Hindawi Publishing CorporationModelling and Simulation in EngineeringVolume 2013 Article ID 839046 13 pageshttpdxdoiorg1011552013839046

Research ArticleInvestigation into the Dynamics and Control of an UnderwaterVehicle-Manipulator System

Mohan Santhakumar

Centre for Robotics and Control Mechanical Engineering Indian Institute of Technology Indore Madhya Pradesh 452017 India

Correspondence should be addressed to Mohan Santhakumar santha radhayahoocoin

Received 12 July 2013 Accepted 19 September 2013

Academic Editor Ahmed Rachid

Copyright copy 2013 Mohan SanthakumarThis is an open access article distributed under theCreativeCommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This study addresses the detailedmodeling and simulation of the dynamic coupling between an underwater vehicle andmanipulatorsystem The dynamic coupling effects due to damping restoring and inertial effects of an underwater manipulator mounted onan autonomous underwater vehicle (AUV) are analyzed by considering the actuator and sensor characteristics A model referencecontrol (MRC) scheme is proposed for the underwater vehicle-manipulator system (UVMS) The effectiveness of the proposedcontrol scheme is demonstrated using numerical simulations along with comparative study between conventional proportional-integral-derivative (PID) control The robustness of the proposed control scheme is also illustrated in the presence of externaldisturbances and parameter uncertainties

1 Introduction

The underwater manipulator has turned into a criticalparttool of underwater vehicles for performing interactivetasks such as opening and closing of valves cutting drillingsampling and laying in the fields of scientific research andocean systems engineering Due to unstructured propertiesof interactive work a good understanding of the dynamicsof a robotic manipulator mounted on a moving underwatervehicle is required for autonomous manipulation tasks [1 2]

The increasing in demand for more efficient precise andaccurate underwater autonomous manipulation has inducedmany researches in this field which includes the dynamicmodel and effective simulation of an underwater manipu-lator mounted on an underwater vehicle The first attempttowards modeling of an underwater vehicle-manipulatorsystem (UVMS) started with the development of a dynamicsimulation algorithm using the Newton-Euler formulationscheme [3 4] Similarly using the Kanersquosmethod a simplifieddynamic model of UVMS was developed and verified usingnumerical simulations [5] A coordinated control schemefor the UVMS using a discrete-time approximation dynamicmodel was developed to compensate for the tracking errorsof the manipulator during vehicle motion [6] The UVMS

dynamic model was formulated using the quasi-Lagrangemethod [4 7] A nonlinear model-based control schemethat controlled the vehicle and manipulator simultaneouslywas developed and investigated [8] In addition to thesestudies some of the researches were focused on estimatinghydrodynamic parameters of these systems [8] the reductionof the interaction effects (dynamic coupling) between themanipulator and the vehicle [9] and the manipulabilityand workspace analysis of the underwater manipulator onremotely operated vehicle (ROV) [10] Also there havebeen many studies on manipulator control for enhancingefficiency of underwater manipulation such as the forcefeedback control of manipulators mounted on ROVs [11]motion planning and control of UVMS [7] computer-basedcontrol and real-time motion compensation of UVMS [12]The workspace-control system for the teleoperated ROV wasproposed by combining the ROV master-slave systems andverified through experiments [13] Despite of these significantresearches most intervention tasks conducted in the fieldstill depend on operatorrsquos skills Therefore much demandand developments are needed in autonomous manipulationwhich gives much attention to and interest in this researchfield Although there have been some research attempts toovercome the parameter uncertainties on underwater robots

2 Modelling and Simulation in Engineering

very few attempts considered the problem of uncertaintiesassociated with time varying parameters on UVMS withmanipulator motion causing dynamic coupling In additionto the coupling effects most of the real-time AUVs areunderactuated in nature (ie the vehicle has fewer numberof control inputs than the total number of independent stateswhichmakes the control scheme complex)which complicatesthe problem

Therefore by considering the above-mentioned issuesthis paper presents the closed-form dynamic equations of anUVMS and the interaction effects between the manipulatorand the vehicle are investigated numerically based on pro-totype vehicle-manipulator parameters This paper also pro-poses a model reference control scheme for the UVMS Thisscheme enables overcoming the difficulty due to parameteruncertainties external variations (eg buoyancy and payloadvariations) and disturbances (eg underwater current) Inthis study the actuator and sensor characteristics such astime constant efficiency saturation limits update rate andsensor noises are considered for numerical simulations Inthe vehicle dynamic modeling off diagonal elements of thesystem matrices are considered as well The effectiveness ofthe proposed control scheme is confirmed with specifiedUVMS tasks

The remainder of this paper is organized as follows Thedynamicmodeling of a general UVMS is derived in Section 2In Section 3 a nonlinear controller for the UVMS based onthe model reference control scheme is discussed and detailedperformance analysis of the UVMS with different operatingconditions is presented in Section 4 Finally Section 5 holdsthe conclusions

2 Mathematical Modeling of UVMS

21 Dynamic Model of the Underwater Vehicle The dynamicmodel of an underwater vehicle is developed through theNewton-Euler formulation using laws of conservation oflinear and angular momentum The equations of motionof such vehicles are highly nonlinear [4] mainly due tohydrodynamic forces which act on the vehicle Generally thevehicle model can be written with respect to either a body-fixed or an earth-fixed frame of reference (refer to Figure 1)

The equations of motion of an underwater vehicle havingsix degrees of freedom with respect to a body-fixed frame ofreference can be written as [4]

M ^ + C (]) ^ +D (]) ^ + g (120578) = 120591119881 (1)

where

M = MRB +M119860

C (]) = CRB (]) + C119860 (

])

D (]) = D119871+D

119876 |]|

(2)

MRB and CRB(]) are the rigid body mass matrix and theCoriolis and centripetal matrix respectively M

119860and C

119860(])

are the added mass matrix and the added Coriolis andcentripetal matrix respectively D

119871and D

119876|^| are the linear

Inertial frame

(fixed)

Vehicle-fixed frame (moving)CB

CG

Manipulatorbase frame

Manipulatorend-effector frame

Surge axis

Sway axis

Heave axis

Yaw axisRoll axis

Pitch axis

Vehicle

Manipulator

M q and

Y v and

K p and

X u and

N r and

Z w and

Sway (y)

Surge (x)

Pitch (120579)

Yaw (120595)

Heave (z)

Roll (120601)

Yt

XtZt

Yb

Xb Zb

Figure 1 Coordinate frame arrangement of an underwater robot

and quadratic dragmatrices respectively g(120578) is the resultantvector of gravity and buoyancy 120591

119881= [119883 119884 119885 119870 119872 119873]

119879

is the resultant input vector of thruster control plane forcesand moments ^ = [119906 V 119908 119901 119902 119903]

119879 is the vector of linearand angular velocities in the vehicle coordinate frame 120578 =[119909 119910 119911 120601 120579 120595]

119879 is the vector of absolute positions andEuler angles (roll pitch and yaw)

The relationship between linear and angular velocities inthe vehicle frame and those in the absolute frame (refer toFigure 1) is given by

= J (120578) ^ (3)

where J(120578) is the kinematic transformation matrix and thistransformation is undefined for 120579 = plusmn90

∘ However mostof the underwater vehicles are designed to operate at pitchangles well below plusmn90

∘ and hence this limitation has nomajor significance here

22 Kinematic Model of the Underwater Manipulator Themathematical model of the underwater manipulator kine-matics is derived in this section

221 Forward Kinematics of the Underwater ManipulatorThe mathematical relations of the end-effector positiontoolcenter point (TCP) or manipulator tip position with theknown joint angles are derived here The mathematical(kinematic) descriptions of the underwater manipulator aredeveloped based on the Denavit-Hartenberg (D-H) param-eter notation [14] The establishment of the link coordinatesystem as shown in Figure 2 yields the D-H parameters

Modelling and Simulation in Engineering 3

Y1

L1

X1

Z1

Y2

L2

X2

Z2

Y3

L3

X3

Z3

Y4

X4

Z4

1205791

Y0

d1

X0

Z0

1205792

1205793

1205794

Figure 2 Establishing link coordinate systems of the manipulator

shown in Table 1 Based on the underwater link parameters inTable 1 the homogeneous transformation matrix [14] whichis derived that specifies the location of the end effector orTCP with respect to the base coordinate system is expressedas

T0

4= [

R0

4P0

4

0 0 0 1

] = T0

1T1

2T2

3T3

4

T119896minus1

119896

=

[

[

[

[

cos 120579119896

minus sin 120579119896

0 119886

119896minus1

sin 120579119896cos120572

119896minus1cos 120579

119896cos120572

119896minus1minussin120572

119896minus1minussin120572

119896minus1119889

119896

sin 120579119896sin120572

119896minus1cos 120579

119896sin120572

119896minus1cos120572

119896minus1cos120572

119896minus1119889

119896

0 0 0 1

]

]

]

]

(4)

The matrix R0

4and the vector P0

4= [119901

119909119901

119910119901

119911]

119879 are therotational matrix and the position vector from the basecoordinates to the end effector respectively From the abovehomogeneous transformation matrix we can obtain the endeffectorrsquos position for feedback control and the elementsfor solving the Jacobian matrix Based on the experimentalunderwater manipulator parameters (refer to Table 1) theforward kinematic solutions are obtained as follows

119901

119909= cos 120579

1(119871

1+ 119871

2cos 120579

2+ 119871

3cos (120579

2+ 120579

3))

119901

119910= sin 120579

1(119871

1+ 119871

2cos 120579

2+ 119871

3cos (120579

2+ 120579

3))

119901

119911= 119871

2sin 120579

2+ 119871

3sin (120579

2+ 120579

3)

(5)

222 Inverse Kinematics of the Underwater Manipulator Inthe workspace-control system each joint of the underwatermanipulator is controlled by the joint angle command calcu-lated from the differential inverse kinematic solutions based

Table 1 D-H parameters of the 3-DOF underwater manipulator

Joint axis(119896)

Link offset(120572

119896minus1)

Link length(119886

119896minus1)

Joint distance(119889

119896)

Joint angle(120579

119896)

1 0∘ 0 0 120579

1

2 90∘119871

10 120579

2

3 0∘119871

20 120579

3

4 0∘119871

30 120579

4= 0∘

on the knownCartesian coordinatesThe closed-form inversekinematic solutions of the 3-DOF underwater manipulatorare described as

120579

1= arctan 2 (119901

119910 119901

119909)

120579

2= arctan 2 (119886119887 minus 119887119888 119886119888 + 119887119889)

120579

3= arctan 2 (sin 120579

3 cos 120579

3)

(6)

where

cos 1205793=

119886

2+ 119887

2minus 119871

2

2minus 119871

2

3

2119871

2119871

3

sin 1205793=radic1 minus cos2120579

3

119886 =

119901

119909

cos 1205791

minus 119871

1 119887 = 119901

119911

119888 = 119871

3cos 120579

3+ 119871

2 119889 = 119871

3sin 120579

3

(7)

23 Dynamic Model of the Underwater Manipulator Thedynamic model of an underwater manipulator is developedthrough the recursive Newton-Euler algorithm In this workit is assumed that the underwater manipulator links are thebuildup of cylindrical elements The effects of the hydrody-namic forces on circular cylindrical elements are describedin the section which mainly consist of added mass effectshydrodynamic drag forces and moments and buoyancyeffects [4] The force and moment interactions between twoadjacent links are as follows

119896f119896=

119896f119896+1

= R119896+1

119896

119896+1f119896+1+ F

119896minus 119898

119896g119896+ b

119896+ p

119896

119896t119896=

119896t119896+1

= R119896+1

119896

119896+1t119896+1+ d

119896119896+1times R119896+1

119896

119896+1f119896+1

+ d119896119896119888

times F119896+ T

119896+ d

119896119896119888

times (minus119898

119896g119896+ p

119896) + d

119896119896119887times b

119896+ n

119896

(8)

p119896= F

119871119896+ F

119863119896+ F

119878119896

F119878119896= D119896

119904

119896k119896

F119863119896=

1003816

1003816

1003816

1003816

1003816

119896k119896

1003816

1003816

1003816

1003816

1003816

119879

D119896

119863

119896k119896

F119871119896=

1003816

1003816

1003816

1003816

1003816

119896k119896

1003816

1003816

1003816

1003816

1003816

119879

D119896

119871

119896k119896

n119896=

119896k119896times (M

119896

119896k119896)

(9)

4 Modelling and Simulation in Engineering

F119896= M

119896(

119896a119896+

119896120572119896times

119896d119896119896119888

+

119896120596

119896times (

119896120596

119896times

119896d119896119896119888))

T119896= I

119896

119896120572119896+

119896120596

119896times (I

119896

119896120596

119896)

119896+1120596

119896+1= R119896

119896+1

119896120596

119896+ z119879 119902

119896+1

119896+1120572119896+1

= R119896

119896+1(

119896120572119896+

119896120596

119896times z119879119902

119896) + z119879 119902

119896+1

119896+1k119896+1

= R119896

119896+1

119896k119896+

119896+1120596

119896+1times

119896+1d119896119896119888

119896+1a119896+1

= R119896

119896+1

119896a119896+

119896+1120572119896+1

times

119896+1d119896+1119896

+

119896+1120596

119896+1times (

119896+1120596

119896+1times

119896+1d119896+1119896

)

(10)

M119896=

[

[

[

[

[

[

119898

119896+

120587120588119903

119896

2119871

119896

10

0 0

0 119898

119896+ 120587120588119903

119896

2119871

1198960

0 0 119898

119896+ 120587120588119903

119896

2119871

119896

]

]

]

]

]

]

I119896=

[

[

[

[

[

[

[

119868

1199090 0

0 119868

119910+

120587120588119903

119896

2119871

119896

3

12

0

0 0 119868

119911+

120587120588119903

119896

2119871

119896

3

12

]

]

]

]

]

]

]

(11)

where 119896 denotes the corresponding joint axis (119896 = 1 2 3)R119896+1

119896is the rotation matrix f

119896is the resultant force vector t

119896

is the resultant moment vector p119896is the linear and quadratic

hydrodynamic friction forces and F119878119896 F

119863119896 and F

119871119896are

vectors of linear skin friction quadratic drag and quadraticlift effects respectively D119896

119904is the linear skin friction matrix

D119896

119871is the diagonal matrix which contains lift coefficientsD119896

119863

is the diagonal matrix which contains drag coefficients g119896is

the gravity force vector b119896is the buoyancy force vector n

119896

is the hydrodynamic moment vector d119896119896119887

is the vector fromthe center of buoyancy of the link d

119896119896119888is the vector from the

center of gravity of the link d119896119896+1

is the vector from joint 119896to 119896 + 1 F

119896is the vector of total forces acting at the center of

mass of link T119896is the vector of total moments acting at the

center ofmass of link a119896is the linear acceleration vector 120572

119896is

the angular acceleration vector k119896is the linear velocity vector

120596119896is the angular velocity vector m

119896is the mass of the link

M119896is the mass and added mass matrix of the link (located

at the center of mass) I119896is the moment of inertia and added

moment of matrix of the link (located at the center of mass)and z119879 is the unit vector along the 119911-axis

The joint torques of each link are represented as

120591

119877119896= z119879 119896t

119896

(12)

The recursive Newton-Euler dynamics algorithm for alllinks symbolically yields the equations of motion for theunderwater manipulatorThe result can be written as follows

M119877(119902) q + C

119877(119902 119902) q +D

119877(119902 119902) q + g

119877(119902) = 120591

119877 (13)

where q is the vector of joint variables and q = [1205791120579

2120579

3]

119879120579

1 120579

2 120579

3are the joint angles of the corresponding underwater

manipulator linksM119877(119902)q is the vector of inertial forces and

moments of the manipulator C119877(119902 119902)q is the vector of Cori-

olis and centripetal effects of the manipulator D119877(119902 119902)q is

the vector of damping effects of the manipulator g119877(119902) is the

restoring vector of themanipulator and 120591119877= [120591

1198771120591

1198772120591

1198773]

119879

is the vector of control inputs

24 Dynamic Model of Vehicle-Manipulator System Themanipulator has an initial velocity equal to the velocity ofthe vehicle This initial velocity should be accounted in themanipulator dynamics Similarly the weight and movementof the manipulator links will affect the vehicle dynamics(these effects are considered as disturbances) and vice versaBy considering the above issues the vehicle and manipulatorequations of motions can be written as follows

M ^ + C (]) ^ +D (]) ^ + g (120578) = 120591119881+ 120590

M119877(119902) q +H119879

2(119902) ^ + C

119877(119902 119902) q +D

119877(119902 119902) q

+ g119877(119902) + C119879

119881(119902 119902 ]) ^ +D119879

119881(119902 119902 ]) ^ = 120591

119877

(14)

where H119879

2(119902) ^ is the vector of reaction forces and moments

between the vehicle and the manipulator C119879

119881(119902 119902 ])^ is the

vector of Coriolis and centripetal effects due to couplingbetween the vehicle and the manipulator and D119879

119881(119902 119902 ])^

is the vector of quadratic drag effects due to the interactionbetween the vehicle and the manipulator 120590 = [120590

119879

119891120590119879

119898]

119879 isthe vector which contains forces and moments disturbancesdue to weight and movement of the manipulator linksConsider

120590119891= R119861

0

0f1

120590119898= R119861

0

0t1minus dvehiclemanipulator times (R

119861

0

0f1)

(15)

where R119861

0and dvehiclemanipulator are the rotation matrix and

position vector from the vehicle-fixed frame to the manip-ulator base frame respectively 0f

1and 0t

1are the vectors

of force and moments of the base frame respectively Thesevectors are derived using (8) and these effects are functionof the manipulator joint coordinates (ie q q and q) andthe vehicle states After evaluating the interaction forces andmoments between the manipulator and the vehicle based onthese vectors the equations of motion of the vehicle can bewritten as

M ^ +H1(119902) ^ + C (]) ^ +D (]) ^ + C

119881(119902 119902 ]) ^

+D119881(119902 119902 ]) ^ + g (120578) +H

2(119902) q + C

1(119902 119902) q

+D1(119902 119902) q + g

1(119902) = 120591

119881

(16)

whereH1(119902) ^ andH

2(119902)q are the added inertia effects due to

the manipulator D1(119902 119902)q is the damping effects due to the

manipulator C1(119902 119902)q is the Coriolis and centripetal effects

due to the manipulator and g1(119902) is the restoring vector due

to the manipulator on the vehicle respectively

Modelling and Simulation in Engineering 5

AUV dynamics

Manipulator dynamics

Trajectory planner

minus

+

minus

+

+

+

+

+

+

+

+

Dynamiccoupling effects

+

+

+

minus

+

++

++

+

++

+

q

q

q

qd

d

dt

q

d

dt

KIR

KDR

KPR

KPV

KDV

KIV

MV

MR (q)

int

int

V

d

R

q

G2

G1

q

J( )minus1

)minus1J( )minus1

F2(q )

HT2 (q)

H2(q)

F1(q )

(middot)

(middot)

(middot)(middot)

120578

120578

120578

120578

120578120578

120578

120578

120578

120578

τ

τ

120578 120578

120578

Figure 3 Block diagram of model reference control

ldquoNot to scalerdquo

Top view

Front viewVehicle

ManipulatorVertical thrusters

Port side thruster

Starboard side thruster Stern control

plane surfaces

Lateral thruster

x

x

y

z

Figure 4 Schematic diagram of UVMS prototype model

3 Model Reference Control

This section discusses the model reference control (MRC)design in terms of feedback linearizationThis control scheme

transforms the nonlinear system dynamics into a linearsystem it compensates for all the nonlinearities in the systemby introducing nonlinear elements in the input side thusmaking the controller design more flexible [15ndash17] Unliketraditional control it can be thought of as ldquoinstantaneouslearningrdquo of the vehicle dynamicsThe individual control lawsof the underwater vehicle and the manipulator are chosensuch that the tracking errors are converging to zero Thetracking errors are defined as = 120578

119889minus120578 and q = q

119889minusq where

119889 denotes the desired (or reference) values The equationsof motion of the UVMS can be expressed in the form givenbelow [15]

M119881^ +H

2(119902) q + F

1(119902 119902 ]) + G

1(120578 119902) = 120591

119881

M119877(119902) q +H119879

2(119902) ^ + F

2(119902 119902 ]) + G

2(119902) = 120591

119877

(17)

where M119881

= M + H1(119902) F

1(119902 119902 ]) F

2(119902 119902 ]) G

2(119902)

and G1(120578 119902) are the vectors of the Coriolis centripetal and

dampingfrictional and restoring effects of the vehicle andthe manipulator respectively

6 Modelling and Simulation in Engineering

The proposed control input vectors given by (18) willcancel out or compensates for the nonlinearities in the systemas

120591119881= M

119881u119881+H

2(119902) q + F

1(119902 119902 ]) + G

1(120578 119902)

120591119877= M

119877(119902) u

119877+H119879

2(119902) ^ + F

2(119902 119902 ]) + G

2(119902)

(18)

where

u119881= J(120578)minus1 (u

120578minus

J (120578) J(120578)minus1120578)

u120578=

119889+ K

119901119881 + K

119889119881

+ K119894119881int 119889119905

u119877= q

119889+ K

119901119877q + K

119889119877q + K

119894119877int q 119889119905

(19)

K119901119881 K

119894119881 and K

119889119881are the proportional integral and

derivative gainmatrices of the vehicle controller respectivelyand K

119901119877 K

119894119877 and K

119889119877are the proportional integral and

derivative gainmatrices of themanipulator controller respec-tively Block diagram representation of the proposed UVMScontroller is presented in Figure 3

The above-mentioned control vectors lead to exponentialstable error dynamics of the vehicle and manipulator whichare given as

+ K119901119881 + K

119889119881

+ K119894119881int 119889119905 = 0

q + K119901119877q + K

119889119877q + K

119894119877int q 119889119905 = 0

(20)

which implies that tracking errors are converging to zero (ie rarr 0 and q rarr 0) and the UVMS follows the given desiredtrajectory [18]

However the above-proposed control scheme assumedthat there are no disturbances and no uncertainties associatedwith the system If the system uncertainties and externaldisturbances are considered for the analysis the system errordynamics become

+ K119901119881 + K

119889119881

+ K119894119881int 119889119905 = M

119881

minus1120591119889119881

q + K119901119877q + K

119889119877q + K

119894119877int q 119889119905 = M

119877

minus1120591119889119877

(21)

where 120591119889119881

and 120591119889119877

are the disturbance vector (which com-bines the internal disturbances such as effect of parameteruncertainties and external disturbances namely underwatercurrent etc) of the vehicle and manipulator controllerrespectively

The closed-loop characteristic equation or polynomial isgiven as

Δ

119888119881 (119904) =

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

119904

2I + 119904K119889119881+ K

119901119881+

K119894119881

119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ

119888119877 (119904) =

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

119904

2I + 119904K119889119877+ K

119901119877+

K119894119877

119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

(22)

The control gain matrices are chosen as diagonal and positivedefinite matrices such as

K119889119881= diag (119896

119889119881119894) K

119901119881= diag (119896

119901119881119894)

K119894119881= diag (119896

119894119881119894) K

119889119877= diag (119896

119889119877119894)

K119901119877= diag (119896

119901119877119894) K

119894119877= diag (119896

119894119877119894)

(23)

Therefore the closed-loop characteristic polynomialbecomes

Δ

119888119881 (119904) =

6

prod

119894=1

(119904

2+ 119904119896

119889119881119894+ 119896

119901119881119894+

119896

119894119881119894

119904

)

Δ

119888119877 (119904) =

119899

prod

119894=1

(119904

2+ 119904119896

119889119877119894+ 119896

119901119877119894+

119896

119894119877119894

119904

)

(24)

and the system error is asymptotically stable as long as thecontroller gain values are all positiveTherefore as long as thedisturbance vectors are bounded the system tracking errorsare converged to zero In other words the system followsthe given desired trajectory Moreover the controller gainmatrices have been chosen in such a way that

120582min K119901119881 gt

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120597120591119889119881

120597

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120582min K119889119881 gt

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120597120591119889119881

120597

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120582min K119901119877 gt

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120597120591119889119877

120597q

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120582min K119889119877 gt

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120597120591119889119877

120597

q

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

(25)

Hence = 0 and q = 0 for all 119905 ge 0 are its unique solutionand it can be observed that the system tracking errors areconverging to zero asymptotically The proposed controlleranalysis does not contain explicit treatment of the parametricuncertainties and external disturbance while taking temporalderivative along the closed-loop system trajectories and it isleft for further research and analysis

4 Performance Analysis of the UVMS

41 Description of the Simulated System We have accom-plished widespread computer-based numerical simulationsto explore the total performance of the proposed UVMS andthe model reference (direct adaptive) control scheme TheUVMS used for this study consists of six degrees of freedom(DOF) vehicle and a 3-DOF spatial manipulator the UVMSarrangement in conceptual design is presented in Figure 4The vehicle is a cylindrical shape (torpedo fish shaped)cruising type with the length of 11m and the diameter of025m The mass of the vehicle is 39 kg The vehicle has fivethrusters in total two propulsion thrusters (in the stern side)two vertical thrusters and one lateral thruster Thereforesurge sway and heave motions are controlled through thesethrusters actuation directly and however yaw and pitchmotions are controlled by differential actuation of propulsionand vertical thrusters Although roll motion is unactuated itcan be controlled itself due to restoring effects [19ndash21] It isknown that a necessary condition for a submersible body to

Modelling and Simulation in Engineering 7

be stable is that the centre of gravity (CG) should lie belowthe centre of buoyancy (CB) For this the vehicle is trimmed(using a float) to have the CB almost vertically above the CGand made to be nearly neutral buoyant Here the roll motionhas nonzero components of restoringmoments that representself-restoring torque for the roll direction With nonzerorestoring terms it may be possible to find continuous statefeedback laws to stabilize the system as a whole In additionto this without loss of generality we can assume that thedamping terms of nonactuated states are sufficiently largerthan their inertia terms which means that the hydrodynamicrestoring forces and torques are large enough to stabilize thenonactuated (roll) states (zero dynamics) which is a commonproperty forAUVs [19]Thismeans that the underwater robotcan be exponentially stabilized by the actuated state controlsalone

The manipulator links are cylindrical in shape and theradii of links 1 2 and 3 are 01m 005m and 005mrespectively The lengths of links 1 2 and 3 are 01m 02mand 02m respectively The link masses (along with oil con-served motors) are 039 kg 157 kg and 157 kg respectivelyHere the links are considered as cylindrical shape becausesuch shape provides uniform hydrodynamic reactions andis one of the primary candidates for possible link geometryfor underwater manipulators Although it is cylindrical ourmathematical framework does not depend on any particularshapes it can be easily accommodated by any other shapesIndeed cylindrical underwater manipulators are available inthe present market [22] Hydrodynamic parameters of theUVMS are estimated using empirical relations based on striptheory This method is verified using the available literaturetherefore these values are reliable and can be used for furtherdevelopments Some parameters like inertia centre of gravityand centre of buoyancy are calculated from the geometricaldesign of the UVMSThe total parameter list of the UVMS isgiven in Tables 2 and 3

We have compared our results with those of traditionalPID controller the following control vectors were consideredfor the vehicle and the manipulator and are given by

120591119881= K

119863119881

+ K119875119881 + K

119868119881int 119889119905

120591119877= K

119863119877q + K

119875119877q + K

119868119877int q 119889119905

(26)

where K119875119881 K

119868119881 K

119863119881 K

119875119877 K

119868119877 and K

119863119877are the propor-

tional integral and derivative gainmatrices of the vehicle andthe manipulator respectively

42 Description of the Tasks Three different tasks with fourdifferent cases have been considered for the simulations Thefirst task is that the vehicle is commanded to track a given3D trajectory without and with the manipulator (at rest or itshome position) and in this condition the vehicle acceleratesfor the initial 20 s and attains the vehicle forward speed of1ms (asymp2 knots) and for the final 20 s the vehicle deceleratesto zero speed The particular desired 3D trajectory (referto Figure 5) has been chosen for this performance analysisbecause this trajectory consists of all four main motions such

Table 2 The parameter list of the UVMS

Parameters ValuesMass of the vehicle (119898V) 39 kgLength of the vehicle (119871V) 11mDiameter of the vehicle (119889V) 025mMoment of inertia of the vehicle119868

119909034 kgm2

119868

119910371 kgm2

119868

119911371 kgm2

Centre of gravity (CG) = (119909119866 119910

119866 119911

119866) (0 0 0) m

Centre of buoyancy (CB) = (119909119861 119910

119861 119911

119861) (0 0 0015) m

Mass of the underwater manipulator links119898

103927 kg

119898

215708 kg

119898

315708 kg

Underwater manipulator link lengths119871

1005m

119871

2020m

119871

3020m

Underwater manipulator link radii119903

1010m

119903

2005m

119903

3005m

Coefficient of drag (119862119863) 125

Coefficient of lift (119862119871) 115

Table 3 The values of hydrodynamic coefficients calculated usingempirical relations based on strip theory

Vehicle added mass derivatives119883

minus117 kg 119870

minus01 kgmrad

119884V minus3484 kg 119872

minus103 kgm

119884

119903104 kgm 119872

119902minus266 kgmrad

119885

minus3483 kg 119873V minus104 kgm

119885

119902minus104 kgm 119873

119903minus265 kgmrad

Vehicle hydrodynamic parameters119883

119906|119906|minus7365 kgm 119883

119906minus212 kgs

119883V|V| minus0737 kgm 119883V minus031 kgs119883

119908|119908|minus0737 kgm 119883

119908minus031 kgs

119883

119902|119902|minus1065 kgmrad 119883

119902minus051 kgms

119883

119903|119903|minus1065 kgmrad 119883

119903minus051 kgms

119884V|V| minus1122 kgm 119884V minus6245 kgs119884

119903|119903|0250 kgmrad 119884

119903012 kgms

119885

119908|119908|minus1122 kgm 119885

119908minus6245 kgs

119885

119902|119902|minus0250 kgmrad 119885

119902012 kgms

119870

119901|119901|minus05975 kgm2rad2 119870

119901minus03125 kgm2s

119872

119908|119908|2244 kgmrad 119872

11990812 kgms

119872

119902|119902|minus1195 kgm2rad2 119872

119902minus5975 kgm2s

119873V|V| minus2244 kgmrad 119873V 12 kgms

as sway in and out and heave up and downThe average valueof sway velocity is 025ms (asymp05 knots) (same value for heaveas well) This task is performed to identify the influences of

8 Modelling and Simulation in Engineering

050

100150

200

05

1015

200

5

10

15

20

Desired 3D pathPID without armMRC without arm

PID with armMRC with arm

z(m

)

y (m)x (m)

Figure 5 Comparative trajectory tracking control results

the underwater manipulator effects during vehicle trackingcontrol In the second task the vehicle is free to move (nocontrol action involved) and the manipulator has a certainrepeated desired trajectory This task is mainly performedto identify the vehicle behavior during manipulator motionIn all the above tasks the initial velocities and positions ofthe vehicle and the manipulator are chosen to be zero andthe initial desired and actual positions and orientations arethe same In the third task two basic trajectories for themanipulator have been chosen for simulations a circulartrajectory (in 3D space) and a rectangular trajectory (in 119910119911plane) along with a straight line in 3D space This is forthe reason that most of the underwater intervention tasksinvolve these types of trajectories and also we can arrangeany spatial trajectory by combining these trajectories For therectangular trajectory we have selected a cubic polynomialfunction as the trajectory function which imposes that thetrajectory is continuous and smooth

In the performance analysis the sensory noises inposition and orientation measurements are introduced andwe have considered Gaussian noise of 001m mean and001m standard deviation for the positionmeasurements and02

∘ mean and 02∘ standard deviation for the orientationmeasurements The thruster dynamic characteristics are alsoincorporated in the simulations All the vehicle thrusters areconsidered as an identical one and the following thrustercharacteristics are considered for the analysis the thrusterresponse delay time is 200ms efficiency is 95and saturationlimits are plusmn20N The vehicle surge thrusters are located at05m from the body centre along the 119909-axis and offset eachside 03m from 119910-axis The lateral thruster is exactly locatedon the body centre and vertical thrusters are placed on the 119909-axis 04m apart from the centre at each side The controllerupdate rate and sensor response time are considered as 100mseach

43 Results and Discussions Here numerical simulationresults are shown and discussed to investigate the dynamic

Table 4 Controller parameter settings for simulations

Vehicle controller parameters Values119870

119901119881diag(42 22 25 0 25 27)

119870

119889119881diag(225 12 13 0 15 13)

119870

119894119881diag(05 02 03 0 25 22)

119870

119875119881diag(180 130 150 0 150 130)

119870

119863119881diag(80 100 100 0 80 90)

119870

119868119881diag(15 12 15 0 16 18)

Manipulator controller parameters Values119870

119901119877diag(5 10 12)

119870

119889119877diag(3 5 8)

119870

119894119877diag(01 02 02)

119870

119875119877diag(60 80 75)

119870

119863119877diag(35 40 50)

119870

119868119877diag(1 15 2)

coupling effects and the effectiveness of the proposed model-based control scheme which is expected to provide anintuitive promising prospective of the proposed approach

431 Underwater Vehicle Tracking a Given 3D Trajectorywith the Underwater Manipulator In this case as mentionedearlier the vehicle is commanded to follow a given 3D desiredtrajectory The desired 3D trajectory is given in Figure 5The controller gain values are tuned based on the geneticalgorithms (GA) for minimizing the integral squared error(ISE) as the costobjective function [23] Here we haveconsidered both the model reference control and the PIDcontrol performance to be almost equal in the ideal situationwhich makes the controller performance comparison quitereasonable and gives much better way of understandingBased on the GA tuning method the controller parametersare obtained and given in Table 4 The same set of controllerparameters are used throughout the entire performanceanalysis

Initially the performance analysis is carried out for thevehicle trajectory tracking without manipulator inclusionThe actual simulated trajectories based on MRC and PID arepresented in Figure 5These results show that both controllersare good enough to track the given trajectory and thetracking errors are within the design limits (error limits forthe vehicle during trajectory tracking are plusmn02m and plusmn02∘in positions and orientations resp) as well The trackingerrors are presented in Figures 6 7 8 9 10 and 11 In thesecond set of simulations the manipulator is included andthe inclusion effects during trajectory tracking of the vehicleare considered Here the manipulator links are folded andarranged in such a way that the influences on the vehicledynamics are small (ie manipulator joint angles are 120579

1=

180

∘ 1205792= 0

∘ and 1205793= 180

∘) The manipulator inclusionshows that there are significant performance changes in thevehicle trajectory tracking especially during the heave andsway motion tracking The heave roll and pitch motionsof the vehicle are greatly influenced by the underwatermanipulator inclusion which are replicated in the results

Modelling and Simulation in Engineering 9

0 50 100 150 200 250 300minus01

minus005

0

005

01

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Trac

king

erro

r inx

(xe) (

m)

Figure 6 Tracking errors in 119909 position for a given 3D trajectory

0 50 100 150 200 250 300minus002

minus001

0

001

002

003

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Trac

king

erro

r iny

(ye) (

m)

Figure 7 Tracking errors in 119910 position for a given 3D trajectory

(refer to Figures 6 to 11) However the manipulator inclusioneffects are better adapted in the model reference control thanin the PID control As can be observed from Figures 8 and10 the manipulator inclusion causes an initial pitch anglevariation drifts the vehicle in the heave direction during thestraight line motion (during acceleration stage) Howeverthese unwanted effects are compensated successfully in themodel reference control and therefore tracking errors do notexceed their design limits

432 Manipulator following a Given Desired 3D Trajectorywith the Freely Moving Underwater Vehicle (without VehicleControl) As mentioned earlier in this section this task ismainly to address the interaction effects and their influences

0 50 100 150 200 250 300minus005

0

005

01

015

02

03

Trac

king

erro

r inz

(ze) (

m)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 8 Tracking errors in 119911 position for a given 3D trajectory

0 50 100 150 200 250 300minus10

minus5

0

5

10

15

20

Trac

king

erro

r in

roll

(120601e) (

deg)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 9 Tracking errors in roll for a given 3D trajectory

on theUVMS For this task the vehicle controller is removedand only the underwater manipulator follows a given desiredcontinuous trajectory The desired values of joint positionsare as follows 120579

1119889= 90

∘ sin (01119905) 1205792119889

= 90

∘ and 1205793119889

=

minus45

∘ The simulation results of this condition are presentedin Figures 12 13 14 15 and 16 From the results it is observedthat the vehicle is started getting drifted from its initialposition and it is moving forward with an average velocityof 002ms (approximately) for the repeated underwatermanipulator movements It shows that the manipulator linksare affected due to the dynamic coupling effects Fromthe results it is observed that the vehicle swims duringmanipulator movements if the vehicle does not have anycontrol actionThese errors and forward speed are increasing

10 Modelling and Simulation in Engineering

0 50 100 150 200 250 300minus15

minus1

minus05

0

05

1

15

Trac

king

erro

r in

pitc

h (120579

e) (

deg)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 10 Tracking errors in pitch for a given 3D trajectory

0 50 100 150 200 250 300minus1

minus05

0

05

1

Trac

king

erro

r in

yaw

(120595e) (

deg)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 11 Tracking errors in yaw for a given 3D trajectory

with the manipulator oscillation frequency and their jointangle magnitudes In addition the direction of the vehiclersquosmovement varies depending on the manipulator positionsand its direction ofmovementsThese results can be extendedto the work towards swimming robots and their dynamicmodeling aspects

433 Underwater Manipulator following a Given DesiredCircular Trajectory with Vehicle Control The circular trajec-tory chosen for the analysis has 02m in diameter and anaverage speed of 00125ms These parameters are chosenwith the consideration of manipulator actuators workspaceand control The results from computer simulations arepresented in Figures 15ndash18 In Figure 15 both desired andactual task space trajectories are plotted and the task spacetracking errors are given in Figures 16ndash18 From the results

0 5 10 15 20minus006

minus004

minus002

0

002

004

006

008

01

012

Posit

ion

erro

rs (m

)

Time (t) (s)

xeyeze

Figure 12 Tracking errors in the vehicle positions (when manipu-lator has motion)

0 5 10 15 20minus3

minus2

minus1

0

1

2

3

4

Attit

ude e

rror

s (de

g)

Time (t) (s)

120601e120579e120595e

Figure 13 Tracking errors in the vehicle orientations (when thevehicle has no control and the manipulator has repeated motion)

it is observed that the manipulator tip tracks the givendesired task space trajectories quite satisfactorily in both PIDand MRC schemes in the ideal conditions (no disturbancesno uncertainties etc) Then in order to demonstrate theadaptability and robustness of the proposed controller anuncertain condition is considered for the simulations Thefollowing conditions are considered for the uncertain condi-tion analysis

(i) the UVMS parameters are assumed to be inaccurate(about 10 for each parameters)

(ii) the manipulator carries a payload of 1 kg at its tip

Modelling and Simulation in Engineering 11

0708

091

minus02minus01

001

02045

046

047

048

049

Desired tool tip positionActual tool tip position

z(m

)

y (m)x (m)

Figure 14 Manipulator tip position in 3D space (when the vehiclehas no control)

06507

07508

085

005

01

015

minus01

minus005

0

005

Desired trajectoryPIDMRC

PID with uncertaintyMRC with uncertainty

z(m

)

y (m)x (m)

Figure 15 Task space (119909119910119911) trajectories (results from the circulartrajectory)

(iii) an unknown ocean current is added in the simulationby properly considering the relative velocity of thein the dynamic model It is assumed to have anirrotational current constant in the inertial frameand the value of the current is considered as ^

119888=

[02 02 01 0 0 0]

119879ms

The results are presented in Figures 15ndash18 and from theseresults it is observed that the proposed controller is goodin adapting the uncertainties and disturbances (refer toFigure 15) Figures 16 and 17 show that tracking errors of119909 and 119910 in both PID and MRC methods are almost thesame and results satisfactorily however the tracking error in119911 substantiates that the proposed controller is comparativelygood in the presence of uncertainties and disturbances

434 Underwater Manipulator following a Given DesiredRectangular Trajectory with Vehicle Control The rectangulartrajectory chosen for the analysis has 04m in width and

0 5 10 15 20 25 30minus002

minus0015

minus001

minus0005

0

0005

001

0015

Time (t) (s)

PIDMRC

PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r inx

(xe) (

m)

Figure 16 Time histories of the manipulator tip position trackingerror in 119909 (circular trajectory)

0 5 10 15 20 25 30minus4

minus3

minus2

minus1

0

1

2

3

4

5

6

MRC

Time (t) (s)

PID PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r iny

(ye) (

m)

times10minus3

Figure 17 Time histories of the manipulator tip position trackingerror in 119910 (circular trajectory)

02m in height in the 119910119911 plane and an average speedof 005ms As mentioned in the last case the trajectoryhas been chosen with the consideration of the manipulatorcharacteristics Two conditions have been considered for theanalysis ideal condition (no disturbances no uncertaintiesetc) and an uncertain condition (the same as the previouscase Section 433) The results from computer simulationsare plotted in Figure 19 In the ideal condition both con-trollers show quite satisfactory performance and in theuncertain condition the proposed controller shows betterperformance

12 Modelling and Simulation in Engineering

MRC

0 5 10 15 20 25 30minus002

0

002

004

006

008

01

012

Time (t) (s)

PID PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r inz

(ze) (

m)

Figure 18 Time histories of the manipulator tip position trackingerror in 119911 (circular trajectory)

064 066 068 07 072

minus020

0202

025

03

035

04

Desired trajectoryPIDMRC

PID with uncertaintyMRC with uncertainty

z(m

)

y (m)x (m)

Figure 19 Task space (119909119910119911) trajectories (results from the rectangu-lar trajectory)

In both trajectory tracking cases the thruster forces donot exceed plusmn5N and the manipulator actuator torques staywithinplusmn015Nmwhich arewell within the range of actuators

5 Conclusions

In this study the interaction effects due to the dynamiccoupling between the vehicle and the manipulator wereinvestigated using closed-form equations which provide ageneralized scheme for formulating the equations of motionof the UVMS The proposed scheme makes it possible toidentify the structure nature and properties of the systemand it simplifies the control design This study also proposeda model reference control approach for an underactuated

UVMS to perform underwater intervention tasks incorpo-rating desired trajectory information Extensive simulationswere carried out to verify and demonstrate the effectivenessof the proposed scheme In particular the performance ofthe model reference controller is compared with that of theconventional PID controller for the given UVMS operationscenarios The obtained results confirm the effectiveness androbustness of the proposed scheme in terms of tracking errorsand control effort in the presence of external disturbancesand parameter uncertainties This research provides a gener-alized framework for modeling and controlling of an UVMSconsidering the dynamic coupling between the vehicle andthe manipulator which is crucial for achieving underwatermanipulation tasks for a variety of scientific industrial andmilitary missions using unmanned underwater vehicles

Conflict of Interests

Authors confirm that this paper has not been publishedelsewhere and is not under consideration by another journalAll authors have approved the manuscript and agree withsubmission toModelling and Simulation in EngineeringTheauthors have no conflict of interests to declare

Acknowledgments

The author would like to acknowledge Professor JinwhanKim for his valuable suggestions and discussions on under-water manipulator This research was supported in partby the World Class University (WCU) program throughthe National Research Foundation of Korea funded by theMinistry of Education Science and Technology (R31-2008-000-10045-0)

References

[1] G Antonelli F Caccavale S Chiaverini and L Villani ldquoTrack-ing control for underwater vehicle-manipulator systems withvelocity estimationrdquo IEEE Journal of Oceanic Engineering vol25 no 3 pp 399ndash413 2000

[2] G Marani S K Choi and J Yuh ldquoUnderwater autonomousmanipulation for intervention missions AUVsrdquo Ocean Engi-neering vol 36 no 1 pp 15ndash23 2009

[3] S McMillan D E Orin and R B McGhee ldquoEfficient dynamicsimulation of an underwater vehicle with a robotic manipula-torrdquo IEEE Transactions on Systems Man and Cybernetics vol25 no 8 pp 1194ndash1206 1995

[4] T I Fossen Guidance and Control of Ocean Vehicles WileyChichester UK 1994

[5] T J Tarn G A Shoults and S P Yang ldquoA dynamic model ofan underwater vehicle with a robotic manipulator using Kanersquosmethodrdquo Autonomous Robots vol 3 no 2-3 pp 269ndash283 1996

[6] H Mahesh J Yuh and R Lakshmi ldquoA Coordinated controlof an underwater vehicle and robotic manipulatorrdquo Journal ofRobotic Systems vol 8 no 3 pp 339ndash370 1991

[7] N Sarkar and T K Podder ldquoCoordinated motion planningand control of autonomous underwater vehicle-manipulatorsystems subject to drag optimizationrdquo IEEE Journal of OceanicEngineering vol 26 no 2 pp 228ndash239 2001

Modelling and Simulation in Engineering 13

[8] T W McLain S M Rock and M J Lee ldquoExperiments inthe coordinated control of an underwater armvehicle systemrdquoAutonomous Robots vol 3 no 2-3 pp 213ndash232 1996

[9] M W Dunnigan and G T Russell ldquoEvaluation and reductionof the dynamic coupling between a manipulator and an under-water vehiclerdquo IEEE Journal of Oceanic Engineering vol 23 no3 pp 260ndash273 1998

[10] B H Jun P M Lee and J Lee ldquoManipulability analysisof underwater robotic arms on ROV and application totask-oriented joint configurationrdquo in Proceedings of the IEEEOCEANS pp 1548ndash1553 November 2004

[11] J H Ryu D S Kwon and P M Lee ldquoControl of underwatermanipulators mounted on an ROV using base force informa-tionrdquo in Proceedings of the IEEE International Conference onRobotics and Automation (ICRA rsquo01) pp 3238ndash3243 May 2001

[12] M Hildebrandt L Christensen J Kerdels J Albiez and FKirchner ldquoRealtime motion compensation for ROV-based tele-operated underwater manipulatorsrdquo in Proceedings of the IEEEOCEANS pp 1ndash6 May 2009

[13] H Shim B H Jun P M Lee H Baek and J Lee ldquoWorkspacecontrol system of underwater tele-operated manipulators on anROVrdquo Ocean Engineering vol 37 no 11-12 pp 1036ndash1047 2010

[14] J J Craig Introduction to Robotics Addison Wesley BostonMass USA 1986

[15] G Antonelli Underwater Robots Motion and Force Control ofVehicle-Manipulator Systems Springer Berlin Germany 2006

[16] K Kim andT Ura ldquoAppliedmodel-based analysis and synthesisfor the dynamics guidance and control of an autonomousundersea vehiclerdquo Mathematical Problems in Engineering vol2010 Article ID 149385 23 pages 2010

[17] T I Fossen Marine Control Systems Guidance Navigationand Control of Ships Rigs and Underwater Vehicles MarineCybernetics AS 2002

[18] J J E Slotine and W Li Applied Nonlinear Control Prentice-Hall Upper Saddle River NJ USA 1991

[19] K Y Pettersen and O Egeland ldquoPosition and attitude control ofan underactuated autonomous underwater vehiclerdquo in Proceed-ings of the 1996 35th IEEE Conference on Decision and Controlpp 987ndash991 Kobe Japan December 1996

[20] T H Koh MW S Lau G Seet and E Low ldquoA control modulescheme for an underactuated underwater robotic vehiclerdquo Jour-nal of Intelligent and Robotic Systems Theory and Applicationsvol 46 no 1 pp 43ndash58 2006

[21] M Santhakumar and T Asokan ldquoInvestigations on the hybridtracking control of an underactuated autonomous underwaterrobotrdquo Advanced Robotics vol 24 no 11 pp 1529ndash1556 2010

[22] ANSALDO Nucleare Underwater Manipulator MARIS 7080Use and Maintenance Manual Ansaldo Nuclear DivisionGenoa Italy 1996

[23] K Deb Optimization for Engineering Design Algorithms andExamples Prentice Hall New Delhi India 2004

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2 Modelling and Simulation in Engineering

very few attempts considered the problem of uncertaintiesassociated with time varying parameters on UVMS withmanipulator motion causing dynamic coupling In additionto the coupling effects most of the real-time AUVs areunderactuated in nature (ie the vehicle has fewer numberof control inputs than the total number of independent stateswhichmakes the control scheme complex)which complicatesthe problem

Therefore by considering the above-mentioned issuesthis paper presents the closed-form dynamic equations of anUVMS and the interaction effects between the manipulatorand the vehicle are investigated numerically based on pro-totype vehicle-manipulator parameters This paper also pro-poses a model reference control scheme for the UVMS Thisscheme enables overcoming the difficulty due to parameteruncertainties external variations (eg buoyancy and payloadvariations) and disturbances (eg underwater current) Inthis study the actuator and sensor characteristics such astime constant efficiency saturation limits update rate andsensor noises are considered for numerical simulations Inthe vehicle dynamic modeling off diagonal elements of thesystem matrices are considered as well The effectiveness ofthe proposed control scheme is confirmed with specifiedUVMS tasks

The remainder of this paper is organized as follows Thedynamicmodeling of a general UVMS is derived in Section 2In Section 3 a nonlinear controller for the UVMS based onthe model reference control scheme is discussed and detailedperformance analysis of the UVMS with different operatingconditions is presented in Section 4 Finally Section 5 holdsthe conclusions

2 Mathematical Modeling of UVMS

21 Dynamic Model of the Underwater Vehicle The dynamicmodel of an underwater vehicle is developed through theNewton-Euler formulation using laws of conservation oflinear and angular momentum The equations of motionof such vehicles are highly nonlinear [4] mainly due tohydrodynamic forces which act on the vehicle Generally thevehicle model can be written with respect to either a body-fixed or an earth-fixed frame of reference (refer to Figure 1)

The equations of motion of an underwater vehicle havingsix degrees of freedom with respect to a body-fixed frame ofreference can be written as [4]

M ^ + C (]) ^ +D (]) ^ + g (120578) = 120591119881 (1)

where

M = MRB +M119860

C (]) = CRB (]) + C119860 (

])

D (]) = D119871+D

119876 |]|

(2)

MRB and CRB(]) are the rigid body mass matrix and theCoriolis and centripetal matrix respectively M

119860and C

119860(])

are the added mass matrix and the added Coriolis andcentripetal matrix respectively D

119871and D

119876|^| are the linear

Inertial frame

(fixed)

Vehicle-fixed frame (moving)CB

CG

Manipulatorbase frame

Manipulatorend-effector frame

Surge axis

Sway axis

Heave axis

Yaw axisRoll axis

Pitch axis

Vehicle

Manipulator

M q and

Y v and

K p and

X u and

N r and

Z w and

Sway (y)

Surge (x)

Pitch (120579)

Yaw (120595)

Heave (z)

Roll (120601)

Yt

XtZt

Yb

Xb Zb

Figure 1 Coordinate frame arrangement of an underwater robot

and quadratic dragmatrices respectively g(120578) is the resultantvector of gravity and buoyancy 120591

119881= [119883 119884 119885 119870 119872 119873]

119879

is the resultant input vector of thruster control plane forcesand moments ^ = [119906 V 119908 119901 119902 119903]

119879 is the vector of linearand angular velocities in the vehicle coordinate frame 120578 =[119909 119910 119911 120601 120579 120595]

119879 is the vector of absolute positions andEuler angles (roll pitch and yaw)

The relationship between linear and angular velocities inthe vehicle frame and those in the absolute frame (refer toFigure 1) is given by

= J (120578) ^ (3)

where J(120578) is the kinematic transformation matrix and thistransformation is undefined for 120579 = plusmn90

∘ However mostof the underwater vehicles are designed to operate at pitchangles well below plusmn90

∘ and hence this limitation has nomajor significance here

22 Kinematic Model of the Underwater Manipulator Themathematical model of the underwater manipulator kine-matics is derived in this section

221 Forward Kinematics of the Underwater ManipulatorThe mathematical relations of the end-effector positiontoolcenter point (TCP) or manipulator tip position with theknown joint angles are derived here The mathematical(kinematic) descriptions of the underwater manipulator aredeveloped based on the Denavit-Hartenberg (D-H) param-eter notation [14] The establishment of the link coordinatesystem as shown in Figure 2 yields the D-H parameters

Modelling and Simulation in Engineering 3

Y1

L1

X1

Z1

Y2

L2

X2

Z2

Y3

L3

X3

Z3

Y4

X4

Z4

1205791

Y0

d1

X0

Z0

1205792

1205793

1205794

Figure 2 Establishing link coordinate systems of the manipulator

shown in Table 1 Based on the underwater link parameters inTable 1 the homogeneous transformation matrix [14] whichis derived that specifies the location of the end effector orTCP with respect to the base coordinate system is expressedas

T0

4= [

R0

4P0

4

0 0 0 1

] = T0

1T1

2T2

3T3

4

T119896minus1

119896

=

[

[

[

[

cos 120579119896

minus sin 120579119896

0 119886

119896minus1

sin 120579119896cos120572

119896minus1cos 120579

119896cos120572

119896minus1minussin120572

119896minus1minussin120572

119896minus1119889

119896

sin 120579119896sin120572

119896minus1cos 120579

119896sin120572

119896minus1cos120572

119896minus1cos120572

119896minus1119889

119896

0 0 0 1

]

]

]

]

(4)

The matrix R0

4and the vector P0

4= [119901

119909119901

119910119901

119911]

119879 are therotational matrix and the position vector from the basecoordinates to the end effector respectively From the abovehomogeneous transformation matrix we can obtain the endeffectorrsquos position for feedback control and the elementsfor solving the Jacobian matrix Based on the experimentalunderwater manipulator parameters (refer to Table 1) theforward kinematic solutions are obtained as follows

119901

119909= cos 120579

1(119871

1+ 119871

2cos 120579

2+ 119871

3cos (120579

2+ 120579

3))

119901

119910= sin 120579

1(119871

1+ 119871

2cos 120579

2+ 119871

3cos (120579

2+ 120579

3))

119901

119911= 119871

2sin 120579

2+ 119871

3sin (120579

2+ 120579

3)

(5)

222 Inverse Kinematics of the Underwater Manipulator Inthe workspace-control system each joint of the underwatermanipulator is controlled by the joint angle command calcu-lated from the differential inverse kinematic solutions based

Table 1 D-H parameters of the 3-DOF underwater manipulator

Joint axis(119896)

Link offset(120572

119896minus1)

Link length(119886

119896minus1)

Joint distance(119889

119896)

Joint angle(120579

119896)

1 0∘ 0 0 120579

1

2 90∘119871

10 120579

2

3 0∘119871

20 120579

3

4 0∘119871

30 120579

4= 0∘

on the knownCartesian coordinatesThe closed-form inversekinematic solutions of the 3-DOF underwater manipulatorare described as

120579

1= arctan 2 (119901

119910 119901

119909)

120579

2= arctan 2 (119886119887 minus 119887119888 119886119888 + 119887119889)

120579

3= arctan 2 (sin 120579

3 cos 120579

3)

(6)

where

cos 1205793=

119886

2+ 119887

2minus 119871

2

2minus 119871

2

3

2119871

2119871

3

sin 1205793=radic1 minus cos2120579

3

119886 =

119901

119909

cos 1205791

minus 119871

1 119887 = 119901

119911

119888 = 119871

3cos 120579

3+ 119871

2 119889 = 119871

3sin 120579

3

(7)

23 Dynamic Model of the Underwater Manipulator Thedynamic model of an underwater manipulator is developedthrough the recursive Newton-Euler algorithm In this workit is assumed that the underwater manipulator links are thebuildup of cylindrical elements The effects of the hydrody-namic forces on circular cylindrical elements are describedin the section which mainly consist of added mass effectshydrodynamic drag forces and moments and buoyancyeffects [4] The force and moment interactions between twoadjacent links are as follows

119896f119896=

119896f119896+1

= R119896+1

119896

119896+1f119896+1+ F

119896minus 119898

119896g119896+ b

119896+ p

119896

119896t119896=

119896t119896+1

= R119896+1

119896

119896+1t119896+1+ d

119896119896+1times R119896+1

119896

119896+1f119896+1

+ d119896119896119888

times F119896+ T

119896+ d

119896119896119888

times (minus119898

119896g119896+ p

119896) + d

119896119896119887times b

119896+ n

119896

(8)

p119896= F

119871119896+ F

119863119896+ F

119878119896

F119878119896= D119896

119904

119896k119896

F119863119896=

1003816

1003816

1003816

1003816

1003816

119896k119896

1003816

1003816

1003816

1003816

1003816

119879

D119896

119863

119896k119896

F119871119896=

1003816

1003816

1003816

1003816

1003816

119896k119896

1003816

1003816

1003816

1003816

1003816

119879

D119896

119871

119896k119896

n119896=

119896k119896times (M

119896

119896k119896)

(9)

4 Modelling and Simulation in Engineering

F119896= M

119896(

119896a119896+

119896120572119896times

119896d119896119896119888

+

119896120596

119896times (

119896120596

119896times

119896d119896119896119888))

T119896= I

119896

119896120572119896+

119896120596

119896times (I

119896

119896120596

119896)

119896+1120596

119896+1= R119896

119896+1

119896120596

119896+ z119879 119902

119896+1

119896+1120572119896+1

= R119896

119896+1(

119896120572119896+

119896120596

119896times z119879119902

119896) + z119879 119902

119896+1

119896+1k119896+1

= R119896

119896+1

119896k119896+

119896+1120596

119896+1times

119896+1d119896119896119888

119896+1a119896+1

= R119896

119896+1

119896a119896+

119896+1120572119896+1

times

119896+1d119896+1119896

+

119896+1120596

119896+1times (

119896+1120596

119896+1times

119896+1d119896+1119896

)

(10)

M119896=

[

[

[

[

[

[

119898

119896+

120587120588119903

119896

2119871

119896

10

0 0

0 119898

119896+ 120587120588119903

119896

2119871

1198960

0 0 119898

119896+ 120587120588119903

119896

2119871

119896

]

]

]

]

]

]

I119896=

[

[

[

[

[

[

[

119868

1199090 0

0 119868

119910+

120587120588119903

119896

2119871

119896

3

12

0

0 0 119868

119911+

120587120588119903

119896

2119871

119896

3

12

]

]

]

]

]

]

]

(11)

where 119896 denotes the corresponding joint axis (119896 = 1 2 3)R119896+1

119896is the rotation matrix f

119896is the resultant force vector t

119896

is the resultant moment vector p119896is the linear and quadratic

hydrodynamic friction forces and F119878119896 F

119863119896 and F

119871119896are

vectors of linear skin friction quadratic drag and quadraticlift effects respectively D119896

119904is the linear skin friction matrix

D119896

119871is the diagonal matrix which contains lift coefficientsD119896

119863

is the diagonal matrix which contains drag coefficients g119896is

the gravity force vector b119896is the buoyancy force vector n

119896

is the hydrodynamic moment vector d119896119896119887

is the vector fromthe center of buoyancy of the link d

119896119896119888is the vector from the

center of gravity of the link d119896119896+1

is the vector from joint 119896to 119896 + 1 F

119896is the vector of total forces acting at the center of

mass of link T119896is the vector of total moments acting at the

center ofmass of link a119896is the linear acceleration vector 120572

119896is

the angular acceleration vector k119896is the linear velocity vector

120596119896is the angular velocity vector m

119896is the mass of the link

M119896is the mass and added mass matrix of the link (located

at the center of mass) I119896is the moment of inertia and added

moment of matrix of the link (located at the center of mass)and z119879 is the unit vector along the 119911-axis

The joint torques of each link are represented as

120591

119877119896= z119879 119896t

119896

(12)

The recursive Newton-Euler dynamics algorithm for alllinks symbolically yields the equations of motion for theunderwater manipulatorThe result can be written as follows

M119877(119902) q + C

119877(119902 119902) q +D

119877(119902 119902) q + g

119877(119902) = 120591

119877 (13)

where q is the vector of joint variables and q = [1205791120579

2120579

3]

119879120579

1 120579

2 120579

3are the joint angles of the corresponding underwater

manipulator linksM119877(119902)q is the vector of inertial forces and

moments of the manipulator C119877(119902 119902)q is the vector of Cori-

olis and centripetal effects of the manipulator D119877(119902 119902)q is

the vector of damping effects of the manipulator g119877(119902) is the

restoring vector of themanipulator and 120591119877= [120591

1198771120591

1198772120591

1198773]

119879

is the vector of control inputs

24 Dynamic Model of Vehicle-Manipulator System Themanipulator has an initial velocity equal to the velocity ofthe vehicle This initial velocity should be accounted in themanipulator dynamics Similarly the weight and movementof the manipulator links will affect the vehicle dynamics(these effects are considered as disturbances) and vice versaBy considering the above issues the vehicle and manipulatorequations of motions can be written as follows

M ^ + C (]) ^ +D (]) ^ + g (120578) = 120591119881+ 120590

M119877(119902) q +H119879

2(119902) ^ + C

119877(119902 119902) q +D

119877(119902 119902) q

+ g119877(119902) + C119879

119881(119902 119902 ]) ^ +D119879

119881(119902 119902 ]) ^ = 120591

119877

(14)

where H119879

2(119902) ^ is the vector of reaction forces and moments

between the vehicle and the manipulator C119879

119881(119902 119902 ])^ is the

vector of Coriolis and centripetal effects due to couplingbetween the vehicle and the manipulator and D119879

119881(119902 119902 ])^

is the vector of quadratic drag effects due to the interactionbetween the vehicle and the manipulator 120590 = [120590

119879

119891120590119879

119898]

119879 isthe vector which contains forces and moments disturbancesdue to weight and movement of the manipulator linksConsider

120590119891= R119861

0

0f1

120590119898= R119861

0

0t1minus dvehiclemanipulator times (R

119861

0

0f1)

(15)

where R119861

0and dvehiclemanipulator are the rotation matrix and

position vector from the vehicle-fixed frame to the manip-ulator base frame respectively 0f

1and 0t

1are the vectors

of force and moments of the base frame respectively Thesevectors are derived using (8) and these effects are functionof the manipulator joint coordinates (ie q q and q) andthe vehicle states After evaluating the interaction forces andmoments between the manipulator and the vehicle based onthese vectors the equations of motion of the vehicle can bewritten as

M ^ +H1(119902) ^ + C (]) ^ +D (]) ^ + C

119881(119902 119902 ]) ^

+D119881(119902 119902 ]) ^ + g (120578) +H

2(119902) q + C

1(119902 119902) q

+D1(119902 119902) q + g

1(119902) = 120591

119881

(16)

whereH1(119902) ^ andH

2(119902)q are the added inertia effects due to

the manipulator D1(119902 119902)q is the damping effects due to the

manipulator C1(119902 119902)q is the Coriolis and centripetal effects

due to the manipulator and g1(119902) is the restoring vector due

to the manipulator on the vehicle respectively

Modelling and Simulation in Engineering 5

AUV dynamics

Manipulator dynamics

Trajectory planner

minus

+

minus

+

+

+

+

+

+

+

+

Dynamiccoupling effects

+

+

+

minus

+

++

++

+

++

+

q

q

q

qd

d

dt

q

d

dt

KIR

KDR

KPR

KPV

KDV

KIV

MV

MR (q)

int

int

V

d

R

q

G2

G1

q

J( )minus1

)minus1J( )minus1

F2(q )

HT2 (q)

H2(q)

F1(q )

(middot)

(middot)

(middot)(middot)

120578

120578

120578

120578

120578120578

120578

120578

120578

120578

τ

τ

120578 120578

120578

Figure 3 Block diagram of model reference control

ldquoNot to scalerdquo

Top view

Front viewVehicle

ManipulatorVertical thrusters

Port side thruster

Starboard side thruster Stern control

plane surfaces

Lateral thruster

x

x

y

z

Figure 4 Schematic diagram of UVMS prototype model

3 Model Reference Control

This section discusses the model reference control (MRC)design in terms of feedback linearizationThis control scheme

transforms the nonlinear system dynamics into a linearsystem it compensates for all the nonlinearities in the systemby introducing nonlinear elements in the input side thusmaking the controller design more flexible [15ndash17] Unliketraditional control it can be thought of as ldquoinstantaneouslearningrdquo of the vehicle dynamicsThe individual control lawsof the underwater vehicle and the manipulator are chosensuch that the tracking errors are converging to zero Thetracking errors are defined as = 120578

119889minus120578 and q = q

119889minusq where

119889 denotes the desired (or reference) values The equationsof motion of the UVMS can be expressed in the form givenbelow [15]

M119881^ +H

2(119902) q + F

1(119902 119902 ]) + G

1(120578 119902) = 120591

119881

M119877(119902) q +H119879

2(119902) ^ + F

2(119902 119902 ]) + G

2(119902) = 120591

119877

(17)

where M119881

= M + H1(119902) F

1(119902 119902 ]) F

2(119902 119902 ]) G

2(119902)

and G1(120578 119902) are the vectors of the Coriolis centripetal and

dampingfrictional and restoring effects of the vehicle andthe manipulator respectively

6 Modelling and Simulation in Engineering

The proposed control input vectors given by (18) willcancel out or compensates for the nonlinearities in the systemas

120591119881= M

119881u119881+H

2(119902) q + F

1(119902 119902 ]) + G

1(120578 119902)

120591119877= M

119877(119902) u

119877+H119879

2(119902) ^ + F

2(119902 119902 ]) + G

2(119902)

(18)

where

u119881= J(120578)minus1 (u

120578minus

J (120578) J(120578)minus1120578)

u120578=

119889+ K

119901119881 + K

119889119881

+ K119894119881int 119889119905

u119877= q

119889+ K

119901119877q + K

119889119877q + K

119894119877int q 119889119905

(19)

K119901119881 K

119894119881 and K

119889119881are the proportional integral and

derivative gainmatrices of the vehicle controller respectivelyand K

119901119877 K

119894119877 and K

119889119877are the proportional integral and

derivative gainmatrices of themanipulator controller respec-tively Block diagram representation of the proposed UVMScontroller is presented in Figure 3

The above-mentioned control vectors lead to exponentialstable error dynamics of the vehicle and manipulator whichare given as

+ K119901119881 + K

119889119881

+ K119894119881int 119889119905 = 0

q + K119901119877q + K

119889119877q + K

119894119877int q 119889119905 = 0

(20)

which implies that tracking errors are converging to zero (ie rarr 0 and q rarr 0) and the UVMS follows the given desiredtrajectory [18]

However the above-proposed control scheme assumedthat there are no disturbances and no uncertainties associatedwith the system If the system uncertainties and externaldisturbances are considered for the analysis the system errordynamics become

+ K119901119881 + K

119889119881

+ K119894119881int 119889119905 = M

119881

minus1120591119889119881

q + K119901119877q + K

119889119877q + K

119894119877int q 119889119905 = M

119877

minus1120591119889119877

(21)

where 120591119889119881

and 120591119889119877

are the disturbance vector (which com-bines the internal disturbances such as effect of parameteruncertainties and external disturbances namely underwatercurrent etc) of the vehicle and manipulator controllerrespectively

The closed-loop characteristic equation or polynomial isgiven as

Δ

119888119881 (119904) =

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

119904

2I + 119904K119889119881+ K

119901119881+

K119894119881

119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ

119888119877 (119904) =

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

119904

2I + 119904K119889119877+ K

119901119877+

K119894119877

119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

(22)

The control gain matrices are chosen as diagonal and positivedefinite matrices such as

K119889119881= diag (119896

119889119881119894) K

119901119881= diag (119896

119901119881119894)

K119894119881= diag (119896

119894119881119894) K

119889119877= diag (119896

119889119877119894)

K119901119877= diag (119896

119901119877119894) K

119894119877= diag (119896

119894119877119894)

(23)

Therefore the closed-loop characteristic polynomialbecomes

Δ

119888119881 (119904) =

6

prod

119894=1

(119904

2+ 119904119896

119889119881119894+ 119896

119901119881119894+

119896

119894119881119894

119904

)

Δ

119888119877 (119904) =

119899

prod

119894=1

(119904

2+ 119904119896

119889119877119894+ 119896

119901119877119894+

119896

119894119877119894

119904

)

(24)

and the system error is asymptotically stable as long as thecontroller gain values are all positiveTherefore as long as thedisturbance vectors are bounded the system tracking errorsare converged to zero In other words the system followsthe given desired trajectory Moreover the controller gainmatrices have been chosen in such a way that

120582min K119901119881 gt

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120597120591119889119881

120597

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120582min K119889119881 gt

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120597120591119889119881

120597

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120582min K119901119877 gt

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120597120591119889119877

120597q

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120582min K119889119877 gt

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120597120591119889119877

120597

q

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

(25)

Hence = 0 and q = 0 for all 119905 ge 0 are its unique solutionand it can be observed that the system tracking errors areconverging to zero asymptotically The proposed controlleranalysis does not contain explicit treatment of the parametricuncertainties and external disturbance while taking temporalderivative along the closed-loop system trajectories and it isleft for further research and analysis

4 Performance Analysis of the UVMS

41 Description of the Simulated System We have accom-plished widespread computer-based numerical simulationsto explore the total performance of the proposed UVMS andthe model reference (direct adaptive) control scheme TheUVMS used for this study consists of six degrees of freedom(DOF) vehicle and a 3-DOF spatial manipulator the UVMSarrangement in conceptual design is presented in Figure 4The vehicle is a cylindrical shape (torpedo fish shaped)cruising type with the length of 11m and the diameter of025m The mass of the vehicle is 39 kg The vehicle has fivethrusters in total two propulsion thrusters (in the stern side)two vertical thrusters and one lateral thruster Thereforesurge sway and heave motions are controlled through thesethrusters actuation directly and however yaw and pitchmotions are controlled by differential actuation of propulsionand vertical thrusters Although roll motion is unactuated itcan be controlled itself due to restoring effects [19ndash21] It isknown that a necessary condition for a submersible body to

Modelling and Simulation in Engineering 7

be stable is that the centre of gravity (CG) should lie belowthe centre of buoyancy (CB) For this the vehicle is trimmed(using a float) to have the CB almost vertically above the CGand made to be nearly neutral buoyant Here the roll motionhas nonzero components of restoringmoments that representself-restoring torque for the roll direction With nonzerorestoring terms it may be possible to find continuous statefeedback laws to stabilize the system as a whole In additionto this without loss of generality we can assume that thedamping terms of nonactuated states are sufficiently largerthan their inertia terms which means that the hydrodynamicrestoring forces and torques are large enough to stabilize thenonactuated (roll) states (zero dynamics) which is a commonproperty forAUVs [19]Thismeans that the underwater robotcan be exponentially stabilized by the actuated state controlsalone

The manipulator links are cylindrical in shape and theradii of links 1 2 and 3 are 01m 005m and 005mrespectively The lengths of links 1 2 and 3 are 01m 02mand 02m respectively The link masses (along with oil con-served motors) are 039 kg 157 kg and 157 kg respectivelyHere the links are considered as cylindrical shape becausesuch shape provides uniform hydrodynamic reactions andis one of the primary candidates for possible link geometryfor underwater manipulators Although it is cylindrical ourmathematical framework does not depend on any particularshapes it can be easily accommodated by any other shapesIndeed cylindrical underwater manipulators are available inthe present market [22] Hydrodynamic parameters of theUVMS are estimated using empirical relations based on striptheory This method is verified using the available literaturetherefore these values are reliable and can be used for furtherdevelopments Some parameters like inertia centre of gravityand centre of buoyancy are calculated from the geometricaldesign of the UVMSThe total parameter list of the UVMS isgiven in Tables 2 and 3

We have compared our results with those of traditionalPID controller the following control vectors were consideredfor the vehicle and the manipulator and are given by

120591119881= K

119863119881

+ K119875119881 + K

119868119881int 119889119905

120591119877= K

119863119877q + K

119875119877q + K

119868119877int q 119889119905

(26)

where K119875119881 K

119868119881 K

119863119881 K

119875119877 K

119868119877 and K

119863119877are the propor-

tional integral and derivative gainmatrices of the vehicle andthe manipulator respectively

42 Description of the Tasks Three different tasks with fourdifferent cases have been considered for the simulations Thefirst task is that the vehicle is commanded to track a given3D trajectory without and with the manipulator (at rest or itshome position) and in this condition the vehicle acceleratesfor the initial 20 s and attains the vehicle forward speed of1ms (asymp2 knots) and for the final 20 s the vehicle deceleratesto zero speed The particular desired 3D trajectory (referto Figure 5) has been chosen for this performance analysisbecause this trajectory consists of all four main motions such

Table 2 The parameter list of the UVMS

Parameters ValuesMass of the vehicle (119898V) 39 kgLength of the vehicle (119871V) 11mDiameter of the vehicle (119889V) 025mMoment of inertia of the vehicle119868

119909034 kgm2

119868

119910371 kgm2

119868

119911371 kgm2

Centre of gravity (CG) = (119909119866 119910

119866 119911

119866) (0 0 0) m

Centre of buoyancy (CB) = (119909119861 119910

119861 119911

119861) (0 0 0015) m

Mass of the underwater manipulator links119898

103927 kg

119898

215708 kg

119898

315708 kg

Underwater manipulator link lengths119871

1005m

119871

2020m

119871

3020m

Underwater manipulator link radii119903

1010m

119903

2005m

119903

3005m

Coefficient of drag (119862119863) 125

Coefficient of lift (119862119871) 115

Table 3 The values of hydrodynamic coefficients calculated usingempirical relations based on strip theory

Vehicle added mass derivatives119883

minus117 kg 119870

minus01 kgmrad

119884V minus3484 kg 119872

minus103 kgm

119884

119903104 kgm 119872

119902minus266 kgmrad

119885

minus3483 kg 119873V minus104 kgm

119885

119902minus104 kgm 119873

119903minus265 kgmrad

Vehicle hydrodynamic parameters119883

119906|119906|minus7365 kgm 119883

119906minus212 kgs

119883V|V| minus0737 kgm 119883V minus031 kgs119883

119908|119908|minus0737 kgm 119883

119908minus031 kgs

119883

119902|119902|minus1065 kgmrad 119883

119902minus051 kgms

119883

119903|119903|minus1065 kgmrad 119883

119903minus051 kgms

119884V|V| minus1122 kgm 119884V minus6245 kgs119884

119903|119903|0250 kgmrad 119884

119903012 kgms

119885

119908|119908|minus1122 kgm 119885

119908minus6245 kgs

119885

119902|119902|minus0250 kgmrad 119885

119902012 kgms

119870

119901|119901|minus05975 kgm2rad2 119870

119901minus03125 kgm2s

119872

119908|119908|2244 kgmrad 119872

11990812 kgms

119872

119902|119902|minus1195 kgm2rad2 119872

119902minus5975 kgm2s

119873V|V| minus2244 kgmrad 119873V 12 kgms

as sway in and out and heave up and downThe average valueof sway velocity is 025ms (asymp05 knots) (same value for heaveas well) This task is performed to identify the influences of

8 Modelling and Simulation in Engineering

050

100150

200

05

1015

200

5

10

15

20

Desired 3D pathPID without armMRC without arm

PID with armMRC with arm

z(m

)

y (m)x (m)

Figure 5 Comparative trajectory tracking control results

the underwater manipulator effects during vehicle trackingcontrol In the second task the vehicle is free to move (nocontrol action involved) and the manipulator has a certainrepeated desired trajectory This task is mainly performedto identify the vehicle behavior during manipulator motionIn all the above tasks the initial velocities and positions ofthe vehicle and the manipulator are chosen to be zero andthe initial desired and actual positions and orientations arethe same In the third task two basic trajectories for themanipulator have been chosen for simulations a circulartrajectory (in 3D space) and a rectangular trajectory (in 119910119911plane) along with a straight line in 3D space This is forthe reason that most of the underwater intervention tasksinvolve these types of trajectories and also we can arrangeany spatial trajectory by combining these trajectories For therectangular trajectory we have selected a cubic polynomialfunction as the trajectory function which imposes that thetrajectory is continuous and smooth

In the performance analysis the sensory noises inposition and orientation measurements are introduced andwe have considered Gaussian noise of 001m mean and001m standard deviation for the positionmeasurements and02

∘ mean and 02∘ standard deviation for the orientationmeasurements The thruster dynamic characteristics are alsoincorporated in the simulations All the vehicle thrusters areconsidered as an identical one and the following thrustercharacteristics are considered for the analysis the thrusterresponse delay time is 200ms efficiency is 95and saturationlimits are plusmn20N The vehicle surge thrusters are located at05m from the body centre along the 119909-axis and offset eachside 03m from 119910-axis The lateral thruster is exactly locatedon the body centre and vertical thrusters are placed on the 119909-axis 04m apart from the centre at each side The controllerupdate rate and sensor response time are considered as 100mseach

43 Results and Discussions Here numerical simulationresults are shown and discussed to investigate the dynamic

Table 4 Controller parameter settings for simulations

Vehicle controller parameters Values119870

119901119881diag(42 22 25 0 25 27)

119870

119889119881diag(225 12 13 0 15 13)

119870

119894119881diag(05 02 03 0 25 22)

119870

119875119881diag(180 130 150 0 150 130)

119870

119863119881diag(80 100 100 0 80 90)

119870

119868119881diag(15 12 15 0 16 18)

Manipulator controller parameters Values119870

119901119877diag(5 10 12)

119870

119889119877diag(3 5 8)

119870

119894119877diag(01 02 02)

119870

119875119877diag(60 80 75)

119870

119863119877diag(35 40 50)

119870

119868119877diag(1 15 2)

coupling effects and the effectiveness of the proposed model-based control scheme which is expected to provide anintuitive promising prospective of the proposed approach

431 Underwater Vehicle Tracking a Given 3D Trajectorywith the Underwater Manipulator In this case as mentionedearlier the vehicle is commanded to follow a given 3D desiredtrajectory The desired 3D trajectory is given in Figure 5The controller gain values are tuned based on the geneticalgorithms (GA) for minimizing the integral squared error(ISE) as the costobjective function [23] Here we haveconsidered both the model reference control and the PIDcontrol performance to be almost equal in the ideal situationwhich makes the controller performance comparison quitereasonable and gives much better way of understandingBased on the GA tuning method the controller parametersare obtained and given in Table 4 The same set of controllerparameters are used throughout the entire performanceanalysis

Initially the performance analysis is carried out for thevehicle trajectory tracking without manipulator inclusionThe actual simulated trajectories based on MRC and PID arepresented in Figure 5These results show that both controllersare good enough to track the given trajectory and thetracking errors are within the design limits (error limits forthe vehicle during trajectory tracking are plusmn02m and plusmn02∘in positions and orientations resp) as well The trackingerrors are presented in Figures 6 7 8 9 10 and 11 In thesecond set of simulations the manipulator is included andthe inclusion effects during trajectory tracking of the vehicleare considered Here the manipulator links are folded andarranged in such a way that the influences on the vehicledynamics are small (ie manipulator joint angles are 120579

1=

180

∘ 1205792= 0

∘ and 1205793= 180

∘) The manipulator inclusionshows that there are significant performance changes in thevehicle trajectory tracking especially during the heave andsway motion tracking The heave roll and pitch motionsof the vehicle are greatly influenced by the underwatermanipulator inclusion which are replicated in the results

Modelling and Simulation in Engineering 9

0 50 100 150 200 250 300minus01

minus005

0

005

01

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Trac

king

erro

r inx

(xe) (

m)

Figure 6 Tracking errors in 119909 position for a given 3D trajectory

0 50 100 150 200 250 300minus002

minus001

0

001

002

003

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Trac

king

erro

r iny

(ye) (

m)

Figure 7 Tracking errors in 119910 position for a given 3D trajectory

(refer to Figures 6 to 11) However the manipulator inclusioneffects are better adapted in the model reference control thanin the PID control As can be observed from Figures 8 and10 the manipulator inclusion causes an initial pitch anglevariation drifts the vehicle in the heave direction during thestraight line motion (during acceleration stage) Howeverthese unwanted effects are compensated successfully in themodel reference control and therefore tracking errors do notexceed their design limits

432 Manipulator following a Given Desired 3D Trajectorywith the Freely Moving Underwater Vehicle (without VehicleControl) As mentioned earlier in this section this task ismainly to address the interaction effects and their influences

0 50 100 150 200 250 300minus005

0

005

01

015

02

03

Trac

king

erro

r inz

(ze) (

m)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 8 Tracking errors in 119911 position for a given 3D trajectory

0 50 100 150 200 250 300minus10

minus5

0

5

10

15

20

Trac

king

erro

r in

roll

(120601e) (

deg)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 9 Tracking errors in roll for a given 3D trajectory

on theUVMS For this task the vehicle controller is removedand only the underwater manipulator follows a given desiredcontinuous trajectory The desired values of joint positionsare as follows 120579

1119889= 90

∘ sin (01119905) 1205792119889

= 90

∘ and 1205793119889

=

minus45

∘ The simulation results of this condition are presentedin Figures 12 13 14 15 and 16 From the results it is observedthat the vehicle is started getting drifted from its initialposition and it is moving forward with an average velocityof 002ms (approximately) for the repeated underwatermanipulator movements It shows that the manipulator linksare affected due to the dynamic coupling effects Fromthe results it is observed that the vehicle swims duringmanipulator movements if the vehicle does not have anycontrol actionThese errors and forward speed are increasing

10 Modelling and Simulation in Engineering

0 50 100 150 200 250 300minus15

minus1

minus05

0

05

1

15

Trac

king

erro

r in

pitc

h (120579

e) (

deg)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 10 Tracking errors in pitch for a given 3D trajectory

0 50 100 150 200 250 300minus1

minus05

0

05

1

Trac

king

erro

r in

yaw

(120595e) (

deg)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 11 Tracking errors in yaw for a given 3D trajectory

with the manipulator oscillation frequency and their jointangle magnitudes In addition the direction of the vehiclersquosmovement varies depending on the manipulator positionsand its direction ofmovementsThese results can be extendedto the work towards swimming robots and their dynamicmodeling aspects

433 Underwater Manipulator following a Given DesiredCircular Trajectory with Vehicle Control The circular trajec-tory chosen for the analysis has 02m in diameter and anaverage speed of 00125ms These parameters are chosenwith the consideration of manipulator actuators workspaceand control The results from computer simulations arepresented in Figures 15ndash18 In Figure 15 both desired andactual task space trajectories are plotted and the task spacetracking errors are given in Figures 16ndash18 From the results

0 5 10 15 20minus006

minus004

minus002

0

002

004

006

008

01

012

Posit

ion

erro

rs (m

)

Time (t) (s)

xeyeze

Figure 12 Tracking errors in the vehicle positions (when manipu-lator has motion)

0 5 10 15 20minus3

minus2

minus1

0

1

2

3

4

Attit

ude e

rror

s (de

g)

Time (t) (s)

120601e120579e120595e

Figure 13 Tracking errors in the vehicle orientations (when thevehicle has no control and the manipulator has repeated motion)

it is observed that the manipulator tip tracks the givendesired task space trajectories quite satisfactorily in both PIDand MRC schemes in the ideal conditions (no disturbancesno uncertainties etc) Then in order to demonstrate theadaptability and robustness of the proposed controller anuncertain condition is considered for the simulations Thefollowing conditions are considered for the uncertain condi-tion analysis

(i) the UVMS parameters are assumed to be inaccurate(about 10 for each parameters)

(ii) the manipulator carries a payload of 1 kg at its tip

Modelling and Simulation in Engineering 11

0708

091

minus02minus01

001

02045

046

047

048

049

Desired tool tip positionActual tool tip position

z(m

)

y (m)x (m)

Figure 14 Manipulator tip position in 3D space (when the vehiclehas no control)

06507

07508

085

005

01

015

minus01

minus005

0

005

Desired trajectoryPIDMRC

PID with uncertaintyMRC with uncertainty

z(m

)

y (m)x (m)

Figure 15 Task space (119909119910119911) trajectories (results from the circulartrajectory)

(iii) an unknown ocean current is added in the simulationby properly considering the relative velocity of thein the dynamic model It is assumed to have anirrotational current constant in the inertial frameand the value of the current is considered as ^

119888=

[02 02 01 0 0 0]

119879ms

The results are presented in Figures 15ndash18 and from theseresults it is observed that the proposed controller is goodin adapting the uncertainties and disturbances (refer toFigure 15) Figures 16 and 17 show that tracking errors of119909 and 119910 in both PID and MRC methods are almost thesame and results satisfactorily however the tracking error in119911 substantiates that the proposed controller is comparativelygood in the presence of uncertainties and disturbances

434 Underwater Manipulator following a Given DesiredRectangular Trajectory with Vehicle Control The rectangulartrajectory chosen for the analysis has 04m in width and

0 5 10 15 20 25 30minus002

minus0015

minus001

minus0005

0

0005

001

0015

Time (t) (s)

PIDMRC

PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r inx

(xe) (

m)

Figure 16 Time histories of the manipulator tip position trackingerror in 119909 (circular trajectory)

0 5 10 15 20 25 30minus4

minus3

minus2

minus1

0

1

2

3

4

5

6

MRC

Time (t) (s)

PID PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r iny

(ye) (

m)

times10minus3

Figure 17 Time histories of the manipulator tip position trackingerror in 119910 (circular trajectory)

02m in height in the 119910119911 plane and an average speedof 005ms As mentioned in the last case the trajectoryhas been chosen with the consideration of the manipulatorcharacteristics Two conditions have been considered for theanalysis ideal condition (no disturbances no uncertaintiesetc) and an uncertain condition (the same as the previouscase Section 433) The results from computer simulationsare plotted in Figure 19 In the ideal condition both con-trollers show quite satisfactory performance and in theuncertain condition the proposed controller shows betterperformance

12 Modelling and Simulation in Engineering

MRC

0 5 10 15 20 25 30minus002

0

002

004

006

008

01

012

Time (t) (s)

PID PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r inz

(ze) (

m)

Figure 18 Time histories of the manipulator tip position trackingerror in 119911 (circular trajectory)

064 066 068 07 072

minus020

0202

025

03

035

04

Desired trajectoryPIDMRC

PID with uncertaintyMRC with uncertainty

z(m

)

y (m)x (m)

Figure 19 Task space (119909119910119911) trajectories (results from the rectangu-lar trajectory)

In both trajectory tracking cases the thruster forces donot exceed plusmn5N and the manipulator actuator torques staywithinplusmn015Nmwhich arewell within the range of actuators

5 Conclusions

In this study the interaction effects due to the dynamiccoupling between the vehicle and the manipulator wereinvestigated using closed-form equations which provide ageneralized scheme for formulating the equations of motionof the UVMS The proposed scheme makes it possible toidentify the structure nature and properties of the systemand it simplifies the control design This study also proposeda model reference control approach for an underactuated

UVMS to perform underwater intervention tasks incorpo-rating desired trajectory information Extensive simulationswere carried out to verify and demonstrate the effectivenessof the proposed scheme In particular the performance ofthe model reference controller is compared with that of theconventional PID controller for the given UVMS operationscenarios The obtained results confirm the effectiveness androbustness of the proposed scheme in terms of tracking errorsand control effort in the presence of external disturbancesand parameter uncertainties This research provides a gener-alized framework for modeling and controlling of an UVMSconsidering the dynamic coupling between the vehicle andthe manipulator which is crucial for achieving underwatermanipulation tasks for a variety of scientific industrial andmilitary missions using unmanned underwater vehicles

Conflict of Interests

Authors confirm that this paper has not been publishedelsewhere and is not under consideration by another journalAll authors have approved the manuscript and agree withsubmission toModelling and Simulation in EngineeringTheauthors have no conflict of interests to declare

Acknowledgments

The author would like to acknowledge Professor JinwhanKim for his valuable suggestions and discussions on under-water manipulator This research was supported in partby the World Class University (WCU) program throughthe National Research Foundation of Korea funded by theMinistry of Education Science and Technology (R31-2008-000-10045-0)

References

[1] G Antonelli F Caccavale S Chiaverini and L Villani ldquoTrack-ing control for underwater vehicle-manipulator systems withvelocity estimationrdquo IEEE Journal of Oceanic Engineering vol25 no 3 pp 399ndash413 2000

[2] G Marani S K Choi and J Yuh ldquoUnderwater autonomousmanipulation for intervention missions AUVsrdquo Ocean Engi-neering vol 36 no 1 pp 15ndash23 2009

[3] S McMillan D E Orin and R B McGhee ldquoEfficient dynamicsimulation of an underwater vehicle with a robotic manipula-torrdquo IEEE Transactions on Systems Man and Cybernetics vol25 no 8 pp 1194ndash1206 1995

[4] T I Fossen Guidance and Control of Ocean Vehicles WileyChichester UK 1994

[5] T J Tarn G A Shoults and S P Yang ldquoA dynamic model ofan underwater vehicle with a robotic manipulator using Kanersquosmethodrdquo Autonomous Robots vol 3 no 2-3 pp 269ndash283 1996

[6] H Mahesh J Yuh and R Lakshmi ldquoA Coordinated controlof an underwater vehicle and robotic manipulatorrdquo Journal ofRobotic Systems vol 8 no 3 pp 339ndash370 1991

[7] N Sarkar and T K Podder ldquoCoordinated motion planningand control of autonomous underwater vehicle-manipulatorsystems subject to drag optimizationrdquo IEEE Journal of OceanicEngineering vol 26 no 2 pp 228ndash239 2001

Modelling and Simulation in Engineering 13

[8] T W McLain S M Rock and M J Lee ldquoExperiments inthe coordinated control of an underwater armvehicle systemrdquoAutonomous Robots vol 3 no 2-3 pp 213ndash232 1996

[9] M W Dunnigan and G T Russell ldquoEvaluation and reductionof the dynamic coupling between a manipulator and an under-water vehiclerdquo IEEE Journal of Oceanic Engineering vol 23 no3 pp 260ndash273 1998

[10] B H Jun P M Lee and J Lee ldquoManipulability analysisof underwater robotic arms on ROV and application totask-oriented joint configurationrdquo in Proceedings of the IEEEOCEANS pp 1548ndash1553 November 2004

[11] J H Ryu D S Kwon and P M Lee ldquoControl of underwatermanipulators mounted on an ROV using base force informa-tionrdquo in Proceedings of the IEEE International Conference onRobotics and Automation (ICRA rsquo01) pp 3238ndash3243 May 2001

[12] M Hildebrandt L Christensen J Kerdels J Albiez and FKirchner ldquoRealtime motion compensation for ROV-based tele-operated underwater manipulatorsrdquo in Proceedings of the IEEEOCEANS pp 1ndash6 May 2009

[13] H Shim B H Jun P M Lee H Baek and J Lee ldquoWorkspacecontrol system of underwater tele-operated manipulators on anROVrdquo Ocean Engineering vol 37 no 11-12 pp 1036ndash1047 2010

[14] J J Craig Introduction to Robotics Addison Wesley BostonMass USA 1986

[15] G Antonelli Underwater Robots Motion and Force Control ofVehicle-Manipulator Systems Springer Berlin Germany 2006

[16] K Kim andT Ura ldquoAppliedmodel-based analysis and synthesisfor the dynamics guidance and control of an autonomousundersea vehiclerdquo Mathematical Problems in Engineering vol2010 Article ID 149385 23 pages 2010

[17] T I Fossen Marine Control Systems Guidance Navigationand Control of Ships Rigs and Underwater Vehicles MarineCybernetics AS 2002

[18] J J E Slotine and W Li Applied Nonlinear Control Prentice-Hall Upper Saddle River NJ USA 1991

[19] K Y Pettersen and O Egeland ldquoPosition and attitude control ofan underactuated autonomous underwater vehiclerdquo in Proceed-ings of the 1996 35th IEEE Conference on Decision and Controlpp 987ndash991 Kobe Japan December 1996

[20] T H Koh MW S Lau G Seet and E Low ldquoA control modulescheme for an underactuated underwater robotic vehiclerdquo Jour-nal of Intelligent and Robotic Systems Theory and Applicationsvol 46 no 1 pp 43ndash58 2006

[21] M Santhakumar and T Asokan ldquoInvestigations on the hybridtracking control of an underactuated autonomous underwaterrobotrdquo Advanced Robotics vol 24 no 11 pp 1529ndash1556 2010

[22] ANSALDO Nucleare Underwater Manipulator MARIS 7080Use and Maintenance Manual Ansaldo Nuclear DivisionGenoa Italy 1996

[23] K Deb Optimization for Engineering Design Algorithms andExamples Prentice Hall New Delhi India 2004

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International Journal of

Modelling and Simulation in Engineering 3

Y1

L1

X1

Z1

Y2

L2

X2

Z2

Y3

L3

X3

Z3

Y4

X4

Z4

1205791

Y0

d1

X0

Z0

1205792

1205793

1205794

Figure 2 Establishing link coordinate systems of the manipulator

shown in Table 1 Based on the underwater link parameters inTable 1 the homogeneous transformation matrix [14] whichis derived that specifies the location of the end effector orTCP with respect to the base coordinate system is expressedas

T0

4= [

R0

4P0

4

0 0 0 1

] = T0

1T1

2T2

3T3

4

T119896minus1

119896

=

[

[

[

[

cos 120579119896

minus sin 120579119896

0 119886

119896minus1

sin 120579119896cos120572

119896minus1cos 120579

119896cos120572

119896minus1minussin120572

119896minus1minussin120572

119896minus1119889

119896

sin 120579119896sin120572

119896minus1cos 120579

119896sin120572

119896minus1cos120572

119896minus1cos120572

119896minus1119889

119896

0 0 0 1

]

]

]

]

(4)

The matrix R0

4and the vector P0

4= [119901

119909119901

119910119901

119911]

119879 are therotational matrix and the position vector from the basecoordinates to the end effector respectively From the abovehomogeneous transformation matrix we can obtain the endeffectorrsquos position for feedback control and the elementsfor solving the Jacobian matrix Based on the experimentalunderwater manipulator parameters (refer to Table 1) theforward kinematic solutions are obtained as follows

119901

119909= cos 120579

1(119871

1+ 119871

2cos 120579

2+ 119871

3cos (120579

2+ 120579

3))

119901

119910= sin 120579

1(119871

1+ 119871

2cos 120579

2+ 119871

3cos (120579

2+ 120579

3))

119901

119911= 119871

2sin 120579

2+ 119871

3sin (120579

2+ 120579

3)

(5)

222 Inverse Kinematics of the Underwater Manipulator Inthe workspace-control system each joint of the underwatermanipulator is controlled by the joint angle command calcu-lated from the differential inverse kinematic solutions based

Table 1 D-H parameters of the 3-DOF underwater manipulator

Joint axis(119896)

Link offset(120572

119896minus1)

Link length(119886

119896minus1)

Joint distance(119889

119896)

Joint angle(120579

119896)

1 0∘ 0 0 120579

1

2 90∘119871

10 120579

2

3 0∘119871

20 120579

3

4 0∘119871

30 120579

4= 0∘

on the knownCartesian coordinatesThe closed-form inversekinematic solutions of the 3-DOF underwater manipulatorare described as

120579

1= arctan 2 (119901

119910 119901

119909)

120579

2= arctan 2 (119886119887 minus 119887119888 119886119888 + 119887119889)

120579

3= arctan 2 (sin 120579

3 cos 120579

3)

(6)

where

cos 1205793=

119886

2+ 119887

2minus 119871

2

2minus 119871

2

3

2119871

2119871

3

sin 1205793=radic1 minus cos2120579

3

119886 =

119901

119909

cos 1205791

minus 119871

1 119887 = 119901

119911

119888 = 119871

3cos 120579

3+ 119871

2 119889 = 119871

3sin 120579

3

(7)

23 Dynamic Model of the Underwater Manipulator Thedynamic model of an underwater manipulator is developedthrough the recursive Newton-Euler algorithm In this workit is assumed that the underwater manipulator links are thebuildup of cylindrical elements The effects of the hydrody-namic forces on circular cylindrical elements are describedin the section which mainly consist of added mass effectshydrodynamic drag forces and moments and buoyancyeffects [4] The force and moment interactions between twoadjacent links are as follows

119896f119896=

119896f119896+1

= R119896+1

119896

119896+1f119896+1+ F

119896minus 119898

119896g119896+ b

119896+ p

119896

119896t119896=

119896t119896+1

= R119896+1

119896

119896+1t119896+1+ d

119896119896+1times R119896+1

119896

119896+1f119896+1

+ d119896119896119888

times F119896+ T

119896+ d

119896119896119888

times (minus119898

119896g119896+ p

119896) + d

119896119896119887times b

119896+ n

119896

(8)

p119896= F

119871119896+ F

119863119896+ F

119878119896

F119878119896= D119896

119904

119896k119896

F119863119896=

1003816

1003816

1003816

1003816

1003816

119896k119896

1003816

1003816

1003816

1003816

1003816

119879

D119896

119863

119896k119896

F119871119896=

1003816

1003816

1003816

1003816

1003816

119896k119896

1003816

1003816

1003816

1003816

1003816

119879

D119896

119871

119896k119896

n119896=

119896k119896times (M

119896

119896k119896)

(9)

4 Modelling and Simulation in Engineering

F119896= M

119896(

119896a119896+

119896120572119896times

119896d119896119896119888

+

119896120596

119896times (

119896120596

119896times

119896d119896119896119888))

T119896= I

119896

119896120572119896+

119896120596

119896times (I

119896

119896120596

119896)

119896+1120596

119896+1= R119896

119896+1

119896120596

119896+ z119879 119902

119896+1

119896+1120572119896+1

= R119896

119896+1(

119896120572119896+

119896120596

119896times z119879119902

119896) + z119879 119902

119896+1

119896+1k119896+1

= R119896

119896+1

119896k119896+

119896+1120596

119896+1times

119896+1d119896119896119888

119896+1a119896+1

= R119896

119896+1

119896a119896+

119896+1120572119896+1

times

119896+1d119896+1119896

+

119896+1120596

119896+1times (

119896+1120596

119896+1times

119896+1d119896+1119896

)

(10)

M119896=

[

[

[

[

[

[

119898

119896+

120587120588119903

119896

2119871

119896

10

0 0

0 119898

119896+ 120587120588119903

119896

2119871

1198960

0 0 119898

119896+ 120587120588119903

119896

2119871

119896

]

]

]

]

]

]

I119896=

[

[

[

[

[

[

[

119868

1199090 0

0 119868

119910+

120587120588119903

119896

2119871

119896

3

12

0

0 0 119868

119911+

120587120588119903

119896

2119871

119896

3

12

]

]

]

]

]

]

]

(11)

where 119896 denotes the corresponding joint axis (119896 = 1 2 3)R119896+1

119896is the rotation matrix f

119896is the resultant force vector t

119896

is the resultant moment vector p119896is the linear and quadratic

hydrodynamic friction forces and F119878119896 F

119863119896 and F

119871119896are

vectors of linear skin friction quadratic drag and quadraticlift effects respectively D119896

119904is the linear skin friction matrix

D119896

119871is the diagonal matrix which contains lift coefficientsD119896

119863

is the diagonal matrix which contains drag coefficients g119896is

the gravity force vector b119896is the buoyancy force vector n

119896

is the hydrodynamic moment vector d119896119896119887

is the vector fromthe center of buoyancy of the link d

119896119896119888is the vector from the

center of gravity of the link d119896119896+1

is the vector from joint 119896to 119896 + 1 F

119896is the vector of total forces acting at the center of

mass of link T119896is the vector of total moments acting at the

center ofmass of link a119896is the linear acceleration vector 120572

119896is

the angular acceleration vector k119896is the linear velocity vector

120596119896is the angular velocity vector m

119896is the mass of the link

M119896is the mass and added mass matrix of the link (located

at the center of mass) I119896is the moment of inertia and added

moment of matrix of the link (located at the center of mass)and z119879 is the unit vector along the 119911-axis

The joint torques of each link are represented as

120591

119877119896= z119879 119896t

119896

(12)

The recursive Newton-Euler dynamics algorithm for alllinks symbolically yields the equations of motion for theunderwater manipulatorThe result can be written as follows

M119877(119902) q + C

119877(119902 119902) q +D

119877(119902 119902) q + g

119877(119902) = 120591

119877 (13)

where q is the vector of joint variables and q = [1205791120579

2120579

3]

119879120579

1 120579

2 120579

3are the joint angles of the corresponding underwater

manipulator linksM119877(119902)q is the vector of inertial forces and

moments of the manipulator C119877(119902 119902)q is the vector of Cori-

olis and centripetal effects of the manipulator D119877(119902 119902)q is

the vector of damping effects of the manipulator g119877(119902) is the

restoring vector of themanipulator and 120591119877= [120591

1198771120591

1198772120591

1198773]

119879

is the vector of control inputs

24 Dynamic Model of Vehicle-Manipulator System Themanipulator has an initial velocity equal to the velocity ofthe vehicle This initial velocity should be accounted in themanipulator dynamics Similarly the weight and movementof the manipulator links will affect the vehicle dynamics(these effects are considered as disturbances) and vice versaBy considering the above issues the vehicle and manipulatorequations of motions can be written as follows

M ^ + C (]) ^ +D (]) ^ + g (120578) = 120591119881+ 120590

M119877(119902) q +H119879

2(119902) ^ + C

119877(119902 119902) q +D

119877(119902 119902) q

+ g119877(119902) + C119879

119881(119902 119902 ]) ^ +D119879

119881(119902 119902 ]) ^ = 120591

119877

(14)

where H119879

2(119902) ^ is the vector of reaction forces and moments

between the vehicle and the manipulator C119879

119881(119902 119902 ])^ is the

vector of Coriolis and centripetal effects due to couplingbetween the vehicle and the manipulator and D119879

119881(119902 119902 ])^

is the vector of quadratic drag effects due to the interactionbetween the vehicle and the manipulator 120590 = [120590

119879

119891120590119879

119898]

119879 isthe vector which contains forces and moments disturbancesdue to weight and movement of the manipulator linksConsider

120590119891= R119861

0

0f1

120590119898= R119861

0

0t1minus dvehiclemanipulator times (R

119861

0

0f1)

(15)

where R119861

0and dvehiclemanipulator are the rotation matrix and

position vector from the vehicle-fixed frame to the manip-ulator base frame respectively 0f

1and 0t

1are the vectors

of force and moments of the base frame respectively Thesevectors are derived using (8) and these effects are functionof the manipulator joint coordinates (ie q q and q) andthe vehicle states After evaluating the interaction forces andmoments between the manipulator and the vehicle based onthese vectors the equations of motion of the vehicle can bewritten as

M ^ +H1(119902) ^ + C (]) ^ +D (]) ^ + C

119881(119902 119902 ]) ^

+D119881(119902 119902 ]) ^ + g (120578) +H

2(119902) q + C

1(119902 119902) q

+D1(119902 119902) q + g

1(119902) = 120591

119881

(16)

whereH1(119902) ^ andH

2(119902)q are the added inertia effects due to

the manipulator D1(119902 119902)q is the damping effects due to the

manipulator C1(119902 119902)q is the Coriolis and centripetal effects

due to the manipulator and g1(119902) is the restoring vector due

to the manipulator on the vehicle respectively

Modelling and Simulation in Engineering 5

AUV dynamics

Manipulator dynamics

Trajectory planner

minus

+

minus

+

+

+

+

+

+

+

+

Dynamiccoupling effects

+

+

+

minus

+

++

++

+

++

+

q

q

q

qd

d

dt

q

d

dt

KIR

KDR

KPR

KPV

KDV

KIV

MV

MR (q)

int

int

V

d

R

q

G2

G1

q

J( )minus1

)minus1J( )minus1

F2(q )

HT2 (q)

H2(q)

F1(q )

(middot)

(middot)

(middot)(middot)

120578

120578

120578

120578

120578120578

120578

120578

120578

120578

τ

τ

120578 120578

120578

Figure 3 Block diagram of model reference control

ldquoNot to scalerdquo

Top view

Front viewVehicle

ManipulatorVertical thrusters

Port side thruster

Starboard side thruster Stern control

plane surfaces

Lateral thruster

x

x

y

z

Figure 4 Schematic diagram of UVMS prototype model

3 Model Reference Control

This section discusses the model reference control (MRC)design in terms of feedback linearizationThis control scheme

transforms the nonlinear system dynamics into a linearsystem it compensates for all the nonlinearities in the systemby introducing nonlinear elements in the input side thusmaking the controller design more flexible [15ndash17] Unliketraditional control it can be thought of as ldquoinstantaneouslearningrdquo of the vehicle dynamicsThe individual control lawsof the underwater vehicle and the manipulator are chosensuch that the tracking errors are converging to zero Thetracking errors are defined as = 120578

119889minus120578 and q = q

119889minusq where

119889 denotes the desired (or reference) values The equationsof motion of the UVMS can be expressed in the form givenbelow [15]

M119881^ +H

2(119902) q + F

1(119902 119902 ]) + G

1(120578 119902) = 120591

119881

M119877(119902) q +H119879

2(119902) ^ + F

2(119902 119902 ]) + G

2(119902) = 120591

119877

(17)

where M119881

= M + H1(119902) F

1(119902 119902 ]) F

2(119902 119902 ]) G

2(119902)

and G1(120578 119902) are the vectors of the Coriolis centripetal and

dampingfrictional and restoring effects of the vehicle andthe manipulator respectively

6 Modelling and Simulation in Engineering

The proposed control input vectors given by (18) willcancel out or compensates for the nonlinearities in the systemas

120591119881= M

119881u119881+H

2(119902) q + F

1(119902 119902 ]) + G

1(120578 119902)

120591119877= M

119877(119902) u

119877+H119879

2(119902) ^ + F

2(119902 119902 ]) + G

2(119902)

(18)

where

u119881= J(120578)minus1 (u

120578minus

J (120578) J(120578)minus1120578)

u120578=

119889+ K

119901119881 + K

119889119881

+ K119894119881int 119889119905

u119877= q

119889+ K

119901119877q + K

119889119877q + K

119894119877int q 119889119905

(19)

K119901119881 K

119894119881 and K

119889119881are the proportional integral and

derivative gainmatrices of the vehicle controller respectivelyand K

119901119877 K

119894119877 and K

119889119877are the proportional integral and

derivative gainmatrices of themanipulator controller respec-tively Block diagram representation of the proposed UVMScontroller is presented in Figure 3

The above-mentioned control vectors lead to exponentialstable error dynamics of the vehicle and manipulator whichare given as

+ K119901119881 + K

119889119881

+ K119894119881int 119889119905 = 0

q + K119901119877q + K

119889119877q + K

119894119877int q 119889119905 = 0

(20)

which implies that tracking errors are converging to zero (ie rarr 0 and q rarr 0) and the UVMS follows the given desiredtrajectory [18]

However the above-proposed control scheme assumedthat there are no disturbances and no uncertainties associatedwith the system If the system uncertainties and externaldisturbances are considered for the analysis the system errordynamics become

+ K119901119881 + K

119889119881

+ K119894119881int 119889119905 = M

119881

minus1120591119889119881

q + K119901119877q + K

119889119877q + K

119894119877int q 119889119905 = M

119877

minus1120591119889119877

(21)

where 120591119889119881

and 120591119889119877

are the disturbance vector (which com-bines the internal disturbances such as effect of parameteruncertainties and external disturbances namely underwatercurrent etc) of the vehicle and manipulator controllerrespectively

The closed-loop characteristic equation or polynomial isgiven as

Δ

119888119881 (119904) =

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

119904

2I + 119904K119889119881+ K

119901119881+

K119894119881

119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ

119888119877 (119904) =

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

119904

2I + 119904K119889119877+ K

119901119877+

K119894119877

119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

(22)

The control gain matrices are chosen as diagonal and positivedefinite matrices such as

K119889119881= diag (119896

119889119881119894) K

119901119881= diag (119896

119901119881119894)

K119894119881= diag (119896

119894119881119894) K

119889119877= diag (119896

119889119877119894)

K119901119877= diag (119896

119901119877119894) K

119894119877= diag (119896

119894119877119894)

(23)

Therefore the closed-loop characteristic polynomialbecomes

Δ

119888119881 (119904) =

6

prod

119894=1

(119904

2+ 119904119896

119889119881119894+ 119896

119901119881119894+

119896

119894119881119894

119904

)

Δ

119888119877 (119904) =

119899

prod

119894=1

(119904

2+ 119904119896

119889119877119894+ 119896

119901119877119894+

119896

119894119877119894

119904

)

(24)

and the system error is asymptotically stable as long as thecontroller gain values are all positiveTherefore as long as thedisturbance vectors are bounded the system tracking errorsare converged to zero In other words the system followsthe given desired trajectory Moreover the controller gainmatrices have been chosen in such a way that

120582min K119901119881 gt

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120597120591119889119881

120597

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120582min K119889119881 gt

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120597120591119889119881

120597

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120582min K119901119877 gt

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120597120591119889119877

120597q

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120582min K119889119877 gt

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120597120591119889119877

120597

q

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

(25)

Hence = 0 and q = 0 for all 119905 ge 0 are its unique solutionand it can be observed that the system tracking errors areconverging to zero asymptotically The proposed controlleranalysis does not contain explicit treatment of the parametricuncertainties and external disturbance while taking temporalderivative along the closed-loop system trajectories and it isleft for further research and analysis

4 Performance Analysis of the UVMS

41 Description of the Simulated System We have accom-plished widespread computer-based numerical simulationsto explore the total performance of the proposed UVMS andthe model reference (direct adaptive) control scheme TheUVMS used for this study consists of six degrees of freedom(DOF) vehicle and a 3-DOF spatial manipulator the UVMSarrangement in conceptual design is presented in Figure 4The vehicle is a cylindrical shape (torpedo fish shaped)cruising type with the length of 11m and the diameter of025m The mass of the vehicle is 39 kg The vehicle has fivethrusters in total two propulsion thrusters (in the stern side)two vertical thrusters and one lateral thruster Thereforesurge sway and heave motions are controlled through thesethrusters actuation directly and however yaw and pitchmotions are controlled by differential actuation of propulsionand vertical thrusters Although roll motion is unactuated itcan be controlled itself due to restoring effects [19ndash21] It isknown that a necessary condition for a submersible body to

Modelling and Simulation in Engineering 7

be stable is that the centre of gravity (CG) should lie belowthe centre of buoyancy (CB) For this the vehicle is trimmed(using a float) to have the CB almost vertically above the CGand made to be nearly neutral buoyant Here the roll motionhas nonzero components of restoringmoments that representself-restoring torque for the roll direction With nonzerorestoring terms it may be possible to find continuous statefeedback laws to stabilize the system as a whole In additionto this without loss of generality we can assume that thedamping terms of nonactuated states are sufficiently largerthan their inertia terms which means that the hydrodynamicrestoring forces and torques are large enough to stabilize thenonactuated (roll) states (zero dynamics) which is a commonproperty forAUVs [19]Thismeans that the underwater robotcan be exponentially stabilized by the actuated state controlsalone

The manipulator links are cylindrical in shape and theradii of links 1 2 and 3 are 01m 005m and 005mrespectively The lengths of links 1 2 and 3 are 01m 02mand 02m respectively The link masses (along with oil con-served motors) are 039 kg 157 kg and 157 kg respectivelyHere the links are considered as cylindrical shape becausesuch shape provides uniform hydrodynamic reactions andis one of the primary candidates for possible link geometryfor underwater manipulators Although it is cylindrical ourmathematical framework does not depend on any particularshapes it can be easily accommodated by any other shapesIndeed cylindrical underwater manipulators are available inthe present market [22] Hydrodynamic parameters of theUVMS are estimated using empirical relations based on striptheory This method is verified using the available literaturetherefore these values are reliable and can be used for furtherdevelopments Some parameters like inertia centre of gravityand centre of buoyancy are calculated from the geometricaldesign of the UVMSThe total parameter list of the UVMS isgiven in Tables 2 and 3

We have compared our results with those of traditionalPID controller the following control vectors were consideredfor the vehicle and the manipulator and are given by

120591119881= K

119863119881

+ K119875119881 + K

119868119881int 119889119905

120591119877= K

119863119877q + K

119875119877q + K

119868119877int q 119889119905

(26)

where K119875119881 K

119868119881 K

119863119881 K

119875119877 K

119868119877 and K

119863119877are the propor-

tional integral and derivative gainmatrices of the vehicle andthe manipulator respectively

42 Description of the Tasks Three different tasks with fourdifferent cases have been considered for the simulations Thefirst task is that the vehicle is commanded to track a given3D trajectory without and with the manipulator (at rest or itshome position) and in this condition the vehicle acceleratesfor the initial 20 s and attains the vehicle forward speed of1ms (asymp2 knots) and for the final 20 s the vehicle deceleratesto zero speed The particular desired 3D trajectory (referto Figure 5) has been chosen for this performance analysisbecause this trajectory consists of all four main motions such

Table 2 The parameter list of the UVMS

Parameters ValuesMass of the vehicle (119898V) 39 kgLength of the vehicle (119871V) 11mDiameter of the vehicle (119889V) 025mMoment of inertia of the vehicle119868

119909034 kgm2

119868

119910371 kgm2

119868

119911371 kgm2

Centre of gravity (CG) = (119909119866 119910

119866 119911

119866) (0 0 0) m

Centre of buoyancy (CB) = (119909119861 119910

119861 119911

119861) (0 0 0015) m

Mass of the underwater manipulator links119898

103927 kg

119898

215708 kg

119898

315708 kg

Underwater manipulator link lengths119871

1005m

119871

2020m

119871

3020m

Underwater manipulator link radii119903

1010m

119903

2005m

119903

3005m

Coefficient of drag (119862119863) 125

Coefficient of lift (119862119871) 115

Table 3 The values of hydrodynamic coefficients calculated usingempirical relations based on strip theory

Vehicle added mass derivatives119883

minus117 kg 119870

minus01 kgmrad

119884V minus3484 kg 119872

minus103 kgm

119884

119903104 kgm 119872

119902minus266 kgmrad

119885

minus3483 kg 119873V minus104 kgm

119885

119902minus104 kgm 119873

119903minus265 kgmrad

Vehicle hydrodynamic parameters119883

119906|119906|minus7365 kgm 119883

119906minus212 kgs

119883V|V| minus0737 kgm 119883V minus031 kgs119883

119908|119908|minus0737 kgm 119883

119908minus031 kgs

119883

119902|119902|minus1065 kgmrad 119883

119902minus051 kgms

119883

119903|119903|minus1065 kgmrad 119883

119903minus051 kgms

119884V|V| minus1122 kgm 119884V minus6245 kgs119884

119903|119903|0250 kgmrad 119884

119903012 kgms

119885

119908|119908|minus1122 kgm 119885

119908minus6245 kgs

119885

119902|119902|minus0250 kgmrad 119885

119902012 kgms

119870

119901|119901|minus05975 kgm2rad2 119870

119901minus03125 kgm2s

119872

119908|119908|2244 kgmrad 119872

11990812 kgms

119872

119902|119902|minus1195 kgm2rad2 119872

119902minus5975 kgm2s

119873V|V| minus2244 kgmrad 119873V 12 kgms

as sway in and out and heave up and downThe average valueof sway velocity is 025ms (asymp05 knots) (same value for heaveas well) This task is performed to identify the influences of

8 Modelling and Simulation in Engineering

050

100150

200

05

1015

200

5

10

15

20

Desired 3D pathPID without armMRC without arm

PID with armMRC with arm

z(m

)

y (m)x (m)

Figure 5 Comparative trajectory tracking control results

the underwater manipulator effects during vehicle trackingcontrol In the second task the vehicle is free to move (nocontrol action involved) and the manipulator has a certainrepeated desired trajectory This task is mainly performedto identify the vehicle behavior during manipulator motionIn all the above tasks the initial velocities and positions ofthe vehicle and the manipulator are chosen to be zero andthe initial desired and actual positions and orientations arethe same In the third task two basic trajectories for themanipulator have been chosen for simulations a circulartrajectory (in 3D space) and a rectangular trajectory (in 119910119911plane) along with a straight line in 3D space This is forthe reason that most of the underwater intervention tasksinvolve these types of trajectories and also we can arrangeany spatial trajectory by combining these trajectories For therectangular trajectory we have selected a cubic polynomialfunction as the trajectory function which imposes that thetrajectory is continuous and smooth

In the performance analysis the sensory noises inposition and orientation measurements are introduced andwe have considered Gaussian noise of 001m mean and001m standard deviation for the positionmeasurements and02

∘ mean and 02∘ standard deviation for the orientationmeasurements The thruster dynamic characteristics are alsoincorporated in the simulations All the vehicle thrusters areconsidered as an identical one and the following thrustercharacteristics are considered for the analysis the thrusterresponse delay time is 200ms efficiency is 95and saturationlimits are plusmn20N The vehicle surge thrusters are located at05m from the body centre along the 119909-axis and offset eachside 03m from 119910-axis The lateral thruster is exactly locatedon the body centre and vertical thrusters are placed on the 119909-axis 04m apart from the centre at each side The controllerupdate rate and sensor response time are considered as 100mseach

43 Results and Discussions Here numerical simulationresults are shown and discussed to investigate the dynamic

Table 4 Controller parameter settings for simulations

Vehicle controller parameters Values119870

119901119881diag(42 22 25 0 25 27)

119870

119889119881diag(225 12 13 0 15 13)

119870

119894119881diag(05 02 03 0 25 22)

119870

119875119881diag(180 130 150 0 150 130)

119870

119863119881diag(80 100 100 0 80 90)

119870

119868119881diag(15 12 15 0 16 18)

Manipulator controller parameters Values119870

119901119877diag(5 10 12)

119870

119889119877diag(3 5 8)

119870

119894119877diag(01 02 02)

119870

119875119877diag(60 80 75)

119870

119863119877diag(35 40 50)

119870

119868119877diag(1 15 2)

coupling effects and the effectiveness of the proposed model-based control scheme which is expected to provide anintuitive promising prospective of the proposed approach

431 Underwater Vehicle Tracking a Given 3D Trajectorywith the Underwater Manipulator In this case as mentionedearlier the vehicle is commanded to follow a given 3D desiredtrajectory The desired 3D trajectory is given in Figure 5The controller gain values are tuned based on the geneticalgorithms (GA) for minimizing the integral squared error(ISE) as the costobjective function [23] Here we haveconsidered both the model reference control and the PIDcontrol performance to be almost equal in the ideal situationwhich makes the controller performance comparison quitereasonable and gives much better way of understandingBased on the GA tuning method the controller parametersare obtained and given in Table 4 The same set of controllerparameters are used throughout the entire performanceanalysis

Initially the performance analysis is carried out for thevehicle trajectory tracking without manipulator inclusionThe actual simulated trajectories based on MRC and PID arepresented in Figure 5These results show that both controllersare good enough to track the given trajectory and thetracking errors are within the design limits (error limits forthe vehicle during trajectory tracking are plusmn02m and plusmn02∘in positions and orientations resp) as well The trackingerrors are presented in Figures 6 7 8 9 10 and 11 In thesecond set of simulations the manipulator is included andthe inclusion effects during trajectory tracking of the vehicleare considered Here the manipulator links are folded andarranged in such a way that the influences on the vehicledynamics are small (ie manipulator joint angles are 120579

1=

180

∘ 1205792= 0

∘ and 1205793= 180

∘) The manipulator inclusionshows that there are significant performance changes in thevehicle trajectory tracking especially during the heave andsway motion tracking The heave roll and pitch motionsof the vehicle are greatly influenced by the underwatermanipulator inclusion which are replicated in the results

Modelling and Simulation in Engineering 9

0 50 100 150 200 250 300minus01

minus005

0

005

01

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Trac

king

erro

r inx

(xe) (

m)

Figure 6 Tracking errors in 119909 position for a given 3D trajectory

0 50 100 150 200 250 300minus002

minus001

0

001

002

003

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Trac

king

erro

r iny

(ye) (

m)

Figure 7 Tracking errors in 119910 position for a given 3D trajectory

(refer to Figures 6 to 11) However the manipulator inclusioneffects are better adapted in the model reference control thanin the PID control As can be observed from Figures 8 and10 the manipulator inclusion causes an initial pitch anglevariation drifts the vehicle in the heave direction during thestraight line motion (during acceleration stage) Howeverthese unwanted effects are compensated successfully in themodel reference control and therefore tracking errors do notexceed their design limits

432 Manipulator following a Given Desired 3D Trajectorywith the Freely Moving Underwater Vehicle (without VehicleControl) As mentioned earlier in this section this task ismainly to address the interaction effects and their influences

0 50 100 150 200 250 300minus005

0

005

01

015

02

03

Trac

king

erro

r inz

(ze) (

m)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 8 Tracking errors in 119911 position for a given 3D trajectory

0 50 100 150 200 250 300minus10

minus5

0

5

10

15

20

Trac

king

erro

r in

roll

(120601e) (

deg)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 9 Tracking errors in roll for a given 3D trajectory

on theUVMS For this task the vehicle controller is removedand only the underwater manipulator follows a given desiredcontinuous trajectory The desired values of joint positionsare as follows 120579

1119889= 90

∘ sin (01119905) 1205792119889

= 90

∘ and 1205793119889

=

minus45

∘ The simulation results of this condition are presentedin Figures 12 13 14 15 and 16 From the results it is observedthat the vehicle is started getting drifted from its initialposition and it is moving forward with an average velocityof 002ms (approximately) for the repeated underwatermanipulator movements It shows that the manipulator linksare affected due to the dynamic coupling effects Fromthe results it is observed that the vehicle swims duringmanipulator movements if the vehicle does not have anycontrol actionThese errors and forward speed are increasing

10 Modelling and Simulation in Engineering

0 50 100 150 200 250 300minus15

minus1

minus05

0

05

1

15

Trac

king

erro

r in

pitc

h (120579

e) (

deg)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 10 Tracking errors in pitch for a given 3D trajectory

0 50 100 150 200 250 300minus1

minus05

0

05

1

Trac

king

erro

r in

yaw

(120595e) (

deg)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 11 Tracking errors in yaw for a given 3D trajectory

with the manipulator oscillation frequency and their jointangle magnitudes In addition the direction of the vehiclersquosmovement varies depending on the manipulator positionsand its direction ofmovementsThese results can be extendedto the work towards swimming robots and their dynamicmodeling aspects

433 Underwater Manipulator following a Given DesiredCircular Trajectory with Vehicle Control The circular trajec-tory chosen for the analysis has 02m in diameter and anaverage speed of 00125ms These parameters are chosenwith the consideration of manipulator actuators workspaceand control The results from computer simulations arepresented in Figures 15ndash18 In Figure 15 both desired andactual task space trajectories are plotted and the task spacetracking errors are given in Figures 16ndash18 From the results

0 5 10 15 20minus006

minus004

minus002

0

002

004

006

008

01

012

Posit

ion

erro

rs (m

)

Time (t) (s)

xeyeze

Figure 12 Tracking errors in the vehicle positions (when manipu-lator has motion)

0 5 10 15 20minus3

minus2

minus1

0

1

2

3

4

Attit

ude e

rror

s (de

g)

Time (t) (s)

120601e120579e120595e

Figure 13 Tracking errors in the vehicle orientations (when thevehicle has no control and the manipulator has repeated motion)

it is observed that the manipulator tip tracks the givendesired task space trajectories quite satisfactorily in both PIDand MRC schemes in the ideal conditions (no disturbancesno uncertainties etc) Then in order to demonstrate theadaptability and robustness of the proposed controller anuncertain condition is considered for the simulations Thefollowing conditions are considered for the uncertain condi-tion analysis

(i) the UVMS parameters are assumed to be inaccurate(about 10 for each parameters)

(ii) the manipulator carries a payload of 1 kg at its tip

Modelling and Simulation in Engineering 11

0708

091

minus02minus01

001

02045

046

047

048

049

Desired tool tip positionActual tool tip position

z(m

)

y (m)x (m)

Figure 14 Manipulator tip position in 3D space (when the vehiclehas no control)

06507

07508

085

005

01

015

minus01

minus005

0

005

Desired trajectoryPIDMRC

PID with uncertaintyMRC with uncertainty

z(m

)

y (m)x (m)

Figure 15 Task space (119909119910119911) trajectories (results from the circulartrajectory)

(iii) an unknown ocean current is added in the simulationby properly considering the relative velocity of thein the dynamic model It is assumed to have anirrotational current constant in the inertial frameand the value of the current is considered as ^

119888=

[02 02 01 0 0 0]

119879ms

The results are presented in Figures 15ndash18 and from theseresults it is observed that the proposed controller is goodin adapting the uncertainties and disturbances (refer toFigure 15) Figures 16 and 17 show that tracking errors of119909 and 119910 in both PID and MRC methods are almost thesame and results satisfactorily however the tracking error in119911 substantiates that the proposed controller is comparativelygood in the presence of uncertainties and disturbances

434 Underwater Manipulator following a Given DesiredRectangular Trajectory with Vehicle Control The rectangulartrajectory chosen for the analysis has 04m in width and

0 5 10 15 20 25 30minus002

minus0015

minus001

minus0005

0

0005

001

0015

Time (t) (s)

PIDMRC

PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r inx

(xe) (

m)

Figure 16 Time histories of the manipulator tip position trackingerror in 119909 (circular trajectory)

0 5 10 15 20 25 30minus4

minus3

minus2

minus1

0

1

2

3

4

5

6

MRC

Time (t) (s)

PID PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r iny

(ye) (

m)

times10minus3

Figure 17 Time histories of the manipulator tip position trackingerror in 119910 (circular trajectory)

02m in height in the 119910119911 plane and an average speedof 005ms As mentioned in the last case the trajectoryhas been chosen with the consideration of the manipulatorcharacteristics Two conditions have been considered for theanalysis ideal condition (no disturbances no uncertaintiesetc) and an uncertain condition (the same as the previouscase Section 433) The results from computer simulationsare plotted in Figure 19 In the ideal condition both con-trollers show quite satisfactory performance and in theuncertain condition the proposed controller shows betterperformance

12 Modelling and Simulation in Engineering

MRC

0 5 10 15 20 25 30minus002

0

002

004

006

008

01

012

Time (t) (s)

PID PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r inz

(ze) (

m)

Figure 18 Time histories of the manipulator tip position trackingerror in 119911 (circular trajectory)

064 066 068 07 072

minus020

0202

025

03

035

04

Desired trajectoryPIDMRC

PID with uncertaintyMRC with uncertainty

z(m

)

y (m)x (m)

Figure 19 Task space (119909119910119911) trajectories (results from the rectangu-lar trajectory)

In both trajectory tracking cases the thruster forces donot exceed plusmn5N and the manipulator actuator torques staywithinplusmn015Nmwhich arewell within the range of actuators

5 Conclusions

In this study the interaction effects due to the dynamiccoupling between the vehicle and the manipulator wereinvestigated using closed-form equations which provide ageneralized scheme for formulating the equations of motionof the UVMS The proposed scheme makes it possible toidentify the structure nature and properties of the systemand it simplifies the control design This study also proposeda model reference control approach for an underactuated

UVMS to perform underwater intervention tasks incorpo-rating desired trajectory information Extensive simulationswere carried out to verify and demonstrate the effectivenessof the proposed scheme In particular the performance ofthe model reference controller is compared with that of theconventional PID controller for the given UVMS operationscenarios The obtained results confirm the effectiveness androbustness of the proposed scheme in terms of tracking errorsand control effort in the presence of external disturbancesand parameter uncertainties This research provides a gener-alized framework for modeling and controlling of an UVMSconsidering the dynamic coupling between the vehicle andthe manipulator which is crucial for achieving underwatermanipulation tasks for a variety of scientific industrial andmilitary missions using unmanned underwater vehicles

Conflict of Interests

Authors confirm that this paper has not been publishedelsewhere and is not under consideration by another journalAll authors have approved the manuscript and agree withsubmission toModelling and Simulation in EngineeringTheauthors have no conflict of interests to declare

Acknowledgments

The author would like to acknowledge Professor JinwhanKim for his valuable suggestions and discussions on under-water manipulator This research was supported in partby the World Class University (WCU) program throughthe National Research Foundation of Korea funded by theMinistry of Education Science and Technology (R31-2008-000-10045-0)

References

[1] G Antonelli F Caccavale S Chiaverini and L Villani ldquoTrack-ing control for underwater vehicle-manipulator systems withvelocity estimationrdquo IEEE Journal of Oceanic Engineering vol25 no 3 pp 399ndash413 2000

[2] G Marani S K Choi and J Yuh ldquoUnderwater autonomousmanipulation for intervention missions AUVsrdquo Ocean Engi-neering vol 36 no 1 pp 15ndash23 2009

[3] S McMillan D E Orin and R B McGhee ldquoEfficient dynamicsimulation of an underwater vehicle with a robotic manipula-torrdquo IEEE Transactions on Systems Man and Cybernetics vol25 no 8 pp 1194ndash1206 1995

[4] T I Fossen Guidance and Control of Ocean Vehicles WileyChichester UK 1994

[5] T J Tarn G A Shoults and S P Yang ldquoA dynamic model ofan underwater vehicle with a robotic manipulator using Kanersquosmethodrdquo Autonomous Robots vol 3 no 2-3 pp 269ndash283 1996

[6] H Mahesh J Yuh and R Lakshmi ldquoA Coordinated controlof an underwater vehicle and robotic manipulatorrdquo Journal ofRobotic Systems vol 8 no 3 pp 339ndash370 1991

[7] N Sarkar and T K Podder ldquoCoordinated motion planningand control of autonomous underwater vehicle-manipulatorsystems subject to drag optimizationrdquo IEEE Journal of OceanicEngineering vol 26 no 2 pp 228ndash239 2001

Modelling and Simulation in Engineering 13

[8] T W McLain S M Rock and M J Lee ldquoExperiments inthe coordinated control of an underwater armvehicle systemrdquoAutonomous Robots vol 3 no 2-3 pp 213ndash232 1996

[9] M W Dunnigan and G T Russell ldquoEvaluation and reductionof the dynamic coupling between a manipulator and an under-water vehiclerdquo IEEE Journal of Oceanic Engineering vol 23 no3 pp 260ndash273 1998

[10] B H Jun P M Lee and J Lee ldquoManipulability analysisof underwater robotic arms on ROV and application totask-oriented joint configurationrdquo in Proceedings of the IEEEOCEANS pp 1548ndash1553 November 2004

[11] J H Ryu D S Kwon and P M Lee ldquoControl of underwatermanipulators mounted on an ROV using base force informa-tionrdquo in Proceedings of the IEEE International Conference onRobotics and Automation (ICRA rsquo01) pp 3238ndash3243 May 2001

[12] M Hildebrandt L Christensen J Kerdels J Albiez and FKirchner ldquoRealtime motion compensation for ROV-based tele-operated underwater manipulatorsrdquo in Proceedings of the IEEEOCEANS pp 1ndash6 May 2009

[13] H Shim B H Jun P M Lee H Baek and J Lee ldquoWorkspacecontrol system of underwater tele-operated manipulators on anROVrdquo Ocean Engineering vol 37 no 11-12 pp 1036ndash1047 2010

[14] J J Craig Introduction to Robotics Addison Wesley BostonMass USA 1986

[15] G Antonelli Underwater Robots Motion and Force Control ofVehicle-Manipulator Systems Springer Berlin Germany 2006

[16] K Kim andT Ura ldquoAppliedmodel-based analysis and synthesisfor the dynamics guidance and control of an autonomousundersea vehiclerdquo Mathematical Problems in Engineering vol2010 Article ID 149385 23 pages 2010

[17] T I Fossen Marine Control Systems Guidance Navigationand Control of Ships Rigs and Underwater Vehicles MarineCybernetics AS 2002

[18] J J E Slotine and W Li Applied Nonlinear Control Prentice-Hall Upper Saddle River NJ USA 1991

[19] K Y Pettersen and O Egeland ldquoPosition and attitude control ofan underactuated autonomous underwater vehiclerdquo in Proceed-ings of the 1996 35th IEEE Conference on Decision and Controlpp 987ndash991 Kobe Japan December 1996

[20] T H Koh MW S Lau G Seet and E Low ldquoA control modulescheme for an underactuated underwater robotic vehiclerdquo Jour-nal of Intelligent and Robotic Systems Theory and Applicationsvol 46 no 1 pp 43ndash58 2006

[21] M Santhakumar and T Asokan ldquoInvestigations on the hybridtracking control of an underactuated autonomous underwaterrobotrdquo Advanced Robotics vol 24 no 11 pp 1529ndash1556 2010

[22] ANSALDO Nucleare Underwater Manipulator MARIS 7080Use and Maintenance Manual Ansaldo Nuclear DivisionGenoa Italy 1996

[23] K Deb Optimization for Engineering Design Algorithms andExamples Prentice Hall New Delhi India 2004

International Journal of

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RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

4 Modelling and Simulation in Engineering

F119896= M

119896(

119896a119896+

119896120572119896times

119896d119896119896119888

+

119896120596

119896times (

119896120596

119896times

119896d119896119896119888))

T119896= I

119896

119896120572119896+

119896120596

119896times (I

119896

119896120596

119896)

119896+1120596

119896+1= R119896

119896+1

119896120596

119896+ z119879 119902

119896+1

119896+1120572119896+1

= R119896

119896+1(

119896120572119896+

119896120596

119896times z119879119902

119896) + z119879 119902

119896+1

119896+1k119896+1

= R119896

119896+1

119896k119896+

119896+1120596

119896+1times

119896+1d119896119896119888

119896+1a119896+1

= R119896

119896+1

119896a119896+

119896+1120572119896+1

times

119896+1d119896+1119896

+

119896+1120596

119896+1times (

119896+1120596

119896+1times

119896+1d119896+1119896

)

(10)

M119896=

[

[

[

[

[

[

119898

119896+

120587120588119903

119896

2119871

119896

10

0 0

0 119898

119896+ 120587120588119903

119896

2119871

1198960

0 0 119898

119896+ 120587120588119903

119896

2119871

119896

]

]

]

]

]

]

I119896=

[

[

[

[

[

[

[

119868

1199090 0

0 119868

119910+

120587120588119903

119896

2119871

119896

3

12

0

0 0 119868

119911+

120587120588119903

119896

2119871

119896

3

12

]

]

]

]

]

]

]

(11)

where 119896 denotes the corresponding joint axis (119896 = 1 2 3)R119896+1

119896is the rotation matrix f

119896is the resultant force vector t

119896

is the resultant moment vector p119896is the linear and quadratic

hydrodynamic friction forces and F119878119896 F

119863119896 and F

119871119896are

vectors of linear skin friction quadratic drag and quadraticlift effects respectively D119896

119904is the linear skin friction matrix

D119896

119871is the diagonal matrix which contains lift coefficientsD119896

119863

is the diagonal matrix which contains drag coefficients g119896is

the gravity force vector b119896is the buoyancy force vector n

119896

is the hydrodynamic moment vector d119896119896119887

is the vector fromthe center of buoyancy of the link d

119896119896119888is the vector from the

center of gravity of the link d119896119896+1

is the vector from joint 119896to 119896 + 1 F

119896is the vector of total forces acting at the center of

mass of link T119896is the vector of total moments acting at the

center ofmass of link a119896is the linear acceleration vector 120572

119896is

the angular acceleration vector k119896is the linear velocity vector

120596119896is the angular velocity vector m

119896is the mass of the link

M119896is the mass and added mass matrix of the link (located

at the center of mass) I119896is the moment of inertia and added

moment of matrix of the link (located at the center of mass)and z119879 is the unit vector along the 119911-axis

The joint torques of each link are represented as

120591

119877119896= z119879 119896t

119896

(12)

The recursive Newton-Euler dynamics algorithm for alllinks symbolically yields the equations of motion for theunderwater manipulatorThe result can be written as follows

M119877(119902) q + C

119877(119902 119902) q +D

119877(119902 119902) q + g

119877(119902) = 120591

119877 (13)

where q is the vector of joint variables and q = [1205791120579

2120579

3]

119879120579

1 120579

2 120579

3are the joint angles of the corresponding underwater

manipulator linksM119877(119902)q is the vector of inertial forces and

moments of the manipulator C119877(119902 119902)q is the vector of Cori-

olis and centripetal effects of the manipulator D119877(119902 119902)q is

the vector of damping effects of the manipulator g119877(119902) is the

restoring vector of themanipulator and 120591119877= [120591

1198771120591

1198772120591

1198773]

119879

is the vector of control inputs

24 Dynamic Model of Vehicle-Manipulator System Themanipulator has an initial velocity equal to the velocity ofthe vehicle This initial velocity should be accounted in themanipulator dynamics Similarly the weight and movementof the manipulator links will affect the vehicle dynamics(these effects are considered as disturbances) and vice versaBy considering the above issues the vehicle and manipulatorequations of motions can be written as follows

M ^ + C (]) ^ +D (]) ^ + g (120578) = 120591119881+ 120590

M119877(119902) q +H119879

2(119902) ^ + C

119877(119902 119902) q +D

119877(119902 119902) q

+ g119877(119902) + C119879

119881(119902 119902 ]) ^ +D119879

119881(119902 119902 ]) ^ = 120591

119877

(14)

where H119879

2(119902) ^ is the vector of reaction forces and moments

between the vehicle and the manipulator C119879

119881(119902 119902 ])^ is the

vector of Coriolis and centripetal effects due to couplingbetween the vehicle and the manipulator and D119879

119881(119902 119902 ])^

is the vector of quadratic drag effects due to the interactionbetween the vehicle and the manipulator 120590 = [120590

119879

119891120590119879

119898]

119879 isthe vector which contains forces and moments disturbancesdue to weight and movement of the manipulator linksConsider

120590119891= R119861

0

0f1

120590119898= R119861

0

0t1minus dvehiclemanipulator times (R

119861

0

0f1)

(15)

where R119861

0and dvehiclemanipulator are the rotation matrix and

position vector from the vehicle-fixed frame to the manip-ulator base frame respectively 0f

1and 0t

1are the vectors

of force and moments of the base frame respectively Thesevectors are derived using (8) and these effects are functionof the manipulator joint coordinates (ie q q and q) andthe vehicle states After evaluating the interaction forces andmoments between the manipulator and the vehicle based onthese vectors the equations of motion of the vehicle can bewritten as

M ^ +H1(119902) ^ + C (]) ^ +D (]) ^ + C

119881(119902 119902 ]) ^

+D119881(119902 119902 ]) ^ + g (120578) +H

2(119902) q + C

1(119902 119902) q

+D1(119902 119902) q + g

1(119902) = 120591

119881

(16)

whereH1(119902) ^ andH

2(119902)q are the added inertia effects due to

the manipulator D1(119902 119902)q is the damping effects due to the

manipulator C1(119902 119902)q is the Coriolis and centripetal effects

due to the manipulator and g1(119902) is the restoring vector due

to the manipulator on the vehicle respectively

Modelling and Simulation in Engineering 5

AUV dynamics

Manipulator dynamics

Trajectory planner

minus

+

minus

+

+

+

+

+

+

+

+

Dynamiccoupling effects

+

+

+

minus

+

++

++

+

++

+

q

q

q

qd

d

dt

q

d

dt

KIR

KDR

KPR

KPV

KDV

KIV

MV

MR (q)

int

int

V

d

R

q

G2

G1

q

J( )minus1

)minus1J( )minus1

F2(q )

HT2 (q)

H2(q)

F1(q )

(middot)

(middot)

(middot)(middot)

120578

120578

120578

120578

120578120578

120578

120578

120578

120578

τ

τ

120578 120578

120578

Figure 3 Block diagram of model reference control

ldquoNot to scalerdquo

Top view

Front viewVehicle

ManipulatorVertical thrusters

Port side thruster

Starboard side thruster Stern control

plane surfaces

Lateral thruster

x

x

y

z

Figure 4 Schematic diagram of UVMS prototype model

3 Model Reference Control

This section discusses the model reference control (MRC)design in terms of feedback linearizationThis control scheme

transforms the nonlinear system dynamics into a linearsystem it compensates for all the nonlinearities in the systemby introducing nonlinear elements in the input side thusmaking the controller design more flexible [15ndash17] Unliketraditional control it can be thought of as ldquoinstantaneouslearningrdquo of the vehicle dynamicsThe individual control lawsof the underwater vehicle and the manipulator are chosensuch that the tracking errors are converging to zero Thetracking errors are defined as = 120578

119889minus120578 and q = q

119889minusq where

119889 denotes the desired (or reference) values The equationsof motion of the UVMS can be expressed in the form givenbelow [15]

M119881^ +H

2(119902) q + F

1(119902 119902 ]) + G

1(120578 119902) = 120591

119881

M119877(119902) q +H119879

2(119902) ^ + F

2(119902 119902 ]) + G

2(119902) = 120591

119877

(17)

where M119881

= M + H1(119902) F

1(119902 119902 ]) F

2(119902 119902 ]) G

2(119902)

and G1(120578 119902) are the vectors of the Coriolis centripetal and

dampingfrictional and restoring effects of the vehicle andthe manipulator respectively

6 Modelling and Simulation in Engineering

The proposed control input vectors given by (18) willcancel out or compensates for the nonlinearities in the systemas

120591119881= M

119881u119881+H

2(119902) q + F

1(119902 119902 ]) + G

1(120578 119902)

120591119877= M

119877(119902) u

119877+H119879

2(119902) ^ + F

2(119902 119902 ]) + G

2(119902)

(18)

where

u119881= J(120578)minus1 (u

120578minus

J (120578) J(120578)minus1120578)

u120578=

119889+ K

119901119881 + K

119889119881

+ K119894119881int 119889119905

u119877= q

119889+ K

119901119877q + K

119889119877q + K

119894119877int q 119889119905

(19)

K119901119881 K

119894119881 and K

119889119881are the proportional integral and

derivative gainmatrices of the vehicle controller respectivelyand K

119901119877 K

119894119877 and K

119889119877are the proportional integral and

derivative gainmatrices of themanipulator controller respec-tively Block diagram representation of the proposed UVMScontroller is presented in Figure 3

The above-mentioned control vectors lead to exponentialstable error dynamics of the vehicle and manipulator whichare given as

+ K119901119881 + K

119889119881

+ K119894119881int 119889119905 = 0

q + K119901119877q + K

119889119877q + K

119894119877int q 119889119905 = 0

(20)

which implies that tracking errors are converging to zero (ie rarr 0 and q rarr 0) and the UVMS follows the given desiredtrajectory [18]

However the above-proposed control scheme assumedthat there are no disturbances and no uncertainties associatedwith the system If the system uncertainties and externaldisturbances are considered for the analysis the system errordynamics become

+ K119901119881 + K

119889119881

+ K119894119881int 119889119905 = M

119881

minus1120591119889119881

q + K119901119877q + K

119889119877q + K

119894119877int q 119889119905 = M

119877

minus1120591119889119877

(21)

where 120591119889119881

and 120591119889119877

are the disturbance vector (which com-bines the internal disturbances such as effect of parameteruncertainties and external disturbances namely underwatercurrent etc) of the vehicle and manipulator controllerrespectively

The closed-loop characteristic equation or polynomial isgiven as

Δ

119888119881 (119904) =

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

119904

2I + 119904K119889119881+ K

119901119881+

K119894119881

119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ

119888119877 (119904) =

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

119904

2I + 119904K119889119877+ K

119901119877+

K119894119877

119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

(22)

The control gain matrices are chosen as diagonal and positivedefinite matrices such as

K119889119881= diag (119896

119889119881119894) K

119901119881= diag (119896

119901119881119894)

K119894119881= diag (119896

119894119881119894) K

119889119877= diag (119896

119889119877119894)

K119901119877= diag (119896

119901119877119894) K

119894119877= diag (119896

119894119877119894)

(23)

Therefore the closed-loop characteristic polynomialbecomes

Δ

119888119881 (119904) =

6

prod

119894=1

(119904

2+ 119904119896

119889119881119894+ 119896

119901119881119894+

119896

119894119881119894

119904

)

Δ

119888119877 (119904) =

119899

prod

119894=1

(119904

2+ 119904119896

119889119877119894+ 119896

119901119877119894+

119896

119894119877119894

119904

)

(24)

and the system error is asymptotically stable as long as thecontroller gain values are all positiveTherefore as long as thedisturbance vectors are bounded the system tracking errorsare converged to zero In other words the system followsthe given desired trajectory Moreover the controller gainmatrices have been chosen in such a way that

120582min K119901119881 gt

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120597120591119889119881

120597

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120582min K119889119881 gt

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120597120591119889119881

120597

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120582min K119901119877 gt

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120597120591119889119877

120597q

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120582min K119889119877 gt

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120597120591119889119877

120597

q

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

(25)

Hence = 0 and q = 0 for all 119905 ge 0 are its unique solutionand it can be observed that the system tracking errors areconverging to zero asymptotically The proposed controlleranalysis does not contain explicit treatment of the parametricuncertainties and external disturbance while taking temporalderivative along the closed-loop system trajectories and it isleft for further research and analysis

4 Performance Analysis of the UVMS

41 Description of the Simulated System We have accom-plished widespread computer-based numerical simulationsto explore the total performance of the proposed UVMS andthe model reference (direct adaptive) control scheme TheUVMS used for this study consists of six degrees of freedom(DOF) vehicle and a 3-DOF spatial manipulator the UVMSarrangement in conceptual design is presented in Figure 4The vehicle is a cylindrical shape (torpedo fish shaped)cruising type with the length of 11m and the diameter of025m The mass of the vehicle is 39 kg The vehicle has fivethrusters in total two propulsion thrusters (in the stern side)two vertical thrusters and one lateral thruster Thereforesurge sway and heave motions are controlled through thesethrusters actuation directly and however yaw and pitchmotions are controlled by differential actuation of propulsionand vertical thrusters Although roll motion is unactuated itcan be controlled itself due to restoring effects [19ndash21] It isknown that a necessary condition for a submersible body to

Modelling and Simulation in Engineering 7

be stable is that the centre of gravity (CG) should lie belowthe centre of buoyancy (CB) For this the vehicle is trimmed(using a float) to have the CB almost vertically above the CGand made to be nearly neutral buoyant Here the roll motionhas nonzero components of restoringmoments that representself-restoring torque for the roll direction With nonzerorestoring terms it may be possible to find continuous statefeedback laws to stabilize the system as a whole In additionto this without loss of generality we can assume that thedamping terms of nonactuated states are sufficiently largerthan their inertia terms which means that the hydrodynamicrestoring forces and torques are large enough to stabilize thenonactuated (roll) states (zero dynamics) which is a commonproperty forAUVs [19]Thismeans that the underwater robotcan be exponentially stabilized by the actuated state controlsalone

The manipulator links are cylindrical in shape and theradii of links 1 2 and 3 are 01m 005m and 005mrespectively The lengths of links 1 2 and 3 are 01m 02mand 02m respectively The link masses (along with oil con-served motors) are 039 kg 157 kg and 157 kg respectivelyHere the links are considered as cylindrical shape becausesuch shape provides uniform hydrodynamic reactions andis one of the primary candidates for possible link geometryfor underwater manipulators Although it is cylindrical ourmathematical framework does not depend on any particularshapes it can be easily accommodated by any other shapesIndeed cylindrical underwater manipulators are available inthe present market [22] Hydrodynamic parameters of theUVMS are estimated using empirical relations based on striptheory This method is verified using the available literaturetherefore these values are reliable and can be used for furtherdevelopments Some parameters like inertia centre of gravityand centre of buoyancy are calculated from the geometricaldesign of the UVMSThe total parameter list of the UVMS isgiven in Tables 2 and 3

We have compared our results with those of traditionalPID controller the following control vectors were consideredfor the vehicle and the manipulator and are given by

120591119881= K

119863119881

+ K119875119881 + K

119868119881int 119889119905

120591119877= K

119863119877q + K

119875119877q + K

119868119877int q 119889119905

(26)

where K119875119881 K

119868119881 K

119863119881 K

119875119877 K

119868119877 and K

119863119877are the propor-

tional integral and derivative gainmatrices of the vehicle andthe manipulator respectively

42 Description of the Tasks Three different tasks with fourdifferent cases have been considered for the simulations Thefirst task is that the vehicle is commanded to track a given3D trajectory without and with the manipulator (at rest or itshome position) and in this condition the vehicle acceleratesfor the initial 20 s and attains the vehicle forward speed of1ms (asymp2 knots) and for the final 20 s the vehicle deceleratesto zero speed The particular desired 3D trajectory (referto Figure 5) has been chosen for this performance analysisbecause this trajectory consists of all four main motions such

Table 2 The parameter list of the UVMS

Parameters ValuesMass of the vehicle (119898V) 39 kgLength of the vehicle (119871V) 11mDiameter of the vehicle (119889V) 025mMoment of inertia of the vehicle119868

119909034 kgm2

119868

119910371 kgm2

119868

119911371 kgm2

Centre of gravity (CG) = (119909119866 119910

119866 119911

119866) (0 0 0) m

Centre of buoyancy (CB) = (119909119861 119910

119861 119911

119861) (0 0 0015) m

Mass of the underwater manipulator links119898

103927 kg

119898

215708 kg

119898

315708 kg

Underwater manipulator link lengths119871

1005m

119871

2020m

119871

3020m

Underwater manipulator link radii119903

1010m

119903

2005m

119903

3005m

Coefficient of drag (119862119863) 125

Coefficient of lift (119862119871) 115

Table 3 The values of hydrodynamic coefficients calculated usingempirical relations based on strip theory

Vehicle added mass derivatives119883

minus117 kg 119870

minus01 kgmrad

119884V minus3484 kg 119872

minus103 kgm

119884

119903104 kgm 119872

119902minus266 kgmrad

119885

minus3483 kg 119873V minus104 kgm

119885

119902minus104 kgm 119873

119903minus265 kgmrad

Vehicle hydrodynamic parameters119883

119906|119906|minus7365 kgm 119883

119906minus212 kgs

119883V|V| minus0737 kgm 119883V minus031 kgs119883

119908|119908|minus0737 kgm 119883

119908minus031 kgs

119883

119902|119902|minus1065 kgmrad 119883

119902minus051 kgms

119883

119903|119903|minus1065 kgmrad 119883

119903minus051 kgms

119884V|V| minus1122 kgm 119884V minus6245 kgs119884

119903|119903|0250 kgmrad 119884

119903012 kgms

119885

119908|119908|minus1122 kgm 119885

119908minus6245 kgs

119885

119902|119902|minus0250 kgmrad 119885

119902012 kgms

119870

119901|119901|minus05975 kgm2rad2 119870

119901minus03125 kgm2s

119872

119908|119908|2244 kgmrad 119872

11990812 kgms

119872

119902|119902|minus1195 kgm2rad2 119872

119902minus5975 kgm2s

119873V|V| minus2244 kgmrad 119873V 12 kgms

as sway in and out and heave up and downThe average valueof sway velocity is 025ms (asymp05 knots) (same value for heaveas well) This task is performed to identify the influences of

8 Modelling and Simulation in Engineering

050

100150

200

05

1015

200

5

10

15

20

Desired 3D pathPID without armMRC without arm

PID with armMRC with arm

z(m

)

y (m)x (m)

Figure 5 Comparative trajectory tracking control results

the underwater manipulator effects during vehicle trackingcontrol In the second task the vehicle is free to move (nocontrol action involved) and the manipulator has a certainrepeated desired trajectory This task is mainly performedto identify the vehicle behavior during manipulator motionIn all the above tasks the initial velocities and positions ofthe vehicle and the manipulator are chosen to be zero andthe initial desired and actual positions and orientations arethe same In the third task two basic trajectories for themanipulator have been chosen for simulations a circulartrajectory (in 3D space) and a rectangular trajectory (in 119910119911plane) along with a straight line in 3D space This is forthe reason that most of the underwater intervention tasksinvolve these types of trajectories and also we can arrangeany spatial trajectory by combining these trajectories For therectangular trajectory we have selected a cubic polynomialfunction as the trajectory function which imposes that thetrajectory is continuous and smooth

In the performance analysis the sensory noises inposition and orientation measurements are introduced andwe have considered Gaussian noise of 001m mean and001m standard deviation for the positionmeasurements and02

∘ mean and 02∘ standard deviation for the orientationmeasurements The thruster dynamic characteristics are alsoincorporated in the simulations All the vehicle thrusters areconsidered as an identical one and the following thrustercharacteristics are considered for the analysis the thrusterresponse delay time is 200ms efficiency is 95and saturationlimits are plusmn20N The vehicle surge thrusters are located at05m from the body centre along the 119909-axis and offset eachside 03m from 119910-axis The lateral thruster is exactly locatedon the body centre and vertical thrusters are placed on the 119909-axis 04m apart from the centre at each side The controllerupdate rate and sensor response time are considered as 100mseach

43 Results and Discussions Here numerical simulationresults are shown and discussed to investigate the dynamic

Table 4 Controller parameter settings for simulations

Vehicle controller parameters Values119870

119901119881diag(42 22 25 0 25 27)

119870

119889119881diag(225 12 13 0 15 13)

119870

119894119881diag(05 02 03 0 25 22)

119870

119875119881diag(180 130 150 0 150 130)

119870

119863119881diag(80 100 100 0 80 90)

119870

119868119881diag(15 12 15 0 16 18)

Manipulator controller parameters Values119870

119901119877diag(5 10 12)

119870

119889119877diag(3 5 8)

119870

119894119877diag(01 02 02)

119870

119875119877diag(60 80 75)

119870

119863119877diag(35 40 50)

119870

119868119877diag(1 15 2)

coupling effects and the effectiveness of the proposed model-based control scheme which is expected to provide anintuitive promising prospective of the proposed approach

431 Underwater Vehicle Tracking a Given 3D Trajectorywith the Underwater Manipulator In this case as mentionedearlier the vehicle is commanded to follow a given 3D desiredtrajectory The desired 3D trajectory is given in Figure 5The controller gain values are tuned based on the geneticalgorithms (GA) for minimizing the integral squared error(ISE) as the costobjective function [23] Here we haveconsidered both the model reference control and the PIDcontrol performance to be almost equal in the ideal situationwhich makes the controller performance comparison quitereasonable and gives much better way of understandingBased on the GA tuning method the controller parametersare obtained and given in Table 4 The same set of controllerparameters are used throughout the entire performanceanalysis

Initially the performance analysis is carried out for thevehicle trajectory tracking without manipulator inclusionThe actual simulated trajectories based on MRC and PID arepresented in Figure 5These results show that both controllersare good enough to track the given trajectory and thetracking errors are within the design limits (error limits forthe vehicle during trajectory tracking are plusmn02m and plusmn02∘in positions and orientations resp) as well The trackingerrors are presented in Figures 6 7 8 9 10 and 11 In thesecond set of simulations the manipulator is included andthe inclusion effects during trajectory tracking of the vehicleare considered Here the manipulator links are folded andarranged in such a way that the influences on the vehicledynamics are small (ie manipulator joint angles are 120579

1=

180

∘ 1205792= 0

∘ and 1205793= 180

∘) The manipulator inclusionshows that there are significant performance changes in thevehicle trajectory tracking especially during the heave andsway motion tracking The heave roll and pitch motionsof the vehicle are greatly influenced by the underwatermanipulator inclusion which are replicated in the results

Modelling and Simulation in Engineering 9

0 50 100 150 200 250 300minus01

minus005

0

005

01

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Trac

king

erro

r inx

(xe) (

m)

Figure 6 Tracking errors in 119909 position for a given 3D trajectory

0 50 100 150 200 250 300minus002

minus001

0

001

002

003

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Trac

king

erro

r iny

(ye) (

m)

Figure 7 Tracking errors in 119910 position for a given 3D trajectory

(refer to Figures 6 to 11) However the manipulator inclusioneffects are better adapted in the model reference control thanin the PID control As can be observed from Figures 8 and10 the manipulator inclusion causes an initial pitch anglevariation drifts the vehicle in the heave direction during thestraight line motion (during acceleration stage) Howeverthese unwanted effects are compensated successfully in themodel reference control and therefore tracking errors do notexceed their design limits

432 Manipulator following a Given Desired 3D Trajectorywith the Freely Moving Underwater Vehicle (without VehicleControl) As mentioned earlier in this section this task ismainly to address the interaction effects and their influences

0 50 100 150 200 250 300minus005

0

005

01

015

02

03

Trac

king

erro

r inz

(ze) (

m)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 8 Tracking errors in 119911 position for a given 3D trajectory

0 50 100 150 200 250 300minus10

minus5

0

5

10

15

20

Trac

king

erro

r in

roll

(120601e) (

deg)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 9 Tracking errors in roll for a given 3D trajectory

on theUVMS For this task the vehicle controller is removedand only the underwater manipulator follows a given desiredcontinuous trajectory The desired values of joint positionsare as follows 120579

1119889= 90

∘ sin (01119905) 1205792119889

= 90

∘ and 1205793119889

=

minus45

∘ The simulation results of this condition are presentedin Figures 12 13 14 15 and 16 From the results it is observedthat the vehicle is started getting drifted from its initialposition and it is moving forward with an average velocityof 002ms (approximately) for the repeated underwatermanipulator movements It shows that the manipulator linksare affected due to the dynamic coupling effects Fromthe results it is observed that the vehicle swims duringmanipulator movements if the vehicle does not have anycontrol actionThese errors and forward speed are increasing

10 Modelling and Simulation in Engineering

0 50 100 150 200 250 300minus15

minus1

minus05

0

05

1

15

Trac

king

erro

r in

pitc

h (120579

e) (

deg)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 10 Tracking errors in pitch for a given 3D trajectory

0 50 100 150 200 250 300minus1

minus05

0

05

1

Trac

king

erro

r in

yaw

(120595e) (

deg)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 11 Tracking errors in yaw for a given 3D trajectory

with the manipulator oscillation frequency and their jointangle magnitudes In addition the direction of the vehiclersquosmovement varies depending on the manipulator positionsand its direction ofmovementsThese results can be extendedto the work towards swimming robots and their dynamicmodeling aspects

433 Underwater Manipulator following a Given DesiredCircular Trajectory with Vehicle Control The circular trajec-tory chosen for the analysis has 02m in diameter and anaverage speed of 00125ms These parameters are chosenwith the consideration of manipulator actuators workspaceand control The results from computer simulations arepresented in Figures 15ndash18 In Figure 15 both desired andactual task space trajectories are plotted and the task spacetracking errors are given in Figures 16ndash18 From the results

0 5 10 15 20minus006

minus004

minus002

0

002

004

006

008

01

012

Posit

ion

erro

rs (m

)

Time (t) (s)

xeyeze

Figure 12 Tracking errors in the vehicle positions (when manipu-lator has motion)

0 5 10 15 20minus3

minus2

minus1

0

1

2

3

4

Attit

ude e

rror

s (de

g)

Time (t) (s)

120601e120579e120595e

Figure 13 Tracking errors in the vehicle orientations (when thevehicle has no control and the manipulator has repeated motion)

it is observed that the manipulator tip tracks the givendesired task space trajectories quite satisfactorily in both PIDand MRC schemes in the ideal conditions (no disturbancesno uncertainties etc) Then in order to demonstrate theadaptability and robustness of the proposed controller anuncertain condition is considered for the simulations Thefollowing conditions are considered for the uncertain condi-tion analysis

(i) the UVMS parameters are assumed to be inaccurate(about 10 for each parameters)

(ii) the manipulator carries a payload of 1 kg at its tip

Modelling and Simulation in Engineering 11

0708

091

minus02minus01

001

02045

046

047

048

049

Desired tool tip positionActual tool tip position

z(m

)

y (m)x (m)

Figure 14 Manipulator tip position in 3D space (when the vehiclehas no control)

06507

07508

085

005

01

015

minus01

minus005

0

005

Desired trajectoryPIDMRC

PID with uncertaintyMRC with uncertainty

z(m

)

y (m)x (m)

Figure 15 Task space (119909119910119911) trajectories (results from the circulartrajectory)

(iii) an unknown ocean current is added in the simulationby properly considering the relative velocity of thein the dynamic model It is assumed to have anirrotational current constant in the inertial frameand the value of the current is considered as ^

119888=

[02 02 01 0 0 0]

119879ms

The results are presented in Figures 15ndash18 and from theseresults it is observed that the proposed controller is goodin adapting the uncertainties and disturbances (refer toFigure 15) Figures 16 and 17 show that tracking errors of119909 and 119910 in both PID and MRC methods are almost thesame and results satisfactorily however the tracking error in119911 substantiates that the proposed controller is comparativelygood in the presence of uncertainties and disturbances

434 Underwater Manipulator following a Given DesiredRectangular Trajectory with Vehicle Control The rectangulartrajectory chosen for the analysis has 04m in width and

0 5 10 15 20 25 30minus002

minus0015

minus001

minus0005

0

0005

001

0015

Time (t) (s)

PIDMRC

PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r inx

(xe) (

m)

Figure 16 Time histories of the manipulator tip position trackingerror in 119909 (circular trajectory)

0 5 10 15 20 25 30minus4

minus3

minus2

minus1

0

1

2

3

4

5

6

MRC

Time (t) (s)

PID PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r iny

(ye) (

m)

times10minus3

Figure 17 Time histories of the manipulator tip position trackingerror in 119910 (circular trajectory)

02m in height in the 119910119911 plane and an average speedof 005ms As mentioned in the last case the trajectoryhas been chosen with the consideration of the manipulatorcharacteristics Two conditions have been considered for theanalysis ideal condition (no disturbances no uncertaintiesetc) and an uncertain condition (the same as the previouscase Section 433) The results from computer simulationsare plotted in Figure 19 In the ideal condition both con-trollers show quite satisfactory performance and in theuncertain condition the proposed controller shows betterperformance

12 Modelling and Simulation in Engineering

MRC

0 5 10 15 20 25 30minus002

0

002

004

006

008

01

012

Time (t) (s)

PID PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r inz

(ze) (

m)

Figure 18 Time histories of the manipulator tip position trackingerror in 119911 (circular trajectory)

064 066 068 07 072

minus020

0202

025

03

035

04

Desired trajectoryPIDMRC

PID with uncertaintyMRC with uncertainty

z(m

)

y (m)x (m)

Figure 19 Task space (119909119910119911) trajectories (results from the rectangu-lar trajectory)

In both trajectory tracking cases the thruster forces donot exceed plusmn5N and the manipulator actuator torques staywithinplusmn015Nmwhich arewell within the range of actuators

5 Conclusions

In this study the interaction effects due to the dynamiccoupling between the vehicle and the manipulator wereinvestigated using closed-form equations which provide ageneralized scheme for formulating the equations of motionof the UVMS The proposed scheme makes it possible toidentify the structure nature and properties of the systemand it simplifies the control design This study also proposeda model reference control approach for an underactuated

UVMS to perform underwater intervention tasks incorpo-rating desired trajectory information Extensive simulationswere carried out to verify and demonstrate the effectivenessof the proposed scheme In particular the performance ofthe model reference controller is compared with that of theconventional PID controller for the given UVMS operationscenarios The obtained results confirm the effectiveness androbustness of the proposed scheme in terms of tracking errorsand control effort in the presence of external disturbancesand parameter uncertainties This research provides a gener-alized framework for modeling and controlling of an UVMSconsidering the dynamic coupling between the vehicle andthe manipulator which is crucial for achieving underwatermanipulation tasks for a variety of scientific industrial andmilitary missions using unmanned underwater vehicles

Conflict of Interests

Authors confirm that this paper has not been publishedelsewhere and is not under consideration by another journalAll authors have approved the manuscript and agree withsubmission toModelling and Simulation in EngineeringTheauthors have no conflict of interests to declare

Acknowledgments

The author would like to acknowledge Professor JinwhanKim for his valuable suggestions and discussions on under-water manipulator This research was supported in partby the World Class University (WCU) program throughthe National Research Foundation of Korea funded by theMinistry of Education Science and Technology (R31-2008-000-10045-0)

References

[1] G Antonelli F Caccavale S Chiaverini and L Villani ldquoTrack-ing control for underwater vehicle-manipulator systems withvelocity estimationrdquo IEEE Journal of Oceanic Engineering vol25 no 3 pp 399ndash413 2000

[2] G Marani S K Choi and J Yuh ldquoUnderwater autonomousmanipulation for intervention missions AUVsrdquo Ocean Engi-neering vol 36 no 1 pp 15ndash23 2009

[3] S McMillan D E Orin and R B McGhee ldquoEfficient dynamicsimulation of an underwater vehicle with a robotic manipula-torrdquo IEEE Transactions on Systems Man and Cybernetics vol25 no 8 pp 1194ndash1206 1995

[4] T I Fossen Guidance and Control of Ocean Vehicles WileyChichester UK 1994

[5] T J Tarn G A Shoults and S P Yang ldquoA dynamic model ofan underwater vehicle with a robotic manipulator using Kanersquosmethodrdquo Autonomous Robots vol 3 no 2-3 pp 269ndash283 1996

[6] H Mahesh J Yuh and R Lakshmi ldquoA Coordinated controlof an underwater vehicle and robotic manipulatorrdquo Journal ofRobotic Systems vol 8 no 3 pp 339ndash370 1991

[7] N Sarkar and T K Podder ldquoCoordinated motion planningand control of autonomous underwater vehicle-manipulatorsystems subject to drag optimizationrdquo IEEE Journal of OceanicEngineering vol 26 no 2 pp 228ndash239 2001

Modelling and Simulation in Engineering 13

[8] T W McLain S M Rock and M J Lee ldquoExperiments inthe coordinated control of an underwater armvehicle systemrdquoAutonomous Robots vol 3 no 2-3 pp 213ndash232 1996

[9] M W Dunnigan and G T Russell ldquoEvaluation and reductionof the dynamic coupling between a manipulator and an under-water vehiclerdquo IEEE Journal of Oceanic Engineering vol 23 no3 pp 260ndash273 1998

[10] B H Jun P M Lee and J Lee ldquoManipulability analysisof underwater robotic arms on ROV and application totask-oriented joint configurationrdquo in Proceedings of the IEEEOCEANS pp 1548ndash1553 November 2004

[11] J H Ryu D S Kwon and P M Lee ldquoControl of underwatermanipulators mounted on an ROV using base force informa-tionrdquo in Proceedings of the IEEE International Conference onRobotics and Automation (ICRA rsquo01) pp 3238ndash3243 May 2001

[12] M Hildebrandt L Christensen J Kerdels J Albiez and FKirchner ldquoRealtime motion compensation for ROV-based tele-operated underwater manipulatorsrdquo in Proceedings of the IEEEOCEANS pp 1ndash6 May 2009

[13] H Shim B H Jun P M Lee H Baek and J Lee ldquoWorkspacecontrol system of underwater tele-operated manipulators on anROVrdquo Ocean Engineering vol 37 no 11-12 pp 1036ndash1047 2010

[14] J J Craig Introduction to Robotics Addison Wesley BostonMass USA 1986

[15] G Antonelli Underwater Robots Motion and Force Control ofVehicle-Manipulator Systems Springer Berlin Germany 2006

[16] K Kim andT Ura ldquoAppliedmodel-based analysis and synthesisfor the dynamics guidance and control of an autonomousundersea vehiclerdquo Mathematical Problems in Engineering vol2010 Article ID 149385 23 pages 2010

[17] T I Fossen Marine Control Systems Guidance Navigationand Control of Ships Rigs and Underwater Vehicles MarineCybernetics AS 2002

[18] J J E Slotine and W Li Applied Nonlinear Control Prentice-Hall Upper Saddle River NJ USA 1991

[19] K Y Pettersen and O Egeland ldquoPosition and attitude control ofan underactuated autonomous underwater vehiclerdquo in Proceed-ings of the 1996 35th IEEE Conference on Decision and Controlpp 987ndash991 Kobe Japan December 1996

[20] T H Koh MW S Lau G Seet and E Low ldquoA control modulescheme for an underactuated underwater robotic vehiclerdquo Jour-nal of Intelligent and Robotic Systems Theory and Applicationsvol 46 no 1 pp 43ndash58 2006

[21] M Santhakumar and T Asokan ldquoInvestigations on the hybridtracking control of an underactuated autonomous underwaterrobotrdquo Advanced Robotics vol 24 no 11 pp 1529ndash1556 2010

[22] ANSALDO Nucleare Underwater Manipulator MARIS 7080Use and Maintenance Manual Ansaldo Nuclear DivisionGenoa Italy 1996

[23] K Deb Optimization for Engineering Design Algorithms andExamples Prentice Hall New Delhi India 2004

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International Journal of

Modelling and Simulation in Engineering 5

AUV dynamics

Manipulator dynamics

Trajectory planner

minus

+

minus

+

+

+

+

+

+

+

+

Dynamiccoupling effects

+

+

+

minus

+

++

++

+

++

+

q

q

q

qd

d

dt

q

d

dt

KIR

KDR

KPR

KPV

KDV

KIV

MV

MR (q)

int

int

V

d

R

q

G2

G1

q

J( )minus1

)minus1J( )minus1

F2(q )

HT2 (q)

H2(q)

F1(q )

(middot)

(middot)

(middot)(middot)

120578

120578

120578

120578

120578120578

120578

120578

120578

120578

τ

τ

120578 120578

120578

Figure 3 Block diagram of model reference control

ldquoNot to scalerdquo

Top view

Front viewVehicle

ManipulatorVertical thrusters

Port side thruster

Starboard side thruster Stern control

plane surfaces

Lateral thruster

x

x

y

z

Figure 4 Schematic diagram of UVMS prototype model

3 Model Reference Control

This section discusses the model reference control (MRC)design in terms of feedback linearizationThis control scheme

transforms the nonlinear system dynamics into a linearsystem it compensates for all the nonlinearities in the systemby introducing nonlinear elements in the input side thusmaking the controller design more flexible [15ndash17] Unliketraditional control it can be thought of as ldquoinstantaneouslearningrdquo of the vehicle dynamicsThe individual control lawsof the underwater vehicle and the manipulator are chosensuch that the tracking errors are converging to zero Thetracking errors are defined as = 120578

119889minus120578 and q = q

119889minusq where

119889 denotes the desired (or reference) values The equationsof motion of the UVMS can be expressed in the form givenbelow [15]

M119881^ +H

2(119902) q + F

1(119902 119902 ]) + G

1(120578 119902) = 120591

119881

M119877(119902) q +H119879

2(119902) ^ + F

2(119902 119902 ]) + G

2(119902) = 120591

119877

(17)

where M119881

= M + H1(119902) F

1(119902 119902 ]) F

2(119902 119902 ]) G

2(119902)

and G1(120578 119902) are the vectors of the Coriolis centripetal and

dampingfrictional and restoring effects of the vehicle andthe manipulator respectively

6 Modelling and Simulation in Engineering

The proposed control input vectors given by (18) willcancel out or compensates for the nonlinearities in the systemas

120591119881= M

119881u119881+H

2(119902) q + F

1(119902 119902 ]) + G

1(120578 119902)

120591119877= M

119877(119902) u

119877+H119879

2(119902) ^ + F

2(119902 119902 ]) + G

2(119902)

(18)

where

u119881= J(120578)minus1 (u

120578minus

J (120578) J(120578)minus1120578)

u120578=

119889+ K

119901119881 + K

119889119881

+ K119894119881int 119889119905

u119877= q

119889+ K

119901119877q + K

119889119877q + K

119894119877int q 119889119905

(19)

K119901119881 K

119894119881 and K

119889119881are the proportional integral and

derivative gainmatrices of the vehicle controller respectivelyand K

119901119877 K

119894119877 and K

119889119877are the proportional integral and

derivative gainmatrices of themanipulator controller respec-tively Block diagram representation of the proposed UVMScontroller is presented in Figure 3

The above-mentioned control vectors lead to exponentialstable error dynamics of the vehicle and manipulator whichare given as

+ K119901119881 + K

119889119881

+ K119894119881int 119889119905 = 0

q + K119901119877q + K

119889119877q + K

119894119877int q 119889119905 = 0

(20)

which implies that tracking errors are converging to zero (ie rarr 0 and q rarr 0) and the UVMS follows the given desiredtrajectory [18]

However the above-proposed control scheme assumedthat there are no disturbances and no uncertainties associatedwith the system If the system uncertainties and externaldisturbances are considered for the analysis the system errordynamics become

+ K119901119881 + K

119889119881

+ K119894119881int 119889119905 = M

119881

minus1120591119889119881

q + K119901119877q + K

119889119877q + K

119894119877int q 119889119905 = M

119877

minus1120591119889119877

(21)

where 120591119889119881

and 120591119889119877

are the disturbance vector (which com-bines the internal disturbances such as effect of parameteruncertainties and external disturbances namely underwatercurrent etc) of the vehicle and manipulator controllerrespectively

The closed-loop characteristic equation or polynomial isgiven as

Δ

119888119881 (119904) =

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

119904

2I + 119904K119889119881+ K

119901119881+

K119894119881

119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ

119888119877 (119904) =

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

119904

2I + 119904K119889119877+ K

119901119877+

K119894119877

119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

(22)

The control gain matrices are chosen as diagonal and positivedefinite matrices such as

K119889119881= diag (119896

119889119881119894) K

119901119881= diag (119896

119901119881119894)

K119894119881= diag (119896

119894119881119894) K

119889119877= diag (119896

119889119877119894)

K119901119877= diag (119896

119901119877119894) K

119894119877= diag (119896

119894119877119894)

(23)

Therefore the closed-loop characteristic polynomialbecomes

Δ

119888119881 (119904) =

6

prod

119894=1

(119904

2+ 119904119896

119889119881119894+ 119896

119901119881119894+

119896

119894119881119894

119904

)

Δ

119888119877 (119904) =

119899

prod

119894=1

(119904

2+ 119904119896

119889119877119894+ 119896

119901119877119894+

119896

119894119877119894

119904

)

(24)

and the system error is asymptotically stable as long as thecontroller gain values are all positiveTherefore as long as thedisturbance vectors are bounded the system tracking errorsare converged to zero In other words the system followsthe given desired trajectory Moreover the controller gainmatrices have been chosen in such a way that

120582min K119901119881 gt

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120597120591119889119881

120597

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120582min K119889119881 gt

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120597120591119889119881

120597

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120582min K119901119877 gt

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120597120591119889119877

120597q

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120582min K119889119877 gt

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120597120591119889119877

120597

q

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

(25)

Hence = 0 and q = 0 for all 119905 ge 0 are its unique solutionand it can be observed that the system tracking errors areconverging to zero asymptotically The proposed controlleranalysis does not contain explicit treatment of the parametricuncertainties and external disturbance while taking temporalderivative along the closed-loop system trajectories and it isleft for further research and analysis

4 Performance Analysis of the UVMS

41 Description of the Simulated System We have accom-plished widespread computer-based numerical simulationsto explore the total performance of the proposed UVMS andthe model reference (direct adaptive) control scheme TheUVMS used for this study consists of six degrees of freedom(DOF) vehicle and a 3-DOF spatial manipulator the UVMSarrangement in conceptual design is presented in Figure 4The vehicle is a cylindrical shape (torpedo fish shaped)cruising type with the length of 11m and the diameter of025m The mass of the vehicle is 39 kg The vehicle has fivethrusters in total two propulsion thrusters (in the stern side)two vertical thrusters and one lateral thruster Thereforesurge sway and heave motions are controlled through thesethrusters actuation directly and however yaw and pitchmotions are controlled by differential actuation of propulsionand vertical thrusters Although roll motion is unactuated itcan be controlled itself due to restoring effects [19ndash21] It isknown that a necessary condition for a submersible body to

Modelling and Simulation in Engineering 7

be stable is that the centre of gravity (CG) should lie belowthe centre of buoyancy (CB) For this the vehicle is trimmed(using a float) to have the CB almost vertically above the CGand made to be nearly neutral buoyant Here the roll motionhas nonzero components of restoringmoments that representself-restoring torque for the roll direction With nonzerorestoring terms it may be possible to find continuous statefeedback laws to stabilize the system as a whole In additionto this without loss of generality we can assume that thedamping terms of nonactuated states are sufficiently largerthan their inertia terms which means that the hydrodynamicrestoring forces and torques are large enough to stabilize thenonactuated (roll) states (zero dynamics) which is a commonproperty forAUVs [19]Thismeans that the underwater robotcan be exponentially stabilized by the actuated state controlsalone

The manipulator links are cylindrical in shape and theradii of links 1 2 and 3 are 01m 005m and 005mrespectively The lengths of links 1 2 and 3 are 01m 02mand 02m respectively The link masses (along with oil con-served motors) are 039 kg 157 kg and 157 kg respectivelyHere the links are considered as cylindrical shape becausesuch shape provides uniform hydrodynamic reactions andis one of the primary candidates for possible link geometryfor underwater manipulators Although it is cylindrical ourmathematical framework does not depend on any particularshapes it can be easily accommodated by any other shapesIndeed cylindrical underwater manipulators are available inthe present market [22] Hydrodynamic parameters of theUVMS are estimated using empirical relations based on striptheory This method is verified using the available literaturetherefore these values are reliable and can be used for furtherdevelopments Some parameters like inertia centre of gravityand centre of buoyancy are calculated from the geometricaldesign of the UVMSThe total parameter list of the UVMS isgiven in Tables 2 and 3

We have compared our results with those of traditionalPID controller the following control vectors were consideredfor the vehicle and the manipulator and are given by

120591119881= K

119863119881

+ K119875119881 + K

119868119881int 119889119905

120591119877= K

119863119877q + K

119875119877q + K

119868119877int q 119889119905

(26)

where K119875119881 K

119868119881 K

119863119881 K

119875119877 K

119868119877 and K

119863119877are the propor-

tional integral and derivative gainmatrices of the vehicle andthe manipulator respectively

42 Description of the Tasks Three different tasks with fourdifferent cases have been considered for the simulations Thefirst task is that the vehicle is commanded to track a given3D trajectory without and with the manipulator (at rest or itshome position) and in this condition the vehicle acceleratesfor the initial 20 s and attains the vehicle forward speed of1ms (asymp2 knots) and for the final 20 s the vehicle deceleratesto zero speed The particular desired 3D trajectory (referto Figure 5) has been chosen for this performance analysisbecause this trajectory consists of all four main motions such

Table 2 The parameter list of the UVMS

Parameters ValuesMass of the vehicle (119898V) 39 kgLength of the vehicle (119871V) 11mDiameter of the vehicle (119889V) 025mMoment of inertia of the vehicle119868

119909034 kgm2

119868

119910371 kgm2

119868

119911371 kgm2

Centre of gravity (CG) = (119909119866 119910

119866 119911

119866) (0 0 0) m

Centre of buoyancy (CB) = (119909119861 119910

119861 119911

119861) (0 0 0015) m

Mass of the underwater manipulator links119898

103927 kg

119898

215708 kg

119898

315708 kg

Underwater manipulator link lengths119871

1005m

119871

2020m

119871

3020m

Underwater manipulator link radii119903

1010m

119903

2005m

119903

3005m

Coefficient of drag (119862119863) 125

Coefficient of lift (119862119871) 115

Table 3 The values of hydrodynamic coefficients calculated usingempirical relations based on strip theory

Vehicle added mass derivatives119883

minus117 kg 119870

minus01 kgmrad

119884V minus3484 kg 119872

minus103 kgm

119884

119903104 kgm 119872

119902minus266 kgmrad

119885

minus3483 kg 119873V minus104 kgm

119885

119902minus104 kgm 119873

119903minus265 kgmrad

Vehicle hydrodynamic parameters119883

119906|119906|minus7365 kgm 119883

119906minus212 kgs

119883V|V| minus0737 kgm 119883V minus031 kgs119883

119908|119908|minus0737 kgm 119883

119908minus031 kgs

119883

119902|119902|minus1065 kgmrad 119883

119902minus051 kgms

119883

119903|119903|minus1065 kgmrad 119883

119903minus051 kgms

119884V|V| minus1122 kgm 119884V minus6245 kgs119884

119903|119903|0250 kgmrad 119884

119903012 kgms

119885

119908|119908|minus1122 kgm 119885

119908minus6245 kgs

119885

119902|119902|minus0250 kgmrad 119885

119902012 kgms

119870

119901|119901|minus05975 kgm2rad2 119870

119901minus03125 kgm2s

119872

119908|119908|2244 kgmrad 119872

11990812 kgms

119872

119902|119902|minus1195 kgm2rad2 119872

119902minus5975 kgm2s

119873V|V| minus2244 kgmrad 119873V 12 kgms

as sway in and out and heave up and downThe average valueof sway velocity is 025ms (asymp05 knots) (same value for heaveas well) This task is performed to identify the influences of

8 Modelling and Simulation in Engineering

050

100150

200

05

1015

200

5

10

15

20

Desired 3D pathPID without armMRC without arm

PID with armMRC with arm

z(m

)

y (m)x (m)

Figure 5 Comparative trajectory tracking control results

the underwater manipulator effects during vehicle trackingcontrol In the second task the vehicle is free to move (nocontrol action involved) and the manipulator has a certainrepeated desired trajectory This task is mainly performedto identify the vehicle behavior during manipulator motionIn all the above tasks the initial velocities and positions ofthe vehicle and the manipulator are chosen to be zero andthe initial desired and actual positions and orientations arethe same In the third task two basic trajectories for themanipulator have been chosen for simulations a circulartrajectory (in 3D space) and a rectangular trajectory (in 119910119911plane) along with a straight line in 3D space This is forthe reason that most of the underwater intervention tasksinvolve these types of trajectories and also we can arrangeany spatial trajectory by combining these trajectories For therectangular trajectory we have selected a cubic polynomialfunction as the trajectory function which imposes that thetrajectory is continuous and smooth

In the performance analysis the sensory noises inposition and orientation measurements are introduced andwe have considered Gaussian noise of 001m mean and001m standard deviation for the positionmeasurements and02

∘ mean and 02∘ standard deviation for the orientationmeasurements The thruster dynamic characteristics are alsoincorporated in the simulations All the vehicle thrusters areconsidered as an identical one and the following thrustercharacteristics are considered for the analysis the thrusterresponse delay time is 200ms efficiency is 95and saturationlimits are plusmn20N The vehicle surge thrusters are located at05m from the body centre along the 119909-axis and offset eachside 03m from 119910-axis The lateral thruster is exactly locatedon the body centre and vertical thrusters are placed on the 119909-axis 04m apart from the centre at each side The controllerupdate rate and sensor response time are considered as 100mseach

43 Results and Discussions Here numerical simulationresults are shown and discussed to investigate the dynamic

Table 4 Controller parameter settings for simulations

Vehicle controller parameters Values119870

119901119881diag(42 22 25 0 25 27)

119870

119889119881diag(225 12 13 0 15 13)

119870

119894119881diag(05 02 03 0 25 22)

119870

119875119881diag(180 130 150 0 150 130)

119870

119863119881diag(80 100 100 0 80 90)

119870

119868119881diag(15 12 15 0 16 18)

Manipulator controller parameters Values119870

119901119877diag(5 10 12)

119870

119889119877diag(3 5 8)

119870

119894119877diag(01 02 02)

119870

119875119877diag(60 80 75)

119870

119863119877diag(35 40 50)

119870

119868119877diag(1 15 2)

coupling effects and the effectiveness of the proposed model-based control scheme which is expected to provide anintuitive promising prospective of the proposed approach

431 Underwater Vehicle Tracking a Given 3D Trajectorywith the Underwater Manipulator In this case as mentionedearlier the vehicle is commanded to follow a given 3D desiredtrajectory The desired 3D trajectory is given in Figure 5The controller gain values are tuned based on the geneticalgorithms (GA) for minimizing the integral squared error(ISE) as the costobjective function [23] Here we haveconsidered both the model reference control and the PIDcontrol performance to be almost equal in the ideal situationwhich makes the controller performance comparison quitereasonable and gives much better way of understandingBased on the GA tuning method the controller parametersare obtained and given in Table 4 The same set of controllerparameters are used throughout the entire performanceanalysis

Initially the performance analysis is carried out for thevehicle trajectory tracking without manipulator inclusionThe actual simulated trajectories based on MRC and PID arepresented in Figure 5These results show that both controllersare good enough to track the given trajectory and thetracking errors are within the design limits (error limits forthe vehicle during trajectory tracking are plusmn02m and plusmn02∘in positions and orientations resp) as well The trackingerrors are presented in Figures 6 7 8 9 10 and 11 In thesecond set of simulations the manipulator is included andthe inclusion effects during trajectory tracking of the vehicleare considered Here the manipulator links are folded andarranged in such a way that the influences on the vehicledynamics are small (ie manipulator joint angles are 120579

1=

180

∘ 1205792= 0

∘ and 1205793= 180

∘) The manipulator inclusionshows that there are significant performance changes in thevehicle trajectory tracking especially during the heave andsway motion tracking The heave roll and pitch motionsof the vehicle are greatly influenced by the underwatermanipulator inclusion which are replicated in the results

Modelling and Simulation in Engineering 9

0 50 100 150 200 250 300minus01

minus005

0

005

01

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Trac

king

erro

r inx

(xe) (

m)

Figure 6 Tracking errors in 119909 position for a given 3D trajectory

0 50 100 150 200 250 300minus002

minus001

0

001

002

003

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Trac

king

erro

r iny

(ye) (

m)

Figure 7 Tracking errors in 119910 position for a given 3D trajectory

(refer to Figures 6 to 11) However the manipulator inclusioneffects are better adapted in the model reference control thanin the PID control As can be observed from Figures 8 and10 the manipulator inclusion causes an initial pitch anglevariation drifts the vehicle in the heave direction during thestraight line motion (during acceleration stage) Howeverthese unwanted effects are compensated successfully in themodel reference control and therefore tracking errors do notexceed their design limits

432 Manipulator following a Given Desired 3D Trajectorywith the Freely Moving Underwater Vehicle (without VehicleControl) As mentioned earlier in this section this task ismainly to address the interaction effects and their influences

0 50 100 150 200 250 300minus005

0

005

01

015

02

03

Trac

king

erro

r inz

(ze) (

m)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 8 Tracking errors in 119911 position for a given 3D trajectory

0 50 100 150 200 250 300minus10

minus5

0

5

10

15

20

Trac

king

erro

r in

roll

(120601e) (

deg)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 9 Tracking errors in roll for a given 3D trajectory

on theUVMS For this task the vehicle controller is removedand only the underwater manipulator follows a given desiredcontinuous trajectory The desired values of joint positionsare as follows 120579

1119889= 90

∘ sin (01119905) 1205792119889

= 90

∘ and 1205793119889

=

minus45

∘ The simulation results of this condition are presentedin Figures 12 13 14 15 and 16 From the results it is observedthat the vehicle is started getting drifted from its initialposition and it is moving forward with an average velocityof 002ms (approximately) for the repeated underwatermanipulator movements It shows that the manipulator linksare affected due to the dynamic coupling effects Fromthe results it is observed that the vehicle swims duringmanipulator movements if the vehicle does not have anycontrol actionThese errors and forward speed are increasing

10 Modelling and Simulation in Engineering

0 50 100 150 200 250 300minus15

minus1

minus05

0

05

1

15

Trac

king

erro

r in

pitc

h (120579

e) (

deg)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 10 Tracking errors in pitch for a given 3D trajectory

0 50 100 150 200 250 300minus1

minus05

0

05

1

Trac

king

erro

r in

yaw

(120595e) (

deg)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 11 Tracking errors in yaw for a given 3D trajectory

with the manipulator oscillation frequency and their jointangle magnitudes In addition the direction of the vehiclersquosmovement varies depending on the manipulator positionsand its direction ofmovementsThese results can be extendedto the work towards swimming robots and their dynamicmodeling aspects

433 Underwater Manipulator following a Given DesiredCircular Trajectory with Vehicle Control The circular trajec-tory chosen for the analysis has 02m in diameter and anaverage speed of 00125ms These parameters are chosenwith the consideration of manipulator actuators workspaceand control The results from computer simulations arepresented in Figures 15ndash18 In Figure 15 both desired andactual task space trajectories are plotted and the task spacetracking errors are given in Figures 16ndash18 From the results

0 5 10 15 20minus006

minus004

minus002

0

002

004

006

008

01

012

Posit

ion

erro

rs (m

)

Time (t) (s)

xeyeze

Figure 12 Tracking errors in the vehicle positions (when manipu-lator has motion)

0 5 10 15 20minus3

minus2

minus1

0

1

2

3

4

Attit

ude e

rror

s (de

g)

Time (t) (s)

120601e120579e120595e

Figure 13 Tracking errors in the vehicle orientations (when thevehicle has no control and the manipulator has repeated motion)

it is observed that the manipulator tip tracks the givendesired task space trajectories quite satisfactorily in both PIDand MRC schemes in the ideal conditions (no disturbancesno uncertainties etc) Then in order to demonstrate theadaptability and robustness of the proposed controller anuncertain condition is considered for the simulations Thefollowing conditions are considered for the uncertain condi-tion analysis

(i) the UVMS parameters are assumed to be inaccurate(about 10 for each parameters)

(ii) the manipulator carries a payload of 1 kg at its tip

Modelling and Simulation in Engineering 11

0708

091

minus02minus01

001

02045

046

047

048

049

Desired tool tip positionActual tool tip position

z(m

)

y (m)x (m)

Figure 14 Manipulator tip position in 3D space (when the vehiclehas no control)

06507

07508

085

005

01

015

minus01

minus005

0

005

Desired trajectoryPIDMRC

PID with uncertaintyMRC with uncertainty

z(m

)

y (m)x (m)

Figure 15 Task space (119909119910119911) trajectories (results from the circulartrajectory)

(iii) an unknown ocean current is added in the simulationby properly considering the relative velocity of thein the dynamic model It is assumed to have anirrotational current constant in the inertial frameand the value of the current is considered as ^

119888=

[02 02 01 0 0 0]

119879ms

The results are presented in Figures 15ndash18 and from theseresults it is observed that the proposed controller is goodin adapting the uncertainties and disturbances (refer toFigure 15) Figures 16 and 17 show that tracking errors of119909 and 119910 in both PID and MRC methods are almost thesame and results satisfactorily however the tracking error in119911 substantiates that the proposed controller is comparativelygood in the presence of uncertainties and disturbances

434 Underwater Manipulator following a Given DesiredRectangular Trajectory with Vehicle Control The rectangulartrajectory chosen for the analysis has 04m in width and

0 5 10 15 20 25 30minus002

minus0015

minus001

minus0005

0

0005

001

0015

Time (t) (s)

PIDMRC

PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r inx

(xe) (

m)

Figure 16 Time histories of the manipulator tip position trackingerror in 119909 (circular trajectory)

0 5 10 15 20 25 30minus4

minus3

minus2

minus1

0

1

2

3

4

5

6

MRC

Time (t) (s)

PID PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r iny

(ye) (

m)

times10minus3

Figure 17 Time histories of the manipulator tip position trackingerror in 119910 (circular trajectory)

02m in height in the 119910119911 plane and an average speedof 005ms As mentioned in the last case the trajectoryhas been chosen with the consideration of the manipulatorcharacteristics Two conditions have been considered for theanalysis ideal condition (no disturbances no uncertaintiesetc) and an uncertain condition (the same as the previouscase Section 433) The results from computer simulationsare plotted in Figure 19 In the ideal condition both con-trollers show quite satisfactory performance and in theuncertain condition the proposed controller shows betterperformance

12 Modelling and Simulation in Engineering

MRC

0 5 10 15 20 25 30minus002

0

002

004

006

008

01

012

Time (t) (s)

PID PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r inz

(ze) (

m)

Figure 18 Time histories of the manipulator tip position trackingerror in 119911 (circular trajectory)

064 066 068 07 072

minus020

0202

025

03

035

04

Desired trajectoryPIDMRC

PID with uncertaintyMRC with uncertainty

z(m

)

y (m)x (m)

Figure 19 Task space (119909119910119911) trajectories (results from the rectangu-lar trajectory)

In both trajectory tracking cases the thruster forces donot exceed plusmn5N and the manipulator actuator torques staywithinplusmn015Nmwhich arewell within the range of actuators

5 Conclusions

In this study the interaction effects due to the dynamiccoupling between the vehicle and the manipulator wereinvestigated using closed-form equations which provide ageneralized scheme for formulating the equations of motionof the UVMS The proposed scheme makes it possible toidentify the structure nature and properties of the systemand it simplifies the control design This study also proposeda model reference control approach for an underactuated

UVMS to perform underwater intervention tasks incorpo-rating desired trajectory information Extensive simulationswere carried out to verify and demonstrate the effectivenessof the proposed scheme In particular the performance ofthe model reference controller is compared with that of theconventional PID controller for the given UVMS operationscenarios The obtained results confirm the effectiveness androbustness of the proposed scheme in terms of tracking errorsand control effort in the presence of external disturbancesand parameter uncertainties This research provides a gener-alized framework for modeling and controlling of an UVMSconsidering the dynamic coupling between the vehicle andthe manipulator which is crucial for achieving underwatermanipulation tasks for a variety of scientific industrial andmilitary missions using unmanned underwater vehicles

Conflict of Interests

Authors confirm that this paper has not been publishedelsewhere and is not under consideration by another journalAll authors have approved the manuscript and agree withsubmission toModelling and Simulation in EngineeringTheauthors have no conflict of interests to declare

Acknowledgments

The author would like to acknowledge Professor JinwhanKim for his valuable suggestions and discussions on under-water manipulator This research was supported in partby the World Class University (WCU) program throughthe National Research Foundation of Korea funded by theMinistry of Education Science and Technology (R31-2008-000-10045-0)

References

[1] G Antonelli F Caccavale S Chiaverini and L Villani ldquoTrack-ing control for underwater vehicle-manipulator systems withvelocity estimationrdquo IEEE Journal of Oceanic Engineering vol25 no 3 pp 399ndash413 2000

[2] G Marani S K Choi and J Yuh ldquoUnderwater autonomousmanipulation for intervention missions AUVsrdquo Ocean Engi-neering vol 36 no 1 pp 15ndash23 2009

[3] S McMillan D E Orin and R B McGhee ldquoEfficient dynamicsimulation of an underwater vehicle with a robotic manipula-torrdquo IEEE Transactions on Systems Man and Cybernetics vol25 no 8 pp 1194ndash1206 1995

[4] T I Fossen Guidance and Control of Ocean Vehicles WileyChichester UK 1994

[5] T J Tarn G A Shoults and S P Yang ldquoA dynamic model ofan underwater vehicle with a robotic manipulator using Kanersquosmethodrdquo Autonomous Robots vol 3 no 2-3 pp 269ndash283 1996

[6] H Mahesh J Yuh and R Lakshmi ldquoA Coordinated controlof an underwater vehicle and robotic manipulatorrdquo Journal ofRobotic Systems vol 8 no 3 pp 339ndash370 1991

[7] N Sarkar and T K Podder ldquoCoordinated motion planningand control of autonomous underwater vehicle-manipulatorsystems subject to drag optimizationrdquo IEEE Journal of OceanicEngineering vol 26 no 2 pp 228ndash239 2001

Modelling and Simulation in Engineering 13

[8] T W McLain S M Rock and M J Lee ldquoExperiments inthe coordinated control of an underwater armvehicle systemrdquoAutonomous Robots vol 3 no 2-3 pp 213ndash232 1996

[9] M W Dunnigan and G T Russell ldquoEvaluation and reductionof the dynamic coupling between a manipulator and an under-water vehiclerdquo IEEE Journal of Oceanic Engineering vol 23 no3 pp 260ndash273 1998

[10] B H Jun P M Lee and J Lee ldquoManipulability analysisof underwater robotic arms on ROV and application totask-oriented joint configurationrdquo in Proceedings of the IEEEOCEANS pp 1548ndash1553 November 2004

[11] J H Ryu D S Kwon and P M Lee ldquoControl of underwatermanipulators mounted on an ROV using base force informa-tionrdquo in Proceedings of the IEEE International Conference onRobotics and Automation (ICRA rsquo01) pp 3238ndash3243 May 2001

[12] M Hildebrandt L Christensen J Kerdels J Albiez and FKirchner ldquoRealtime motion compensation for ROV-based tele-operated underwater manipulatorsrdquo in Proceedings of the IEEEOCEANS pp 1ndash6 May 2009

[13] H Shim B H Jun P M Lee H Baek and J Lee ldquoWorkspacecontrol system of underwater tele-operated manipulators on anROVrdquo Ocean Engineering vol 37 no 11-12 pp 1036ndash1047 2010

[14] J J Craig Introduction to Robotics Addison Wesley BostonMass USA 1986

[15] G Antonelli Underwater Robots Motion and Force Control ofVehicle-Manipulator Systems Springer Berlin Germany 2006

[16] K Kim andT Ura ldquoAppliedmodel-based analysis and synthesisfor the dynamics guidance and control of an autonomousundersea vehiclerdquo Mathematical Problems in Engineering vol2010 Article ID 149385 23 pages 2010

[17] T I Fossen Marine Control Systems Guidance Navigationand Control of Ships Rigs and Underwater Vehicles MarineCybernetics AS 2002

[18] J J E Slotine and W Li Applied Nonlinear Control Prentice-Hall Upper Saddle River NJ USA 1991

[19] K Y Pettersen and O Egeland ldquoPosition and attitude control ofan underactuated autonomous underwater vehiclerdquo in Proceed-ings of the 1996 35th IEEE Conference on Decision and Controlpp 987ndash991 Kobe Japan December 1996

[20] T H Koh MW S Lau G Seet and E Low ldquoA control modulescheme for an underactuated underwater robotic vehiclerdquo Jour-nal of Intelligent and Robotic Systems Theory and Applicationsvol 46 no 1 pp 43ndash58 2006

[21] M Santhakumar and T Asokan ldquoInvestigations on the hybridtracking control of an underactuated autonomous underwaterrobotrdquo Advanced Robotics vol 24 no 11 pp 1529ndash1556 2010

[22] ANSALDO Nucleare Underwater Manipulator MARIS 7080Use and Maintenance Manual Ansaldo Nuclear DivisionGenoa Italy 1996

[23] K Deb Optimization for Engineering Design Algorithms andExamples Prentice Hall New Delhi India 2004

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RotatingMachinery

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

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Shock and Vibration

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Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

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Electrical and Computer Engineering

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Advances inOptoElectronics

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Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

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DistributedSensor Networks

International Journal of

6 Modelling and Simulation in Engineering

The proposed control input vectors given by (18) willcancel out or compensates for the nonlinearities in the systemas

120591119881= M

119881u119881+H

2(119902) q + F

1(119902 119902 ]) + G

1(120578 119902)

120591119877= M

119877(119902) u

119877+H119879

2(119902) ^ + F

2(119902 119902 ]) + G

2(119902)

(18)

where

u119881= J(120578)minus1 (u

120578minus

J (120578) J(120578)minus1120578)

u120578=

119889+ K

119901119881 + K

119889119881

+ K119894119881int 119889119905

u119877= q

119889+ K

119901119877q + K

119889119877q + K

119894119877int q 119889119905

(19)

K119901119881 K

119894119881 and K

119889119881are the proportional integral and

derivative gainmatrices of the vehicle controller respectivelyand K

119901119877 K

119894119877 and K

119889119877are the proportional integral and

derivative gainmatrices of themanipulator controller respec-tively Block diagram representation of the proposed UVMScontroller is presented in Figure 3

The above-mentioned control vectors lead to exponentialstable error dynamics of the vehicle and manipulator whichare given as

+ K119901119881 + K

119889119881

+ K119894119881int 119889119905 = 0

q + K119901119877q + K

119889119877q + K

119894119877int q 119889119905 = 0

(20)

which implies that tracking errors are converging to zero (ie rarr 0 and q rarr 0) and the UVMS follows the given desiredtrajectory [18]

However the above-proposed control scheme assumedthat there are no disturbances and no uncertainties associatedwith the system If the system uncertainties and externaldisturbances are considered for the analysis the system errordynamics become

+ K119901119881 + K

119889119881

+ K119894119881int 119889119905 = M

119881

minus1120591119889119881

q + K119901119877q + K

119889119877q + K

119894119877int q 119889119905 = M

119877

minus1120591119889119877

(21)

where 120591119889119881

and 120591119889119877

are the disturbance vector (which com-bines the internal disturbances such as effect of parameteruncertainties and external disturbances namely underwatercurrent etc) of the vehicle and manipulator controllerrespectively

The closed-loop characteristic equation or polynomial isgiven as

Δ

119888119881 (119904) =

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

119904

2I + 119904K119889119881+ K

119901119881+

K119894119881

119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

Δ

119888119877 (119904) =

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

119904

2I + 119904K119889119877+ K

119901119877+

K119894119877

119904

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

(22)

The control gain matrices are chosen as diagonal and positivedefinite matrices such as

K119889119881= diag (119896

119889119881119894) K

119901119881= diag (119896

119901119881119894)

K119894119881= diag (119896

119894119881119894) K

119889119877= diag (119896

119889119877119894)

K119901119877= diag (119896

119901119877119894) K

119894119877= diag (119896

119894119877119894)

(23)

Therefore the closed-loop characteristic polynomialbecomes

Δ

119888119881 (119904) =

6

prod

119894=1

(119904

2+ 119904119896

119889119881119894+ 119896

119901119881119894+

119896

119894119881119894

119904

)

Δ

119888119877 (119904) =

119899

prod

119894=1

(119904

2+ 119904119896

119889119877119894+ 119896

119901119877119894+

119896

119894119877119894

119904

)

(24)

and the system error is asymptotically stable as long as thecontroller gain values are all positiveTherefore as long as thedisturbance vectors are bounded the system tracking errorsare converged to zero In other words the system followsthe given desired trajectory Moreover the controller gainmatrices have been chosen in such a way that

120582min K119901119881 gt

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120597120591119889119881

120597

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120582min K119889119881 gt

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120597120591119889119881

120597

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120582min K119901119877 gt

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120597120591119889119877

120597q

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120582min K119889119877 gt

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

120597120591119889119877

120597

q

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

1003817

(25)

Hence = 0 and q = 0 for all 119905 ge 0 are its unique solutionand it can be observed that the system tracking errors areconverging to zero asymptotically The proposed controlleranalysis does not contain explicit treatment of the parametricuncertainties and external disturbance while taking temporalderivative along the closed-loop system trajectories and it isleft for further research and analysis

4 Performance Analysis of the UVMS

41 Description of the Simulated System We have accom-plished widespread computer-based numerical simulationsto explore the total performance of the proposed UVMS andthe model reference (direct adaptive) control scheme TheUVMS used for this study consists of six degrees of freedom(DOF) vehicle and a 3-DOF spatial manipulator the UVMSarrangement in conceptual design is presented in Figure 4The vehicle is a cylindrical shape (torpedo fish shaped)cruising type with the length of 11m and the diameter of025m The mass of the vehicle is 39 kg The vehicle has fivethrusters in total two propulsion thrusters (in the stern side)two vertical thrusters and one lateral thruster Thereforesurge sway and heave motions are controlled through thesethrusters actuation directly and however yaw and pitchmotions are controlled by differential actuation of propulsionand vertical thrusters Although roll motion is unactuated itcan be controlled itself due to restoring effects [19ndash21] It isknown that a necessary condition for a submersible body to

Modelling and Simulation in Engineering 7

be stable is that the centre of gravity (CG) should lie belowthe centre of buoyancy (CB) For this the vehicle is trimmed(using a float) to have the CB almost vertically above the CGand made to be nearly neutral buoyant Here the roll motionhas nonzero components of restoringmoments that representself-restoring torque for the roll direction With nonzerorestoring terms it may be possible to find continuous statefeedback laws to stabilize the system as a whole In additionto this without loss of generality we can assume that thedamping terms of nonactuated states are sufficiently largerthan their inertia terms which means that the hydrodynamicrestoring forces and torques are large enough to stabilize thenonactuated (roll) states (zero dynamics) which is a commonproperty forAUVs [19]Thismeans that the underwater robotcan be exponentially stabilized by the actuated state controlsalone

The manipulator links are cylindrical in shape and theradii of links 1 2 and 3 are 01m 005m and 005mrespectively The lengths of links 1 2 and 3 are 01m 02mand 02m respectively The link masses (along with oil con-served motors) are 039 kg 157 kg and 157 kg respectivelyHere the links are considered as cylindrical shape becausesuch shape provides uniform hydrodynamic reactions andis one of the primary candidates for possible link geometryfor underwater manipulators Although it is cylindrical ourmathematical framework does not depend on any particularshapes it can be easily accommodated by any other shapesIndeed cylindrical underwater manipulators are available inthe present market [22] Hydrodynamic parameters of theUVMS are estimated using empirical relations based on striptheory This method is verified using the available literaturetherefore these values are reliable and can be used for furtherdevelopments Some parameters like inertia centre of gravityand centre of buoyancy are calculated from the geometricaldesign of the UVMSThe total parameter list of the UVMS isgiven in Tables 2 and 3

We have compared our results with those of traditionalPID controller the following control vectors were consideredfor the vehicle and the manipulator and are given by

120591119881= K

119863119881

+ K119875119881 + K

119868119881int 119889119905

120591119877= K

119863119877q + K

119875119877q + K

119868119877int q 119889119905

(26)

where K119875119881 K

119868119881 K

119863119881 K

119875119877 K

119868119877 and K

119863119877are the propor-

tional integral and derivative gainmatrices of the vehicle andthe manipulator respectively

42 Description of the Tasks Three different tasks with fourdifferent cases have been considered for the simulations Thefirst task is that the vehicle is commanded to track a given3D trajectory without and with the manipulator (at rest or itshome position) and in this condition the vehicle acceleratesfor the initial 20 s and attains the vehicle forward speed of1ms (asymp2 knots) and for the final 20 s the vehicle deceleratesto zero speed The particular desired 3D trajectory (referto Figure 5) has been chosen for this performance analysisbecause this trajectory consists of all four main motions such

Table 2 The parameter list of the UVMS

Parameters ValuesMass of the vehicle (119898V) 39 kgLength of the vehicle (119871V) 11mDiameter of the vehicle (119889V) 025mMoment of inertia of the vehicle119868

119909034 kgm2

119868

119910371 kgm2

119868

119911371 kgm2

Centre of gravity (CG) = (119909119866 119910

119866 119911

119866) (0 0 0) m

Centre of buoyancy (CB) = (119909119861 119910

119861 119911

119861) (0 0 0015) m

Mass of the underwater manipulator links119898

103927 kg

119898

215708 kg

119898

315708 kg

Underwater manipulator link lengths119871

1005m

119871

2020m

119871

3020m

Underwater manipulator link radii119903

1010m

119903

2005m

119903

3005m

Coefficient of drag (119862119863) 125

Coefficient of lift (119862119871) 115

Table 3 The values of hydrodynamic coefficients calculated usingempirical relations based on strip theory

Vehicle added mass derivatives119883

minus117 kg 119870

minus01 kgmrad

119884V minus3484 kg 119872

minus103 kgm

119884

119903104 kgm 119872

119902minus266 kgmrad

119885

minus3483 kg 119873V minus104 kgm

119885

119902minus104 kgm 119873

119903minus265 kgmrad

Vehicle hydrodynamic parameters119883

119906|119906|minus7365 kgm 119883

119906minus212 kgs

119883V|V| minus0737 kgm 119883V minus031 kgs119883

119908|119908|minus0737 kgm 119883

119908minus031 kgs

119883

119902|119902|minus1065 kgmrad 119883

119902minus051 kgms

119883

119903|119903|minus1065 kgmrad 119883

119903minus051 kgms

119884V|V| minus1122 kgm 119884V minus6245 kgs119884

119903|119903|0250 kgmrad 119884

119903012 kgms

119885

119908|119908|minus1122 kgm 119885

119908minus6245 kgs

119885

119902|119902|minus0250 kgmrad 119885

119902012 kgms

119870

119901|119901|minus05975 kgm2rad2 119870

119901minus03125 kgm2s

119872

119908|119908|2244 kgmrad 119872

11990812 kgms

119872

119902|119902|minus1195 kgm2rad2 119872

119902minus5975 kgm2s

119873V|V| minus2244 kgmrad 119873V 12 kgms

as sway in and out and heave up and downThe average valueof sway velocity is 025ms (asymp05 knots) (same value for heaveas well) This task is performed to identify the influences of

8 Modelling and Simulation in Engineering

050

100150

200

05

1015

200

5

10

15

20

Desired 3D pathPID without armMRC without arm

PID with armMRC with arm

z(m

)

y (m)x (m)

Figure 5 Comparative trajectory tracking control results

the underwater manipulator effects during vehicle trackingcontrol In the second task the vehicle is free to move (nocontrol action involved) and the manipulator has a certainrepeated desired trajectory This task is mainly performedto identify the vehicle behavior during manipulator motionIn all the above tasks the initial velocities and positions ofthe vehicle and the manipulator are chosen to be zero andthe initial desired and actual positions and orientations arethe same In the third task two basic trajectories for themanipulator have been chosen for simulations a circulartrajectory (in 3D space) and a rectangular trajectory (in 119910119911plane) along with a straight line in 3D space This is forthe reason that most of the underwater intervention tasksinvolve these types of trajectories and also we can arrangeany spatial trajectory by combining these trajectories For therectangular trajectory we have selected a cubic polynomialfunction as the trajectory function which imposes that thetrajectory is continuous and smooth

In the performance analysis the sensory noises inposition and orientation measurements are introduced andwe have considered Gaussian noise of 001m mean and001m standard deviation for the positionmeasurements and02

∘ mean and 02∘ standard deviation for the orientationmeasurements The thruster dynamic characteristics are alsoincorporated in the simulations All the vehicle thrusters areconsidered as an identical one and the following thrustercharacteristics are considered for the analysis the thrusterresponse delay time is 200ms efficiency is 95and saturationlimits are plusmn20N The vehicle surge thrusters are located at05m from the body centre along the 119909-axis and offset eachside 03m from 119910-axis The lateral thruster is exactly locatedon the body centre and vertical thrusters are placed on the 119909-axis 04m apart from the centre at each side The controllerupdate rate and sensor response time are considered as 100mseach

43 Results and Discussions Here numerical simulationresults are shown and discussed to investigate the dynamic

Table 4 Controller parameter settings for simulations

Vehicle controller parameters Values119870

119901119881diag(42 22 25 0 25 27)

119870

119889119881diag(225 12 13 0 15 13)

119870

119894119881diag(05 02 03 0 25 22)

119870

119875119881diag(180 130 150 0 150 130)

119870

119863119881diag(80 100 100 0 80 90)

119870

119868119881diag(15 12 15 0 16 18)

Manipulator controller parameters Values119870

119901119877diag(5 10 12)

119870

119889119877diag(3 5 8)

119870

119894119877diag(01 02 02)

119870

119875119877diag(60 80 75)

119870

119863119877diag(35 40 50)

119870

119868119877diag(1 15 2)

coupling effects and the effectiveness of the proposed model-based control scheme which is expected to provide anintuitive promising prospective of the proposed approach

431 Underwater Vehicle Tracking a Given 3D Trajectorywith the Underwater Manipulator In this case as mentionedearlier the vehicle is commanded to follow a given 3D desiredtrajectory The desired 3D trajectory is given in Figure 5The controller gain values are tuned based on the geneticalgorithms (GA) for minimizing the integral squared error(ISE) as the costobjective function [23] Here we haveconsidered both the model reference control and the PIDcontrol performance to be almost equal in the ideal situationwhich makes the controller performance comparison quitereasonable and gives much better way of understandingBased on the GA tuning method the controller parametersare obtained and given in Table 4 The same set of controllerparameters are used throughout the entire performanceanalysis

Initially the performance analysis is carried out for thevehicle trajectory tracking without manipulator inclusionThe actual simulated trajectories based on MRC and PID arepresented in Figure 5These results show that both controllersare good enough to track the given trajectory and thetracking errors are within the design limits (error limits forthe vehicle during trajectory tracking are plusmn02m and plusmn02∘in positions and orientations resp) as well The trackingerrors are presented in Figures 6 7 8 9 10 and 11 In thesecond set of simulations the manipulator is included andthe inclusion effects during trajectory tracking of the vehicleare considered Here the manipulator links are folded andarranged in such a way that the influences on the vehicledynamics are small (ie manipulator joint angles are 120579

1=

180

∘ 1205792= 0

∘ and 1205793= 180

∘) The manipulator inclusionshows that there are significant performance changes in thevehicle trajectory tracking especially during the heave andsway motion tracking The heave roll and pitch motionsof the vehicle are greatly influenced by the underwatermanipulator inclusion which are replicated in the results

Modelling and Simulation in Engineering 9

0 50 100 150 200 250 300minus01

minus005

0

005

01

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Trac

king

erro

r inx

(xe) (

m)

Figure 6 Tracking errors in 119909 position for a given 3D trajectory

0 50 100 150 200 250 300minus002

minus001

0

001

002

003

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Trac

king

erro

r iny

(ye) (

m)

Figure 7 Tracking errors in 119910 position for a given 3D trajectory

(refer to Figures 6 to 11) However the manipulator inclusioneffects are better adapted in the model reference control thanin the PID control As can be observed from Figures 8 and10 the manipulator inclusion causes an initial pitch anglevariation drifts the vehicle in the heave direction during thestraight line motion (during acceleration stage) Howeverthese unwanted effects are compensated successfully in themodel reference control and therefore tracking errors do notexceed their design limits

432 Manipulator following a Given Desired 3D Trajectorywith the Freely Moving Underwater Vehicle (without VehicleControl) As mentioned earlier in this section this task ismainly to address the interaction effects and their influences

0 50 100 150 200 250 300minus005

0

005

01

015

02

03

Trac

king

erro

r inz

(ze) (

m)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 8 Tracking errors in 119911 position for a given 3D trajectory

0 50 100 150 200 250 300minus10

minus5

0

5

10

15

20

Trac

king

erro

r in

roll

(120601e) (

deg)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 9 Tracking errors in roll for a given 3D trajectory

on theUVMS For this task the vehicle controller is removedand only the underwater manipulator follows a given desiredcontinuous trajectory The desired values of joint positionsare as follows 120579

1119889= 90

∘ sin (01119905) 1205792119889

= 90

∘ and 1205793119889

=

minus45

∘ The simulation results of this condition are presentedin Figures 12 13 14 15 and 16 From the results it is observedthat the vehicle is started getting drifted from its initialposition and it is moving forward with an average velocityof 002ms (approximately) for the repeated underwatermanipulator movements It shows that the manipulator linksare affected due to the dynamic coupling effects Fromthe results it is observed that the vehicle swims duringmanipulator movements if the vehicle does not have anycontrol actionThese errors and forward speed are increasing

10 Modelling and Simulation in Engineering

0 50 100 150 200 250 300minus15

minus1

minus05

0

05

1

15

Trac

king

erro

r in

pitc

h (120579

e) (

deg)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 10 Tracking errors in pitch for a given 3D trajectory

0 50 100 150 200 250 300minus1

minus05

0

05

1

Trac

king

erro

r in

yaw

(120595e) (

deg)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 11 Tracking errors in yaw for a given 3D trajectory

with the manipulator oscillation frequency and their jointangle magnitudes In addition the direction of the vehiclersquosmovement varies depending on the manipulator positionsand its direction ofmovementsThese results can be extendedto the work towards swimming robots and their dynamicmodeling aspects

433 Underwater Manipulator following a Given DesiredCircular Trajectory with Vehicle Control The circular trajec-tory chosen for the analysis has 02m in diameter and anaverage speed of 00125ms These parameters are chosenwith the consideration of manipulator actuators workspaceand control The results from computer simulations arepresented in Figures 15ndash18 In Figure 15 both desired andactual task space trajectories are plotted and the task spacetracking errors are given in Figures 16ndash18 From the results

0 5 10 15 20minus006

minus004

minus002

0

002

004

006

008

01

012

Posit

ion

erro

rs (m

)

Time (t) (s)

xeyeze

Figure 12 Tracking errors in the vehicle positions (when manipu-lator has motion)

0 5 10 15 20minus3

minus2

minus1

0

1

2

3

4

Attit

ude e

rror

s (de

g)

Time (t) (s)

120601e120579e120595e

Figure 13 Tracking errors in the vehicle orientations (when thevehicle has no control and the manipulator has repeated motion)

it is observed that the manipulator tip tracks the givendesired task space trajectories quite satisfactorily in both PIDand MRC schemes in the ideal conditions (no disturbancesno uncertainties etc) Then in order to demonstrate theadaptability and robustness of the proposed controller anuncertain condition is considered for the simulations Thefollowing conditions are considered for the uncertain condi-tion analysis

(i) the UVMS parameters are assumed to be inaccurate(about 10 for each parameters)

(ii) the manipulator carries a payload of 1 kg at its tip

Modelling and Simulation in Engineering 11

0708

091

minus02minus01

001

02045

046

047

048

049

Desired tool tip positionActual tool tip position

z(m

)

y (m)x (m)

Figure 14 Manipulator tip position in 3D space (when the vehiclehas no control)

06507

07508

085

005

01

015

minus01

minus005

0

005

Desired trajectoryPIDMRC

PID with uncertaintyMRC with uncertainty

z(m

)

y (m)x (m)

Figure 15 Task space (119909119910119911) trajectories (results from the circulartrajectory)

(iii) an unknown ocean current is added in the simulationby properly considering the relative velocity of thein the dynamic model It is assumed to have anirrotational current constant in the inertial frameand the value of the current is considered as ^

119888=

[02 02 01 0 0 0]

119879ms

The results are presented in Figures 15ndash18 and from theseresults it is observed that the proposed controller is goodin adapting the uncertainties and disturbances (refer toFigure 15) Figures 16 and 17 show that tracking errors of119909 and 119910 in both PID and MRC methods are almost thesame and results satisfactorily however the tracking error in119911 substantiates that the proposed controller is comparativelygood in the presence of uncertainties and disturbances

434 Underwater Manipulator following a Given DesiredRectangular Trajectory with Vehicle Control The rectangulartrajectory chosen for the analysis has 04m in width and

0 5 10 15 20 25 30minus002

minus0015

minus001

minus0005

0

0005

001

0015

Time (t) (s)

PIDMRC

PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r inx

(xe) (

m)

Figure 16 Time histories of the manipulator tip position trackingerror in 119909 (circular trajectory)

0 5 10 15 20 25 30minus4

minus3

minus2

minus1

0

1

2

3

4

5

6

MRC

Time (t) (s)

PID PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r iny

(ye) (

m)

times10minus3

Figure 17 Time histories of the manipulator tip position trackingerror in 119910 (circular trajectory)

02m in height in the 119910119911 plane and an average speedof 005ms As mentioned in the last case the trajectoryhas been chosen with the consideration of the manipulatorcharacteristics Two conditions have been considered for theanalysis ideal condition (no disturbances no uncertaintiesetc) and an uncertain condition (the same as the previouscase Section 433) The results from computer simulationsare plotted in Figure 19 In the ideal condition both con-trollers show quite satisfactory performance and in theuncertain condition the proposed controller shows betterperformance

12 Modelling and Simulation in Engineering

MRC

0 5 10 15 20 25 30minus002

0

002

004

006

008

01

012

Time (t) (s)

PID PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r inz

(ze) (

m)

Figure 18 Time histories of the manipulator tip position trackingerror in 119911 (circular trajectory)

064 066 068 07 072

minus020

0202

025

03

035

04

Desired trajectoryPIDMRC

PID with uncertaintyMRC with uncertainty

z(m

)

y (m)x (m)

Figure 19 Task space (119909119910119911) trajectories (results from the rectangu-lar trajectory)

In both trajectory tracking cases the thruster forces donot exceed plusmn5N and the manipulator actuator torques staywithinplusmn015Nmwhich arewell within the range of actuators

5 Conclusions

In this study the interaction effects due to the dynamiccoupling between the vehicle and the manipulator wereinvestigated using closed-form equations which provide ageneralized scheme for formulating the equations of motionof the UVMS The proposed scheme makes it possible toidentify the structure nature and properties of the systemand it simplifies the control design This study also proposeda model reference control approach for an underactuated

UVMS to perform underwater intervention tasks incorpo-rating desired trajectory information Extensive simulationswere carried out to verify and demonstrate the effectivenessof the proposed scheme In particular the performance ofthe model reference controller is compared with that of theconventional PID controller for the given UVMS operationscenarios The obtained results confirm the effectiveness androbustness of the proposed scheme in terms of tracking errorsand control effort in the presence of external disturbancesand parameter uncertainties This research provides a gener-alized framework for modeling and controlling of an UVMSconsidering the dynamic coupling between the vehicle andthe manipulator which is crucial for achieving underwatermanipulation tasks for a variety of scientific industrial andmilitary missions using unmanned underwater vehicles

Conflict of Interests

Authors confirm that this paper has not been publishedelsewhere and is not under consideration by another journalAll authors have approved the manuscript and agree withsubmission toModelling and Simulation in EngineeringTheauthors have no conflict of interests to declare

Acknowledgments

The author would like to acknowledge Professor JinwhanKim for his valuable suggestions and discussions on under-water manipulator This research was supported in partby the World Class University (WCU) program throughthe National Research Foundation of Korea funded by theMinistry of Education Science and Technology (R31-2008-000-10045-0)

References

[1] G Antonelli F Caccavale S Chiaverini and L Villani ldquoTrack-ing control for underwater vehicle-manipulator systems withvelocity estimationrdquo IEEE Journal of Oceanic Engineering vol25 no 3 pp 399ndash413 2000

[2] G Marani S K Choi and J Yuh ldquoUnderwater autonomousmanipulation for intervention missions AUVsrdquo Ocean Engi-neering vol 36 no 1 pp 15ndash23 2009

[3] S McMillan D E Orin and R B McGhee ldquoEfficient dynamicsimulation of an underwater vehicle with a robotic manipula-torrdquo IEEE Transactions on Systems Man and Cybernetics vol25 no 8 pp 1194ndash1206 1995

[4] T I Fossen Guidance and Control of Ocean Vehicles WileyChichester UK 1994

[5] T J Tarn G A Shoults and S P Yang ldquoA dynamic model ofan underwater vehicle with a robotic manipulator using Kanersquosmethodrdquo Autonomous Robots vol 3 no 2-3 pp 269ndash283 1996

[6] H Mahesh J Yuh and R Lakshmi ldquoA Coordinated controlof an underwater vehicle and robotic manipulatorrdquo Journal ofRobotic Systems vol 8 no 3 pp 339ndash370 1991

[7] N Sarkar and T K Podder ldquoCoordinated motion planningand control of autonomous underwater vehicle-manipulatorsystems subject to drag optimizationrdquo IEEE Journal of OceanicEngineering vol 26 no 2 pp 228ndash239 2001

Modelling and Simulation in Engineering 13

[8] T W McLain S M Rock and M J Lee ldquoExperiments inthe coordinated control of an underwater armvehicle systemrdquoAutonomous Robots vol 3 no 2-3 pp 213ndash232 1996

[9] M W Dunnigan and G T Russell ldquoEvaluation and reductionof the dynamic coupling between a manipulator and an under-water vehiclerdquo IEEE Journal of Oceanic Engineering vol 23 no3 pp 260ndash273 1998

[10] B H Jun P M Lee and J Lee ldquoManipulability analysisof underwater robotic arms on ROV and application totask-oriented joint configurationrdquo in Proceedings of the IEEEOCEANS pp 1548ndash1553 November 2004

[11] J H Ryu D S Kwon and P M Lee ldquoControl of underwatermanipulators mounted on an ROV using base force informa-tionrdquo in Proceedings of the IEEE International Conference onRobotics and Automation (ICRA rsquo01) pp 3238ndash3243 May 2001

[12] M Hildebrandt L Christensen J Kerdels J Albiez and FKirchner ldquoRealtime motion compensation for ROV-based tele-operated underwater manipulatorsrdquo in Proceedings of the IEEEOCEANS pp 1ndash6 May 2009

[13] H Shim B H Jun P M Lee H Baek and J Lee ldquoWorkspacecontrol system of underwater tele-operated manipulators on anROVrdquo Ocean Engineering vol 37 no 11-12 pp 1036ndash1047 2010

[14] J J Craig Introduction to Robotics Addison Wesley BostonMass USA 1986

[15] G Antonelli Underwater Robots Motion and Force Control ofVehicle-Manipulator Systems Springer Berlin Germany 2006

[16] K Kim andT Ura ldquoAppliedmodel-based analysis and synthesisfor the dynamics guidance and control of an autonomousundersea vehiclerdquo Mathematical Problems in Engineering vol2010 Article ID 149385 23 pages 2010

[17] T I Fossen Marine Control Systems Guidance Navigationand Control of Ships Rigs and Underwater Vehicles MarineCybernetics AS 2002

[18] J J E Slotine and W Li Applied Nonlinear Control Prentice-Hall Upper Saddle River NJ USA 1991

[19] K Y Pettersen and O Egeland ldquoPosition and attitude control ofan underactuated autonomous underwater vehiclerdquo in Proceed-ings of the 1996 35th IEEE Conference on Decision and Controlpp 987ndash991 Kobe Japan December 1996

[20] T H Koh MW S Lau G Seet and E Low ldquoA control modulescheme for an underactuated underwater robotic vehiclerdquo Jour-nal of Intelligent and Robotic Systems Theory and Applicationsvol 46 no 1 pp 43ndash58 2006

[21] M Santhakumar and T Asokan ldquoInvestigations on the hybridtracking control of an underactuated autonomous underwaterrobotrdquo Advanced Robotics vol 24 no 11 pp 1529ndash1556 2010

[22] ANSALDO Nucleare Underwater Manipulator MARIS 7080Use and Maintenance Manual Ansaldo Nuclear DivisionGenoa Italy 1996

[23] K Deb Optimization for Engineering Design Algorithms andExamples Prentice Hall New Delhi India 2004

International Journal of

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RotatingMachinery

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Civil EngineeringAdvances in

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Electrical and Computer Engineering

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Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

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International Journal of

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Navigation and Observation

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DistributedSensor Networks

International Journal of

Modelling and Simulation in Engineering 7

be stable is that the centre of gravity (CG) should lie belowthe centre of buoyancy (CB) For this the vehicle is trimmed(using a float) to have the CB almost vertically above the CGand made to be nearly neutral buoyant Here the roll motionhas nonzero components of restoringmoments that representself-restoring torque for the roll direction With nonzerorestoring terms it may be possible to find continuous statefeedback laws to stabilize the system as a whole In additionto this without loss of generality we can assume that thedamping terms of nonactuated states are sufficiently largerthan their inertia terms which means that the hydrodynamicrestoring forces and torques are large enough to stabilize thenonactuated (roll) states (zero dynamics) which is a commonproperty forAUVs [19]Thismeans that the underwater robotcan be exponentially stabilized by the actuated state controlsalone

The manipulator links are cylindrical in shape and theradii of links 1 2 and 3 are 01m 005m and 005mrespectively The lengths of links 1 2 and 3 are 01m 02mand 02m respectively The link masses (along with oil con-served motors) are 039 kg 157 kg and 157 kg respectivelyHere the links are considered as cylindrical shape becausesuch shape provides uniform hydrodynamic reactions andis one of the primary candidates for possible link geometryfor underwater manipulators Although it is cylindrical ourmathematical framework does not depend on any particularshapes it can be easily accommodated by any other shapesIndeed cylindrical underwater manipulators are available inthe present market [22] Hydrodynamic parameters of theUVMS are estimated using empirical relations based on striptheory This method is verified using the available literaturetherefore these values are reliable and can be used for furtherdevelopments Some parameters like inertia centre of gravityand centre of buoyancy are calculated from the geometricaldesign of the UVMSThe total parameter list of the UVMS isgiven in Tables 2 and 3

We have compared our results with those of traditionalPID controller the following control vectors were consideredfor the vehicle and the manipulator and are given by

120591119881= K

119863119881

+ K119875119881 + K

119868119881int 119889119905

120591119877= K

119863119877q + K

119875119877q + K

119868119877int q 119889119905

(26)

where K119875119881 K

119868119881 K

119863119881 K

119875119877 K

119868119877 and K

119863119877are the propor-

tional integral and derivative gainmatrices of the vehicle andthe manipulator respectively

42 Description of the Tasks Three different tasks with fourdifferent cases have been considered for the simulations Thefirst task is that the vehicle is commanded to track a given3D trajectory without and with the manipulator (at rest or itshome position) and in this condition the vehicle acceleratesfor the initial 20 s and attains the vehicle forward speed of1ms (asymp2 knots) and for the final 20 s the vehicle deceleratesto zero speed The particular desired 3D trajectory (referto Figure 5) has been chosen for this performance analysisbecause this trajectory consists of all four main motions such

Table 2 The parameter list of the UVMS

Parameters ValuesMass of the vehicle (119898V) 39 kgLength of the vehicle (119871V) 11mDiameter of the vehicle (119889V) 025mMoment of inertia of the vehicle119868

119909034 kgm2

119868

119910371 kgm2

119868

119911371 kgm2

Centre of gravity (CG) = (119909119866 119910

119866 119911

119866) (0 0 0) m

Centre of buoyancy (CB) = (119909119861 119910

119861 119911

119861) (0 0 0015) m

Mass of the underwater manipulator links119898

103927 kg

119898

215708 kg

119898

315708 kg

Underwater manipulator link lengths119871

1005m

119871

2020m

119871

3020m

Underwater manipulator link radii119903

1010m

119903

2005m

119903

3005m

Coefficient of drag (119862119863) 125

Coefficient of lift (119862119871) 115

Table 3 The values of hydrodynamic coefficients calculated usingempirical relations based on strip theory

Vehicle added mass derivatives119883

minus117 kg 119870

minus01 kgmrad

119884V minus3484 kg 119872

minus103 kgm

119884

119903104 kgm 119872

119902minus266 kgmrad

119885

minus3483 kg 119873V minus104 kgm

119885

119902minus104 kgm 119873

119903minus265 kgmrad

Vehicle hydrodynamic parameters119883

119906|119906|minus7365 kgm 119883

119906minus212 kgs

119883V|V| minus0737 kgm 119883V minus031 kgs119883

119908|119908|minus0737 kgm 119883

119908minus031 kgs

119883

119902|119902|minus1065 kgmrad 119883

119902minus051 kgms

119883

119903|119903|minus1065 kgmrad 119883

119903minus051 kgms

119884V|V| minus1122 kgm 119884V minus6245 kgs119884

119903|119903|0250 kgmrad 119884

119903012 kgms

119885

119908|119908|minus1122 kgm 119885

119908minus6245 kgs

119885

119902|119902|minus0250 kgmrad 119885

119902012 kgms

119870

119901|119901|minus05975 kgm2rad2 119870

119901minus03125 kgm2s

119872

119908|119908|2244 kgmrad 119872

11990812 kgms

119872

119902|119902|minus1195 kgm2rad2 119872

119902minus5975 kgm2s

119873V|V| minus2244 kgmrad 119873V 12 kgms

as sway in and out and heave up and downThe average valueof sway velocity is 025ms (asymp05 knots) (same value for heaveas well) This task is performed to identify the influences of

8 Modelling and Simulation in Engineering

050

100150

200

05

1015

200

5

10

15

20

Desired 3D pathPID without armMRC without arm

PID with armMRC with arm

z(m

)

y (m)x (m)

Figure 5 Comparative trajectory tracking control results

the underwater manipulator effects during vehicle trackingcontrol In the second task the vehicle is free to move (nocontrol action involved) and the manipulator has a certainrepeated desired trajectory This task is mainly performedto identify the vehicle behavior during manipulator motionIn all the above tasks the initial velocities and positions ofthe vehicle and the manipulator are chosen to be zero andthe initial desired and actual positions and orientations arethe same In the third task two basic trajectories for themanipulator have been chosen for simulations a circulartrajectory (in 3D space) and a rectangular trajectory (in 119910119911plane) along with a straight line in 3D space This is forthe reason that most of the underwater intervention tasksinvolve these types of trajectories and also we can arrangeany spatial trajectory by combining these trajectories For therectangular trajectory we have selected a cubic polynomialfunction as the trajectory function which imposes that thetrajectory is continuous and smooth

In the performance analysis the sensory noises inposition and orientation measurements are introduced andwe have considered Gaussian noise of 001m mean and001m standard deviation for the positionmeasurements and02

∘ mean and 02∘ standard deviation for the orientationmeasurements The thruster dynamic characteristics are alsoincorporated in the simulations All the vehicle thrusters areconsidered as an identical one and the following thrustercharacteristics are considered for the analysis the thrusterresponse delay time is 200ms efficiency is 95and saturationlimits are plusmn20N The vehicle surge thrusters are located at05m from the body centre along the 119909-axis and offset eachside 03m from 119910-axis The lateral thruster is exactly locatedon the body centre and vertical thrusters are placed on the 119909-axis 04m apart from the centre at each side The controllerupdate rate and sensor response time are considered as 100mseach

43 Results and Discussions Here numerical simulationresults are shown and discussed to investigate the dynamic

Table 4 Controller parameter settings for simulations

Vehicle controller parameters Values119870

119901119881diag(42 22 25 0 25 27)

119870

119889119881diag(225 12 13 0 15 13)

119870

119894119881diag(05 02 03 0 25 22)

119870

119875119881diag(180 130 150 0 150 130)

119870

119863119881diag(80 100 100 0 80 90)

119870

119868119881diag(15 12 15 0 16 18)

Manipulator controller parameters Values119870

119901119877diag(5 10 12)

119870

119889119877diag(3 5 8)

119870

119894119877diag(01 02 02)

119870

119875119877diag(60 80 75)

119870

119863119877diag(35 40 50)

119870

119868119877diag(1 15 2)

coupling effects and the effectiveness of the proposed model-based control scheme which is expected to provide anintuitive promising prospective of the proposed approach

431 Underwater Vehicle Tracking a Given 3D Trajectorywith the Underwater Manipulator In this case as mentionedearlier the vehicle is commanded to follow a given 3D desiredtrajectory The desired 3D trajectory is given in Figure 5The controller gain values are tuned based on the geneticalgorithms (GA) for minimizing the integral squared error(ISE) as the costobjective function [23] Here we haveconsidered both the model reference control and the PIDcontrol performance to be almost equal in the ideal situationwhich makes the controller performance comparison quitereasonable and gives much better way of understandingBased on the GA tuning method the controller parametersare obtained and given in Table 4 The same set of controllerparameters are used throughout the entire performanceanalysis

Initially the performance analysis is carried out for thevehicle trajectory tracking without manipulator inclusionThe actual simulated trajectories based on MRC and PID arepresented in Figure 5These results show that both controllersare good enough to track the given trajectory and thetracking errors are within the design limits (error limits forthe vehicle during trajectory tracking are plusmn02m and plusmn02∘in positions and orientations resp) as well The trackingerrors are presented in Figures 6 7 8 9 10 and 11 In thesecond set of simulations the manipulator is included andthe inclusion effects during trajectory tracking of the vehicleare considered Here the manipulator links are folded andarranged in such a way that the influences on the vehicledynamics are small (ie manipulator joint angles are 120579

1=

180

∘ 1205792= 0

∘ and 1205793= 180

∘) The manipulator inclusionshows that there are significant performance changes in thevehicle trajectory tracking especially during the heave andsway motion tracking The heave roll and pitch motionsof the vehicle are greatly influenced by the underwatermanipulator inclusion which are replicated in the results

Modelling and Simulation in Engineering 9

0 50 100 150 200 250 300minus01

minus005

0

005

01

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Trac

king

erro

r inx

(xe) (

m)

Figure 6 Tracking errors in 119909 position for a given 3D trajectory

0 50 100 150 200 250 300minus002

minus001

0

001

002

003

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Trac

king

erro

r iny

(ye) (

m)

Figure 7 Tracking errors in 119910 position for a given 3D trajectory

(refer to Figures 6 to 11) However the manipulator inclusioneffects are better adapted in the model reference control thanin the PID control As can be observed from Figures 8 and10 the manipulator inclusion causes an initial pitch anglevariation drifts the vehicle in the heave direction during thestraight line motion (during acceleration stage) Howeverthese unwanted effects are compensated successfully in themodel reference control and therefore tracking errors do notexceed their design limits

432 Manipulator following a Given Desired 3D Trajectorywith the Freely Moving Underwater Vehicle (without VehicleControl) As mentioned earlier in this section this task ismainly to address the interaction effects and their influences

0 50 100 150 200 250 300minus005

0

005

01

015

02

03

Trac

king

erro

r inz

(ze) (

m)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 8 Tracking errors in 119911 position for a given 3D trajectory

0 50 100 150 200 250 300minus10

minus5

0

5

10

15

20

Trac

king

erro

r in

roll

(120601e) (

deg)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 9 Tracking errors in roll for a given 3D trajectory

on theUVMS For this task the vehicle controller is removedand only the underwater manipulator follows a given desiredcontinuous trajectory The desired values of joint positionsare as follows 120579

1119889= 90

∘ sin (01119905) 1205792119889

= 90

∘ and 1205793119889

=

minus45

∘ The simulation results of this condition are presentedin Figures 12 13 14 15 and 16 From the results it is observedthat the vehicle is started getting drifted from its initialposition and it is moving forward with an average velocityof 002ms (approximately) for the repeated underwatermanipulator movements It shows that the manipulator linksare affected due to the dynamic coupling effects Fromthe results it is observed that the vehicle swims duringmanipulator movements if the vehicle does not have anycontrol actionThese errors and forward speed are increasing

10 Modelling and Simulation in Engineering

0 50 100 150 200 250 300minus15

minus1

minus05

0

05

1

15

Trac

king

erro

r in

pitc

h (120579

e) (

deg)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 10 Tracking errors in pitch for a given 3D trajectory

0 50 100 150 200 250 300minus1

minus05

0

05

1

Trac

king

erro

r in

yaw

(120595e) (

deg)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 11 Tracking errors in yaw for a given 3D trajectory

with the manipulator oscillation frequency and their jointangle magnitudes In addition the direction of the vehiclersquosmovement varies depending on the manipulator positionsand its direction ofmovementsThese results can be extendedto the work towards swimming robots and their dynamicmodeling aspects

433 Underwater Manipulator following a Given DesiredCircular Trajectory with Vehicle Control The circular trajec-tory chosen for the analysis has 02m in diameter and anaverage speed of 00125ms These parameters are chosenwith the consideration of manipulator actuators workspaceand control The results from computer simulations arepresented in Figures 15ndash18 In Figure 15 both desired andactual task space trajectories are plotted and the task spacetracking errors are given in Figures 16ndash18 From the results

0 5 10 15 20minus006

minus004

minus002

0

002

004

006

008

01

012

Posit

ion

erro

rs (m

)

Time (t) (s)

xeyeze

Figure 12 Tracking errors in the vehicle positions (when manipu-lator has motion)

0 5 10 15 20minus3

minus2

minus1

0

1

2

3

4

Attit

ude e

rror

s (de

g)

Time (t) (s)

120601e120579e120595e

Figure 13 Tracking errors in the vehicle orientations (when thevehicle has no control and the manipulator has repeated motion)

it is observed that the manipulator tip tracks the givendesired task space trajectories quite satisfactorily in both PIDand MRC schemes in the ideal conditions (no disturbancesno uncertainties etc) Then in order to demonstrate theadaptability and robustness of the proposed controller anuncertain condition is considered for the simulations Thefollowing conditions are considered for the uncertain condi-tion analysis

(i) the UVMS parameters are assumed to be inaccurate(about 10 for each parameters)

(ii) the manipulator carries a payload of 1 kg at its tip

Modelling and Simulation in Engineering 11

0708

091

minus02minus01

001

02045

046

047

048

049

Desired tool tip positionActual tool tip position

z(m

)

y (m)x (m)

Figure 14 Manipulator tip position in 3D space (when the vehiclehas no control)

06507

07508

085

005

01

015

minus01

minus005

0

005

Desired trajectoryPIDMRC

PID with uncertaintyMRC with uncertainty

z(m

)

y (m)x (m)

Figure 15 Task space (119909119910119911) trajectories (results from the circulartrajectory)

(iii) an unknown ocean current is added in the simulationby properly considering the relative velocity of thein the dynamic model It is assumed to have anirrotational current constant in the inertial frameand the value of the current is considered as ^

119888=

[02 02 01 0 0 0]

119879ms

The results are presented in Figures 15ndash18 and from theseresults it is observed that the proposed controller is goodin adapting the uncertainties and disturbances (refer toFigure 15) Figures 16 and 17 show that tracking errors of119909 and 119910 in both PID and MRC methods are almost thesame and results satisfactorily however the tracking error in119911 substantiates that the proposed controller is comparativelygood in the presence of uncertainties and disturbances

434 Underwater Manipulator following a Given DesiredRectangular Trajectory with Vehicle Control The rectangulartrajectory chosen for the analysis has 04m in width and

0 5 10 15 20 25 30minus002

minus0015

minus001

minus0005

0

0005

001

0015

Time (t) (s)

PIDMRC

PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r inx

(xe) (

m)

Figure 16 Time histories of the manipulator tip position trackingerror in 119909 (circular trajectory)

0 5 10 15 20 25 30minus4

minus3

minus2

minus1

0

1

2

3

4

5

6

MRC

Time (t) (s)

PID PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r iny

(ye) (

m)

times10minus3

Figure 17 Time histories of the manipulator tip position trackingerror in 119910 (circular trajectory)

02m in height in the 119910119911 plane and an average speedof 005ms As mentioned in the last case the trajectoryhas been chosen with the consideration of the manipulatorcharacteristics Two conditions have been considered for theanalysis ideal condition (no disturbances no uncertaintiesetc) and an uncertain condition (the same as the previouscase Section 433) The results from computer simulationsare plotted in Figure 19 In the ideal condition both con-trollers show quite satisfactory performance and in theuncertain condition the proposed controller shows betterperformance

12 Modelling and Simulation in Engineering

MRC

0 5 10 15 20 25 30minus002

0

002

004

006

008

01

012

Time (t) (s)

PID PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r inz

(ze) (

m)

Figure 18 Time histories of the manipulator tip position trackingerror in 119911 (circular trajectory)

064 066 068 07 072

minus020

0202

025

03

035

04

Desired trajectoryPIDMRC

PID with uncertaintyMRC with uncertainty

z(m

)

y (m)x (m)

Figure 19 Task space (119909119910119911) trajectories (results from the rectangu-lar trajectory)

In both trajectory tracking cases the thruster forces donot exceed plusmn5N and the manipulator actuator torques staywithinplusmn015Nmwhich arewell within the range of actuators

5 Conclusions

In this study the interaction effects due to the dynamiccoupling between the vehicle and the manipulator wereinvestigated using closed-form equations which provide ageneralized scheme for formulating the equations of motionof the UVMS The proposed scheme makes it possible toidentify the structure nature and properties of the systemand it simplifies the control design This study also proposeda model reference control approach for an underactuated

UVMS to perform underwater intervention tasks incorpo-rating desired trajectory information Extensive simulationswere carried out to verify and demonstrate the effectivenessof the proposed scheme In particular the performance ofthe model reference controller is compared with that of theconventional PID controller for the given UVMS operationscenarios The obtained results confirm the effectiveness androbustness of the proposed scheme in terms of tracking errorsand control effort in the presence of external disturbancesand parameter uncertainties This research provides a gener-alized framework for modeling and controlling of an UVMSconsidering the dynamic coupling between the vehicle andthe manipulator which is crucial for achieving underwatermanipulation tasks for a variety of scientific industrial andmilitary missions using unmanned underwater vehicles

Conflict of Interests

Authors confirm that this paper has not been publishedelsewhere and is not under consideration by another journalAll authors have approved the manuscript and agree withsubmission toModelling and Simulation in EngineeringTheauthors have no conflict of interests to declare

Acknowledgments

The author would like to acknowledge Professor JinwhanKim for his valuable suggestions and discussions on under-water manipulator This research was supported in partby the World Class University (WCU) program throughthe National Research Foundation of Korea funded by theMinistry of Education Science and Technology (R31-2008-000-10045-0)

References

[1] G Antonelli F Caccavale S Chiaverini and L Villani ldquoTrack-ing control for underwater vehicle-manipulator systems withvelocity estimationrdquo IEEE Journal of Oceanic Engineering vol25 no 3 pp 399ndash413 2000

[2] G Marani S K Choi and J Yuh ldquoUnderwater autonomousmanipulation for intervention missions AUVsrdquo Ocean Engi-neering vol 36 no 1 pp 15ndash23 2009

[3] S McMillan D E Orin and R B McGhee ldquoEfficient dynamicsimulation of an underwater vehicle with a robotic manipula-torrdquo IEEE Transactions on Systems Man and Cybernetics vol25 no 8 pp 1194ndash1206 1995

[4] T I Fossen Guidance and Control of Ocean Vehicles WileyChichester UK 1994

[5] T J Tarn G A Shoults and S P Yang ldquoA dynamic model ofan underwater vehicle with a robotic manipulator using Kanersquosmethodrdquo Autonomous Robots vol 3 no 2-3 pp 269ndash283 1996

[6] H Mahesh J Yuh and R Lakshmi ldquoA Coordinated controlof an underwater vehicle and robotic manipulatorrdquo Journal ofRobotic Systems vol 8 no 3 pp 339ndash370 1991

[7] N Sarkar and T K Podder ldquoCoordinated motion planningand control of autonomous underwater vehicle-manipulatorsystems subject to drag optimizationrdquo IEEE Journal of OceanicEngineering vol 26 no 2 pp 228ndash239 2001

Modelling and Simulation in Engineering 13

[8] T W McLain S M Rock and M J Lee ldquoExperiments inthe coordinated control of an underwater armvehicle systemrdquoAutonomous Robots vol 3 no 2-3 pp 213ndash232 1996

[9] M W Dunnigan and G T Russell ldquoEvaluation and reductionof the dynamic coupling between a manipulator and an under-water vehiclerdquo IEEE Journal of Oceanic Engineering vol 23 no3 pp 260ndash273 1998

[10] B H Jun P M Lee and J Lee ldquoManipulability analysisof underwater robotic arms on ROV and application totask-oriented joint configurationrdquo in Proceedings of the IEEEOCEANS pp 1548ndash1553 November 2004

[11] J H Ryu D S Kwon and P M Lee ldquoControl of underwatermanipulators mounted on an ROV using base force informa-tionrdquo in Proceedings of the IEEE International Conference onRobotics and Automation (ICRA rsquo01) pp 3238ndash3243 May 2001

[12] M Hildebrandt L Christensen J Kerdels J Albiez and FKirchner ldquoRealtime motion compensation for ROV-based tele-operated underwater manipulatorsrdquo in Proceedings of the IEEEOCEANS pp 1ndash6 May 2009

[13] H Shim B H Jun P M Lee H Baek and J Lee ldquoWorkspacecontrol system of underwater tele-operated manipulators on anROVrdquo Ocean Engineering vol 37 no 11-12 pp 1036ndash1047 2010

[14] J J Craig Introduction to Robotics Addison Wesley BostonMass USA 1986

[15] G Antonelli Underwater Robots Motion and Force Control ofVehicle-Manipulator Systems Springer Berlin Germany 2006

[16] K Kim andT Ura ldquoAppliedmodel-based analysis and synthesisfor the dynamics guidance and control of an autonomousundersea vehiclerdquo Mathematical Problems in Engineering vol2010 Article ID 149385 23 pages 2010

[17] T I Fossen Marine Control Systems Guidance Navigationand Control of Ships Rigs and Underwater Vehicles MarineCybernetics AS 2002

[18] J J E Slotine and W Li Applied Nonlinear Control Prentice-Hall Upper Saddle River NJ USA 1991

[19] K Y Pettersen and O Egeland ldquoPosition and attitude control ofan underactuated autonomous underwater vehiclerdquo in Proceed-ings of the 1996 35th IEEE Conference on Decision and Controlpp 987ndash991 Kobe Japan December 1996

[20] T H Koh MW S Lau G Seet and E Low ldquoA control modulescheme for an underactuated underwater robotic vehiclerdquo Jour-nal of Intelligent and Robotic Systems Theory and Applicationsvol 46 no 1 pp 43ndash58 2006

[21] M Santhakumar and T Asokan ldquoInvestigations on the hybridtracking control of an underactuated autonomous underwaterrobotrdquo Advanced Robotics vol 24 no 11 pp 1529ndash1556 2010

[22] ANSALDO Nucleare Underwater Manipulator MARIS 7080Use and Maintenance Manual Ansaldo Nuclear DivisionGenoa Italy 1996

[23] K Deb Optimization for Engineering Design Algorithms andExamples Prentice Hall New Delhi India 2004

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 Modelling and Simulation in Engineering

050

100150

200

05

1015

200

5

10

15

20

Desired 3D pathPID without armMRC without arm

PID with armMRC with arm

z(m

)

y (m)x (m)

Figure 5 Comparative trajectory tracking control results

the underwater manipulator effects during vehicle trackingcontrol In the second task the vehicle is free to move (nocontrol action involved) and the manipulator has a certainrepeated desired trajectory This task is mainly performedto identify the vehicle behavior during manipulator motionIn all the above tasks the initial velocities and positions ofthe vehicle and the manipulator are chosen to be zero andthe initial desired and actual positions and orientations arethe same In the third task two basic trajectories for themanipulator have been chosen for simulations a circulartrajectory (in 3D space) and a rectangular trajectory (in 119910119911plane) along with a straight line in 3D space This is forthe reason that most of the underwater intervention tasksinvolve these types of trajectories and also we can arrangeany spatial trajectory by combining these trajectories For therectangular trajectory we have selected a cubic polynomialfunction as the trajectory function which imposes that thetrajectory is continuous and smooth

In the performance analysis the sensory noises inposition and orientation measurements are introduced andwe have considered Gaussian noise of 001m mean and001m standard deviation for the positionmeasurements and02

∘ mean and 02∘ standard deviation for the orientationmeasurements The thruster dynamic characteristics are alsoincorporated in the simulations All the vehicle thrusters areconsidered as an identical one and the following thrustercharacteristics are considered for the analysis the thrusterresponse delay time is 200ms efficiency is 95and saturationlimits are plusmn20N The vehicle surge thrusters are located at05m from the body centre along the 119909-axis and offset eachside 03m from 119910-axis The lateral thruster is exactly locatedon the body centre and vertical thrusters are placed on the 119909-axis 04m apart from the centre at each side The controllerupdate rate and sensor response time are considered as 100mseach

43 Results and Discussions Here numerical simulationresults are shown and discussed to investigate the dynamic

Table 4 Controller parameter settings for simulations

Vehicle controller parameters Values119870

119901119881diag(42 22 25 0 25 27)

119870

119889119881diag(225 12 13 0 15 13)

119870

119894119881diag(05 02 03 0 25 22)

119870

119875119881diag(180 130 150 0 150 130)

119870

119863119881diag(80 100 100 0 80 90)

119870

119868119881diag(15 12 15 0 16 18)

Manipulator controller parameters Values119870

119901119877diag(5 10 12)

119870

119889119877diag(3 5 8)

119870

119894119877diag(01 02 02)

119870

119875119877diag(60 80 75)

119870

119863119877diag(35 40 50)

119870

119868119877diag(1 15 2)

coupling effects and the effectiveness of the proposed model-based control scheme which is expected to provide anintuitive promising prospective of the proposed approach

431 Underwater Vehicle Tracking a Given 3D Trajectorywith the Underwater Manipulator In this case as mentionedearlier the vehicle is commanded to follow a given 3D desiredtrajectory The desired 3D trajectory is given in Figure 5The controller gain values are tuned based on the geneticalgorithms (GA) for minimizing the integral squared error(ISE) as the costobjective function [23] Here we haveconsidered both the model reference control and the PIDcontrol performance to be almost equal in the ideal situationwhich makes the controller performance comparison quitereasonable and gives much better way of understandingBased on the GA tuning method the controller parametersare obtained and given in Table 4 The same set of controllerparameters are used throughout the entire performanceanalysis

Initially the performance analysis is carried out for thevehicle trajectory tracking without manipulator inclusionThe actual simulated trajectories based on MRC and PID arepresented in Figure 5These results show that both controllersare good enough to track the given trajectory and thetracking errors are within the design limits (error limits forthe vehicle during trajectory tracking are plusmn02m and plusmn02∘in positions and orientations resp) as well The trackingerrors are presented in Figures 6 7 8 9 10 and 11 In thesecond set of simulations the manipulator is included andthe inclusion effects during trajectory tracking of the vehicleare considered Here the manipulator links are folded andarranged in such a way that the influences on the vehicledynamics are small (ie manipulator joint angles are 120579

1=

180

∘ 1205792= 0

∘ and 1205793= 180

∘) The manipulator inclusionshows that there are significant performance changes in thevehicle trajectory tracking especially during the heave andsway motion tracking The heave roll and pitch motionsof the vehicle are greatly influenced by the underwatermanipulator inclusion which are replicated in the results

Modelling and Simulation in Engineering 9

0 50 100 150 200 250 300minus01

minus005

0

005

01

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Trac

king

erro

r inx

(xe) (

m)

Figure 6 Tracking errors in 119909 position for a given 3D trajectory

0 50 100 150 200 250 300minus002

minus001

0

001

002

003

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Trac

king

erro

r iny

(ye) (

m)

Figure 7 Tracking errors in 119910 position for a given 3D trajectory

(refer to Figures 6 to 11) However the manipulator inclusioneffects are better adapted in the model reference control thanin the PID control As can be observed from Figures 8 and10 the manipulator inclusion causes an initial pitch anglevariation drifts the vehicle in the heave direction during thestraight line motion (during acceleration stage) Howeverthese unwanted effects are compensated successfully in themodel reference control and therefore tracking errors do notexceed their design limits

432 Manipulator following a Given Desired 3D Trajectorywith the Freely Moving Underwater Vehicle (without VehicleControl) As mentioned earlier in this section this task ismainly to address the interaction effects and their influences

0 50 100 150 200 250 300minus005

0

005

01

015

02

03

Trac

king

erro

r inz

(ze) (

m)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 8 Tracking errors in 119911 position for a given 3D trajectory

0 50 100 150 200 250 300minus10

minus5

0

5

10

15

20

Trac

king

erro

r in

roll

(120601e) (

deg)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 9 Tracking errors in roll for a given 3D trajectory

on theUVMS For this task the vehicle controller is removedand only the underwater manipulator follows a given desiredcontinuous trajectory The desired values of joint positionsare as follows 120579

1119889= 90

∘ sin (01119905) 1205792119889

= 90

∘ and 1205793119889

=

minus45

∘ The simulation results of this condition are presentedin Figures 12 13 14 15 and 16 From the results it is observedthat the vehicle is started getting drifted from its initialposition and it is moving forward with an average velocityof 002ms (approximately) for the repeated underwatermanipulator movements It shows that the manipulator linksare affected due to the dynamic coupling effects Fromthe results it is observed that the vehicle swims duringmanipulator movements if the vehicle does not have anycontrol actionThese errors and forward speed are increasing

10 Modelling and Simulation in Engineering

0 50 100 150 200 250 300minus15

minus1

minus05

0

05

1

15

Trac

king

erro

r in

pitc

h (120579

e) (

deg)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 10 Tracking errors in pitch for a given 3D trajectory

0 50 100 150 200 250 300minus1

minus05

0

05

1

Trac

king

erro

r in

yaw

(120595e) (

deg)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 11 Tracking errors in yaw for a given 3D trajectory

with the manipulator oscillation frequency and their jointangle magnitudes In addition the direction of the vehiclersquosmovement varies depending on the manipulator positionsand its direction ofmovementsThese results can be extendedto the work towards swimming robots and their dynamicmodeling aspects

433 Underwater Manipulator following a Given DesiredCircular Trajectory with Vehicle Control The circular trajec-tory chosen for the analysis has 02m in diameter and anaverage speed of 00125ms These parameters are chosenwith the consideration of manipulator actuators workspaceand control The results from computer simulations arepresented in Figures 15ndash18 In Figure 15 both desired andactual task space trajectories are plotted and the task spacetracking errors are given in Figures 16ndash18 From the results

0 5 10 15 20minus006

minus004

minus002

0

002

004

006

008

01

012

Posit

ion

erro

rs (m

)

Time (t) (s)

xeyeze

Figure 12 Tracking errors in the vehicle positions (when manipu-lator has motion)

0 5 10 15 20minus3

minus2

minus1

0

1

2

3

4

Attit

ude e

rror

s (de

g)

Time (t) (s)

120601e120579e120595e

Figure 13 Tracking errors in the vehicle orientations (when thevehicle has no control and the manipulator has repeated motion)

it is observed that the manipulator tip tracks the givendesired task space trajectories quite satisfactorily in both PIDand MRC schemes in the ideal conditions (no disturbancesno uncertainties etc) Then in order to demonstrate theadaptability and robustness of the proposed controller anuncertain condition is considered for the simulations Thefollowing conditions are considered for the uncertain condi-tion analysis

(i) the UVMS parameters are assumed to be inaccurate(about 10 for each parameters)

(ii) the manipulator carries a payload of 1 kg at its tip

Modelling and Simulation in Engineering 11

0708

091

minus02minus01

001

02045

046

047

048

049

Desired tool tip positionActual tool tip position

z(m

)

y (m)x (m)

Figure 14 Manipulator tip position in 3D space (when the vehiclehas no control)

06507

07508

085

005

01

015

minus01

minus005

0

005

Desired trajectoryPIDMRC

PID with uncertaintyMRC with uncertainty

z(m

)

y (m)x (m)

Figure 15 Task space (119909119910119911) trajectories (results from the circulartrajectory)

(iii) an unknown ocean current is added in the simulationby properly considering the relative velocity of thein the dynamic model It is assumed to have anirrotational current constant in the inertial frameand the value of the current is considered as ^

119888=

[02 02 01 0 0 0]

119879ms

The results are presented in Figures 15ndash18 and from theseresults it is observed that the proposed controller is goodin adapting the uncertainties and disturbances (refer toFigure 15) Figures 16 and 17 show that tracking errors of119909 and 119910 in both PID and MRC methods are almost thesame and results satisfactorily however the tracking error in119911 substantiates that the proposed controller is comparativelygood in the presence of uncertainties and disturbances

434 Underwater Manipulator following a Given DesiredRectangular Trajectory with Vehicle Control The rectangulartrajectory chosen for the analysis has 04m in width and

0 5 10 15 20 25 30minus002

minus0015

minus001

minus0005

0

0005

001

0015

Time (t) (s)

PIDMRC

PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r inx

(xe) (

m)

Figure 16 Time histories of the manipulator tip position trackingerror in 119909 (circular trajectory)

0 5 10 15 20 25 30minus4

minus3

minus2

minus1

0

1

2

3

4

5

6

MRC

Time (t) (s)

PID PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r iny

(ye) (

m)

times10minus3

Figure 17 Time histories of the manipulator tip position trackingerror in 119910 (circular trajectory)

02m in height in the 119910119911 plane and an average speedof 005ms As mentioned in the last case the trajectoryhas been chosen with the consideration of the manipulatorcharacteristics Two conditions have been considered for theanalysis ideal condition (no disturbances no uncertaintiesetc) and an uncertain condition (the same as the previouscase Section 433) The results from computer simulationsare plotted in Figure 19 In the ideal condition both con-trollers show quite satisfactory performance and in theuncertain condition the proposed controller shows betterperformance

12 Modelling and Simulation in Engineering

MRC

0 5 10 15 20 25 30minus002

0

002

004

006

008

01

012

Time (t) (s)

PID PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r inz

(ze) (

m)

Figure 18 Time histories of the manipulator tip position trackingerror in 119911 (circular trajectory)

064 066 068 07 072

minus020

0202

025

03

035

04

Desired trajectoryPIDMRC

PID with uncertaintyMRC with uncertainty

z(m

)

y (m)x (m)

Figure 19 Task space (119909119910119911) trajectories (results from the rectangu-lar trajectory)

In both trajectory tracking cases the thruster forces donot exceed plusmn5N and the manipulator actuator torques staywithinplusmn015Nmwhich arewell within the range of actuators

5 Conclusions

In this study the interaction effects due to the dynamiccoupling between the vehicle and the manipulator wereinvestigated using closed-form equations which provide ageneralized scheme for formulating the equations of motionof the UVMS The proposed scheme makes it possible toidentify the structure nature and properties of the systemand it simplifies the control design This study also proposeda model reference control approach for an underactuated

UVMS to perform underwater intervention tasks incorpo-rating desired trajectory information Extensive simulationswere carried out to verify and demonstrate the effectivenessof the proposed scheme In particular the performance ofthe model reference controller is compared with that of theconventional PID controller for the given UVMS operationscenarios The obtained results confirm the effectiveness androbustness of the proposed scheme in terms of tracking errorsand control effort in the presence of external disturbancesand parameter uncertainties This research provides a gener-alized framework for modeling and controlling of an UVMSconsidering the dynamic coupling between the vehicle andthe manipulator which is crucial for achieving underwatermanipulation tasks for a variety of scientific industrial andmilitary missions using unmanned underwater vehicles

Conflict of Interests

Authors confirm that this paper has not been publishedelsewhere and is not under consideration by another journalAll authors have approved the manuscript and agree withsubmission toModelling and Simulation in EngineeringTheauthors have no conflict of interests to declare

Acknowledgments

The author would like to acknowledge Professor JinwhanKim for his valuable suggestions and discussions on under-water manipulator This research was supported in partby the World Class University (WCU) program throughthe National Research Foundation of Korea funded by theMinistry of Education Science and Technology (R31-2008-000-10045-0)

References

[1] G Antonelli F Caccavale S Chiaverini and L Villani ldquoTrack-ing control for underwater vehicle-manipulator systems withvelocity estimationrdquo IEEE Journal of Oceanic Engineering vol25 no 3 pp 399ndash413 2000

[2] G Marani S K Choi and J Yuh ldquoUnderwater autonomousmanipulation for intervention missions AUVsrdquo Ocean Engi-neering vol 36 no 1 pp 15ndash23 2009

[3] S McMillan D E Orin and R B McGhee ldquoEfficient dynamicsimulation of an underwater vehicle with a robotic manipula-torrdquo IEEE Transactions on Systems Man and Cybernetics vol25 no 8 pp 1194ndash1206 1995

[4] T I Fossen Guidance and Control of Ocean Vehicles WileyChichester UK 1994

[5] T J Tarn G A Shoults and S P Yang ldquoA dynamic model ofan underwater vehicle with a robotic manipulator using Kanersquosmethodrdquo Autonomous Robots vol 3 no 2-3 pp 269ndash283 1996

[6] H Mahesh J Yuh and R Lakshmi ldquoA Coordinated controlof an underwater vehicle and robotic manipulatorrdquo Journal ofRobotic Systems vol 8 no 3 pp 339ndash370 1991

[7] N Sarkar and T K Podder ldquoCoordinated motion planningand control of autonomous underwater vehicle-manipulatorsystems subject to drag optimizationrdquo IEEE Journal of OceanicEngineering vol 26 no 2 pp 228ndash239 2001

Modelling and Simulation in Engineering 13

[8] T W McLain S M Rock and M J Lee ldquoExperiments inthe coordinated control of an underwater armvehicle systemrdquoAutonomous Robots vol 3 no 2-3 pp 213ndash232 1996

[9] M W Dunnigan and G T Russell ldquoEvaluation and reductionof the dynamic coupling between a manipulator and an under-water vehiclerdquo IEEE Journal of Oceanic Engineering vol 23 no3 pp 260ndash273 1998

[10] B H Jun P M Lee and J Lee ldquoManipulability analysisof underwater robotic arms on ROV and application totask-oriented joint configurationrdquo in Proceedings of the IEEEOCEANS pp 1548ndash1553 November 2004

[11] J H Ryu D S Kwon and P M Lee ldquoControl of underwatermanipulators mounted on an ROV using base force informa-tionrdquo in Proceedings of the IEEE International Conference onRobotics and Automation (ICRA rsquo01) pp 3238ndash3243 May 2001

[12] M Hildebrandt L Christensen J Kerdels J Albiez and FKirchner ldquoRealtime motion compensation for ROV-based tele-operated underwater manipulatorsrdquo in Proceedings of the IEEEOCEANS pp 1ndash6 May 2009

[13] H Shim B H Jun P M Lee H Baek and J Lee ldquoWorkspacecontrol system of underwater tele-operated manipulators on anROVrdquo Ocean Engineering vol 37 no 11-12 pp 1036ndash1047 2010

[14] J J Craig Introduction to Robotics Addison Wesley BostonMass USA 1986

[15] G Antonelli Underwater Robots Motion and Force Control ofVehicle-Manipulator Systems Springer Berlin Germany 2006

[16] K Kim andT Ura ldquoAppliedmodel-based analysis and synthesisfor the dynamics guidance and control of an autonomousundersea vehiclerdquo Mathematical Problems in Engineering vol2010 Article ID 149385 23 pages 2010

[17] T I Fossen Marine Control Systems Guidance Navigationand Control of Ships Rigs and Underwater Vehicles MarineCybernetics AS 2002

[18] J J E Slotine and W Li Applied Nonlinear Control Prentice-Hall Upper Saddle River NJ USA 1991

[19] K Y Pettersen and O Egeland ldquoPosition and attitude control ofan underactuated autonomous underwater vehiclerdquo in Proceed-ings of the 1996 35th IEEE Conference on Decision and Controlpp 987ndash991 Kobe Japan December 1996

[20] T H Koh MW S Lau G Seet and E Low ldquoA control modulescheme for an underactuated underwater robotic vehiclerdquo Jour-nal of Intelligent and Robotic Systems Theory and Applicationsvol 46 no 1 pp 43ndash58 2006

[21] M Santhakumar and T Asokan ldquoInvestigations on the hybridtracking control of an underactuated autonomous underwaterrobotrdquo Advanced Robotics vol 24 no 11 pp 1529ndash1556 2010

[22] ANSALDO Nucleare Underwater Manipulator MARIS 7080Use and Maintenance Manual Ansaldo Nuclear DivisionGenoa Italy 1996

[23] K Deb Optimization for Engineering Design Algorithms andExamples Prentice Hall New Delhi India 2004

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Modelling and Simulation in Engineering 9

0 50 100 150 200 250 300minus01

minus005

0

005

01

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Trac

king

erro

r inx

(xe) (

m)

Figure 6 Tracking errors in 119909 position for a given 3D trajectory

0 50 100 150 200 250 300minus002

minus001

0

001

002

003

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Trac

king

erro

r iny

(ye) (

m)

Figure 7 Tracking errors in 119910 position for a given 3D trajectory

(refer to Figures 6 to 11) However the manipulator inclusioneffects are better adapted in the model reference control thanin the PID control As can be observed from Figures 8 and10 the manipulator inclusion causes an initial pitch anglevariation drifts the vehicle in the heave direction during thestraight line motion (during acceleration stage) Howeverthese unwanted effects are compensated successfully in themodel reference control and therefore tracking errors do notexceed their design limits

432 Manipulator following a Given Desired 3D Trajectorywith the Freely Moving Underwater Vehicle (without VehicleControl) As mentioned earlier in this section this task ismainly to address the interaction effects and their influences

0 50 100 150 200 250 300minus005

0

005

01

015

02

03

Trac

king

erro

r inz

(ze) (

m)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 8 Tracking errors in 119911 position for a given 3D trajectory

0 50 100 150 200 250 300minus10

minus5

0

5

10

15

20

Trac

king

erro

r in

roll

(120601e) (

deg)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 9 Tracking errors in roll for a given 3D trajectory

on theUVMS For this task the vehicle controller is removedand only the underwater manipulator follows a given desiredcontinuous trajectory The desired values of joint positionsare as follows 120579

1119889= 90

∘ sin (01119905) 1205792119889

= 90

∘ and 1205793119889

=

minus45

∘ The simulation results of this condition are presentedin Figures 12 13 14 15 and 16 From the results it is observedthat the vehicle is started getting drifted from its initialposition and it is moving forward with an average velocityof 002ms (approximately) for the repeated underwatermanipulator movements It shows that the manipulator linksare affected due to the dynamic coupling effects Fromthe results it is observed that the vehicle swims duringmanipulator movements if the vehicle does not have anycontrol actionThese errors and forward speed are increasing

10 Modelling and Simulation in Engineering

0 50 100 150 200 250 300minus15

minus1

minus05

0

05

1

15

Trac

king

erro

r in

pitc

h (120579

e) (

deg)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 10 Tracking errors in pitch for a given 3D trajectory

0 50 100 150 200 250 300minus1

minus05

0

05

1

Trac

king

erro

r in

yaw

(120595e) (

deg)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 11 Tracking errors in yaw for a given 3D trajectory

with the manipulator oscillation frequency and their jointangle magnitudes In addition the direction of the vehiclersquosmovement varies depending on the manipulator positionsand its direction ofmovementsThese results can be extendedto the work towards swimming robots and their dynamicmodeling aspects

433 Underwater Manipulator following a Given DesiredCircular Trajectory with Vehicle Control The circular trajec-tory chosen for the analysis has 02m in diameter and anaverage speed of 00125ms These parameters are chosenwith the consideration of manipulator actuators workspaceand control The results from computer simulations arepresented in Figures 15ndash18 In Figure 15 both desired andactual task space trajectories are plotted and the task spacetracking errors are given in Figures 16ndash18 From the results

0 5 10 15 20minus006

minus004

minus002

0

002

004

006

008

01

012

Posit

ion

erro

rs (m

)

Time (t) (s)

xeyeze

Figure 12 Tracking errors in the vehicle positions (when manipu-lator has motion)

0 5 10 15 20minus3

minus2

minus1

0

1

2

3

4

Attit

ude e

rror

s (de

g)

Time (t) (s)

120601e120579e120595e

Figure 13 Tracking errors in the vehicle orientations (when thevehicle has no control and the manipulator has repeated motion)

it is observed that the manipulator tip tracks the givendesired task space trajectories quite satisfactorily in both PIDand MRC schemes in the ideal conditions (no disturbancesno uncertainties etc) Then in order to demonstrate theadaptability and robustness of the proposed controller anuncertain condition is considered for the simulations Thefollowing conditions are considered for the uncertain condi-tion analysis

(i) the UVMS parameters are assumed to be inaccurate(about 10 for each parameters)

(ii) the manipulator carries a payload of 1 kg at its tip

Modelling and Simulation in Engineering 11

0708

091

minus02minus01

001

02045

046

047

048

049

Desired tool tip positionActual tool tip position

z(m

)

y (m)x (m)

Figure 14 Manipulator tip position in 3D space (when the vehiclehas no control)

06507

07508

085

005

01

015

minus01

minus005

0

005

Desired trajectoryPIDMRC

PID with uncertaintyMRC with uncertainty

z(m

)

y (m)x (m)

Figure 15 Task space (119909119910119911) trajectories (results from the circulartrajectory)

(iii) an unknown ocean current is added in the simulationby properly considering the relative velocity of thein the dynamic model It is assumed to have anirrotational current constant in the inertial frameand the value of the current is considered as ^

119888=

[02 02 01 0 0 0]

119879ms

The results are presented in Figures 15ndash18 and from theseresults it is observed that the proposed controller is goodin adapting the uncertainties and disturbances (refer toFigure 15) Figures 16 and 17 show that tracking errors of119909 and 119910 in both PID and MRC methods are almost thesame and results satisfactorily however the tracking error in119911 substantiates that the proposed controller is comparativelygood in the presence of uncertainties and disturbances

434 Underwater Manipulator following a Given DesiredRectangular Trajectory with Vehicle Control The rectangulartrajectory chosen for the analysis has 04m in width and

0 5 10 15 20 25 30minus002

minus0015

minus001

minus0005

0

0005

001

0015

Time (t) (s)

PIDMRC

PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r inx

(xe) (

m)

Figure 16 Time histories of the manipulator tip position trackingerror in 119909 (circular trajectory)

0 5 10 15 20 25 30minus4

minus3

minus2

minus1

0

1

2

3

4

5

6

MRC

Time (t) (s)

PID PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r iny

(ye) (

m)

times10minus3

Figure 17 Time histories of the manipulator tip position trackingerror in 119910 (circular trajectory)

02m in height in the 119910119911 plane and an average speedof 005ms As mentioned in the last case the trajectoryhas been chosen with the consideration of the manipulatorcharacteristics Two conditions have been considered for theanalysis ideal condition (no disturbances no uncertaintiesetc) and an uncertain condition (the same as the previouscase Section 433) The results from computer simulationsare plotted in Figure 19 In the ideal condition both con-trollers show quite satisfactory performance and in theuncertain condition the proposed controller shows betterperformance

12 Modelling and Simulation in Engineering

MRC

0 5 10 15 20 25 30minus002

0

002

004

006

008

01

012

Time (t) (s)

PID PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r inz

(ze) (

m)

Figure 18 Time histories of the manipulator tip position trackingerror in 119911 (circular trajectory)

064 066 068 07 072

minus020

0202

025

03

035

04

Desired trajectoryPIDMRC

PID with uncertaintyMRC with uncertainty

z(m

)

y (m)x (m)

Figure 19 Task space (119909119910119911) trajectories (results from the rectangu-lar trajectory)

In both trajectory tracking cases the thruster forces donot exceed plusmn5N and the manipulator actuator torques staywithinplusmn015Nmwhich arewell within the range of actuators

5 Conclusions

In this study the interaction effects due to the dynamiccoupling between the vehicle and the manipulator wereinvestigated using closed-form equations which provide ageneralized scheme for formulating the equations of motionof the UVMS The proposed scheme makes it possible toidentify the structure nature and properties of the systemand it simplifies the control design This study also proposeda model reference control approach for an underactuated

UVMS to perform underwater intervention tasks incorpo-rating desired trajectory information Extensive simulationswere carried out to verify and demonstrate the effectivenessof the proposed scheme In particular the performance ofthe model reference controller is compared with that of theconventional PID controller for the given UVMS operationscenarios The obtained results confirm the effectiveness androbustness of the proposed scheme in terms of tracking errorsand control effort in the presence of external disturbancesand parameter uncertainties This research provides a gener-alized framework for modeling and controlling of an UVMSconsidering the dynamic coupling between the vehicle andthe manipulator which is crucial for achieving underwatermanipulation tasks for a variety of scientific industrial andmilitary missions using unmanned underwater vehicles

Conflict of Interests

Authors confirm that this paper has not been publishedelsewhere and is not under consideration by another journalAll authors have approved the manuscript and agree withsubmission toModelling and Simulation in EngineeringTheauthors have no conflict of interests to declare

Acknowledgments

The author would like to acknowledge Professor JinwhanKim for his valuable suggestions and discussions on under-water manipulator This research was supported in partby the World Class University (WCU) program throughthe National Research Foundation of Korea funded by theMinistry of Education Science and Technology (R31-2008-000-10045-0)

References

[1] G Antonelli F Caccavale S Chiaverini and L Villani ldquoTrack-ing control for underwater vehicle-manipulator systems withvelocity estimationrdquo IEEE Journal of Oceanic Engineering vol25 no 3 pp 399ndash413 2000

[2] G Marani S K Choi and J Yuh ldquoUnderwater autonomousmanipulation for intervention missions AUVsrdquo Ocean Engi-neering vol 36 no 1 pp 15ndash23 2009

[3] S McMillan D E Orin and R B McGhee ldquoEfficient dynamicsimulation of an underwater vehicle with a robotic manipula-torrdquo IEEE Transactions on Systems Man and Cybernetics vol25 no 8 pp 1194ndash1206 1995

[4] T I Fossen Guidance and Control of Ocean Vehicles WileyChichester UK 1994

[5] T J Tarn G A Shoults and S P Yang ldquoA dynamic model ofan underwater vehicle with a robotic manipulator using Kanersquosmethodrdquo Autonomous Robots vol 3 no 2-3 pp 269ndash283 1996

[6] H Mahesh J Yuh and R Lakshmi ldquoA Coordinated controlof an underwater vehicle and robotic manipulatorrdquo Journal ofRobotic Systems vol 8 no 3 pp 339ndash370 1991

[7] N Sarkar and T K Podder ldquoCoordinated motion planningand control of autonomous underwater vehicle-manipulatorsystems subject to drag optimizationrdquo IEEE Journal of OceanicEngineering vol 26 no 2 pp 228ndash239 2001

Modelling and Simulation in Engineering 13

[8] T W McLain S M Rock and M J Lee ldquoExperiments inthe coordinated control of an underwater armvehicle systemrdquoAutonomous Robots vol 3 no 2-3 pp 213ndash232 1996

[9] M W Dunnigan and G T Russell ldquoEvaluation and reductionof the dynamic coupling between a manipulator and an under-water vehiclerdquo IEEE Journal of Oceanic Engineering vol 23 no3 pp 260ndash273 1998

[10] B H Jun P M Lee and J Lee ldquoManipulability analysisof underwater robotic arms on ROV and application totask-oriented joint configurationrdquo in Proceedings of the IEEEOCEANS pp 1548ndash1553 November 2004

[11] J H Ryu D S Kwon and P M Lee ldquoControl of underwatermanipulators mounted on an ROV using base force informa-tionrdquo in Proceedings of the IEEE International Conference onRobotics and Automation (ICRA rsquo01) pp 3238ndash3243 May 2001

[12] M Hildebrandt L Christensen J Kerdels J Albiez and FKirchner ldquoRealtime motion compensation for ROV-based tele-operated underwater manipulatorsrdquo in Proceedings of the IEEEOCEANS pp 1ndash6 May 2009

[13] H Shim B H Jun P M Lee H Baek and J Lee ldquoWorkspacecontrol system of underwater tele-operated manipulators on anROVrdquo Ocean Engineering vol 37 no 11-12 pp 1036ndash1047 2010

[14] J J Craig Introduction to Robotics Addison Wesley BostonMass USA 1986

[15] G Antonelli Underwater Robots Motion and Force Control ofVehicle-Manipulator Systems Springer Berlin Germany 2006

[16] K Kim andT Ura ldquoAppliedmodel-based analysis and synthesisfor the dynamics guidance and control of an autonomousundersea vehiclerdquo Mathematical Problems in Engineering vol2010 Article ID 149385 23 pages 2010

[17] T I Fossen Marine Control Systems Guidance Navigationand Control of Ships Rigs and Underwater Vehicles MarineCybernetics AS 2002

[18] J J E Slotine and W Li Applied Nonlinear Control Prentice-Hall Upper Saddle River NJ USA 1991

[19] K Y Pettersen and O Egeland ldquoPosition and attitude control ofan underactuated autonomous underwater vehiclerdquo in Proceed-ings of the 1996 35th IEEE Conference on Decision and Controlpp 987ndash991 Kobe Japan December 1996

[20] T H Koh MW S Lau G Seet and E Low ldquoA control modulescheme for an underactuated underwater robotic vehiclerdquo Jour-nal of Intelligent and Robotic Systems Theory and Applicationsvol 46 no 1 pp 43ndash58 2006

[21] M Santhakumar and T Asokan ldquoInvestigations on the hybridtracking control of an underactuated autonomous underwaterrobotrdquo Advanced Robotics vol 24 no 11 pp 1529ndash1556 2010

[22] ANSALDO Nucleare Underwater Manipulator MARIS 7080Use and Maintenance Manual Ansaldo Nuclear DivisionGenoa Italy 1996

[23] K Deb Optimization for Engineering Design Algorithms andExamples Prentice Hall New Delhi India 2004

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 Modelling and Simulation in Engineering

0 50 100 150 200 250 300minus15

minus1

minus05

0

05

1

15

Trac

king

erro

r in

pitc

h (120579

e) (

deg)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 10 Tracking errors in pitch for a given 3D trajectory

0 50 100 150 200 250 300minus1

minus05

0

05

1

Trac

king

erro

r in

yaw

(120595e) (

deg)

Time (t) (s)

PID without armMRC without arm

PID with armMRC with arm

Figure 11 Tracking errors in yaw for a given 3D trajectory

with the manipulator oscillation frequency and their jointangle magnitudes In addition the direction of the vehiclersquosmovement varies depending on the manipulator positionsand its direction ofmovementsThese results can be extendedto the work towards swimming robots and their dynamicmodeling aspects

433 Underwater Manipulator following a Given DesiredCircular Trajectory with Vehicle Control The circular trajec-tory chosen for the analysis has 02m in diameter and anaverage speed of 00125ms These parameters are chosenwith the consideration of manipulator actuators workspaceand control The results from computer simulations arepresented in Figures 15ndash18 In Figure 15 both desired andactual task space trajectories are plotted and the task spacetracking errors are given in Figures 16ndash18 From the results

0 5 10 15 20minus006

minus004

minus002

0

002

004

006

008

01

012

Posit

ion

erro

rs (m

)

Time (t) (s)

xeyeze

Figure 12 Tracking errors in the vehicle positions (when manipu-lator has motion)

0 5 10 15 20minus3

minus2

minus1

0

1

2

3

4

Attit

ude e

rror

s (de

g)

Time (t) (s)

120601e120579e120595e

Figure 13 Tracking errors in the vehicle orientations (when thevehicle has no control and the manipulator has repeated motion)

it is observed that the manipulator tip tracks the givendesired task space trajectories quite satisfactorily in both PIDand MRC schemes in the ideal conditions (no disturbancesno uncertainties etc) Then in order to demonstrate theadaptability and robustness of the proposed controller anuncertain condition is considered for the simulations Thefollowing conditions are considered for the uncertain condi-tion analysis

(i) the UVMS parameters are assumed to be inaccurate(about 10 for each parameters)

(ii) the manipulator carries a payload of 1 kg at its tip

Modelling and Simulation in Engineering 11

0708

091

minus02minus01

001

02045

046

047

048

049

Desired tool tip positionActual tool tip position

z(m

)

y (m)x (m)

Figure 14 Manipulator tip position in 3D space (when the vehiclehas no control)

06507

07508

085

005

01

015

minus01

minus005

0

005

Desired trajectoryPIDMRC

PID with uncertaintyMRC with uncertainty

z(m

)

y (m)x (m)

Figure 15 Task space (119909119910119911) trajectories (results from the circulartrajectory)

(iii) an unknown ocean current is added in the simulationby properly considering the relative velocity of thein the dynamic model It is assumed to have anirrotational current constant in the inertial frameand the value of the current is considered as ^

119888=

[02 02 01 0 0 0]

119879ms

The results are presented in Figures 15ndash18 and from theseresults it is observed that the proposed controller is goodin adapting the uncertainties and disturbances (refer toFigure 15) Figures 16 and 17 show that tracking errors of119909 and 119910 in both PID and MRC methods are almost thesame and results satisfactorily however the tracking error in119911 substantiates that the proposed controller is comparativelygood in the presence of uncertainties and disturbances

434 Underwater Manipulator following a Given DesiredRectangular Trajectory with Vehicle Control The rectangulartrajectory chosen for the analysis has 04m in width and

0 5 10 15 20 25 30minus002

minus0015

minus001

minus0005

0

0005

001

0015

Time (t) (s)

PIDMRC

PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r inx

(xe) (

m)

Figure 16 Time histories of the manipulator tip position trackingerror in 119909 (circular trajectory)

0 5 10 15 20 25 30minus4

minus3

minus2

minus1

0

1

2

3

4

5

6

MRC

Time (t) (s)

PID PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r iny

(ye) (

m)

times10minus3

Figure 17 Time histories of the manipulator tip position trackingerror in 119910 (circular trajectory)

02m in height in the 119910119911 plane and an average speedof 005ms As mentioned in the last case the trajectoryhas been chosen with the consideration of the manipulatorcharacteristics Two conditions have been considered for theanalysis ideal condition (no disturbances no uncertaintiesetc) and an uncertain condition (the same as the previouscase Section 433) The results from computer simulationsare plotted in Figure 19 In the ideal condition both con-trollers show quite satisfactory performance and in theuncertain condition the proposed controller shows betterperformance

12 Modelling and Simulation in Engineering

MRC

0 5 10 15 20 25 30minus002

0

002

004

006

008

01

012

Time (t) (s)

PID PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r inz

(ze) (

m)

Figure 18 Time histories of the manipulator tip position trackingerror in 119911 (circular trajectory)

064 066 068 07 072

minus020

0202

025

03

035

04

Desired trajectoryPIDMRC

PID with uncertaintyMRC with uncertainty

z(m

)

y (m)x (m)

Figure 19 Task space (119909119910119911) trajectories (results from the rectangu-lar trajectory)

In both trajectory tracking cases the thruster forces donot exceed plusmn5N and the manipulator actuator torques staywithinplusmn015Nmwhich arewell within the range of actuators

5 Conclusions

In this study the interaction effects due to the dynamiccoupling between the vehicle and the manipulator wereinvestigated using closed-form equations which provide ageneralized scheme for formulating the equations of motionof the UVMS The proposed scheme makes it possible toidentify the structure nature and properties of the systemand it simplifies the control design This study also proposeda model reference control approach for an underactuated

UVMS to perform underwater intervention tasks incorpo-rating desired trajectory information Extensive simulationswere carried out to verify and demonstrate the effectivenessof the proposed scheme In particular the performance ofthe model reference controller is compared with that of theconventional PID controller for the given UVMS operationscenarios The obtained results confirm the effectiveness androbustness of the proposed scheme in terms of tracking errorsand control effort in the presence of external disturbancesand parameter uncertainties This research provides a gener-alized framework for modeling and controlling of an UVMSconsidering the dynamic coupling between the vehicle andthe manipulator which is crucial for achieving underwatermanipulation tasks for a variety of scientific industrial andmilitary missions using unmanned underwater vehicles

Conflict of Interests

Authors confirm that this paper has not been publishedelsewhere and is not under consideration by another journalAll authors have approved the manuscript and agree withsubmission toModelling and Simulation in EngineeringTheauthors have no conflict of interests to declare

Acknowledgments

The author would like to acknowledge Professor JinwhanKim for his valuable suggestions and discussions on under-water manipulator This research was supported in partby the World Class University (WCU) program throughthe National Research Foundation of Korea funded by theMinistry of Education Science and Technology (R31-2008-000-10045-0)

References

[1] G Antonelli F Caccavale S Chiaverini and L Villani ldquoTrack-ing control for underwater vehicle-manipulator systems withvelocity estimationrdquo IEEE Journal of Oceanic Engineering vol25 no 3 pp 399ndash413 2000

[2] G Marani S K Choi and J Yuh ldquoUnderwater autonomousmanipulation for intervention missions AUVsrdquo Ocean Engi-neering vol 36 no 1 pp 15ndash23 2009

[3] S McMillan D E Orin and R B McGhee ldquoEfficient dynamicsimulation of an underwater vehicle with a robotic manipula-torrdquo IEEE Transactions on Systems Man and Cybernetics vol25 no 8 pp 1194ndash1206 1995

[4] T I Fossen Guidance and Control of Ocean Vehicles WileyChichester UK 1994

[5] T J Tarn G A Shoults and S P Yang ldquoA dynamic model ofan underwater vehicle with a robotic manipulator using Kanersquosmethodrdquo Autonomous Robots vol 3 no 2-3 pp 269ndash283 1996

[6] H Mahesh J Yuh and R Lakshmi ldquoA Coordinated controlof an underwater vehicle and robotic manipulatorrdquo Journal ofRobotic Systems vol 8 no 3 pp 339ndash370 1991

[7] N Sarkar and T K Podder ldquoCoordinated motion planningand control of autonomous underwater vehicle-manipulatorsystems subject to drag optimizationrdquo IEEE Journal of OceanicEngineering vol 26 no 2 pp 228ndash239 2001

Modelling and Simulation in Engineering 13

[8] T W McLain S M Rock and M J Lee ldquoExperiments inthe coordinated control of an underwater armvehicle systemrdquoAutonomous Robots vol 3 no 2-3 pp 213ndash232 1996

[9] M W Dunnigan and G T Russell ldquoEvaluation and reductionof the dynamic coupling between a manipulator and an under-water vehiclerdquo IEEE Journal of Oceanic Engineering vol 23 no3 pp 260ndash273 1998

[10] B H Jun P M Lee and J Lee ldquoManipulability analysisof underwater robotic arms on ROV and application totask-oriented joint configurationrdquo in Proceedings of the IEEEOCEANS pp 1548ndash1553 November 2004

[11] J H Ryu D S Kwon and P M Lee ldquoControl of underwatermanipulators mounted on an ROV using base force informa-tionrdquo in Proceedings of the IEEE International Conference onRobotics and Automation (ICRA rsquo01) pp 3238ndash3243 May 2001

[12] M Hildebrandt L Christensen J Kerdels J Albiez and FKirchner ldquoRealtime motion compensation for ROV-based tele-operated underwater manipulatorsrdquo in Proceedings of the IEEEOCEANS pp 1ndash6 May 2009

[13] H Shim B H Jun P M Lee H Baek and J Lee ldquoWorkspacecontrol system of underwater tele-operated manipulators on anROVrdquo Ocean Engineering vol 37 no 11-12 pp 1036ndash1047 2010

[14] J J Craig Introduction to Robotics Addison Wesley BostonMass USA 1986

[15] G Antonelli Underwater Robots Motion and Force Control ofVehicle-Manipulator Systems Springer Berlin Germany 2006

[16] K Kim andT Ura ldquoAppliedmodel-based analysis and synthesisfor the dynamics guidance and control of an autonomousundersea vehiclerdquo Mathematical Problems in Engineering vol2010 Article ID 149385 23 pages 2010

[17] T I Fossen Marine Control Systems Guidance Navigationand Control of Ships Rigs and Underwater Vehicles MarineCybernetics AS 2002

[18] J J E Slotine and W Li Applied Nonlinear Control Prentice-Hall Upper Saddle River NJ USA 1991

[19] K Y Pettersen and O Egeland ldquoPosition and attitude control ofan underactuated autonomous underwater vehiclerdquo in Proceed-ings of the 1996 35th IEEE Conference on Decision and Controlpp 987ndash991 Kobe Japan December 1996

[20] T H Koh MW S Lau G Seet and E Low ldquoA control modulescheme for an underactuated underwater robotic vehiclerdquo Jour-nal of Intelligent and Robotic Systems Theory and Applicationsvol 46 no 1 pp 43ndash58 2006

[21] M Santhakumar and T Asokan ldquoInvestigations on the hybridtracking control of an underactuated autonomous underwaterrobotrdquo Advanced Robotics vol 24 no 11 pp 1529ndash1556 2010

[22] ANSALDO Nucleare Underwater Manipulator MARIS 7080Use and Maintenance Manual Ansaldo Nuclear DivisionGenoa Italy 1996

[23] K Deb Optimization for Engineering Design Algorithms andExamples Prentice Hall New Delhi India 2004

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Modelling and Simulation in Engineering 11

0708

091

minus02minus01

001

02045

046

047

048

049

Desired tool tip positionActual tool tip position

z(m

)

y (m)x (m)

Figure 14 Manipulator tip position in 3D space (when the vehiclehas no control)

06507

07508

085

005

01

015

minus01

minus005

0

005

Desired trajectoryPIDMRC

PID with uncertaintyMRC with uncertainty

z(m

)

y (m)x (m)

Figure 15 Task space (119909119910119911) trajectories (results from the circulartrajectory)

(iii) an unknown ocean current is added in the simulationby properly considering the relative velocity of thein the dynamic model It is assumed to have anirrotational current constant in the inertial frameand the value of the current is considered as ^

119888=

[02 02 01 0 0 0]

119879ms

The results are presented in Figures 15ndash18 and from theseresults it is observed that the proposed controller is goodin adapting the uncertainties and disturbances (refer toFigure 15) Figures 16 and 17 show that tracking errors of119909 and 119910 in both PID and MRC methods are almost thesame and results satisfactorily however the tracking error in119911 substantiates that the proposed controller is comparativelygood in the presence of uncertainties and disturbances

434 Underwater Manipulator following a Given DesiredRectangular Trajectory with Vehicle Control The rectangulartrajectory chosen for the analysis has 04m in width and

0 5 10 15 20 25 30minus002

minus0015

minus001

minus0005

0

0005

001

0015

Time (t) (s)

PIDMRC

PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r inx

(xe) (

m)

Figure 16 Time histories of the manipulator tip position trackingerror in 119909 (circular trajectory)

0 5 10 15 20 25 30minus4

minus3

minus2

minus1

0

1

2

3

4

5

6

MRC

Time (t) (s)

PID PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r iny

(ye) (

m)

times10minus3

Figure 17 Time histories of the manipulator tip position trackingerror in 119910 (circular trajectory)

02m in height in the 119910119911 plane and an average speedof 005ms As mentioned in the last case the trajectoryhas been chosen with the consideration of the manipulatorcharacteristics Two conditions have been considered for theanalysis ideal condition (no disturbances no uncertaintiesetc) and an uncertain condition (the same as the previouscase Section 433) The results from computer simulationsare plotted in Figure 19 In the ideal condition both con-trollers show quite satisfactory performance and in theuncertain condition the proposed controller shows betterperformance

12 Modelling and Simulation in Engineering

MRC

0 5 10 15 20 25 30minus002

0

002

004

006

008

01

012

Time (t) (s)

PID PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r inz

(ze) (

m)

Figure 18 Time histories of the manipulator tip position trackingerror in 119911 (circular trajectory)

064 066 068 07 072

minus020

0202

025

03

035

04

Desired trajectoryPIDMRC

PID with uncertaintyMRC with uncertainty

z(m

)

y (m)x (m)

Figure 19 Task space (119909119910119911) trajectories (results from the rectangu-lar trajectory)

In both trajectory tracking cases the thruster forces donot exceed plusmn5N and the manipulator actuator torques staywithinplusmn015Nmwhich arewell within the range of actuators

5 Conclusions

In this study the interaction effects due to the dynamiccoupling between the vehicle and the manipulator wereinvestigated using closed-form equations which provide ageneralized scheme for formulating the equations of motionof the UVMS The proposed scheme makes it possible toidentify the structure nature and properties of the systemand it simplifies the control design This study also proposeda model reference control approach for an underactuated

UVMS to perform underwater intervention tasks incorpo-rating desired trajectory information Extensive simulationswere carried out to verify and demonstrate the effectivenessof the proposed scheme In particular the performance ofthe model reference controller is compared with that of theconventional PID controller for the given UVMS operationscenarios The obtained results confirm the effectiveness androbustness of the proposed scheme in terms of tracking errorsand control effort in the presence of external disturbancesand parameter uncertainties This research provides a gener-alized framework for modeling and controlling of an UVMSconsidering the dynamic coupling between the vehicle andthe manipulator which is crucial for achieving underwatermanipulation tasks for a variety of scientific industrial andmilitary missions using unmanned underwater vehicles

Conflict of Interests

Authors confirm that this paper has not been publishedelsewhere and is not under consideration by another journalAll authors have approved the manuscript and agree withsubmission toModelling and Simulation in EngineeringTheauthors have no conflict of interests to declare

Acknowledgments

The author would like to acknowledge Professor JinwhanKim for his valuable suggestions and discussions on under-water manipulator This research was supported in partby the World Class University (WCU) program throughthe National Research Foundation of Korea funded by theMinistry of Education Science and Technology (R31-2008-000-10045-0)

References

[1] G Antonelli F Caccavale S Chiaverini and L Villani ldquoTrack-ing control for underwater vehicle-manipulator systems withvelocity estimationrdquo IEEE Journal of Oceanic Engineering vol25 no 3 pp 399ndash413 2000

[2] G Marani S K Choi and J Yuh ldquoUnderwater autonomousmanipulation for intervention missions AUVsrdquo Ocean Engi-neering vol 36 no 1 pp 15ndash23 2009

[3] S McMillan D E Orin and R B McGhee ldquoEfficient dynamicsimulation of an underwater vehicle with a robotic manipula-torrdquo IEEE Transactions on Systems Man and Cybernetics vol25 no 8 pp 1194ndash1206 1995

[4] T I Fossen Guidance and Control of Ocean Vehicles WileyChichester UK 1994

[5] T J Tarn G A Shoults and S P Yang ldquoA dynamic model ofan underwater vehicle with a robotic manipulator using Kanersquosmethodrdquo Autonomous Robots vol 3 no 2-3 pp 269ndash283 1996

[6] H Mahesh J Yuh and R Lakshmi ldquoA Coordinated controlof an underwater vehicle and robotic manipulatorrdquo Journal ofRobotic Systems vol 8 no 3 pp 339ndash370 1991

[7] N Sarkar and T K Podder ldquoCoordinated motion planningand control of autonomous underwater vehicle-manipulatorsystems subject to drag optimizationrdquo IEEE Journal of OceanicEngineering vol 26 no 2 pp 228ndash239 2001

Modelling and Simulation in Engineering 13

[8] T W McLain S M Rock and M J Lee ldquoExperiments inthe coordinated control of an underwater armvehicle systemrdquoAutonomous Robots vol 3 no 2-3 pp 213ndash232 1996

[9] M W Dunnigan and G T Russell ldquoEvaluation and reductionof the dynamic coupling between a manipulator and an under-water vehiclerdquo IEEE Journal of Oceanic Engineering vol 23 no3 pp 260ndash273 1998

[10] B H Jun P M Lee and J Lee ldquoManipulability analysisof underwater robotic arms on ROV and application totask-oriented joint configurationrdquo in Proceedings of the IEEEOCEANS pp 1548ndash1553 November 2004

[11] J H Ryu D S Kwon and P M Lee ldquoControl of underwatermanipulators mounted on an ROV using base force informa-tionrdquo in Proceedings of the IEEE International Conference onRobotics and Automation (ICRA rsquo01) pp 3238ndash3243 May 2001

[12] M Hildebrandt L Christensen J Kerdels J Albiez and FKirchner ldquoRealtime motion compensation for ROV-based tele-operated underwater manipulatorsrdquo in Proceedings of the IEEEOCEANS pp 1ndash6 May 2009

[13] H Shim B H Jun P M Lee H Baek and J Lee ldquoWorkspacecontrol system of underwater tele-operated manipulators on anROVrdquo Ocean Engineering vol 37 no 11-12 pp 1036ndash1047 2010

[14] J J Craig Introduction to Robotics Addison Wesley BostonMass USA 1986

[15] G Antonelli Underwater Robots Motion and Force Control ofVehicle-Manipulator Systems Springer Berlin Germany 2006

[16] K Kim andT Ura ldquoAppliedmodel-based analysis and synthesisfor the dynamics guidance and control of an autonomousundersea vehiclerdquo Mathematical Problems in Engineering vol2010 Article ID 149385 23 pages 2010

[17] T I Fossen Marine Control Systems Guidance Navigationand Control of Ships Rigs and Underwater Vehicles MarineCybernetics AS 2002

[18] J J E Slotine and W Li Applied Nonlinear Control Prentice-Hall Upper Saddle River NJ USA 1991

[19] K Y Pettersen and O Egeland ldquoPosition and attitude control ofan underactuated autonomous underwater vehiclerdquo in Proceed-ings of the 1996 35th IEEE Conference on Decision and Controlpp 987ndash991 Kobe Japan December 1996

[20] T H Koh MW S Lau G Seet and E Low ldquoA control modulescheme for an underactuated underwater robotic vehiclerdquo Jour-nal of Intelligent and Robotic Systems Theory and Applicationsvol 46 no 1 pp 43ndash58 2006

[21] M Santhakumar and T Asokan ldquoInvestigations on the hybridtracking control of an underactuated autonomous underwaterrobotrdquo Advanced Robotics vol 24 no 11 pp 1529ndash1556 2010

[22] ANSALDO Nucleare Underwater Manipulator MARIS 7080Use and Maintenance Manual Ansaldo Nuclear DivisionGenoa Italy 1996

[23] K Deb Optimization for Engineering Design Algorithms andExamples Prentice Hall New Delhi India 2004

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

12 Modelling and Simulation in Engineering

MRC

0 5 10 15 20 25 30minus002

0

002

004

006

008

01

012

Time (t) (s)

PID PID with uncertaintyMRC with uncertainty

Tip

posit

ion

erro

r inz

(ze) (

m)

Figure 18 Time histories of the manipulator tip position trackingerror in 119911 (circular trajectory)

064 066 068 07 072

minus020

0202

025

03

035

04

Desired trajectoryPIDMRC

PID with uncertaintyMRC with uncertainty

z(m

)

y (m)x (m)

Figure 19 Task space (119909119910119911) trajectories (results from the rectangu-lar trajectory)

In both trajectory tracking cases the thruster forces donot exceed plusmn5N and the manipulator actuator torques staywithinplusmn015Nmwhich arewell within the range of actuators

5 Conclusions

In this study the interaction effects due to the dynamiccoupling between the vehicle and the manipulator wereinvestigated using closed-form equations which provide ageneralized scheme for formulating the equations of motionof the UVMS The proposed scheme makes it possible toidentify the structure nature and properties of the systemand it simplifies the control design This study also proposeda model reference control approach for an underactuated

UVMS to perform underwater intervention tasks incorpo-rating desired trajectory information Extensive simulationswere carried out to verify and demonstrate the effectivenessof the proposed scheme In particular the performance ofthe model reference controller is compared with that of theconventional PID controller for the given UVMS operationscenarios The obtained results confirm the effectiveness androbustness of the proposed scheme in terms of tracking errorsand control effort in the presence of external disturbancesand parameter uncertainties This research provides a gener-alized framework for modeling and controlling of an UVMSconsidering the dynamic coupling between the vehicle andthe manipulator which is crucial for achieving underwatermanipulation tasks for a variety of scientific industrial andmilitary missions using unmanned underwater vehicles

Conflict of Interests

Authors confirm that this paper has not been publishedelsewhere and is not under consideration by another journalAll authors have approved the manuscript and agree withsubmission toModelling and Simulation in EngineeringTheauthors have no conflict of interests to declare

Acknowledgments

The author would like to acknowledge Professor JinwhanKim for his valuable suggestions and discussions on under-water manipulator This research was supported in partby the World Class University (WCU) program throughthe National Research Foundation of Korea funded by theMinistry of Education Science and Technology (R31-2008-000-10045-0)

References

[1] G Antonelli F Caccavale S Chiaverini and L Villani ldquoTrack-ing control for underwater vehicle-manipulator systems withvelocity estimationrdquo IEEE Journal of Oceanic Engineering vol25 no 3 pp 399ndash413 2000

[2] G Marani S K Choi and J Yuh ldquoUnderwater autonomousmanipulation for intervention missions AUVsrdquo Ocean Engi-neering vol 36 no 1 pp 15ndash23 2009

[3] S McMillan D E Orin and R B McGhee ldquoEfficient dynamicsimulation of an underwater vehicle with a robotic manipula-torrdquo IEEE Transactions on Systems Man and Cybernetics vol25 no 8 pp 1194ndash1206 1995

[4] T I Fossen Guidance and Control of Ocean Vehicles WileyChichester UK 1994

[5] T J Tarn G A Shoults and S P Yang ldquoA dynamic model ofan underwater vehicle with a robotic manipulator using Kanersquosmethodrdquo Autonomous Robots vol 3 no 2-3 pp 269ndash283 1996

[6] H Mahesh J Yuh and R Lakshmi ldquoA Coordinated controlof an underwater vehicle and robotic manipulatorrdquo Journal ofRobotic Systems vol 8 no 3 pp 339ndash370 1991

[7] N Sarkar and T K Podder ldquoCoordinated motion planningand control of autonomous underwater vehicle-manipulatorsystems subject to drag optimizationrdquo IEEE Journal of OceanicEngineering vol 26 no 2 pp 228ndash239 2001

Modelling and Simulation in Engineering 13

[8] T W McLain S M Rock and M J Lee ldquoExperiments inthe coordinated control of an underwater armvehicle systemrdquoAutonomous Robots vol 3 no 2-3 pp 213ndash232 1996

[9] M W Dunnigan and G T Russell ldquoEvaluation and reductionof the dynamic coupling between a manipulator and an under-water vehiclerdquo IEEE Journal of Oceanic Engineering vol 23 no3 pp 260ndash273 1998

[10] B H Jun P M Lee and J Lee ldquoManipulability analysisof underwater robotic arms on ROV and application totask-oriented joint configurationrdquo in Proceedings of the IEEEOCEANS pp 1548ndash1553 November 2004

[11] J H Ryu D S Kwon and P M Lee ldquoControl of underwatermanipulators mounted on an ROV using base force informa-tionrdquo in Proceedings of the IEEE International Conference onRobotics and Automation (ICRA rsquo01) pp 3238ndash3243 May 2001

[12] M Hildebrandt L Christensen J Kerdels J Albiez and FKirchner ldquoRealtime motion compensation for ROV-based tele-operated underwater manipulatorsrdquo in Proceedings of the IEEEOCEANS pp 1ndash6 May 2009

[13] H Shim B H Jun P M Lee H Baek and J Lee ldquoWorkspacecontrol system of underwater tele-operated manipulators on anROVrdquo Ocean Engineering vol 37 no 11-12 pp 1036ndash1047 2010

[14] J J Craig Introduction to Robotics Addison Wesley BostonMass USA 1986

[15] G Antonelli Underwater Robots Motion and Force Control ofVehicle-Manipulator Systems Springer Berlin Germany 2006

[16] K Kim andT Ura ldquoAppliedmodel-based analysis and synthesisfor the dynamics guidance and control of an autonomousundersea vehiclerdquo Mathematical Problems in Engineering vol2010 Article ID 149385 23 pages 2010

[17] T I Fossen Marine Control Systems Guidance Navigationand Control of Ships Rigs and Underwater Vehicles MarineCybernetics AS 2002

[18] J J E Slotine and W Li Applied Nonlinear Control Prentice-Hall Upper Saddle River NJ USA 1991

[19] K Y Pettersen and O Egeland ldquoPosition and attitude control ofan underactuated autonomous underwater vehiclerdquo in Proceed-ings of the 1996 35th IEEE Conference on Decision and Controlpp 987ndash991 Kobe Japan December 1996

[20] T H Koh MW S Lau G Seet and E Low ldquoA control modulescheme for an underactuated underwater robotic vehiclerdquo Jour-nal of Intelligent and Robotic Systems Theory and Applicationsvol 46 no 1 pp 43ndash58 2006

[21] M Santhakumar and T Asokan ldquoInvestigations on the hybridtracking control of an underactuated autonomous underwaterrobotrdquo Advanced Robotics vol 24 no 11 pp 1529ndash1556 2010

[22] ANSALDO Nucleare Underwater Manipulator MARIS 7080Use and Maintenance Manual Ansaldo Nuclear DivisionGenoa Italy 1996

[23] K Deb Optimization for Engineering Design Algorithms andExamples Prentice Hall New Delhi India 2004

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Modelling and Simulation in Engineering 13

[8] T W McLain S M Rock and M J Lee ldquoExperiments inthe coordinated control of an underwater armvehicle systemrdquoAutonomous Robots vol 3 no 2-3 pp 213ndash232 1996

[9] M W Dunnigan and G T Russell ldquoEvaluation and reductionof the dynamic coupling between a manipulator and an under-water vehiclerdquo IEEE Journal of Oceanic Engineering vol 23 no3 pp 260ndash273 1998

[10] B H Jun P M Lee and J Lee ldquoManipulability analysisof underwater robotic arms on ROV and application totask-oriented joint configurationrdquo in Proceedings of the IEEEOCEANS pp 1548ndash1553 November 2004

[11] J H Ryu D S Kwon and P M Lee ldquoControl of underwatermanipulators mounted on an ROV using base force informa-tionrdquo in Proceedings of the IEEE International Conference onRobotics and Automation (ICRA rsquo01) pp 3238ndash3243 May 2001

[12] M Hildebrandt L Christensen J Kerdels J Albiez and FKirchner ldquoRealtime motion compensation for ROV-based tele-operated underwater manipulatorsrdquo in Proceedings of the IEEEOCEANS pp 1ndash6 May 2009

[13] H Shim B H Jun P M Lee H Baek and J Lee ldquoWorkspacecontrol system of underwater tele-operated manipulators on anROVrdquo Ocean Engineering vol 37 no 11-12 pp 1036ndash1047 2010

[14] J J Craig Introduction to Robotics Addison Wesley BostonMass USA 1986

[15] G Antonelli Underwater Robots Motion and Force Control ofVehicle-Manipulator Systems Springer Berlin Germany 2006

[16] K Kim andT Ura ldquoAppliedmodel-based analysis and synthesisfor the dynamics guidance and control of an autonomousundersea vehiclerdquo Mathematical Problems in Engineering vol2010 Article ID 149385 23 pages 2010

[17] T I Fossen Marine Control Systems Guidance Navigationand Control of Ships Rigs and Underwater Vehicles MarineCybernetics AS 2002

[18] J J E Slotine and W Li Applied Nonlinear Control Prentice-Hall Upper Saddle River NJ USA 1991

[19] K Y Pettersen and O Egeland ldquoPosition and attitude control ofan underactuated autonomous underwater vehiclerdquo in Proceed-ings of the 1996 35th IEEE Conference on Decision and Controlpp 987ndash991 Kobe Japan December 1996

[20] T H Koh MW S Lau G Seet and E Low ldquoA control modulescheme for an underactuated underwater robotic vehiclerdquo Jour-nal of Intelligent and Robotic Systems Theory and Applicationsvol 46 no 1 pp 43ndash58 2006

[21] M Santhakumar and T Asokan ldquoInvestigations on the hybridtracking control of an underactuated autonomous underwaterrobotrdquo Advanced Robotics vol 24 no 11 pp 1529ndash1556 2010

[22] ANSALDO Nucleare Underwater Manipulator MARIS 7080Use and Maintenance Manual Ansaldo Nuclear DivisionGenoa Italy 1996

[23] K Deb Optimization for Engineering Design Algorithms andExamples Prentice Hall New Delhi India 2004

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of