An Advanced Autonomous Underwater VehicleDesign and Control Strategy

Jiaxing Che‡, Joseph Cernio‡, Joseph Prainito‡, Michael Zuba†, Chengyu Cao‡,Jun-Hong Cui† and Kazem Kazerounian‡,

‡Mechanical Engineering Department, University of Connecticut, Storrs, CT, USA†Computer Science & Engineering Department, University of Connecticut, Storrs, CT, USA

{jiaxing.che, joseph.cernio, joseph.prainito, zuba, ccao, jcui, kazem}@engr.uconn.edu

Abstract—In this paper, an advanced design of an Autonomous Underwater Vehicle (AUV) is presented. The design is driven only by four water pumps. The different power combinations of the four motors provides the force and moment for propulsion and maneuvering. No control surfaces are needed in this design, which make the manufacturing cost of such a vehicle minimal and more reliable. Based on the propulsion method of the vehicle, a nonlinear AUV dynamic model is studied. This nonlinear model is linearized at the operation point. A control strategy of the AUV is proposed including attitude control and auto-pilot design. Simulation results for the attitude control loop are presented to validate this approach.

Index Terms— Autonomous Underwater Vehicles, AttitudeControl, Auto-Pilot design, AUV modeling

I. INTRODUCTION

The ocean is a harsh and dynamic environment. Therefore,it still remains mysterious and relatively unexplored. Bodiesof water will play a vital role in mankind’s future - notably forfood resources, energy, materials and climate effects. In orderto leverage these aforementioned items we require a platformto explore the underwater environment. One such platform isthat of an autonomous underwater vehicle (AUV). Underwatervehicle design and their control strategies have drawn largeresearch attention.

This paper presents an AUV design and control strategyto facilitate the advancement of autonomous underwater net-works. The current design is in the prototype stages anda relatively low cost but fully functional vehicle has beendesigned and fabricated. The control hardware will containvarious devices from acoustic modems and inertial measure-ment units (IMUs) and compasses. The control strategy ofthe AUV includes modeling, attitude control and a auto-pilotdesign. Simulation results will be presented in order to studyand improve our design.

The rest of the paper is as follows: Section II will discuss the mechanical design of the AUV, Section III will introduce our proof of concept for testing, Section IV will present our control system design in detail, in Section V we provide simulation results and validate our design and finally in Section VI we provide our conclusions and future work.

II. MECHANICAL DESIGN

This full-scale platform utilizes a vectored-thrust propulsionsystem powered by four low-cost submersible bilge pumpsforming four water-jet thrusters with reducing end nozzles.

This provides an optimal thrust to flow rate ratio. By differ-entiating the power combinations of four motors, the force and moment needed for the propulsion and maneuvering are generated. The machine design has two working modes. Mode 1, as shown in Figure 1 is the non-vectored-thurst mode. In this mode, the force vector is one degree of freedom (DOF) pointing to the back and two DOF of moment to manipulate the pitch and yaw angle. Mode 2 is the vectored-thrust mode. In this mode, the vehicle utilizes the same concept of the quadcopter. Together, it provides 1 DOF of thrust force and 3 DOF of moment. Mode 2 further enables the vehicle to change the roll angle. The advantage of the vector approach is that it only uses four motors for propulsion and full maneuvering (in three angles). The manufacturing cost is low compared to that of a more deep-water design that would require more control surfaces.

Fig. 1. Mechanical Design and Propulsion System

III. PROOF OF CONCEPT TESTING

The proof of concept system has been designed to be passively stable. In initial testing, this criterion has been sufficiently met with a self-righting time of approximately 1 second from a complete roll over. A large and versatile cargo bay allows the testing of a variety of component sizes and shapes. Initial testing of the propulsion system in a swimming pool environment has displayed an acceptable cruising speed and turn radius.

978-1-4673-0831-1/12/$31.00 ©2012 IEEE

Fig. 2. Future Design Objective

The test procedure includes balance alignment in static anddynamic working point:

Static balance and alignment: With all the motor power set to zero. We adjust the fluid level to make the buoyancy force equal. Additionally, we adjust the position of the buoyancy to make the attitude of the AUV straight in the water. The fluid level and position of the buoyancy control unit is adjustable.

This static balancing and alignment can make the vehiclenaturally closed to the desired system. When the closed loopcontrol system is applied to this vehicle, the control lawcan compensate these unbalanced and misaligned factors.However, the initial alignment can still reduce the controleffort. The control signal is with in limited amplitude due tothe physical constraint. Initial alignment also helps to ensurethat the vehicle parameter falls into the range which is fullycontrollable for the control signal with limited amplitude.

Fig. 3. Swimming Pool Test of Prototype

IV. CONTROL SYSTEM DESIGN

A. Dynamic model of the AUV

In this section, the dynamic model from the actuator (4motors) and the position is studied. This part can be decoupled

Fig. 4. Prototype Side View

into three subsections and provides the formulation for the control strategy. The general approach of the modeling of a remotely operated vehicle (ROV), an AUV or other underwater vehicles are discussed in [1], [2] [3], [4]. In this paper, some results are revisited, further simplification of the model are derived to help design a more efficient control system.

1) Actuator Dynamics: In our work an actuator is thewater pumps. The dynamic relation of the setting value ofthe speed controller and real-time speed of motor is describedin Equation (1). A single lag model is used to model the real-time speed ωi of the motor i and the setting input value ui.

ωi(s) =1

Tms+ 1ui(s) (1)

2) Force and Moment Generation Process: This part ana-lyzes how the force and moment are generated and applied to the AUV. There are three types of force applied on the vehicle, weight and buoyancy force and moment, water pump propulsion force and moment and AUV fluid dynamic force and moment

a) Weight and Buoyancy: The gravitational force andbuoyant force are defined in terms of the global coordinate system so they must be transformed to the local coordinate systems.

Fw = mg[ − sin θ cos θ sinφ cos θ cosφ

](2)

The buoyancy force is as

FB = −ρgV [ − sin θ cos θ sinφ cos θ cosφ]

(3)

Where g is the gravitational acceleration, ρ is the fluid densityand V is the volume of the fluid displaced by the vehicle. Themoments generated by these forces can be expressed in termsof the positions of the center of mass C and the center of thebuoyancy B [1].

GW = RC × FW , GB = RB × FB (4)

Where RC and RB are the respective positions of the centerof mass and the center of buoyancy in the local coordinatesystem.

The AUV designed in this paper is aligned to be neutrally buoyant which means Fw = FB . It is also aligned to be naturally stable, which means the two of three Euler angles φ, θ are close to zero. The moment generated by the buoyancy force and gravity force can be simplified as follows.

τxs = GW • d • sin(φ) ≈ GW • d • φ (5)

τys = GW • d • sin(θ) ≈ GW • d • θ (6)

Where d is the distance from the gravity center and buoyancycenter. The stabilization moments τxs, τys are always tryingto maintain stability, which means the larger the d, the morestable the vehicle.

b) Water Pump Propulsion Force and Moment: Thequadcopter model is well studied in [5]. Similarly, the resultantforce and moment of a thruster configuration consisting of Nthrusters can be expressed as the vector sum of the force andmoment form each individual thruster:

FT =∑N

FTi (7)

GT =∑N

GTi +∑N

RTi × FTi (8)

Where RTi is the position of the ith thruster in local coordi-nates. The magnitudes of the thruster and torque generated bythe ith thruster can be expressed as:

|FTi| = KTiρn2iD

4i (9)

|GTi| = KQiρn2iD

5i (10)

Where Di is the diameter of the thruster, ni is the angular speed of the thruster shaft and KTi and KQi are the thruster and torque coefficients of the thruster. The major problem that is encountered in thruster modeling is that they behave as highly nonlinear actuators. Therefore, the thruster and torque coefficients cannot be represented as being constant but rather must be expressed as functions of the advanced coefficient. J = V/nD. Where V is the axial speed of the thruster.

Ti = bω2i (11)

mv =

⎡⎣ 0

0mg

⎤⎦−R(Θ)

⎡⎣ 0

0Tb

⎤⎦ (12)

Tb =

⎡⎣ 1

00

⎤⎦ b(ω2

1 + ω22 + ω2

3 + ω24) (13)

τyt = lb(−ω21 − ω2

2 + ω23 + ω2

4) (14)

τzt = lb(ω21 − ω2

2 − ω23 + ω2

4) (15)

⎡⎢⎢⎣Tτxτyτz

⎤⎥⎥⎦ =

⎡⎢⎢⎣

−b −b −b −b0 0 0 0

−lb −lb lb lblb −lb −lb lb

⎤⎥⎥⎦

⎡⎢⎢⎣ω21

ω22

ω23

ω24

⎤⎥⎥⎦ (16)

Linearize the above equation at a operation points:[ω1 ω2 ω3 ω4

]T=

[ω0 ω0 ω0 ω0

]T

ΔT = −bω0

[1 1 1 1

]⎡⎢⎢⎣

Δω1

Δω2

Δω3

Δω4

⎤⎥⎥⎦ (17)

Δτy = lbω0

[ −1 −1 1 1]⎡⎢⎢⎣

Δω1

Δω2

Δω3

Δω4

⎤⎥⎥⎦ (18)

Δτz = lbω0

[1 −1 −1 1

]⎡⎢⎢⎣

Δω1

Δω2

Δω3

Δω4

⎤⎥⎥⎦ (19)

The control law design needs to discover a power combina-tion of the vector

[Δω1 Δω2 Δω3 Δω4

]Tto generate

the ΔT , Δτy , Δτz .the following equation is a candidate toachieve this goal.⎡

⎢⎢⎣Δω1

Δω2

Δω3

Δω4

⎤⎥⎥⎦ = −

⎡⎢⎢⎣

1111

⎤⎥⎥⎦ bω0ΔTb

+

⎡⎢⎢⎣

−1−111

⎤⎥⎥⎦ lbω0Δτy +

⎡⎢⎢⎣

1−1−11

⎤⎥⎥⎦ lbω0Δτz

(20)

Equation (20) is used to derive the control law in the followingsection.

c) AUV Fluid Dynamic Force and Moment: The AUVbody has a complex shape and therefore the modeling of the complex behavior is almost impractical. From the control system point of view, the most important thing is the simplified model at the operation points.

The drag equation of fluid is:

fD =1

2ρv2CdA (21)

Where ρ is the density of the fluid, v is the speed of theobject relative to the fluid, Cd is the drag coefficient, A is the reference area. In the vector form:

FD =1

2ρ

⎡⎣ CdxAx 0 0

0 CdyAy 00 0 CdzAz

⎤⎦⎡⎣ sign(vx)v

2x

sign(vy)v2y

sign(vz)v2z

⎤⎦CdA

(22)

Where Cdx, Cdy, Cdz and Ax, Ay , Az, are the damping coefficients for the x, y, z directions.Similarly for the rotational moment is:

τD = −1

2

⎡⎣ Cωx 0 0

0 Cωy 00 0 Cωz

⎤⎦⎡⎣ sign(ωx)ω

2x

sign(ωy)ω2y

sign(ωz)ω2z

⎤⎦ (23)

To summarize, the overall force f b and moment τ applied toAUV is as follows:

f b = Tb + FD (24)

τ =

⎡⎣ τxsτyy0

⎤⎦+

⎡⎣ 0τytτzt

⎤⎦+ τD (25)

where Tb fD τxs τys τyt τzt and τD are defined in Equations (13), (22), (5), (6), (14) ,(15).

3) Rigid Dynamics of the AUV Body: This section discussesthe relationship of the body force, velocity and angular veloc-ity, attitude and position in the navigation reference frame.

Revisiting the notations in [6], the equations of motion for arigid body subject to body force fb ∈ R3 and torque τb ∈ R3

applied at the center of mass and specified with respect to the

body coordinate frame is given by the Newton-Euler equationin the body coordinate which can be written as:[

mI 00 I

] [vb

ωb

]+

[ωb ×mvb

ωb × Iωb

]=

[f b

τb

](26)

Where vb ∈ R3 is the body velocity vector, ωb ∈ R3 is the body angular velocity vector, m ∈ R, specifies the mass, I ∈ R3×3 is an identity matrix and I ∈ R3×3 is an inertial matrix. The effects of added mass [1] will influence the total mass m and total moment of inertial matrix J. There will be large uncertainties in those parameters.

The position and velocity of the AUV center of gravity aregiven by P ∈ R3 and vp = P ∈ R3, respectively, expressed tothe spatial frame in North-East-Down orientation. Let R ∈ SObe the rotation matrix of the body axes relative to the spatialaxes and vector. R can be parameterized by the ZYX Eulerangles with φ, θ and ψ about the x, y and z axes respectively.

R(Θ) = exp(zψ) exp(yθ) exp(xφ)

=

⎡⎣ cθcψ sφsθcψ − cφsψ cφsθcψ + sθsψcθsψ sφsθcψ + cφcψ cφsθsψ − sθcψ−sθ sφcθ cφcθ

⎤⎦ (27)

Where x =[1 0 0

]T,y =

[0 1 0

]T,z =[

0 0 1]T

and cθ and sθ are abbreviations for cos(θ)and sin(θ) respectively and similarly for the other terms.By differentiating R(Θ) respect to time, we have the stateequations of the Euler angles Θ =

[φ θ ψ

]T, which are

Θ = Ψ(Θ)ωb

⎡⎣ φθψ

⎤⎦ =

⎡⎣ 1 sθtθ cφtθ

0 cφ −sφ0 sφcθ cφ/cθ

⎤⎦ωb (28)

Where tθ is an abbreviation for tan(θ). In the ZYX Euler an-gle parameterization of rotation matrix, there are singularities

at θ = ±π/2. For the following discussion, we assume that thetrajectory of AUV does not pass through the singularities. Ifthe trajectory is required to pass through the singularities, wecan simply switch to another chart parameterizing the rotationmatrix. By using the fact that vb = Pvb, we can rewrite themotion equations of a rigid body as:

⎡⎢⎢⎣

pmv

ΘIωb

⎤⎥⎥⎦ =

⎡⎢⎢⎣

vRT (Θ)f b

Ψ(Θ)ωb

τ − ωb × Iωb

⎤⎥⎥⎦

p =

⎡⎣ xyz

⎤⎦ ,Θ =

⎡⎣ φθψ

⎤⎦

(29)

Equation (29) summarize the overall dynamic model of the AUV, where f b and τ are defined in Equations (24) and (25).

B. Attitude Control of the AUV

Based on the dynamic model of the AUV, this sectionstudies the control law design to control the attitude of theAUV. This part is also the foundation of the auto-pilot designin the next section. Here a PID control law for pitch andyaw angle control is presented. Simulation results are alsopresented in the following section.

Based on the analysis of Equation (20), the overall controllaw is given as follows:

u =

⎡⎢⎢⎣ω1

ω2

ω3

ω4

⎤⎥⎥⎦ =

⎡⎢⎢⎣

1111

⎤⎥⎥⎦ uT +

⎡⎢⎢⎣

−1−111

⎤⎥⎥⎦ uτy

+

⎡⎢⎢⎣

1−1−11

⎤⎥⎥⎦uτz

(30)

Where uT , uτy , uτz is the control channel for the total thrust,pitch angle and yaw angle. Letting θd, φd be the desired pitchand yaw angle, eτy = θd − θ and eτx = φd − φ, the controllaw is given as follows:

uτy = kpyeτy + kdyeτy + kiy

∫eτy (31)

uτz = kpyeτz + kdz eτz + kiz

∫eτz (32)

C. Auto-Pilot Design of the AUV

In this section the auto-pilot design of the AUV is discussed.The control system structure is shown in Figure 5, a pathfollowing controller must make real time decisions to generatethe attitude command and thrust command base on the currentposition and velocity and the desired trajectory. The thrustcontrol signal uT is generated based on the desired velocity.The attitude command θd, φd is also generated from the pathfollowing controller. The control laws are well studied in [7],[8], [9], due to the time and page limitation, the details of thepath following algorithm are not discussed in this paper.

Fig. 5. Diagram for the auto-pilot design for the AUV

V. SIMULATION RESULTS

A. Open Loop Response

The AUV dynamic model described in Equation (29) is implemented in Matlab Simulink. The simulation parameters, I moments of inertia and m AUV body mass, are closed to the AUV body design. The other coefficients are tuned such that the response of the Simulink model is closed to the real response, at least they are in the same time and space scale. Figure 6 is the natural response of the AUV with an initial Euler angle φ0 = 2 0 o and θ0 = 1 0 o. The gravity and buoyancy force can make the vehicle balance by itself. It can be seen that the pitch response is a lot slower than the roll response. This is due to the damping coefficients τD in the pitch direction is much larger that in the roll directions. These coefficients are based on the experiment experience. The roll angle recovery time is much shorter than the pitch angle. Due to the rigid body coupling of the three angles, there is still a little response in the yaw direction, after the dynamic transient, yaw angle ψ can maintain equilibrium at any value. The acceleration curve, shown in Figure 7, is also studied to determine the parameter of the thrusters. Based on the maximum cruse speed, the thrust coefficients b is chosen to make the data close to the real model.

B. Closed loop Response

When the control signal uτy and uτz is implemented asdefined in Equation (31), (32), the attitude response is shownin Figure 8 and Figure 9. The RPM command sent to thefour water pumps is shown in Figure 10 and the verticaldisplacement is shown in Figure 11.

VI. CONCLUSIONS

In this paper, a novel design of a low cost autonomous underwater vehicle driven by four water pumps is developed. The dynamic model of the AUV is derived and simplified for the control system design. Based on the linearized model, a control strategy is designed for the attitude control. Simulation results validated this design. The auto-pilot system structure is also presented.

Future design work is to include the addition of a water-tight containment vessel to house the required electronics, suchas the modem boards, motor controllers and microcontrollers.Additionally, an active ballasting system is necessary to adjustthe buoyancy force in real-time.

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Fig. 6. Natural Angular Response

Fig. 7. Acceleration Curve

Fig. 8. Pitch Command Tracking

Fig. 9. Yaw Command Tracking

Fig. 10. Control signal (RPM) command for the four water pumps

Fig. 11. AUV vertical velocity