Local Hand Control for Tezpur University Bionic HandGrasping ∗

Nayan M. Kakoty and Shyamanta M. HazarikaBiomimetic and Cognitive Robotics Lab

School of EngineeringTezpur University, INDIA

{nkakoty,smh}@tezu.ernet.in

ABSTRACTTezpur University (TU) Bionic Hand is a biomimetic ex-treme upper limb prosthesis. The Hand is intended to emu-late grasping operations involved during 70% of daily livingactivities and have been developed using a biomimetic ap-proach. This paper focus on the development of a local handcontrol for grasping by TU Bionic Hand. Grasp primitives:finger joint angular positions and joint torques are derivedthrough kinematic and dynamic analysis. TU Bionic Handemulates the grasp types following the dynamic constraintsof human hand. The joint angle trajectories and velocityprofiles of the Hand finger are in close approximation tothose of the human finger.

1. INTRODUCTIONA prosthetic hand needs to mimic the human hand both infunctionality and geometry. Higher functionality and con-trollability leads to stable grasping and therefore expectedto be readily accepted by amputees. But instead of a greatstride for prosthetic hands with optimal performance char-acteristics i.e. characteristics close to the human hand, therestill is a gap between state of the art prosthesis and humanhand grasping. The need for improving the functionality andcontrollability of the prosthesis arises from the desire to useprostheses as if it is a natural part of the body during DailyLiving Activities (DLA). To have such a prosthesis control,

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the control schema should satisfy the dynamic constraintsof human hand [18].

In previous research intending towards a human-like controlfor prosthesis, Electromyogram (EMG) signals have beenwidely used as an interface tool for prosthetic hands [1, 5].Successful results on EMG recognition would bring a su-perior control and replicates the neural control of humanhand. However, most of these are followed by only withon/off control for prosthetic arms depending on the resultsof EMG recognition [8, 13]. Current control schemes arenon-intuitive in the sense that the user is required to learnto associate muscle remnants actions to unrelated posturesof the prosthesis [4]. Further control is still rudimentary be-ing limited to a few hand postures or a simple proportionalestimate of force. In order to bridge the gap towards hu-man like control, a Local Hand Control (LHC) replicatingthe muskuloskeletal control of human hand is needed. Thiscan be implemented through a kinematic and dynamic anal-ysis of the prosthesis satisfying the dynamic constraints ofhuman hand.

To overcome the limitation of previous kinematic model ig-noring the state-space for multifingered robotic hand, Mon-tana [16] has provided a configuration-space description ofthe kinematics of the fingers plus-object system. A kine-matic model is developed for a dexterous end-effector topredict tendon tensions and tip forces during grasping andshows similar joint motion behavior to that of the humanhand [21]. Derivation of kinematic and dynamic equationsfor biomechanical analysis of human hand has been reportedin [19]. Robotic finger control technique using inverse kine-matics to find the joint angular position have been reportedin [22]. Inspite of all these great stride, none of the controlbased on above analysis are anywhere close to the naturalhand.

We concentrated on the development of a LHC for TezpurUniversity (TU) Bionic Hand. Grasp primitives: finger jointangular positions and joint torques are derived through kine-matic and dynamic analysis. The analysis explores the dy-namic constraints of human hand finger. The simulationresults shows that the joint angle trajectories and velocityprofiles of the prosthetic hand finger are in close approxima-tion to those of the human finger.

The rest of the paper is structured as follows: TU BionicHand and the proposed control architecture are described

in section 2. Section 3 describes the LHC following thekinematic and dynamic analysis of the Hand. The resultsobtained for TU Bionic Hand finger joint trajectories andvelocity are discussed in section 4. The paper concludeswith final comments are in section 5.

2. TU BIONIC HANDTU Bionic Hand shown in Figure 1 has been developed in-spired by human hand anatomy. For details on design anddevelopment of TU Bionic Hand, please refer to [11]. Forcompleteness of the paper, we are presenting a brief descrip-tion of TU Bionic Hand.

Figure 1: Ventral view of theTU Bionic Hand

TU Bionic Hand consists of five digits: four fingers and onethumb. Each finger consists of three links replicating thedistal, middle and proximal phalanx. The links are con-nected through revolute joints corresponding to distal in-terphalangeal (DIP) joint, proximal interphalangeal (PIP)joint and metacarpophalangeal (MCP) joint of human hand.Thumb consist of two links. The palm is two piece and canmove inward and outward to form grasps. The prototypejoint range motion and dimensions closely resembles the hu-man hand as tabulated in [11].

Table 1: Specification of the Actuating MotorsParameter ValueGear Ratio 0.03No load Speed 250 Revolutions per minuteNo Load Torque 0.0764 NmDiameter 160 mmLength 300 mmDiameter of motor pulley 10 mm

Abduction and adduction is not implemented in TU BionicHand. N + 1 tendon system is used as media to transmitforces from actuators to the joints. For N + 1 tendon system,see [17, chapter 5: p 299]. Extensor and flexor tendonsare placed on the dorsal and ventral side of each finger and

connected to individual actuation unit (a DC geared motor)embedded in the palm. The motors for flexion are placed onthe ventral side and for extension are placed on the dorsalside of the palm. Tendons are connected to the pulley ofthe motors, passing through a series of hollow guides. Thedeveloped prototype possess a total of (3 × 3 of fingers +2 of thumb + 1 of the palm + 3 of wrist) = 15 Degrees ofFreedom (DoF). Each finger tip is equipped with film likeforce sensors to measure the fingertip force applied on theobject to be grasped.

2.1 Control ArchtiectureFigure 2 shows the “LHC” within the control architecturefor TU Bionic Hand. The control is two layered: SuperiorHand Control (SHC) and LHC.

Prosthetic Hand equipped with Force Sensor

Fingertip force sensor feedback

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Supe

rior

Han

d C

ontr

ol Grasp Planning

Evoked Action Potentials or Electromyogram

Grasp Recognition Architecture

Machine Learning

Visual Feedback

Loc

al H

and

Con

trol

Grasp Primitives

PID Control

Kinematic Analysis

Dynamic Analysis

Actuation of Motors corresponding to the Grasp Recognized

Transformation of the Grasp Type into the fingers to be actuated

Grasp Type

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Figure 2: Schematic of Two Layered Control Archi-tecture. The dotted region highlights the LHC

In an earlier paper [12], we presented details of the SHC andhave shown an average recognition rate of 97.5% for the sixgrasp types: power, palm-up, oblique, hook, pinch and pre-cision. SHC provides the information about the grasp typeattempted by the user based on the forearm EMG signals.On recognition of the grasp type, classification architecturecommands the LHC to actuate the corresponding motors onthe prototype to replicate the identified grasp.

The LHC is the interface between the SHC and the pros-thetic hand. LHC identifies the fingers to be actuated forperforming recognized grasp. The finger actuation is con-trolled through a proportional-integral-derivative controller(PID) customized with fingertip force sensor. Based on thekinematic and dynamic analysis of the finger, grasp primi-tives i.e. finger joint angular positions and joint torques aredetermined. The Hand perform the six grasp types followingthe dynamic constraints of human hand.

3. LOCAL HAND CONTROLThe LHC is responsible for controlling the finger joint angu-lar positions and velocities following the dynamic constraintsof human hand [14]. The detailed LHC is shown in Fig-ure 3 wherein K, J, F and Td are motor constant, inertiaof finger links, frictional constant of the motor and externaldisturbance torque. The kinematic and dynamic analysisare computed in 40 msec., the PID controller settles the fin-gertip force at desired value in a period of 200 msec. andthe actuator outputs the desired force at the fingertip in aperiod of 8 msec.

Actuator

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+ + Fa

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Kinematic

Analysis (as detailed in

section 5.1)

Dynamic

Analysis (as detailed in

section 5.2)

(�1, �2, �3)�

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(�1,

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Controller (Kp + sKd + Ki/s)

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20 msec

20 msec

200 msec

8 msec

Figure 3: Detailed schematic diagram of LHC withproportional gain Kp = 200, differential gain KD =10 and integral gain KI = 100

The LHC maps the identified grasp type into the actuationof the corresponding motors [13]. Kinematic and Dynamicanalysis leads to evaluation of grasp primitives - finger jointangular position and joint torques. The finger joint angu-lar positions are obtained as detailed in 3.1. The desiredjoint torques τ = {τ1, τ2, τ3} calculated in accordance to thefinger model as detailed in section 3.2 are applied to theMCP, PIP and DIP. Using equation 17, the desired forceat the fingertips are calculated. The controller sends theactuating signal to the motors at time t = T0. On estab-lishing contact between the fingertip and the object beinggrasped, the force sensor sends a signal to the controller attime t = T1 and the controller stops the actuating signal.The time duration of actuation of the motor is calculatedas δt = T1 − T0. On establishing contact by fingertip withthe object to be grasped, the extensor motor is stalled. Theflexor motor torque is controlled to prevent the fingertipforce from exceeding the desired force. From the force sen-sor, the actual force is measured. The difference between themeasured force and desired force is the error to minimize. Atypical PID controller is used to reduce the error. The LHCprevents the fingertip force from exceeding a critical valuewith the joints at a pose for the grasp attempted. Followingthe neuromuscular time constraint [9], LHC commands theprosthesis to form the attempted grasp in an approximateperiod of 250 msec.

3.1 Kinematic AnalysisTo discuss the kinematics and dynamics of a finger, we con-sider a planner schematic structure of the index finger; asshown in Figure 4; wherein each link Li(i = 1, 2, 3) corre-sponds to the proximal, middle and distal phalanges. MCP,PIP and DIP joint angles are θ1, θ2 and θ3 respectively. Theinitial forward kinematics based on Denavit-Hartenberg (D-

H) parameters of the schematic representation in Figure 4is presented in Appendix-I.

Yo

Y1

Y2

�3 23

L3 DIP �2

L2

PIP 22

L1 �1

MCP 21

Xo

Zo

Z1

Z2 X1

X2

Figure 4: A planner schematic structure of the indexfinger

Direct kinematic equations are used to obtain the fingertipposition and orientation according to the joint angles. Withthree revolute joints, the finger has three rotational DoF (θ̄= {θ1, θ2, θ3}T ) leading to the finger end effector having pose(x̄ = {x , y , α}T ). For kinematic analysis, the first step is toestablish the mapping from joint angles (the vector of threegeneralized rotational coordinates θ̄ ={θ1, θ2, θ3}T ) to linkend point position and orientation of the finger for a givenset of link lengths L̄ = {L1, L2, L3}. From the Denavit-Hertenberg parameters of the finger as stated in Table 2, thefingertip pose x̄ with respect to the base frame (Xo, Yo, Zo)can be computed as:

x̄ = G(θ̄) =

2

4

Gx (θ̄)Gy(θ̄)Gα(θ̄)

3

5 (1)

2

4

xyα

3

5 =

2

4

L1C1 + L2C12 + L3C123

L1S1 + L2S12 + L3S123

θ1 + θ2 + θ3

3

5 (2)

where G(θ̄) is the geometric model defined by the trigono-metric equations for the end point position {x , y}T and ori-entation {α} of the last link as a function of θ̄ and linklengths of the finger L̄. C1 ,C12 and C123 denotes cos(θ1 ),cos(θ1 + θ2 ) and cos(θ1 + θ2 + θ3 ) and S1 ,S12 and S123 de-notes sin(θ1 ), sin(θ1 + θ2 ) and sin(θ1 + θ2 + θ3 ) respectively.

Since flexion and extension is performed by pulling and re-leasing the flexor and extensor tendons, the joint angles de-pends on the tendon length pulled (lm) and released (lm′)by the motors [10]. Tendon length while the finger is max-imally extended is lo = L1 + L2 + L3 . When the finger is

flexed, the flexor tendon is pulled by the motor. Let lx bethe resulting flexor tendon length and θ1 , θ2, θ3 be the jointangles respectively. Change in flexor tendon length lm is thedifference of lo and lx.

lm = lo − lx

= (L1 + L2 + L3 ) −(L1C1 + L2C12 + L3C123 ) (3)

In order to replicate the motion feature of human fingerinto the prototype, we considered the dynamic constraintsof human fingers. Following the anatomical and empiricalstudies on linear relationship between finger joints presentedin [14], following constraints which relates one joint angle toanother are used:

θ1 = 0.5θ2 (4)

θ2 = 1.5θ3 (5)

Substituting the above constraints i.e, equations (4) and (5)into equation (3), we have the following relation between θ1

and lm.

lm = (L1 + L2 + L3 ) − (L1 cos(θ1 )

+L2 cos(2.θ1 ) + L3 cos(4.θ1/3 )) (6)

In a similar way, the length of the extensor tendon releasedby the motor is given as:

lm′ = (L1 + L2 + L3 ) + (L1 cos(θ1 )

+L2 cos(2.θ1 ) + L3 cos(4.θ1 /3 )) (7)

Since, lm is the length of the tendon pulled by the motor;lm can be computed using equation 7 given diameter of thepulley connected to the motor, d; time of rotation of themotor, δt and revolution per minute of the motor, N .

lm = πdN δt (8)

The values of d and N are known a priori as tabulated inTable 1. δt is computed from force sensory feedback. Thestart time is achieved from initiation of the actuating sig-nal to the motor and the time of contact is on receiving afeedback signal from fingertip sensor.

3.2 Dynamic AnalysisFor dynamic analysis, we refer to the schematic represen-tation of the finger in Figure 5. Tendon routing the fingerjoints d1, d2 and d3 are the distance of the center of mass ofthe phalanges from the respective joints MCP, PIP and DIP(E1, E2 and E3) respectively. I1, I2 and I3 are the moment ofinertias of the three phalanges about an axis passing throughtheir center of masses. m1, m2 and m3 are the masses of theproximal, middle and distal phalanges respectively. a and bare half the finger width and distance of the tendon guidesform the finger joints. Lagrangian method was used to de-rive the mathematical model of the finger [17]. The tendonswere assumed to be inextensible and inertial effects of thepulley and all frictional effects are neglected. The dynamicequation can be written starting from the Lagrangian for-mulation as:

[M (θ)]θ̈ + [C (θ, θ̇)] + G(θ) = τ (9)

where [M(θ)] is 3 x 3 mass matrix of the finger; C[θ, θ̇] is3 x 1 vector and includes the coriolis terms and centrifugalterms, G(θ) is 3 x 1 vector of the gravity terms and τ is 3

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Z o

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pulley

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b

b

Figure 5: Schematic of the finger representing ten-don routing, center of mass and moment of inertiasof the phalanges in the finger

x 1 generalized torque input vector on phalanges (producedby tendons).

The chain like nature of a manipulator leads us to considerhow forces and moments propagate from one link to thenext originating at the actuator. Typically the finger appliessome force on the object to be grasped with the free end.We wish to solve for the joint torques which must be actingto keep the system in static equilibrium. In considering thestatic forces in a manipulator, we first lock all the joints sothat the manipulator becomes a structure at the point thefinger touches the object to be grasped. We then considereach link in this structure and write a force moment balancerelationship in terms of the link frames. Finally, we computewhat static force must be acting about the joint axis for themanipulator to be in static equilibrium.

The joint torques exactly balances the finger tip force inthe static equilibrium situations. The Jacobian transposemaps finger tip forces into equivalent joint torques [17]. Therotational kinetic input to the end effector is the net ofthree torques (τ = {τ1, τ2, τ3}T ) at MCP, PIP and DIPjoints respectively to produce the output wrench vector (W̄= {fx, fy , τz}T ). The transformation from joint torques τwhich balances the wrench vector W̄ is given by,

τ̄ = J(θ̄)T (W̄ )

=

" −L1S1−L2S12−L3S123 −L2S12−L3S123 −L3S123

L1C1+L2C12+L3C123 L2C12+L3C123 L3C123

1 1 1

#T

.

"

fx

fy

τz

#

where J(θ̄) is the Jacobian matrix relating the joint space tothe finger tip space. It is partial derivatives of the geometric

model of the link chain given by equation 2 with respect toθ̄. Next, we wish to describe how forces applied at the end ofthe tendons are related to the torque applied at the joints.Following [17], the extension function 1 for the flexor andextensor tendons are given as:

h1 (θ)=lm+2p

a2 +b2 cos(tan−1(a/b)+θ1/2 )−2b−R2 θ2−R3 θ3

(10)

h2 (θ) = lm′ + R1θ1 + R2 θ2 + R3 θ3 (11)

The coupling function relating the tendon force and the jointtorques is computed as:

Hc =

2

4

dh1/dθ1 dh2/dθ1

dh1/dθ2 dh2/dθ2

dh1/dθ3 dh2/dθ3

3

5 (12)

Now the joint torque in terms of tendon force is given as:

τ̄ = Hc.F (13)

=

2

4

−√

a2 + b2sin(tan−1(a/b) + θ1/2) R1

−R2 R2

−R3 R3

3

5

.

»

F1

F2

–

(14)

where F1 and F2 are the forces on the flexor and extensortendons respectively.

Considering the motor torque for flexion of the finger as T1

and r as the radius of the pulley connected to the motor, wehave

F1 = T1/r (15)

For a serial manipulator with pivoted joints τz = 0. Fol-lowing the work reported in [7], we measured the force inthe direction of the object to be grasped i.e. fx using thesensors placed at the fingertip and fy = 0 assumed. Consid-ering these, equation 10 becomes

τ̄ = J(θ̄)T (W̄ )

=

"−L1S1 − L2S12 − L3S123 −L2S12 − L3S123 −L3S123

L1C1 + L2C12 + L3C123 L2C12 + L3C123 L3C123

1 1 1

#T

.

"

fx00

#

(16)

From equation 14 and 16, we have fx, desired fingertip forceas follows:

1Extension function measures the displacement of the endof the tendon as a function of the joint angles of the finger

fx =−

p

(a2 + b2 )(sin(tan−1((a/b) + θ1/2)F1 + R1F2

−L1S1 − L2S12 − L3S123

(17)

4. RESULTS AND DISCUSSIONSThe LHC emulates the grasps type in the Hand followingthe dynamic constraints of human hand finger through aPID controller. We have used RoboAnalyzer V.4 [20] forkinematic and dynamic analysis of the prosthetic hand. Wereport analysis for the hand performing a pinch grasp. Thepinch grasp is used for grasping small object like pen, penciletc. Preshaping of the grasp is performed by flexing theindex finger and thumb in opposition. For our experiment,the index finger and the thumb moves towards each otherfrom a tip to tip angular distance of 175◦. The object tobe grasped is hold between the index finger and the thumb.The other fingers remain fully extended during execution ofthe grasp. Figure 6 shows the index and thumb end positionduring pinch grasp.

0 10 20 30 40 50 60 70 80 90 100−80

−60

−40

−20

0

20

40

60

80

100

120

Ang

ular

Pos

ition

in D

egre

e

Time in msec

Figure 6: End Position of the Index Fin-ger and Thumb during Pinch Grasp

On establishing contact with the object to be grasped ataround 80-100 msec, finger end positions are retained. Fig-ure 7(A), (B) and (C) shows the MCP, PIP and DIP jointtrajectories of the index finger for TU Bionic Hand. Thesehas been derived following inverse and forward kinematicsimulations as stated in [20]. It has been found that the PIPjoint moves at a rate of 2.06 (i.e. y/x in Figure 7) times tothat of the MCP joint and 1.61 (i.e. y/z in Figure 7) times tothat of the DIP joint; which follows the dynamic constraintsof the human hand closely as stated in equation 4 and 5.The finger joint trajectories of human hand as reported in[15] is shown in Figure 7(D). As can be seen, the finger jointtrajectories of the Hand are in close approximation to thehuman finger joint trajectories.

Figure 8(a) shows the velocity profiles of prosthetic handindex finger joints. Velocity profile of human hand fingersas reported in [3] is shown in Figure 8(b). The velocity pro-files of TU Bionic Hand are in line with the velocity profileof human fingers. This also satisfies the statement that the“velocity profiles of the finger joints are bell shaped” as re-ported in [2].

�

�

�

A

B

C

�

�

�

x

y

z

D

Figure 7: Joint Trajectories of Prosthetic Hand In-dex Fingers: (A) MCP Joint (B) PIP Joint (C) DIPJoint. (D) Human Hand Index Finger (Figure ’c’adapted from [15]).

Figure 8: Velocity profiles of (a) Prosthetic HandIndex Finger Joints (b) Human Hand Finger MCP(solid line) and PIP (dotted line) joints (Figure ’b’adapted from [3]).

5. FINAL COMMENTSDevelopment of a LHC for TU Bionic following the dynamicconstraints of human hand is reported. The grasp primi-tives: finger joint angular positions and joint torques arederived through kinematics and dynamics. The simulationresults depicts that TU Bionic Hand follows the human handdynamic constraints closely. The joint angle trajectories andvelocity profiles of the prosthetic hand finger are in close ap-proximation to those of human finger. Embedment of thecontrol architecture for the developed TU Bionic hand ispart of ongoing research.

AcknowledgmentThe authors gratefully acknowledge Prof. S. K. Saha fromthe Indian Institute of Technology, Delhi, INDIA for hishelpful suggestions and comments in carrying forward theresearch reported here. Financial support received from De-partment of Electronics and Information Technology, Gov-ernment of India through its project Design and Develop-ment of Cost-effective Bio-signals Controlled Prosthetic Hand;1(9)/2008-ME & TMD is gratefully acknowledged.

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Appendix-IThe Denavit-Hartenberg parameters [6] describing the fingerkinematics are illustrated in Table 2; where θi is the jointangle from the Xi−1 axis to the Xi axis about the Zi−1 axis,d1 is the distance from the origin of the (i− 1)th coordinateframe to the intersection of the Zi−1 axis with the Xi−1

axis along the Zi−1 axis, ai is the offset distance from theintersection of the Zi−1 axis with the Xi axis and αi is theoffset angle from the Zi−1 axis to the Zi axis about the Xi

axis with i = 1, 2, 3.

Table 2: Denavit-Hartenberg Parameters of the Fin-ger

Link αi−1 ai−1 di θi

1 0 0 0 θ1

2 0 L1 = 30 mm 0 θ2

3 0 L2 = 25 mm 0 θ3