Development of an Above Knee Prosthesis using MR Damper

and Leg Simulator

Jung-Hoon Kim and Jun-Ho Oh

Machine Control Laboratory, Dept. of Mechanical Engineering, KAIST373-1, Kusong-dong, Yusong-gu, Taejon, 305-701, Republic of KoreaE-mail: maysmile@ohzlab.kaist.ac.kr , junhoh@ohzlab.kaist.ac.kr

Abstract

Because conventional above-knee prostheses are passivetype device with constant mechanical properties, kneejoint motions are not similar to that of normal persons.On the other hand, active type prostheses can improveswing phase gait but these are expensive, heavy andconsume large energy. So the semi-active type prosthesesare presented. We propose to use the rotary MR damper.The torque dissipation in the knee joint can be controlledby the magnetic field induced by solenoid. The 3 DOF legsimulator has been also developed to generate various hipmotions and analyze the results of walking motions. Thissimulator is useful in designing suitable prosthesis for thehandicapped. Tracking control of knee joint angle wasperformed with this leg simulator. The experiment showsthat the proposed prosthesis system has goodperformance in swing phase. As a controller, we appliedthe repetitive controller in conjunction with a computedcontrol law and PD control law. This algorithm reducedRMS tracking error as the repetitions of the tracking.Moreover, the proposed prosthesis system is adaptable towalking speed.

1 Introduction

The gait of human is periodic repetitions of the stancephase in which a foot is on the ground and the swingphase in which the lower lamb moves after toe-off. Thefunctional requirements of above-knee(AK) prosthesesare providing knee locking during stance phase anddamping during the swing phase. Many kinds ofconventional AK prostheses are based on the passive typemechanism with constant mechanical properties such asfriction, spring and damping coefficients. However, thesedesigns are unable to realize the natural gait due to thelack of active knee joint control. On the other hand, activetype prosthesis such as hydraulic actuator, can producethe natural gait similar to that of normal persons easily,

but it is expensive, heavy and consumes large energy.[1]Therefore, the semi-active type prostheses have beendeveloped because they have the best features of passiveand active system. In 1983, A.Bar et al. applied on-offcontrol using four solenoid valves and realized the 16damping level. They divided the walking cycle into tenstages and gave the appropriate damping level at eachstage. However, this device could not give smoothtransitions between damping level. [2] The Magnetoreological fluid(MR fluid) is the materialthat reversibly changes from a linear viscous fluid to asemisolid with a controllable yield strength when exposedto a magnetic field. The rotary MR damper is filled withthis material and the torque dissipation is controlled byapplying current to the solenoid. It is possible to realizemore natural gait than that of passive mechanism bycontrolling knee joint using MR damper In this study, MR damper satisfying the specification ofAK prosthesis is developed and the controller withmicroprocessor is designed. The prosthesis is assembledinto the 3 DOF leg simulator and tracking control of kneejoint angle for normal gait is performed. The leg simulatoris very useful tool in the design of suitable prosthesis forthe handicapped and in the analysis of walking motion.Finally, the gait period is estimated with the gyro sensorthat is attached into the thigh and the tracking control isperformed for the reference knee angle that is generatedbased on the gait period.

2 The Above Knee prosthesis systemComposed of Damper

2.1 System Modeling

The amputee’s swing leg is modeled as a two-link rigidbody chain representing the thigh and the shank in sagittalplane motion. The knee is modeled as a hinge joint withthe damper in figure 1. The ankle and the center of massare assumed to be fixed. The subscript 1,2 denotes thigh

0-7803-6475-9/01/$10.00© 2001 IEEE

Proceedings of the 2001 IEEE International Conference on Robotics & Automation

Seoul, Korea • May 21-26, 2001

3686

and shank . im are mass ,

ia are distance from the masscenter ,

iI are moment of inertia in the mass center, 1l is the

length of thigh, hx is horizontal movement of hip, and

hy isvertical movement of hip. The equations of motion can bewritten as

−=

+

+

=++

k

h

u

u

K

K

C

C

MM

MM

BuKCM

10

11

)(),()(

2

1

2

1

2

1

2221

1211

ηη

ηηηηη

&&

&&

&&& (1)

where

+−−++

=222221212

212122

122111

)cos(

)cos()(

amIalm

almlmamIM

ηηηη

η

: inertial matrix

−−−

=2121212

2221212

)sin(

)sin(),(

ηηηηηη

ηη&

&&

alm

almC

: Centripetal and Coriolis torques

++

+++=

)sinsin(cos

)sinsin)(cos()(

22222

1111211

gyxam

gyxlmamK

hh

hh

ηηηηηη

η&&&&

&&&&

: Gravitational torque and hip acceleration terms

=

2

1

ηη

η : vector of the thigh and shank angles

=

k

h

u

uu : input vector of the hip and knee torques

Figure 1 The amputee’s swing leg model

If it is assumed that the hip torque and the thigh angleare accord with normal person’s, all we has to consider incontrolling the knee angle is 2nd equation of (1). In ourexperiment, leg simulator generates hip torque and thighangle of normal person. So, the equation of motion to beconsidered is written as

),,(),( 22222121 hhk yxKCMMu &&&&&&&&& ηηηηη +++= (2)

Because we assumed that the knee is only composed ofthe damper,

ku is the torque acting on the damper.

2.2 Damper Model

The relation between angular velocity and dissipationtorque is represented as

)()( wsignBTTcwuT fk ++== (3)

where c is the damping coefficient when no field and itis came from pressure drop in the duct of the damper.

)(BT is the variable torque which can be controlled bymagnetic field. This model is shown in figure 2. Theoperating point moves parallel to the coefficient whenconstant magnetic field is applied.

Figure 2. MR damper Model

2.3 Basic Control Law

In order to track the desired knee angle, PD feedbackcontrol and computed torque method are introduced. Thecomputed torque terms cancel the nonlinear terms in thedynamic model and linearize the knee joint dynamicsystem. The control signal which tracks the desired knee angle

2dη is written as

)(),(

)(

22

222121

ηηηηη

KC

eKeKMMu pvdc

+++++=

&

&&&&& (4)

where

2dη : desired knee angle trajectory

22 ηη −= de : tracking error

vp KK , : control gain ),,(2 hh yxK &&&&η term is simplified into )(2 ηK in eqn. (4) ,since the hip accelerations

hh yx , are small.

T

)(BT

fTw

c

)()( BTTwsigncwT f ++=

3687

Then, the control input T(B) is chosen as

1) if 0>w

<

>=

otherwiseT

Tif

TTifT

BT

p

p

BpB

00)(maxmax

(5)

2) if 0<w

−>

−<=

otherwiseT

Tif

TTifT

BT

p

p

BpB

00)(maxmax

(6)

where, maxBT : maximum variable torque

)(wsignTcwuT fkp −−=

3 Design of the Damper for Above KneeProsthesis

Figure 3 Structure of the damper

The rotary MR damper is made of the rotary cylinderwhich is filled with MR fluid and of which two ports areconnected each other. In this damper, the pressure drop inthe duct acts as a resistant force to the rotation.[3,4,5] Therelation between torque dissipation and pressure is givenby

fD T

PVT +

∆=

π2 (7)

where DV = Volumetric displacement

fT = Frictional torqueP∆ = pressure drop

The pressure drop in a valve mode device is composedof viscous component and an applied field dependentinduced yield stress component.[6]

g

LHcPP yp )(τ

η +∆=∆ (8)

where ηP∆ = pressure drop due to viscous flow

pc = 2 ~ 3 )(Hyτ = variable yield stress (controlled by magnetic field)

L = field lengthg = gap length

If the magnetic field is induced by moving a permanentmagnet instead of applying current to a solenoid, it hasadvantage in power consumption, but there exist timedelay in operating motor additionally.[3,4] Because fastresponse time is needed in tracking knee angle, a solenoidis selected as a magnetic field induction device. The structure of MR damper is shown in figure 3.Magnetic filed is applied in the upper plate of choke(choke: narrow and long passage, in which pressure dropis affected by viscosity ) and cross section of choke isrectangular. Magnet core is made of silicon steel, theresistance of coil is 10.6Ω and inductance is 1H. As acurrent supplier, PWM generator and amplifier are used.In addition, the upper plate of choke is made ofnonmagnetic material and the lower plate of choke ismade of soft steel in order to minimize the leakage flux.The gap of damper is selected as 2mm. [3,4]

Figure 4 Relation between PWM duty, torque andangular velocity (duty 100 correspond to 2 Ampere)

Figure 5 Controller for the MR damper

3688

Figure 4 shows the relation between PWM duty, torquedissipation and angular velocity for the damper. Figure 5shows the controller for the MR damper. It is composedof TMS320F240 DSP, AD converter, ROM, RAM, PWMAMP and serial communication module.

4 Leg Simulator

The leg simulator is used for generating the variousmovements of human thigh. This simulator shortens timeof developing AK prostheses and makes it possible to getreliable results from lots of experiments. The simulator infigure 6 has 3 DOF – horizontal, vertical and rotationalmovement. The linear actuator and ball screw generatehorizontal and vertical movements. Hip motor generateship rotation. Because only the acceleration terms affectthe dynamics of knee in the equation (2), we have no needto consider constant horizontal speed in

hx . i.e thesimulator have no reason to go on forward. The author’sgait data was used for reference data. The hip trajectoryand angle are shown in figure 7 & 8.

Figure 6. Appearance of Leg Simulator

Figure 7 Hip trajectory of Leg simulator

Figure 8 Hip angle of Leg simulator

5 Tracking Control of Knee Angle

Figure 9 AK prosthesis using MR damper

MR damper is attached in the thigh of simulator asshown in figure 9 and tracking control of knee angle isperformed. Repetitive controller in conjunction with aPD control law and computed control law is used for thecontrol algorithm. Repetitive control law is useful forknown periodic reference commands. Its control input iscalculated using the information of the error signal in thepreceding periods and can be expressed as follows

)1()()(1 +Φ+=+ kekuku jjj (9)

where Φ is the learning gain, k is time step in theperiod and the subscript indicates the repetition number. Itis reported that the repetitive control law with a computedtorque control law, or a PD control law, assures goodtracking performance when the desired trajectory is

3689

periodic and the period is known.[8] Moreover, It isdesirable to include a anti-windup concept when theactuator is operating at its saturation limit.[9] Tracking control of the knee angle have been carried outto examine the performance of the controller. Figure10(A) is the knee tracking error when PD control law andcomputed torque law are adopted. RMS errors are morethan 4° as the repetition.

1η is assumed to be known inthe experiment.

Figure 10 Comparison of RMS tracking erroras the repetition

Figure 10(B) is the knee tracking error when repetitivecontroller in conjunction with a PD control law andcomputed control law is used. This RMS error convergesas the repetition and the deviation of error is also small. Figure 11 shows the tracking control of knee as therepetition. Only initial angle was set to be coincided withthe reference as a initial condition, initial angular velocityand acceleration was set to zero in the experiment.

Figure 11 Relative knee joint angle tracking of PD + Computed torque + Repetitive control method

The time interval between 0.1sec and 0.4sec correspondsto the stance phase, in which the weight is applied on theground in the real environment. Large error was found in

this interval because the resistant force from the groundwas not applied to the foot. If the resistant force is appliedto the damper in the real environment, the damper shouldgive a maximum torque to achieve stability.

6 Estimation of Gait Period Using Gyro

In order to design the controller adaptable to the walkingspeed, the gait period should be estimated. Gyro sensor isattached to the thigh because person moves the thighactively. Gait period is estimated by measuring the zerocrossing interval of gyro signal.[7] Initial gait period isassumed to the normal walking speed and the updatedvalue of estimated value is determined by

)()()1( kekTkT α+=+ (10)

where )()()( kTkTke m −= : k-th error )(kT : k-th estimation period

)(kTm : k-th measurement period

α : weighting factor

After generating the reference knee angle trajectorybased on the estimated period, the tracking of thetrajectory has been performed. The result is represented infigure 12. At the transition of gyro signal from minus toplus sign, the period is estimated by the equation (10) andnew reference profile is generated. In the experiment, legsimulator is operated repeatedly with the 1.15sec period.At the start, the damper is maintained passively withoutcontrol until first zero crossing point is detected.

Figure 12 Knee joint angle tracking and estimation ofperiod

Relative knee joint angle is minus sign at the start since

3690

the proposed AK prosthesis is now the structure that canbe folded down inversely. In the estimation of period, αis 0.5 and initial period is assumed to 1 sec. The estimatedperiod converges in the 5~6 repetitions as shown in the figure.

7 Conclusion

In this study, we proposed rotary MR damper usingmicroprocessor as a control device for AK prosthesis. Wedesigned the MR damper that is controlled by applyingcurrent to a solenoid. The damper was attached into kneeof leg simulator and experimental tracking control ofabove knee angle was carried out. Leg simulator wasdesigned and this robot made it possible to developintelligent AK prosthesis. As the controller for tracking ofrepetitive reference profile, repetitive controller inconjunction with a PD control law and computed controllaw was adopted. Consequently, the algorithm reducedRMS tracking error and possibility of application for AKprosthesis was proved. Using gyro sensor attached in thethigh, the gait period was estimated and real timefeedback control adaptable to walking speed wasperformed based on the estimated period. As a futurework, structural reinforcement should be carried out toresist the sufficient weight at stance phase even thoughthe damper is passive condition without power supply.

Reference

[1] T.K.Wang, M.S.Ju and Y.G.Tsuei, "Adaptive Controlof Above Knee Electro-Hydraulic Prosthesis," Journal ofBiomechanical Engineering, Vol. 114, pp.421-424, 1992

[2] A.Bar, G.Ishai, P. Meretsky and Y. Koren, "AdaptiveMicrocomputer Control of An Artificial Knee in LevelWalking," Journal of Biomedical Engineering , Vol. 5,145-150,1983

[3] J.H. Kim, J.H Oh, "The design of low-power MRdamper using permanent magnet," In Prec. of the KSME2000 Spring Annual Meeting A, pp.433-439, 2000

[4] J.H. Kim, "A study on the design of valve mode MRdamper using permanent magnetic circuit," M.Eng. Thesis,Dept of Mechanical Engineering, KAIST, 1999

[5] S.H. Kim, "Constrained Rotary MR Damper Designand Its Application," M.Eng. Thesis, Dept of MechanicalEngineering, KAIST, 1998

[6] J.D.Carlson, D.M.Catanzarite and K.A.St. Clair,"Commercial Magneto-Rheological Fluid Devices",International Journal of Modern Physics B, Vol. 10, pp.

2857-2865, 1996

[7] J.C. Cho, "A Study on Control for Above-KneeProsthesis through Gait Analysis," M.Eng. Thesis, Dept ofMechanical Engineering, KAIST, 1998

[8] Tsai, M. C., Anwar, G. and Tomizuka, M., "DiscreteTime Repetitive Control for Robot Manipulators", IEEEInternational Conf. On Robotics and Automation, pp.1341-1346, Philadelphia, PN, 1988

[9] Y.S. Ryu and R.W. Longman, "Use of Anti-ResetWindup in Integral Control Based Learning andRepetitive Control," IEEE Int. Conf. on Systems, Man,and Cybernetics, Vol 3, pp. 2617 -2622, 1994

3691