Design of Variable-Damping Control for ProstheticKnee based on a Simulated Biped

Jie Zhao∗, Karsten Berns∗, Roberto de Souza Baptista†, Antonio Padilha L. Bo†∗Robotics Research Lab, Department of Computer Science, TU Kaiserslautern, Kaiserslautern, Germany

{zhao, berns}@cs.uni-kl.de†Automation and Robotics Laboratory, Unversity of Brasılia, Brasılia, Brazil

baptista@ieee.org, antonio.plb@lara.unb.br

Abstract—This paper presents a new variable-damping con-troller for a prosthetic knee. The development is also based ona novel approach: using a simulated biped robot for evaluatingdifferent prosthesis designs and controllers before real tests areconducted on humans. The simulated biped incorporates severalfeatures of human walking, such as functional morphology,exploitation of inherent dynamics, hierarchical control network,combination of feed-forward and feedback controllers and phase-dependent modulation and so on. Based on this virtual model ofhuman walking, we have studied biomechanical aspects of kneeduring walking and then developed a controller based on thedamping profile developed by simulated bipedal robot throughouta gait cycle. This controller has been evaluated on a modifiedversion of the simulated biped, in which a model of a prostheticleg under construction has been incorporated. This simulatedbiped is 1.8 m in height and 76 kg in weight with 21 degreesof freedom. Results of such experiments for walking on flatand rough terrains have provided satisfactory outputs, includingimproved robustness.

I. INTRODUCTION

Amputation of lower limbs, either due to trauma, infectionsor other causes, may potentially decrease considerably the per-son’s quality of life. Walking is obviously of prior importanceamong the basic movements affected. This paper is related tothe use of new tools in the development of control strategies forartificial legs, since current prosthetic legs are not yet capableof completely restoring functionalities.

To improve walking capability for handicapped peopleresearchers examine various solutions. For instance, in thefield of functional stimulation and neuroprosthesics [1], [2],the control approach uses electromyographic signals capturedfrom muscles and nerves as stimulations to activate prosthesis.Another class of solution is the use of powered joints like thatpresented in [3] in which an ankle is controlled during thetoe-off to optimize energy efficiency and to increase stability.The powered knee prosthesis GeniumTM [4] developed byOtto Bock is commercially available. This microprocessor-controlled knee can anticipate movements of users and adaptinstantaneously in order to function as close to a natural legas possible. Nevertheless, the performance of this artificialknee under different walking conditions is not clear [5].Some researchers are looking into biological aspects of kneejoint during walking and then trying to transfer the findingsinto robotics or prosthetic legs. Based on electromyographanalysis [6]–[8] proposed a central control unit generatingcommands for synergistic muscle primitives and reflex actions.In accordance with their work, human walking tends to be

combined of five phases which can be affiliating to kineticor kinematic events: weight acceptance, leg propulsion, trunkstabilization,leg swing, and heel strike [9]. Found by [10],maximum energy consumed in walking comes from the legswing phase, which starts from the toe-off event and ends justwhen heel strike event is achieved. The knee joint is alwayskeeping stiffen to provide enough support for human in stancephase while it is providing damping to prevent hyperflexionand hyperextension. Therefore, a variable-damping knee pros-thesis with the capability of performing those functionalitiesis required. These knee prostheses are normally controlledby microcontroller or DSP to modulate the damping ratiosand adapt to different walking scenarios. Variable-dampingcontrolled knee prostheses have some advantages over passiveknee prostheses [11]. These advantages covers enhanced kneestability, more smoothness of knee gait and adaptation todifferent walking velocities.

The suggested methodology results from a kinematic andkinetic analysis based on a simulated biped, as shown in Fig. 1.The bipedal robot has human-like features, including 21 DoFs,the weight up to 76 kg and the height over to 1.8 m. TheNewton Game Dynamics1 is applied for dynamic calculationof rigid body. A biologically motivated control method isapplied to control this biped and capture the kinematic anddynamical data set from different experiment scenarios [9].The control architecture is designed as a hierarchical systemof feed-forward and feedback control units. A central patterngenerator coordinates the stimulation and synchronization ofvarious control units. Instead of using a dynamic model ofbiped, reflex controllers and motor patterns play the mostimportant roles in regulating locomotion of the biped. In nextsections, we describes working principles of this prosthetic legand its mechanical designs. We then study the kinematic anddynamical data captured from simulated biped, from whichwe extract a damping profile during leg swing phase within agait cycle. Afterwards, a finite-state machine that regulates theswitching of different phases is suggested. In accordance withthis profile, the corresponding variable-damping controller forinteresting walking phases is developed. At last, this controlleris tested within a simulated biped with a leg prosthesis andresults are demonstrated.

II. MECHANICAL DESIGN OF THE PROSTHESIS

The knee module of the ongoing prosthetic knee project isa polycentric knee mechanism with adjustable damping ratios.

1www.newtondynamics.com

A polycentric knee consists of any type of mechanism in whichthe center of rotation varies according to the angular position[12].

As in various polycentric knee designs, our polycentricmechanism is based on a four-bar linkage system [13]. Ina four-bar linkage system, the length of the bars determinesthe trajectory of the instantaneous center of rotation [14].The particular trajectory of a specific design brings manyadvantages to polycentric knees when compared to mono-centric ones [12]. In the stance phase if the instantaneouscenter of rotation is positioned posterior the Trochanter-Knee-Ankle (TKA) line, the system is considered a stable weightbearing system. Furthermore, if the instantaneous center ofrotation is located above the mechanical center of rotationof the mechanism, keeping the knee straight will require lesseffort from the user and will increase leverage for the residuallimb. In the swing phase the angular motion of the four-barlinkage mechanism may shorten its total length compared tothe full extension position. This characteristic is exploited toprovide foot clearance during the swing phase. The trajectoryof the instantaneous center of rotation also influences thedynamics of the mechanism, therefore the polycentric kneecan be designed to ease acceleration during the flexion anddeceleration during extension. In sum: the four-bar linkagemechanism applied to the design of prosthetic knees brings thefollowing advantages when compared to monocentic: stabilityin stance phase, total length shortening, and acceleration anddeceralation enhancement in swing phase.

Besides the advantages of the polycentric knee design, amagnetorheological piston is integrated to the prosthetic kneeto provide damping adjustment of the mechanism. Magne-torheological fluids alter its viscosity in the presence of amagnetic field. A piston, or damper, filled with this type offluid provides a continuously variable damping force controlledby a desired input [15]. In our project we used a commerciallyavailable magnetorheological piston from Lord Corporation. Inthis device, the magnetic field through the magnetorheologicalfluid is induced through an electric current, which is the controlinput to adjust the damping coefficient of the system.

The prosthetic knee prototype is currently in the finishingphase of production as shown in Fig. 1. The goal of this projectis to investigate different control strategies taking into accounthuman in the loop for above the knee amputees.

Fig. 1: Mechanical configuration of prosthesis in a simulatedbiped and prototype.

III. BIOMECHANICAL ANALYSIS OF KNEE JOINT

Understanding human walking and the dynamic propertiesin each phase is important for designing assistive devices thatmay improve gait robustness and performance. In this section,the knee biomechanics during different gait phases is studiedfor designing improved prosthetic knees. [6], [7] found thatwalking can be divided into five subdivisions, as shown inFig. 2, in which the knee biomechanics can be detailedlystudied.

A. Biomechanical Events at Knee joint

Through simulating a biped in a dynamic environment2within scenario of flat ground walking, kinematic data of kneealong gait cycle can be observed as in Fig. 3.

1) We consider that the first phase weight acceptancestarts just after full contact with ground of the swingleg, namely after both heels and toes contact. In thisphase the former leg supports the weight of uppertrunk. The former knee begins to flex until around20◦, that performs like a compressed spring withstored potential energy. In this phase, the knee canbe modeled as an angular spring.

2) When the maximum compression is achieved, theknee extends until maximum stance extension ap-proaches. This extension phase is called leg propul-sion, which makes the knee again act as an angularspring. The stiffness of knee keeps the same level asthat in first phase.

3) The third phase is characterized by double supportduring which stabilization of the body posture isguaranteed. By analyzing kinematics of knee, we findthat the knee begins to flex again for preparing legswing.

4) After happening of the toe-off event, the swing phasestarts, transferring the leg in front of the body, andthe flexion ends when knee angle achieves at around60◦. It extends consequently until knee of swing legis totally stretched. This phase includes both kneeflexion and extension. Observing torque and angle ofknee, we can theoretically calculate the work W andpower P on knee joint as following:

W = τ · θ (1)P = τ · θ. (2)

Where τ denotes the torque and θ and θ are individu-ally the joint revolution and velocity. The knee powerconsumption is generally negative (see Fig. 3) since ithinders knee angular velocity. Therefore in the swingphase, the knee can be modeled as a variable damper.

5) As soon as the swing leg’s knee is locked or itsheel contacts with ground, the last phase begins.It manages the foot impact during heel strike andprovides control concerning full contact of the foot.The knee should be again stiff to handle the impactof body weight.

2The detailed architecture, i.e. biologically inspired control of a dynamicallywalking bipedal robot can be found in [9]

Fig. 2: Walking phases for both legs and sensor events for switching phases [9].

B. Extraction of Damping Profile

As shown in Fig. 3, the knee generates a positive, resistivemoment during leg extension in swing phase. This negativepower portion of the gait cycle can be effectively modeledas a variable damper, as shown by biomechanical analysis inSec. III-A. Therefore, using Eq. 3, the effective damping co-efficient of the knee throughout swing extension is calculated:

Bk =τk

θk. (3)

The effective damping variable Bk is the ratio between theknee torque τk and knee velocity θk. By using the data setillustrated in Fig.3, one can calculate the damping coefficientdirectly as shown in 4. From Fig 4, we see the knee dampingBk decreases sharply when knee starts to flex from stancephase. Then Bk is mostly performing as a linear function ofknee angle up to the maximum value of knee flexion,. Afterextension of knee joint, Bk is nearly a linear function of kneeangle between 20◦ and 50◦. The damping coefficient alongincreasing and decreasing knee angle have the same courseduring swing phase. Since in the stance phase, the knee jointis stiff to keep stability of the upper body, we then think itsdamping coefficient goes very high. Thus we only consider thedamping coefficient in leg swing phase. According to Fig. 4,the damping coefficient can be represented as a function ofknee angle:

Bk(θk) =

Bklow+Bkup

−Bklow

θkup − θklow

· (θk − θklow) , if θk > θklow

∞, otherwise(4)

In Eq. 4 θklowand θkup

mean a range in which knee joint canbe modeled as a variable damper whereas Bklow

and Bkup

denote respectively the damping coefficient at θklowand θkup

.

IV. FINITE-STATE MACHINE FOR WALKING PHASES

From a biomechanical point of view, it is known thatwalking can be divided into distinct phases. However, forcontrolling a prosthetic leg based on these different walkingphases, those events and their features must be estimated inreal-time. We have to use limited sensors mounted withinprosthetic leg to decide the happening of critical events that

Fig. 3: Angle, velocity, torque and power consumption at kneejoint. The solid lines indicate mean values while dashed linesdenotes maximum and minimum values. The vertical dashedline denotes the toe-off event.

walking phase is transferred from one state to another. Theexisted sensors on prosthetic leg are encoders on each joint

Fig. 4: Knee damping coefficient along the knee angle duringgait cycle.

and four load cells on each foot. As existence of a hierarchicalcontrol architecture, sensor informations are introduced intothe Central Pattern Generators, i.e. CPG, which plays the roleas a central controller triggering state of walking phases.

A finite-state machine for cyclic walking is instrumentedto present a health knee, as illustrated in Fig. 2. Transitions ofgait phases are activated by three events, i.e., toe off, lockedknee and full contact. Therefore, the whole five gait phasescan be actually arranged in three states, which are respectivelyStabilization (ST), Swing (SW) and Heel Strike (HS). In orderto successfully activate the state machine, following variablesare required:

• Knee angle (θk) indicates the relative angle of kneejoint. Fully extended knee angle denotes θk = 0.Maximum knee angle is 2 rad/s.

• Ankle angkle (θa) denotes the relative angle of anklejoint in sagittal plane. Neutral position θa0

is setat the position that human is standing still. Angleof ankle is set larger than neutral angle θa0 whenplantarflexion is happening, whereas is smaller whenthere is dorsiflexion.

• Foot load (Fl) means loaded force on the foot basedon four force sensors respectively mounted on innertoe, outer toe, inner heel and outer heel. With

Fl =Fforce − Flow

Fup − Flow, if Fl ∈ [0, 1], (5)

where Fforce is the measured force, whereas Flow

and Fup indicating individually the lower and upperthreshold of vertical force on feet. Besides, the valueof Fl is limited in [0, 1]. It can be divided into HeelContact(H) and Toe Contact(T), in which 1 means fullcontact while 0 denotes no contact at all.

The elaborate descriptions are shown as follows:

1) When the heel strikes on the ground, the landing kneejoint bends a little due strong impact of upper body.However it maintains around equilibrium positionto support the weight of upper body, acting as alocked mechanism. After the forward transferring ofthe center of mass, the stored energy will be released.

Meanwhile the opposite knee prepares to start theswing. State switches when following two kinematicevents happened:• the ground contact detected by force sensors

mounted on feet is smaller than a predefinedthreshold value, e.g. Fl < Fthreshold1

and• due to plantarflexion of ankle joint, it grows

up till larger than neutral angle, e.g. θa > θa0.

2) Swing phase completely starts after toe-off. The kneeis bended due to the inertia of knee. The oppositeknee is again extended to the neutral angle to supportbody. As the knee flexes beyond θklow

, dampingcontrol has been applied to resist hyperflexion. Theposition tracking in flexion phase is not necessarysince it utilizes the passive dynamics of knee joint.The damping coefficient is slightly increased alongknee angle until knee extension comes. The kneeextension is caused by the gravity of leg and torquegenerated at hip joint which make leg extend andmove forward. As in beginning of extension, kneeacts as a passive joint and therefore no controlleris required. Once knee angle achieves the θkup

, forresisting hyperextension, a damper controller is thusneeded. Knee velocity is then gradually decreaseddue to resisted torques. When knee joint passes overθklow

and approaches the equilibrium position, a lockmechanism will prevent the knee hyperextension. Thenext state Heel Strike happens when:• the knee angle θk > θkthreshold2

; or• the ground contact Fl > Fthreshold2

which means heel of swing leg starts to landon the ground.

3) Heel Strike is responsible for reducing the groundimpact and for generating a lowering of toes afterheel strike. Instead of modeling the knee joint asa variable damper, a locked mechanism within kneejoint to support the impact of landing of upper bodyis suggested. It turns again to Stabilization phase, iffollowing condition is fulfilled:• H > Hthreshold.

It means the heel strike is finished and the foot hasmade full contact with the ground.

Fig. 5: Transitions of finite state machine regulating gaitphases.

V. SIMULATION AND RESULTS

In this section, a simulated biped and the simulationenvironment are introduced firstly. A biologically motivated

control for a biped is briefly presented. Utilizing the gait phaseanalysis and variable-damping control, simulation results on abiped with a virtual leg prosthesis are then illustrated.

The leg prosthesis consists of one knee joint and anklejoints in both sagittal and frontal plane. Except for the variable-damping controlled knee joint, other joints are passive ele-ments with fixed stiffness and damping. A sliding joint isplaced in between top of the amputee and knee joint, whereasanother is situated between knee and ankle joint. Those twosliding joints, which are shown in Fig. 1, provide a constantstiffness and lock mechanism that are applied to lock knee inlate swing phase and stance phase.

In this paper, we have implemented the simulation of cyclicwalking in a flat platform and then obtained the data fromsimulation which are used as kind of biomechanical data.To test adaptation of the suggested methodology, walking onrough terrain is performed as well.

A. Normal Walking on Even Terrain

The first tests conducted using the simulated biped werebased on normal walking at the speed of 1.21 m/s. It providesa detailed evaluation of the calculated damping coefficient andthe mechanism of the leg prosthesis. The kinetic and kinematicanalysis give insight into joint trajectories and necessary jointtorques. Angles trajectories of joints over the course of a gait

Fig. 6: Joint angles over the course of gait cycle. The solidlines in left-handed figures represent mean values of prostheticjoints over 15 steps of normal walking, whereas those in right-handed figures show mean values of health leg. The dashedlines mark the minimum and maximum values. The verticaldashed line denotes the transition from stance to swing.

cycle, which are respectively hip joint in sagittal plane, kneejoint and ankle joints, are shown in Fig. 6. 15 consecutivesteps of walking on flat ground are averaged by manuallytagging the sampling data from one heel strike to next. Positive

values indicates individually a joint flexion ,abduction ordorsiflexion, while negative values denote extension, adductionor plantarflexion. The solid lines show the up-to-dateaveragevalues of joints along gait cycle, where dashed lines illustratethe maximum and minimum values. The vertical dashed linearound 69% is the location of the transition from stance toswing. The left column figures show the joints in prostheticlegs and figures on right one illustrate those joints in a healthyleg. The average duration of gait cycle is 1.35 s.

In Fig. 6, hip angles in frontal plane for prosthetic legand healthy leg are generally similar, which means amputeeswith this prosthesis do not need to adjust the amplitude of hipswing in swing phase and postures during swing phase. Wealso found that the course of the knee angle at prosthetic leghas closely the same profile of that in a health leg. That meansthe variable damping control has fulfilled the functionalityas required. But since we have only the passive joints forankle, in which stiffness and torque control are both required,therefore, we see some differences between the prosthetic legand the healthy leg. Since in healthy leg, the ankle joint insagittal plane is actively controlled, meaning reflex controllersand motor patterns are applied at joint. The lateral stabilityis normally maintained by a stiffness control at ankle joint infrontal plane. However due to the missing of stiffness control,the lateral stability can not be guaranteed during the stancephase. Fig. 7 illustrates torques of joints in both legs. The

Fig. 7: Joint torques over the course of gait cycle.

torque here is a combination of pure motor torque and torquegenerated by a virtual spring or/and damper. Again, plots in theleft column represent mean, minimum and maximum values ofjoint torques in the prosthetic leg, where the right ones denotethose values of joint torques in the intact leg. Torques at hipfrontal joint in both legs perform very close to each other.This means amputees do not need to generate more energy toswing the leg. Coming to knee joints, based on the calculateddamping profile, the prosthetic knee produces enough torques

to restrain its locomotion and therefore achieve a very human-like walking gait.

B. Walking on Rough Terrain

The following series of tests were conducted on roughterrain. The simulated terrain is built with roughness up to3.3 cm, which is equivalent to randomly placing rocks orsimilar obstacles with this maximum height throughout theterrain. The kinematic and kinetic data from prosthetic leg areillustrated in Fig. 8, in which mean angles and torques for hip,knee and ankle are shown in solid lines, where dashed linesdenote the maximum and minimum values. The kinematic datashows that the average angle values are similar with thosevalues in normal walking, but due to the rough ground, anglevalues can vary in a wider range than those in normal walking.However, with variable-damping control, the biped can stillwalk very smoothly on this uneven terrain. Looking into thecourse of knee angle and joint, we found that the torquegenerated by damper is less than that in normal walking. Thisis because protrudence on the ground curtails duration of swingphase and extends stance phase. Ankle vibration in frontalplane, that results from unevenness on the ground, has impactespecially on lateral stability. In this case, a constant stiffnesscontrol limits its adaptation to various environments. Hencea variable-stiffness controller could be more comfortable foramputees in different walking scenarios.

Fig. 8: Joint angles and torques over the course of gait cycle.

VI. CONCLUSION

We have discussed a methodology of designing a variable-damping controller for a leg prosthesis in this paper. Forcontrolling the phase-dependent prosthesis, we have firstlystudied the biomechanical aspects of knee joint along walkingcycle and then defined a finite-state machine to identify phasesof interest. We have then performed simulations and obtained

such data from a virtual model of human walking. Afterwards,we have analyzed the kinetic and kinematic data and extracteda damping profile along walking cycle. At last, we have testedthis methodology within this simulation environment both onflat ground and rough terrain. This is one great advantageof the proposed method, since the control strategy may beevaluated without any risk for humans. The resulting gaitwas satisfactory and robust to different environments. Futureworks include testing the developed control strategy on thereal prosthetic knee under development and expanding theproposed methodology for both active knee and ankle control.

ACKNOWLEDGMENT

We would like to thank DAAD3 and CAPES4 for fundingthis work.

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3www.daad.de4www.capes.gov.br