Energy Regeneration-Based Hybrid Control For Transfemoral .
Energy Regeneration-Based Hybrid Controlfor Transfemoral Prosthetic LegsUsing Four-Bar MechanismHanz RichterByoung-Ho KimDept. of Mechanical EngineeringCleveland State UniversityCleveland, USAh.richter@csuohio.eduDept. of Mechatronics EngineeringKyungsung UniversityBusan, Republic of Koreakimbh@ks.ac.krAbstract—This paper presents an energy regeneration-basedhybrid control method for transfemoral prosthetic legs using afour-bar linkage mechanism. To do that, we consider a model oftransfemoral prosthetic leg with three-degrees of freedom thatemploys a knee mechanism using a four-bar linkage mechanism.We also focus on suggesting a practical strategy for effectiveimplementation rather than a complex algorithm. In this point ofview, we devise a hybrid controller for the prosthetic leg. Actually,the motions of the hip mechanism of the leg are controlled bya PID control method and the knee joint is controlled by animpedance control method. We also consider an electrical energyregeneration module for effective energy utilization. Throughan exemplary walk simulation, we show the availability of thehybrid controller for such a transfemoral prosthetic leg and alsoaddress the advantages of using such a four-bar mechanism andan energy regeneration module for effective driving the kneejoint. It is finally concluded that the proposed hybrid controllercan be applied for effective control of transfemoral prostheticlegs using such a four-bar mechanism.Index Terms—transfemoral prosthetic leg, four-bar linkagemechanism, energy regeneration, hybrid controlI. I NTRODUCTIONIt is well-known that the objective of research on transfemoral prosthesis is to replace a leg missing above the kneeas an artificial limb. This effort is very helpful for amputeesto regain normal movement. Initially, many passive prostheseswere developed and used by transfemoral amputees [1]. In fact,these passive prostheses put a lot of strain on their hip jointsbecause those mechanisms are somewhat heavy and have nopower to drive any joint. Thus, transfemoral amputees walkingwith these passive prostheses consume much more energyduring walking compared to healthy people [2]. Especially,the hip joints with these passive prostheses have several timesmore burden than the normal hip joints [3]. This burden canbe alleviated by using a powered prosthesis [4].Actually, there are many challenges in developing the powered transfemoral prosthesis, as shown in Fig. 1, in terms ofmechanical design, effective energy utilization and control,biomimetic motion planning, and so on. Recently, in order todevelop an effective powered transfemoral prosthesis, manystudies have been actively conducted [5] - [8]. Sup, et. al.978-1-5090-6683-4/18/ 31.00 2018 IEEEFig. 1. A powered transfemoral prosthetic leg using a four-bar linkagemechanism (Copyright: Cleveland FES Center, Cleveland, USA)presented a remarkable consideration on design of poweredtransfemoral prostheses [5]. Actually, related to driving theknee joint mechanism, they considered a slider-crank mechanism and a pneumatically actuated powered-tethered device.An embedded control system has been specified for effectivecontrol of a prosthetic leg mechanism [7]. A user-orientedtransfemoral prosthesis approach is also remarkable for effective walking because it considers a whole-body awareness [8].And a remote controller using a high-speed CAN Bus has beenproposed for a transfemoral prosthesis [9]. However, they didnot show the performance of their prosthesis in terms of a leg.In fact, although a prosthesis is an independent part, once it isattached to a person, it is no longer an independent part. Thatis, the control performance of the prosthesis could be affectedby the style of the hip movement of an amputee. Therefore,it is necessary to consider the overall dynamic characteristicsof the leg with a prosthesis to achieve more comfortable walkperformance.In terms of effective energy utilization, a remarkable framework of energy regeneration has been presented [10] and anoptimal control method has been proposed for effective controlof transfemoral prostheses using such an energy regeneration[11]. They showed the feasibility of their optimal controlapproach for a proper combination of control performanceand energy recycling. Nevertheless, more simplification of the2516
overall control algorithm remains a challenge.The objective of this paper is to present an energyregeneration-based hybrid control method for effective control of transfemoral prosthetic legs using a four-bar linkagemechanism. Our focus is to devise a practical strategy foreffective implementation rather than a complex algorithm.The features of using a four-bar mechanism and an energyregeneration module are also discussed in terms of effectiveenergy utilization. It is finally shown that our approach isavailable for effective control of transfemoral prosthetic legsusing such a four-bar mechanism.II. M ODELING AND C ONTROL OF T RANSFEMORALP ROSTHETIC L EGrepresents the generalized force and torque vector that supportsthe external force activated in the leg.The generalized force and torque vector in (1) is given by Tu f1 τ2 τ3(2)where f1 represents the force for the vertical motion of theoverall hip joint. τ2 and τ3 represent the torques for the rotational motion of the hip joint and the knee joint, respectively.In our consideration, the vertical force and rotational torque ofthe hip joint are supplied by using an external power source.But the knee joint torque is made by an embedded self-powermodule as shown in Fig. 3.This section reveals a typical model of transfemoral prosthetic leg mechanisms and describes its dynamic relationship.Fig. 1 shows a situation that an amputee is testing theperformance of a powered transfemoral prosthetic leg using afour-bar linkage mechanism through walking on a treadmill. Inorder to deal with the control problem of such a transfemoralprosthetic leg, the human walk has been simplified as a bipedalrobot walk as shown in Fig. 2, where the prosthetic leg is onlyconsidered for the control problem.Fig. 3. A prosthetic knee system using a four-bar mechanism and a self-powermoduleIn fact, the knee system shown in Fig. 3 utilizes a kind offour-bar linkage mechanism driven by an electric motor. Thismechanism is a typical electro-mechanical system and veryuseful in terms of torque utilization. Actually, the torque fordriving the knee joint can be expressed as follows.τ3 n(q3 )τm(3)where the torque ratio n(q3 ) relating the drive motor space tothe knee joint space can be driven bya1 a4 sin(q3 qDAC0 )n(q3 ) p2η (a1 ) (a4 )2 2a1 a4 cos(q3 qDAC0 )(4)(1)here a1 is the length of the link DA in the four-bar mechanismand a4 represents the length of the line AC. η denotes the ratiorelating the rotation angle of the linear actuator to its linearmovement, and qDAC0 is the angle A of the virtual triangleconsisting of DAC at the initial configuration. Note that thejoint motion of the linear actuator is the same as that of thedrive motor because the belt drive ratio is 1:1.Based on the motor relationship and the electric network,the torque of the drive motor τm can be determined bywhere q, q̇ and q̈ are the n 1 vectors of joint angular position,velocity and acceleration, respectively. u is the n 1 vectorof generalized force and torque supplied by actuators. M (q)is a n n symmetric positive definite inertia matrix. B(q)[q̇ q̇]and C(q)[(q̇)2 ] are n 1 vectors representing the Coriolisand centrifugal terms. g(q) is the n 1 vector of gravity. uL1km (rvc τbemf )(5)Rwhere km represents the motor constant, and the resistance ofthe network R is determined by the sum of the resistance ofthe armature Ra and the additional resistance Rs . The role ofthe parameter r is to divide the voltage of the capacitor vc ,Fig. 2. A bipedal robot walkThe dynamic equation of the prosthetic leg in Fig. 2 isgenerally described by the following form at the joint space[12]:M (q)q̈ B(q)[q̇ q̇] C(q)[(q̇)2 ] g(q) uL u2517τm
and it can be adjusted to a value between 1 and -1. The backelectro-mechanical force τbemf can be expressed by1(km )2 n(q3a )q̇3a(6)Rrepresents the actual angular velocity of the kneeτbemf where q̇3ajoint.Then, we propose a hybrid controller for the operation ofthe prosthetic leg as follows. It is actually made by combiningthe conventional PID(Proportional, Integral, and Derivative)controller and an impedance controller. Firstly, the vertical androtational motions of the hip are controlled by the PID controllaw as follows.Xf1 kp1 δh1 kd1 δv1 ki1δh1(7)Xτ2 kp2 δq2 kd2 δw2 ki2δq2(8)where kpj , kdj , and kij represent the proportional, derivative,and integral gains for the jth motion. The parameters of δh1and δv1 are the position and velocity errors of the verticalmovement of the hip, respectively. δq2 and δw2 represent therotational angular position and velocity errors of the hip joint.Secondly, the motion of the knee joint is controlled by thefollowing impedance control law:As a result, using (3) and (7) (13), we can control thetransfemoral prosthetic leg shown in Fig. 2. The availabilityof the specified hybrid control approach is shown in the nextsection.III. WALK S IMULATION AND D ISCUSSIONTo demonstrate the usefulness of the proposed hybrid controller, this section provides an exemplary walk simulationusing the transfemoral prosthetic leg in Fig. 2 and interestingdiscussions.For effective simulation, we performed a repetitive steppingwalk of the transfemoral prosthetic leg on a treadmill as shownin Fig. 2. By observing the walk style of a human [13]- [15],the trajectories set for the walking task were planned as Fig.4. Especially, note that the y-directional motion of the leg hasbeen constrained on 0.2 m. The z-directional trajectories of thehip joint and the foot can be described by combining a cubicand triangular functions, but they have been omitted becauseof the limited space.1.210.80.6τm kpm δqm kdm q̇ma(9)where δqm and q̇ma are the position error and the actualangular velocity of the drive motor, respectively, and kpmand kdm represent the proportional and damping gains for theactuator. The actual angle and angular velocity of the drivemotor can be determined byp(a1 )2 (a4 )2 2a1 a4 cos(q3a qDAC0 ) lCD0qma η(10)q̇ma n(q3a )q̇3a(11)0.40.20-0.2-0.402.4 2.8 3.2 3.640.30.250.20.150.10.05(12)0-0.05Simultaneously, the real-time voltage of the capacitor considering discharge and recharge can be determined by1vc (t dt) vc (t) ic (t)dtC2Fig. 4. Trajectories set for the walking task: (a) z-directional movement of thehip, (b) x-directional movement of the foot, and (c) z-directional movementof the foot.here lCD0 and q3a represent the length of the line CD at theinitial configuration and the actual angle of the knee joint,respectively.Since the knee joint is actually driven by using the embedded self-power module, the torque of the knee joint can bemade by controlling the parameter r which is determined byusing (3), (5) and (9) as follows.R(τm τbemf ).r k m vc0.4 0.8 1.2 1.6(13)where C and ic (t) represent the capacitance and current parameters of the capacitor, respectively, and dt is the samplingtime. Practically, the voltage of the capacitor can be increasedwhen the current is negative, and this activity is helpful for along time walk after attaching the prosthetic leg.-0.1-0.4 -0.3 -0.2 -0.100.10.20.30.4Fig. 5. Trajectory of the foot in the xz-planar space for the prosthetic walkThe trajectory of the foot in the xz-planar space for thewalking task can be shown as Fig. 5. It forms a kind of iterativeloop. The foot trajectory given in this study proceeds actuallyin the order of A B C D B C E A, where the pointA is the starting or end position. The stage from A to B is for2518
a ready step to start the recursive walk, and the stage from Eto A is to finish the recursive walk. The stage from C to D,or from C to E, means a lifting operation of the heel of thefoot to enter the swing phase. Such a repetitive walking canbe performed by following the closed loop B C D.Our simulation has been performed under the conditionthat the initial posture of the leg is an upright posture, andeach part should follow the trajectory assigned in Fig. 4.The corresponding system parameters for this simulation werespecified in Table I. Especially, the reaction force at thefoot was calculated by using stiffness relationship, where thestiffness of the treadmill was set to 37000 N/m. The frictioncoefficient of the treadmill was set to 0.25, and the initialvoltage of the self-power module was assigned as 20 V. Thegain parameters for the hybrid controller described in SectionII were assigned as Table II. The sampling time for the controlof each walk was set to 5 ms.200-20-40-60-80-100-12000.4 0.8 1.2 1.622.4 2.8 3.2 3.64Fig. 7. Trajectory following result for the rotational motion of the hip joint:(a) desired trajectory and (b) actual trajectory.20TABLE IS YSTEM PARAMETERS FOR THE WALK SIMULATIONParameterlength of thigh (l2 )length of shank (l3 )mass of hip (m1 )mass of thigh (m2 )mass of shank (m3 )DC motor constant (km )armature resistance (R)setting resistance(Rs )capacitance mkgkgkgNm/AΩΩF-40-60-80-100-1200TABLE IIG AIN PARAMETERS FOR THE HYBRID CONTROLLERj12mPID controllerkpjkdjkij685003425 1712.54001.40.2-0.4 0.8 1.2 1.622.4 2.8 3.2 3.64Fig. 8. Trajectory following result for the rotational motion of the knee joint:(a) desired trajectory and (b) actual trajectory.0.3Impedance .8-0.05-0.1-0.4 -0.3 -0.2 -0.10.600.10.20.30.4Fig. 9. Trajectory following result of the foot in the xz-planar space: (a)desired trajectory and (b) actual trajectory.0.40.2000.4 0.8 1.2 1.622.4 2.8 3.2 3.64Fig. 6. Trajectory following result for the vertical motion of the hip: (a)desired trajectory and (b) actual trajectory.Through this simulation, we confirmed the desired andactual trajectories for the vertical motion of the hip and therotational motion of the hip joint, and they have been shownin Fig. 6 and Fig. 7. Fig. 8 shows the desired and actualangular trajectories of the knee joint for the walk. From these2519
3000figures, it can be seen that the actual trajectories follow theirdesired trajectories satisfactorily. Also, the resultant trajectoryfollowing result of the foot in the xz-planar space has beenplotted in Fig. 9. Specifically, the actual trajectory deviatessignificantly from the desired trajectory at points B, D, andE in Fig. 9, but after those points, the actual trajectory hasbeen properly controlled. This phenomenon can be seen asthe effect of the reaction force shown in Fig. 10, which isactually caused from landing of the foot on the walk surfaceor take off. From Fig. 8, we can also recognize that the motionof the knee joint can be affected by the reaction 00.4 0.8 1.2 1.622.4 2.8 3.2 3.642400Fig. 12. Torques supporting the rotational motion of the hip joint: (a) desiredtorque and (b) actual torque.180030201200106000000.4 0.8 1.2 1.622.4 2.8 3.2 3.64-10Fig. 10. Reaction force to the z-directionAlso, we confirmed the desired and actual force profilesfor the vertical motion of the hip and the desired and actualtorques for the rotational motion of the hip joint as shown inFig. 11 and Fig. 12, respectively. In particular, we can see thata relatively large torque value appears when the foot touchesdown on the walk surface repeatedly at 0.4 s and 2.4 s.30002400180012006000-600-1200-1800-2400-300000.4 0.8 1.2 1.622.4 2.8 3.2 3.64Fig. 11. Forces supporting the vertical motion of the hip: (a) desired forceand (b) actual force.Fig. 13 shows the torque performance of the drive motorfor the actuation of the knee joint, where the torque range isconfirmed to be within 20 Nm. It is very reasonable range for-20-3000.4 0.8 1.2 1.622.4 2.8 3.2 3.64Fig. 13. Torques of the drive motor for the actuation of the knee joint: (a)desired torque and (b) actual torque.practical implementation. This advantage could be obtained byemploying the four-bar mechanism shown in Fig. 3 to drivethe knee joint. Actually, the four-bar mechanism enables us toutilize the torque ratio in (3) and (11), and the ratio in thisstudy has been illustrated in Fig. 14. Note that the torque ratiois not constant and depends on the motion of the knee joint.Also, we can confirm that a large change of torque at pointsD and E in Fig. 13 reliably support the response shown inFig. 8.In addition, the control parameter for effective supplying theembedded self-power into the drive motor and the voltage ofthe capacitor which changes in real time have been shown inFig. 15 and Fig. 16, respectively. Actually, we can confirmthat the initial voltage of the capacitor is 20 V, and it isgradually reduced by being used in real time for the kneejoint motion. This gentle pattern is due to the fact that somevoltage is recharged in the course of the knee motion. Recently,a performance test on a knee controller has been performed[16]. In fact, this effort to improve the performance of suchenergy recharging is very important to increase the time of2520
9.8000.4 0.8 1.2 1.622.4 2.8 3.2 3.604Fig. 14. Torques ratios relating the drive motor space to the knee joint space:(a) the ratio determined by the desired angular trajectory of the knee jointq3d and (b) the ratio by the actual angular trajectory q3a .22.4 2.8 3.2 3.64Fig. 16. Voltage profile of the capacitor0.8four-bar mechanism. One of interesting future works will bethe study on effective energy recharging by considering morepractical walking strategy.0.6R EFERENCES0.4[1] S. B. O’Sullivan and T. J. Schmitz, Physical Rehabilitation, 5th ed., F.A.Davis Company, 2007.[2] R. Waters, J. Perry, D. Antonelli, and H. Hislop, “Energy cost of walkingamputees: the influence of level of amputation,” Jour. of Bone and JointSurgery, vol. 58A, pp. 42–46, 1976.[3] D. A. Winter, The Biomechanics and Motor Control of Human Gait:Normal, Elderly and Pathological, 2nd ed., Waterloo, ON, University ofWaterloo Press, 1991.[4] G. K. Klute, J. Czerniecki, and B. Hannaford, “Development of poweredprosthetic lower limb,” Proc. of the 1st National Meeting, VeteransAffairs Rehabilitation Research and Development Service, 1998.[5] F. Sup, A. Bohara, and M. Goldfarb, “Design and contol of a poweredtransfemoral prosthesis,” The International Jour. of Robotics Research,vol. 27, no. 2, pp. 263–273, February 2008.[6] S. K. Au and H. M. Herr, “Powered ankle-foot prosthesis,” IEEERobotics & Automation Magazine, vol. 15, no. 3, pp. 52–59, 2008.[7] B. E. Lawson, J. E. Mitchell, D. Truex, A. Shultz, E. Ledoux, and M.Goldfarb, “A robotic leg prosthesis-design, control, and implementation,”IEEE Robotics & Automation Magazine, pp. 70–81, December 2014.[8] L. Ambrozic, M. Gorsic, J. Geeroms, L. Flynn, R. M. Lova, R. Kamnik,M. Munih, and N. Vitiello, “Cyberlegs-a user-oriented robotic transfemoral prosthesis with whole-body awareness control,” IEEE Robotics& Automation Magazine, pp. 82–93, December 2014.[9] T. Lenzi, L. J. Hargrove, and J. W. Sensinger, “Speed-adaptationmechanism-robotic prostheses can actively regulate joint torque,” IEEERobotics & Automation Magazine, pp. 94–107, December 2014.[10] H. Richter, “A framework for control of robots with energy regeneration,” ASME Jour. of Dynamic Systems, Measurement, and Control,vol. 137, no. 9, pp. 091004-1–11, September 2015.[11] G. Khademi, H. Mohammadi, H. Richter, and D. Simon, “Optimal mixedtracking/impedance control with application to transfemoral prostheseswith energy regeneration,” IEEE Trans. on Biomedical Engineering, vol.65, no. 4, pp. 894–910, April 2018.[12] J. J. Craig, Introduction to robotics mechanics and control, 3rd. ed.Prentice Hall, 2004.[13] J. Perry, Gait Analysis, SLACK, INC., 1992.[14] C. C. Norkin and P. K. Levan
But the knee joint torque is made by an embedded self-power module as shown in Fig. 3. Fig. 3. A prosthetic knee system using a four-bar mechanism and a self-power module In fact, the knee system shown in Fig. 3 utilizes a kind of four-bar linkage mechanism driven by an electric motor. This mechanism is a typical electro-mechanical system and very
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