DEVELOPMENT AND EXPERIMENTAL VALIDATION OF AN … · Holly Warner Doctoral student Dept. of Mechanical Eng. Cleveland State University Cleveland, OH, 44115 Email: [email protected]

Proceedings of the ASME 2018 Dynamic Systems and Control ConferenceDSCC2018

September 30-October 3, 2018, Atlanta, Georgia, USA

DSCC2018-9091

DEVELOPMENT AND EXPERIMENTAL VALIDATION OF AN ENERGYREGENERATIVE PROSTHETIC KNEE CONTROLLER AND PROTOTYPE

Poya Khalaf∗Doctoral student

Dept. of Mechanical Eng.Cleveland State University

Cleveland, OH, 44115Email: [email protected]

Holly WarnerDoctoral student



Elizabeth HardinPrincipal Investigator

Cleveland FES Center, Motion Study LaboratoryCleveland VA Medical Center


Hanz RichterProfessor



Dan SimonProfessor

Dept. of Electrical Eng. and Computer Sci.Cleveland State University


DONT FORGET THE VIDEO

ABSTRACTWe present the design, control, and experimental evaluation

of an energy regenerative powered transfemoral prosthesis. Ourprosthesis prototype is comprised of a passive ankle and a pow-ered knee joint. The knee joint is actuated by an ultracapacitorbased regenerative drive mechanism. A novel varying impedancecontrol approach controls the prosthesis in both the stance andswing phase of the gait cycle, while explicitly considering en-ergy regeneration. This control method varies the impedance ofthe knee joint based on the amount of force exerted on the shankof the prosthesis. Furthermore, the controller promotes energyregeneration by precisely injecting a designated amount of neg-ative damping into the system. Our control approach leads to afew tuning parameters that cover all of the gait phases for walk-ing and all of the tested walking speeds and eliminates the needfor tedious target impedance scheduling. Experimental evalu-ation is done with an amputee test subject walking at different

∗Address all correspondence to this author.

speeds on a treadmill. The results validate the effectiveness of thecontrol method. In addition, net energy regeneration is achievedwhile walking with near-natural gait across all speeds.

INTRODUCTIONEnergetically passive prostheses enable walking for people

with lower limb amputations by using damping and spring-likeelements [1]. Accordingly, passive prostheses cannot providenet positive power. Able-bodied gait, on the other hand, requirespositive power output at the ankle and knee joints [2]. This re-sults in an increase in energy consumption for amputees duringwalking [3, 4].

Powered prostheses have been shown to reduce themetabolic cost of transport by providing positive net work [5–7].However, one main drawback of powered prostheses that hin-ders their widespread use is their power consumption. For theVanderbilt leg, which includes both a powered knee and ankle, awalking distance of about 9-12 km and a battery life of approxi-mately 1.8 hours of continual walking have been reported [8, 9].

1 Copyright c© 2018 by ASME

The Empower ankle (Ottobock, Duderstadt, Germany) can pro-vide a battery life of up to eight hours [10]. The Power Knee(Ossur, Reykjavik, Iceland) has a battery life of approximatelytwelve hours depending on usage and a charging time of threeand one half hours [11]. Considering power consuming daily ac-tivities beyond the average walking pace for which these valuesare reported, such as fast walking or climbing stairs, the afore-mentioned powered prostheses would have to be recharged sev-eral times daily for an amputee with a moderately active lifestyle.

Energy regeneration technologies have gained much atten-tion due to their potential to reduce the energy cost of systems,allowing them to work for longer periods of time with lower op-erational costs. Use of energy regeneration technologies in pow-ered prostheses specifically can provide longer battery life andmore generous ranges of locomotion, making them more prac-tical for daily use. The concept of energy regeneration is un-derstood here to be the process of recovering energy that wouldotherwise be dissipated and storing it for later use.

The potential to recover energy in powered lower limb pros-theses can be seen when considering power flows occurring inable-bodied walking. During able-bodied gait, the knee mostlyacts as a brake, absorbing/dissipating power, while the ankle actsas a motor, providing power [2, 12]. In a powered prostheticleg, the energy dissipated by the knee joint has the potential tobe stored and reused to reduce the overall power consumption.

Papers discussing energy regeneration in powered prosthe-ses are scarce in the research literature. An MIT group devel-oped a regenerative transfemoral prosthesis in the 1980s [13–15].Their conclusions suggested the use of larger capacitances,which were not available at the time. Arizona State Univer-sity has created a powered robotic ankle that uses energy storingelastic elements in series with an electric motor [16–19]. In apowered ankle prosthesis simulation, Everarts et al. [20] also usean elastic element in series with an electric motor to reduce thepeak power and regenerate energy. Tucker et al. [21] developedan analytical model of a regenerative powered transfemoral pros-thesis. A regeneration manifold is found that limits the actuatordamping which can be achieved while regenerating energy.

Many powered lower limb prostheses use impedance con-trol [5, 6, 17, 22, 23]. Impedance control emulates the behav-ior of physical springs and dampers; any active, variable, andnonlinear behavior can be achieved. For prostheses power isproduced by varying the joint impedance during different gaitphases. However, the advantages of impedance control overmechanical springs and dampers, as with any powered controlmethod, come at the price of energy consumption.

The general approach for controlling powered lower limbprostheses is to use a finite state impedance controller which di-vides the gait into discrete states [5–9, 22–27]. Each state has itsseparate controller and transitions between states are triggeredby sensors placed on the prostheses. The control parameters foreach state are tuned to individual subjects and different walking

speeds. A five state controller with three gains per state acrossthree walking speeds can lead to as many as 5×3×3= 45 tuningparameters in addition to gait-phase switching rules [8]. Moreelaborate methods add variation of the impedance parametersbased on joint angles or measured forces during the finite statesto reduce the number of tunable parameters [28, 29]. We referreaders to a comprehensive survey [1] of control strategies usedfor powered lower extremity prostheses.

We present an overview of the design, control, and experi-mental evaluation of an ultracapacitor based regenerative pow-ered prosthetic knee. A previously introduced framework for an-alyzing regenerative robotic systems [30–33] is used to designand model the powered prosthesis. Ultracapacitors, also knownas supercapacitors, provide an efficient means of storing andreusing energy [34] that is lightweight and durable and has highpower densities and the ability to rapidly charge and dischargewithout damage. This is the first known publication of a humantrial with an electro-mechanical energy-regenerative prosthesis.In addition, a novel varying impedance control approach drivesthe prosthesis in both stance and swing phase, while explicitlydealing with energy regeneration. Our control method varies theimpedance of the knee joint based on the amount of force exertedon the shank. This approach provides a natural variation in theimpedance of the knee and leads to far fewer tuning parameterscompared to some other approaches [6–9]. In addition, the con-troller allows walking at different speeds without the need forretuning, and with a simple adjustment, the same tuning can beused for different subjects. The prosthesis is evaluated experi-mentally by having an amputee test subject walk with the deviceon a treadmill.

THE REGENERATIVE PROSTHESIS MODELWe have previously developed a framework for analyzing

robotic systems having regenerative actuators or drive mecha-nisms [30–33]. Based on this framework, each actuator of aregenerative robotic system is classified as either conventional,external power is used for actuation, or regenerative, energy stor-ing elements store and reuse excess energy from the robot. Theconventional actuators are termed fully-active while the regener-ative actuators are termed semi-active. This framework is used asa basis for analyzing and modeling our regenerative prosthesis.

Our prosthetic leg prototype, depicted in Fig. 1, is comprisedof a powered regenerative knee joint and a passive ankle joint.To model the system, the prosthesis, excluding the regenerativedrive mechanism, can be thought of as a four degree of freedomstandard open-chain robotic system. The first three degrees offreedom are the horizontal motion, vertical motion, and rotationof the prosthesis socket in the sagittal plane; the fourth degree offreedom corresponds to flexion/extension of the knee joint. The


Figure 1. PROSTHETIC KNEE PROTOTYPE WITH OTTOBOCK TRI-TON VERTICAL SHOCK FOOT.

equation of motion for this system can be expressed as

D◦(q)q̈+C(q, q̇)q̇+R ◦(q, q̇)+g(q)+T = τ (1)

where q is the 4 × 1 vector of joint coordinates, D◦(q) is theinertia matrix, C(q, q̇) is a matrix accounting for Coriolis andcentrifugal effects, R ◦(q, q̇) is a general nonlinear damping term,T is the vector of external forces and moments reflected to themanipulator joints, and g(q) is the gravity vector.

The motion of the prosthesis socket (q1, q2, and q3) is con-trolled by the human subject and can be thought of as fully-active, injecting energy into the system. The prosthetic knee isconnected to a regenerative (semi-active) drive mechanism com-prised of a transmission with velocity ratio n, inertia m, and vis-cous damping coefficient b, a DC motor/generator with torqueconstant α and resistance R, an ultracapacitor with capacitanceC, and a four quadrant motor driver with voltage ratio r. Figure 2depicts a schematic of the regenerative drive mechanism. The in-ertial and frictional effects of the motor are assumed to have beenreflected to the transmission and are thereby included in m and b.In the most general case, the transmission ratio can be a functionof the knee joint angle. The voltage ratio r represents the ratioof motor voltage and capacitor voltage. Since the motor driverdoes not boost the capacitor voltage, r is constrained to [−1,1].A value r < 0 corresponds to applying reverse polarity voltage tothe DC motor.

Bond graphs [35] are used to facilitate the system represen-tation and equation derivation. From the bond graph model inFig. 2, the interfacing force τ4 for the knee joint is found as

τ4 =−mn2q̈4 − (bn2 +a2

R)q̇4 +

arR

Vcap (2)

where Vcap is the capacitor voltage, and a = αn. Substituting τ4from Eqn. (2) into Eqn. (1) and absorbing the terms containing q̇and q̈ into the left-hand side, the complete model of the prosthe-sis with the regenerative drive mechanism is obtained

D(q)q̈+C(q, q̇)q̇+R (q, q̇)+g+T = u (3)

where D and R result from augmenting D◦ and R ◦,

D44 = D◦44 +mn2q̈4

R4 = R ◦4 +(bn2 +a2R )q̇4

(4)

The first three joints are actively controlled by the human subject(u1−3). For the knee joint

u4 =arR

Vcap (5)

Semi-active Virtual Control StrategyThe semi-active virtual control strategy (SVC) provides a

means for controlling semi-active joints [30–32, 36]. To controlthe semi-active knee joint, a virtual control law τd is initiallydesigned for u4 in Eqn. (3). A virtual matching law is then foundthat can be solved for r

u4 =arR

Vcap = τd (6)

The virtual control (τd) can be of any form to achieve desiredcontrol objectives. Moreover, provided exact virtual matching ofEqn. (6), properties of the virtual design such as stability, track-ing performance, robustness, etc. will also apply to the actualsystem [30]. For this system virtual matching is always possibleas long as the capacitor voltage is high enough. Note that thesemi-active virtual control method decouples the system fromthe ultracapacitor model by placing Vcap in feedback of the vir-tual control law [33]. This is a major advantage because it allowsmodeling, analysis, and control of regenerative systems withoutinvolving the complexities of ultracapacitor models.


TF 1 GY 1 MTF Cτ4

_q4

n

R : b I : m

α

R : R

r V

i

Transmission

Rotor

R

r CMotor

Driver

q1

q2

q3

q4

τ4

Figure 2. THE PROSTHETIC LEG WITH THE REGENERATIVE DRIVE MECHANISM AND ITS BOND GRAPH REPRESENTATION. THE FIRST THREEJOINTS OF THE PROSTHESIS ARE ACTUATED BY THE HUMAN SUBJECT AND ARE CONSIDERED FULLY-ACTIVE. THE KNEE JOINT IS REGEN-ERATIVE AND CONSIDERED SEMI-ACTIVE.

Regenerated Energy in the Knee JointEnergy provided to the capacitor between any two arbitrary

times t1 and t2 can be derived from the bond graph of Fig. 2,

∆Es =∫ t2

t1Vcapi dt (7)

where i is the capacitor current. By deriving i from the bondgraph and using Eqn. (2), Eqn. (7) can be written in terms of thevirtual control

∆Es =∫ t2

t1

(τd q̇4 −

Ra2

(τd)2)

dt (8)

A detailed derivation can be found in [33]. A value of ∆Es > 0indicates energy regeneration and ∆Es < 0 indicates energy con-sumption. As a result of SVC, ∆Es is independent of the ultraca-pacitor model and is only a function of the control law τd , jointvelocities q̇, and joint parameters R and a.

THE VARYING IMPEDANCE CONTROL METHODWe use a novel varying impedance control method to con-

trol the prosthetic knee. Our approach changes the impedanceof the knee joint based on the amount of force applied to theprosthesis’ shank. This provides a continuous variation of theknee impedance during the gait cycle and enables a soft transi-tion between the stance and swing phases of gait. Moreover, our

approach leads to far fewer tuning parameters when comparedto finite state impedance control. Five parameters that are in-dependent of walking speed are identified. Furthermore, oncethe controller is tuned, the same tuning can be used for differentsubjects with just a simple adjustment.

The equation describing the control structure is

τd =−(Bh +B)q̇4 −FFs

Kq4 −Ks(q4 −q◦4) (9)

where B and Bh are virtual damping coefficients, F is the shankforce, Fs is a normalization factor, K and Ks are virtual springstiffnesses, and q◦4 is the equilibrium point of the virtual spring.We explain the controller’s functionality in the stance and swingphases separately.

Swing PhaseIn the swing phase the shank force F is zero and Eqn. (9)

reduces to

τd =−(Bh +B)q̇4 −Ks(q4 −q◦4) (10)

We mainly rely on the kinetic energy of the prosthesis at the be-ginning of the swing phase to extend the knee. The virtual stiff-ness Ks can be used to further propel the leg if the knee jointdoes not fully extend before heel strike. During tests with theprototype, we observed that this was not the case and set Ks tozero.


Virtual damping constant Bh prevents the mechanical hardstop from making contact at the end of the swing phase and onlybecomes active when the knee angle approaches full extension,meaning that the screw displacement becomes less than a certainthreshold.

Bh =

{bh q4 < qthreshold0 q4 > qthreshold

(11)

This could, however, be achieved mechanically by installing asoft stop insert, avoiding the need to expend extra electrical en-ergy.

The purpose of the virtual damping constant B is to regen-erate energy in the swing phase. The damping constant is setby considering the regenerated energy Eqn. (8) under the casewhere τd =−Bq̇4

∆Es =∫ t2

t1−(

B+Ra2

B2)

q̇24 dt (12)

From Eqn. (12) it can be seen that energy is regenerated (∆Es >0) only if

−a2

R< B < 0 (13)

Equation (13) suggests that power can only be regenerated with avirtual damper if negative damping constants are used. Negativedamping constants in the range of Eqn. (13) reduce the dampingof the overall system but not to the extent of causing instability.Assuming that q̇4 is mostly governed by the system dynamicsand varying B in the range of Eqn. (13) has negligible effect onq̇4, we can differentiate Eqn. (12) with respect to B and set it tozero to find the optimum damping constant for regeneration

B∗ =− a2

2R(14)

and the optimum energy regenerated

∆E∗s =∫ t2

t1

a2

4Rq̇24 dt (15)

Stance PhaseOnce the foot makes contact with the ground, the shank

force F is non-zero, reinstating the full control law Eqn. (9). Thevirtual spring K dominates the control in stance phase due to thesmaller knee velocities. Also, the virtual spring constant K is

typically set to much larger values compared to Ks. The stancephase control reduces to

τd ≈− FFs

Kq4 (16)

The normalization factor Fs is the measured shank force F whenthe amputee is fully supported by the prosthetic leg.

During stance phase the behavior of the control law dictatesthat as the user shifts his or her weight to the prosthetic leg, theknee will stiffen, providing the amputee with the necessary sup-port even when the knee remains slightly flexed. This is in con-trast to the slow collapse of, for example, a hydraulic knee jointunder matching conditions. During late stance when the amputeeprepares for swing phase and begins to transfer his or her weightto the opposing leg, the proposed control law causes the pros-thesis to soften, initializing the knee flexion required to enterswing phase. Each of these transitions are accomplished withoutswitching between multiple sets of control gains.

Controller Tuning ProcedureTuning the control law therefore requires the selection of

five values. These are bh, qthreshold , K, Ks, and q◦4. Notedly, B isautomatically determined by system parameters; see Eqn. (14).The parameter bh is set to be a little larger than the magnitude ofB so that it cancels the negative damping. The smallest sufficientvalue of qthreshold to prevent the hard stop is chosen, typically acouple of millimeters. K is determined by trial and error suchthat the amputee feels well supported. Ks and q◦4 are nonzeroonly when needed and are increased until the knee fully extendsunder the user’s volition. Once this initial tuning is completed, itis expected that other amputees could reuse the same tuning pa-rameters. The value for Fs, which is specific to the user’s weight,would only need to be updated. None of the tuning parametersare dependent on the user’s selected speed either. These featuresof the controller make tuning efforts minimal and very straight-forward compared to finite state impedance controllers.

THE PROSTHESIS PROTOTYPE AND EXPERIMENTALSETUP

The prototype used for this work was constructed from off-the-shelf components with an emphasis on creating a low-cost,proof-of-concept system. The overall system can be divided intothe following categories: actuation, power storage, control, andsensing. A schematic of the system is given in Fig. 3.

The knee structure was built such that standard pyramidadapters are available at both the thigh and ankle interfaces.Also, it should be noted in relation to stance phase that whenthe knee is completely straight it can enter a mechanically self-locking region, depending on the location of the user’s center of


Capacitor Side Current Sensor

Ultracapacitors

dSPACE System

V Command

V Cap

iCap

iMotor

Motor Driver

M1

B−

B+

M2

Motor Side Current Sensor

Prosthetic Leg/Screw/DC Motor

q4; _q4

F

V Motor

Figure 3. PROSTHETIC LEG SYSTEM OVERVIEW INDICATING POWER AND INFORMATION PATHS

mass. Under this condition q4 = q̇4 = 0 rad, eliminating activepower usage and saving energy. The knee attached to a socketand an Ottobock Triton Vertical Shock foot is shown in Fig. 1.

A 12 V DC motor-driven lead screw (ULTRAMOTION)actuates the knee joint by use of the crank-slider architecture.Power is supplied to the motor from four ultracapacitors linkedin series by balancing circuitry (Maxwell Technologies, BKIT-MCINT). These capacitors are rated for up to 2.7 V and at 650 Feach (Maxwell Technologies, BCAP0650 P270 K04), determin-ing a maximum operating voltage of 10.8 V. Regulating thepower flow to and from the motor, a 10 A SyRen motor driverwas selected (DimensionEngineering). This device is capable offour-quadrant operation. The analog control signal sent to themotor driver are generated by the dSPACE system, specificallythe DS1104. The control software run by this system was devel-oped in Simulink with the more complex computations writtendirectly in MATLAB code.

A variety of sensors were installed for both control feed-back and performance evaluation. For feedback, motor position,which is kinematically related to knee angle, was measured by anencoder, from which velocity could be computed. Additionally,two strain gages were adhered to the foot and then calibrated toproduce shank force. The capacitor voltage was measured foruse in the semiactive virtual control method. To be able to eval-uate the energy regeneration capacity of the prosthesis, currentsensors were installed at both the input and output to the motordriver; see Fig. 3 for the wiring schematic. The voltage applied

to the motor as well as the voltage across the capacitors, as previ-ously mentioned, were recorded. Combining these two pairs ofmeasurements provides information regarding the power usageand the efficiency of the motor driver. All data with exceptionof the knee position were passed through a digital filter with acutoff frequency of 24 Hz.

Human trials with an amputee subject were completed at theLouis Stokes Cleveland VA Medical Center as approved by itsinternal institutional review board. A 35-year-old male (81.7 kg,175.3 cm) with a right transfemoral amputation volunteered totrial the leg; see Fig. 4. The test subject walks with a FreedomInnovations Plie microprocessor-controlled passive knee in com-bination with an Ottobock Triton Vertical Shock foot on a dailybasis. The subject used his personal socket and daily foot for allof the trials. All components were fit by a certified prosthetist.

Three speeds were selected for the trial protocol, which wasexecuted on a treadmill. These were the amputee’s preferredspeed while using his everyday leg and plus and minus 0.15 m/s,giving 0.6 m/s, 0.75 m/s, and 0.9 m/s. All test data were takenon the same day. The amputee was provided two periods of atleast 15 minutes on previous, non-consecutive days to familiarizehimself with the experimental prosthesis.

TEST RESULTSThe controller was tuned by trial and error based on the am-

putee’s feedback and the guidelines previously described. The


Figure 4. TEST SUBJECT WALKING WITH THE PROSTHESIS PRO-TOTYPE (COPYRIGHT CLEVELAND FES CENTER, CLEVELAND,USA).

Table 1. CONTROLLER TUNING PARAMETERS.

K (N/mm) Ks (N/mm) B (Ns/mm)

200 0 -1.743

bh (Ns/mm) q◦4 (mm) qthreshold (mm)

2.5 0 2

final parameters are provided in Tab. 1. K, the spring constantdominating the stance phase, was tuned before the trial so thatthe leg could hold the weight of one of the authors. This gainwas then fine-tuned with the test subject while he walked on atreadmill. The swing phase spring constant Ks and accordinglyq◦4 were zero because the test subject’s gait pattern caused theprosthesis to fully extend without aid. B was computed based onthe constants a and R that were identified for the actuator. Bhoverrides the negative damping during late swing phase, whichis defined as qthreshold = 2 mm of screw travel before full exten-sion. Note that the same tuning was used for all tests and walkingspeeds.

Figure 5 shows the prosthetic knee angle as derived fromthe motor position for three walking speeds, slow (0.6 m/s),preferred (0.75 m/s), and fast (0.9 m/s). It can be seen thatas walking speed increases the maximum angle of the knee inthe swing phase also increases slightly, which is consistent withable-bodied gait [37]. However, the increase in maximum angleis less pronounced when comparing the preferred and fast speedsas opposed to the slow and preferred speeds, especially whenconsidering the larger standard deviation band of the fast speed.This could be due to a singularity in the slider-crank mechanism

of the knee actuator. The knee shows almost none of the flex-ion in the stance phase that is usually seen in able-bodied walk-ing [2,12]. This behavior, having little to no flexion in the stancephase, is typical, however, for most powered and passive pros-theses [6, 7, 38–42]. While our controller had the ability to re-cover knee flexion in the stance phase, it was observed that thetest subject would fully extend the knee joint before foot strikeinstead of using this feature, potentially due to previous walk-ing habits and/or a lack of confidence in the prosthesis’ ability tosupport the amputee’s weight while flexed. The weight of the de-vice might have also aided this outcome. A similar lack of stanceflexion has been seen in below knee amputee gait data [43], sug-gesting the possibility that this phenomenon is due to the pros-thetic ankle.

Figure 5 also shows the electrical power flows for the threetested walking speeds. Power flows are given for the capaci-tor and motor side of the motor driver. Positive power indicatespower consumption while negative power indicates power regen-eration. In the stance phase, very little power is consumed. Inable-bodied gait, the knee joint uses positive power while it is be-ing extended during mid-stance [2]. As previously explained, forour tests the knee was fully extended during stance and supportedthe weight of the amputee without the need for energy expendi-ture. Hence the controller only needs to provide sufficient powerto stabilize the knee. In the swing phase the negative dampingterm of Eqn. (9) becomes dominant, and power is regeneratedand stored in the ultracapacitor. With increased walking speedthe peak value of the regenerated power increases. In addition,not all of the regenerated power is stored in the capacitor, and aportion of it (0.7 Watts) is consumed by the motor driver.

As was observed from the power plots, energy regenerationwas possible under the test conditions. Integrating the powermeasurements yields total energy regenerated. This is shown forboth the motor and capacitor sides of the motor driver and acrossall speeds in Fig. 6. As speed increases, it is clear from the mo-tor side values that energy regenerated increases. However, ap-proximately one half or more of the regenerated energy does notreach the capacitor bank to be stored. Efficiency does increasesignificantly between the slow speed and both higher rates, sug-gesting that the efficiency of the motor driver is affected by thereturn voltage and/or current applied. There is a less significantincrease between the preferred and fast walking speeds. This islikely partially due to the previously mentioned singularity in thecrank-slider. It is also true that the hard stop prevention damp-ing will use more energy at higher swing speeds, causing lessenergy to be available for storage. Comparing these results withable-bodied data, in [2] the range of available energy is about15-30 J for slow to fast paced walking, respectively. It thereforeseems likely that there is still significant energy to be capturedbeyond what we have accomplished. Indeed, a regeneration po-tential is known to exist during the stance phase of able-bodiedgait [2]. Our current results do not include energy recovery from


Figure 5. AVERAGE KNEE ANGLE AND POWER FLOWS FOR THREE WALKING SPEEDS. THE GREY BANDS SHOW ONE STANDARD DEVIATIONFROM THE AVERAGE TRAJECTORIES. THE SLOW, PREFERRED, AND FAST WALKING SPEEDS ARE 0.6, 0.75, AND 0.9 METERS PER SECOND,RESPECTIVELY. POSITIVE POWER INDICATES POWER CONSUMPTION. NEGATIVE POWER INDICATES POWER REGENERATION.

Slow Preferred Fast

Walking Speeds

0

0.5

1

1.5

2

2.5

Regenera

ted E

nerg

y (

J)

Motor side

Capacitor side

Figure 6. AVERAGE ENERGY REGENERATED IN EACH GAIT CYCLEFOR THREE WALKING SPEEDS. REGENERATED ENERGIES AREREPORTED FOR THE CAPACITOR SIDE AND THE MOTOR SIDE OFTHE MOTOR DRIVER.

this region.

CONCLUSIONSWithin this work we have developed a powered knee pros-

thesis and controller, emphasizing control simplicity and energyregeneration. An experimental trial conducted with an amputeetest subject validated the control method and achieved energyregeneration. Furthermore, basic features of able-bodied gaitwere replicated in testing, including swing phase knee flexionand transitions between gait phases.

Three traits of the proposed control law differentiate it fromalternative methods. First, it has only five parameters, and theyare intuitive for the individual adjusting the gains. This makesthe tuning process relatively easy; tuning was able to be com-pleted in a matter of minutes while conducting the test. Second,guidelines for tuning for energy regeneration can be developedanalytically. Lastly, our approach only provides power to theknee joint when needed, yielding further energy savings.

Considering longer periods of operation in the future, sev-eral items must be addressed. As with any system with finiteon-board power storage, operation must be stopped once charge(indicated by Vcap) drops below an acceptable threshold. Atthis point the system must be recharged. It is important to notethat two alternative conditions, self-sustained operation or evencharge buildup, can also occur in a system with energy regenera-tion. Achieving either of these conditions is dependent on systemparameters and trajectories. If charging occurs during operation,


the regenerated power from the knee can be used for operating apowered ankle, which is a primary long-term goal of this work.

As suggested by the results, the prototype suffers from sev-eral sources of energy loss. Additionally, there are some lossesthat are not even reflected in the measurements taken. In the nexthardware iteration, an improved actuator, including the motor,motor driver, and screw, will aid in eliminating these losses. Be-cause the energy regenerated is directly dependent on the motorparameters, a more optimal motor can be selected with this inmind. A different four-quadrant motor driver should be identi-fied to better transfer the power available for regeneration at lowwalking speeds. The current screw is a lead screw with a ratedefficiency of about 60%. Replacing it with a ballscrew can easilyraise this value above 90%. In addition, the energy regeneratedby the negative damping is inversely proportional to electrical re-sistance (R), Eqn. (15). By embedding the electronics and elim-inating the lengthy tether used in the test, further improvementsin energy regeneration are possible.

ACKNOWLEDGMENTThis work was supported by the National Science Founda-

tion, grants #1344954 and #1536035.

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DEVELOPMENT AND EXPERIMENTAL VALIDATION OF AN … · Holly Warner Doctoral student Dept. of Mechanical Eng. Cleveland State University Cleveland, OH, 44115 Email: [email protected]