Experimental comparison of torque control methods on an ankleexoskeleton during human walking

Juanjuan Zhang1,2,∗, Chien Chern Cheah2, Steven H. Collins1,3

Abstract— Few comparisons have been performed acrosstorque controllers for exoskeletons, and differences amongdevices have made interpretation difficult. In this study, wedesigned, developed and compared the torque-tracking perfor-mance of nine control methods, including variations on classicalfeedback control, model-based control, adaptive control and it-erative learning. Each was tested with four high-level controllersthat determined desired torque based on time, joint angle, aneuromuscular model, or electromyography. Controllers wereimplemented on a tethered ankle exoskeleton with series elasticactuation. Measurements were taken while one human subjectwalked on a treadmill at 1.25 m·s-1 for one hundred steady-state steps. The combination of proportional control withdamping injection and iterative learning resulted in the lowesterrors for all high-level controllers. With time-based desiredtorque, root-mean-squared errors were 0.6 N·m (1.3% of peakdesired torque) step by step, and 0.1 N·m (0.2%) on average.These results indicate that model-free, integration-free feedbackcontrol is suited to the uncertain dynamics of the human-robotsystem, while iterative learning is effective in the cyclic task ofwalking.

Index Terms— Rehabilitation Robotics, Ankle Exoskeleton,Torque Control, Human-Robot Interaction

I. INTRODUCTION

Exoskeletons have been used for performance restoration [1]and enhancement [2]. Recently, the importance of the naturaldynamics of the human body [3], energy input [4] and comfortof human-robot interactions [5, 6] have been given increasedattention in exoskeleton applications. In these approaches to ex-oskeleton assistance torque control is crucial. In such systems,series-elastic actuators [7] are commonly used to provide low-error torque tracking in the presence of unknown and changinghuman dynamics.

It has been a common interest for the lower-limb exoskeletoncommunity to improve locomotion performance. The anklejoint has drawn attention for effort reduction in walking [8]since it produces more mechanical work than other joints[9]. Better ankle joint torque tracking would therefore benefitexperimental studies. Such techniques are also expected toextend to knee and hip exoskeletons, for which the controlproblem is similar.

This material is based upon work supported by the National ScienceFoundation under Grant No. IIS-1355716 and by the Singapore EconomicDevelopment Board NTU-CMU Dual PhD Scholarship.

1Dept. Mechanical Engineering, Carnegie Mellon University, USA.2School of Electrical and Electronic Engineering, Nanyang Technological

University, Singapore.3Robotics Institute, Carnegie Mellon University, USA.∗Corresponding author: J. Zhang. Dept. Mechanical Engineering,

Carnegie Mellon University, 5000 Forbes Ave. Pittsburgh, Pennsylvania15213, USA. Email:juanjuaz@andrew.cmu.edu

Control of exoskeletons is normally hierarchical, with high-level controllers determining behavior-related desired torquesand torque control lying at a lower level. Therefore, in thisstudy we refer to torque controllers as low-level controllersand desired torque generators as high-level controllers.

Many low-level control methods have been employed fortorque or position tracking in exoskeletons, including classi-cal feedback control [6], model-based control [5], adaptivecontrol [10] and iterative learning control [11]. However, itremains unclear which method has the best performance, orhow performance may vary with high-level controllers.

High-level controllers based on time [4], joint angle [12],neuromuscular models [6], and electromyographic measure-ments [8] have been used to assist human walking. Each may beadvantageous insomeassistanceparadigms,andeachgeneratesdesired torques with different dynamics.

The topic of exoskeleton torque control has not drawnas much attention as high-level control and biomechanicsoutcomes. In cases where torque control has been addresseddirectly, it has typically been investigated under unrealisticconditions, i.e., during benchtop tests rather than human-robotinteractions [13], and results have often not been reportedquantitatively [14]. Moreover, little has been reported on therelative performance of different torque controllers on thesame platform, making differentiation among candidate meth-ods difficult. This study aims to compare the torque-trackingperformance of prominent torque controllers, under realisticexperimental conditions, with multiple high-level controllers,in a single exoskeleton platform. These results are expected tohelp guide the selection and tuning of exoskeleton torque con-trollers, particularly in lower-limb exoskeletons for locomotionassistance.

II. METHODS

Nine torque controllers, including variations and combi-nations of classical feedback control, model-based control,adaptive control and iterative learning, were experimentallycompared in this study. Each was tested separately with fourhigh-level controllers that determined desired torque basedon time, ankle angle, a neuromuscular model, or electro-myography. Controllers were implemented on a tethered ankleexoskeleton with series-elastic actuation and tuned to minimizeerror. Under each high- and low-level controller combination,the exoskeleton was tested with one subject who walked onehundred steady-state steps on a treadmill. The root meansquared torque errors were calculated for each step and for anaveraged step.

2015 IEEE International Conference on Robotics and Automation (ICRA)Washington State Convention CenterSeattle, Washington, May 26-30, 2015

978-1-4799-6923-4/15/$31.00 ©2015 IEEE 5584

A System Schematic

transmission

exoskeleton

B Device Photo

off-board motor

Fig. 1. Schematic and photo of the tethered ankle exoskeleton system.(A) Schematic of the system that consists of an off-board motor, a Bowdencable transmission and an exoskeleton frame; (B) Photo of the exoskeletonworn by a human.

A. Exoskeleton Testbed

The ankle exoskeleton testbed used in experiments consistedof an off-board geared electric motor with real-time driver, aflexibleBowdencable transmissionwithseriescompliance,andan exoskeleton that interfaced with the human body (Fig. 1).

A dedicated real-time control system sampled sensor data at5000 Hz, which were then filtered at 200 Hz. The desired motorvelocity commands were generated at 500 Hz. The motor unitwas composed of a low-inertia 1.6 kW AC servo motor anda 5:1 planetary gear. Motor input voltage was regulated by amotor driver running in velocity control mode, which providessmoother torque tracking in series elastic actuators [15]. Adigital optical encoder was used to measure motor position.

The flexible Bowden cable that transmitted forces was com-posed of a coiled-steel outer conduit and a 0.003 m diameterVectranr inner rope, and was 2 m in length. A coil spring withan effective stiffness of 190 N·m·rad-1 was attached at the endof the rope to provide increased compliance.

The exoskeleton frame generated a plantarflexion torquewhich was measured using strain gauges on the heel lever with1000 Hz signal conditioning. Joint angle was measured using adigital optical encoder. Muscle activity was measured using awired electromyography system for one high-level controller.

The components of the system interacted as in Fig. 2. Thehigh-level controller used time, t, exoskeleton joint angle, θa, orelectromyography (EMG) to determine the desired torque, τdes.The low-level controller tracked torque by changing the desiredmotor velocity, θ̇m,des determined by desired torque, measuredtorque, τ , motor angle, θm, and/or exoskeleton angle. A motordriver regulated motor velocity. Motor motion was transmittedthrough the Bowden cable to one end of a series springand generated exoskeleton torque together with exoskeletonmotion. Both the human and the series spring exerted torqueson the exoskeleton frame and led to exoskeleton rotation.

B. Controllers

Nine prominent low-level torque control methods werecompared in this study in combination with four high-levelassistance controllers. High-level controllers generated desiredtorque, which low-level controllers tracked.

EMG Signal

Δθ

θa

θm

τh

τ

τdes

θdes

.

Low Level

Control

Motor

System

Trans-

missionSeries

Spring

Exo

Frame

High Level

ControlHuman

+_ θ’m

Time

-τh

Fig. 2. Flowchart of the control system. High Level Control and LowLevel Control are the two blocks to be varied and tested in this study.

1) Low-Level Torque Controllers: Desired motor velocitywas commanded to a dedicated hardware motor controller forall torque controllers investigated:

θ̇m,des = ∆θm,desT -1 = [θm,des−θm]T -1 (1)

where θ̇m,des is the commanded motor velocity; T is a constantrelated to motor position rise time; ∆θm,des is the desired motordisplacement; θm,des is the desired motor position; θm is themeasured motor position.L1: Proportional Control with Damping Injection (PD)

This controller was a variant of the classical proportional-derivative control of torque, with the derivative term replacedby damping injection [16]:

∆θm,des =−Kpeτ −Kdθ̇m (2)

where Kp is proportional gain, eτ = τ − τdes is torque error,τ is measured exoskeleton torque, τdes is desired exoskeletontorque, Kd is damping gain, and θ̇m is measured motor velocity.Lower noise was obtained with damping injection than with thederivative of torque error because motor position was measuredby a digital encoder while torque was measured by analog straingauges subject to electromagnetic interference.L2: Proportional Control with Damping Injection andError-Dependent Gains (PD+EDG)

This controller was the same as L1, except that the propor-tional gain was error-dependent [17, 18]:

Kp = min[ceil( |eτ |hτ

)hk,Kmax]

∆θm,des = −Kpeτ −Kdθ̇m(3)

where operation ‘ceil’ rounds the element to the next smallestinteger, Kp is the error-dependent proportional gain, hτ and hkare torque error and proportional gain step sizes, and Kmax isthe maximum allowable gain. This controller was intended tolimit overshoot and oscillations during torque tracking.L3: Proportional Control with Damping Injection andPrevious-Error Compensation (PD+PEC)

This controller was the same as L1, except that desired torquewas altered based on torque error from the previous time step[as done in 19]:

τ ′des = τdes− eτ ,prev∆θm,des = −Kpec(τ− τ ′des)−Kdθ̇m

(4)

where τ ′des is the compensated desired torque and eτ ,prev is thetorque error from the previous time step. This was intended toincrease control response for large errors.

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L4: Proportional-Integral Control with Damping Injec-tion (PID)

This controller was a variant of the classical proportional-integral-derivative control, with the derivative term replacedby damping injection:

∆θm,des =−Kpeτ −Ki∫ t

t0 eτ dt−Kdθ̇m

where Ki is the gain on the integral of torque error, and t0 is thetime at which the stance phase of current step begins.L5: Proportional Control with Damping Injection andModel-based Compensation (PD+M)

This controller combined the feedback controller of L1and a model-based feed-forward term, which was intendedto anticipate changes in desired motor position due to eitherexoskeleton joint displacements or changes in desired jointtorque:

∆θm,des = −Kpeτ −Kdθ̇m +(θmdl−θm)θmdl = θaR̃− τdesK̃-1

c

where θmdl is model-based motor position compensation, θm ismeasured motor position, θa is measured exoskeleton anklejoint angle, R̃ is estimated total gear ratio from motor toexoskeleton joint, and K̃c is estimated total stiffness of thetransmission with respect to the motor displacement.L6: Passivity-based Adaptive Control (PAS)

This provably stable adaptive controller was based on adynamic model of the motor, transmission and exoskeleton.It is described as

∆θm,des =−Kpeτ −Kss+Yd(τ, τ̇r, τ̈r, θ̇a)Γ̂

where Ks is the sliding control gain and s is a sliding vector:

s = τ̇− τ̇des +λeτ = τ̇− τ̇r

where λ is a positive scalar and τr is a virtual reference torque.Yd is a regressor defined as

Yd(τ, τ̇r, τ̈r, θ̇a) = [τ τ̇r τ̈r θ̇a],

whichexpresses thedynamicsasa linearcombinationof systemparameters. Γ is the system parameter vector. Its estimate Γ̂ wasupdated by the law

˙̂Γ =−LY T

d s,

where L is a positive definite parameter adaptation gain matrix.This controller was intended to reduce model uncertainties

by parameter adaptation and address unknown human-robotinteractions.L7: Iterative Learning of Desired Motor Position (LRN)

This controller updates a desired motor position trajectoryfor the next step using torque errors of the current step [11, 20]:

θm,des(i,n+1) = βθm,des(i,n)−KLeflt(i,n)∆θm,des(i,n) = θm,des(i+D,n)−θm(i,n)

where i is the time index or number of control cycles elapsedwithin this step, n is this step and n+1 is the next step, KL is theiterative learning gain, and D is an estimate of the delay betweencommanding and achieving a change in motor position. Currenttorqueerror therebyupdatesdesiredmotorposition for thesame

time index on the next step, while commanded motor velocity atthis time index is based on a preview of desired motor positionlater in the same step.

β ∈ [0, 1] is a weighting term on the learned trajectory toadd “forgetting” into learning. eflt is the filtered torque errortrajectory, initially an array of zeros, expressed as

eflt(i,n) = (1−µ)eflt(i,n-1)+µeτ(i,n)

where µ ∈ [0, 1] is a weighting term on the learned error.This controller exploits the cyclic nature of the task to

accommodate complex dynamics without an explicit model.L8: Iterative Learning of Desired Motor Position +Proportional-Damping Compensation (LRN+PD)

This controller combined iterative learning (L7) withproportional-damping control (L1) compensation [11, 21]. Mo-tor commands arose primarily from the learned feed-forwardtrajectory, while feedback control compensated for step-by-step variations in desired torque:

θ LRNm,des(i,n+1) = βθ LRN

m,des(i,n)−KLeflt(i,n)θm,des(i,n) = θ LRN

m,des(i+D,n)−Kpeτ(i,n)−Kdθ̇m(i,n)

∆θm,des(i,n) = θm,des(i,n)−θm(i,n)

L9: Proportional Control with Damping Injection +Iterative Learning Compensation (PD+LRN)

This controller combined proportional-damping control (L1)with iterative learning (L7) compensation [11, 21]. Motorcommands arose primarily from feedback control, with learnedfeed-forward compensation for consistent tracking errors:

∆θ LRNm,des(i,n+1) = β∆θ LRN

m,des(i,n)−KLeflt(i,n)∆θm,des(i,n) = −Kpeτ(i,n)−Kdθ̇m(i,n)

+∆θ LRNm,des(i+D,n)

2) High-Level Assistance Controllers: During the stancephase, desired torque τdes was determined by high-level con-trollers H1-H4 detailed below. During the swing phase, motorposition control was employed to allow free human anklemovement while maintaining minimal cable slack:

∆θm,des = θaR̃−θm (5)

where R̃ is the estimated gear ratio from motor to exoskeleton.H1: Time Based Desired Torque Trajectory (TIME)

0 0.25 0.5 0.75

25

50

Time (s)

De

sire

d T

orq

ue

(N

. m)

Fig. 3. High-level control based on a fixed trajectory in time

This high-level controller set desired torque as a function oftime. We used a curve (Fig. 3) that resembled a scaled-down

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version of the human ankle moment during unassisted walking[9] with a stance period of 0.66 s.H2: Joint Angle Based Desired Torque (ANGLE)

Ankle Angle (rad)

Plantar�exion

[θ’a,2 τ’2]

Dorsi�exion

[θa,1 τ1]

[θa,3 τ3]

[θa,4 τ4]

[θa,0 τ0]

An

kle

To

rqu

e (

N. m

)

0

θa

torque

0

45.2

-0.2 0.2

Fig. 4. High-level control based on ankle joint angle

This high-level controller set desired torque as a functionof ankle angle and phase of the gait cycle [12]. We used apiece-wise linear curve that resembled a scaled-down versionof the human ankle moment during unassisted walking (Fig. 4),calculated as τdes =

τi−τi-1θa,i−θa,i-1

(θa − θa,i-1), i ∈ {1,2,3,4}, inwhich (θa,i,τi) defines a node in torque-angle space. The node(θa,2,τ2) marked the transition from the Dorsiflexion phase, inwhich ankle velocity was negative, to the Plantarflexion phase,in which ankle velocity was positive. Since the exact transitionpoint varied on each step, the angle and torque at the moment oftransition, (θ ′a,2,τ

′2) replaced (θa,2,τ2) for calculating desired

torque in the first portion of Plantarflexion, i.e., when i = 3.H3: Neuromuscular Model Based Desired Torque (NMM)

This high-level controller set desired torque using a virtualmuscle and neural system model. The virtual muscle tookhuman ankle position and velocity as inputs and generated avirtual joint torque which was conditioned and used as desiredtorque. The virtual torque was also fed into the virtual neuralsystem where it was delayed and linearly scaled to generatethe stimulation signal of the virtual muscle. This virtual reflexmechanism realized a form of positive feedback in the model.A complete description of the reflex-based muscle model wasavailable in [6].H4: Electromyography Based Desired Torque (EMG)

This high-level controller set desired torque in proportion toEMG measurements [8] from the subject’s gastrocnemius mus-cle. Electrical activity was measured using surface electrodes,high-pass filtered at 20 Hz, rectified, low-pass filtered at 6 Hz,offset by a small value of -0.008, and amplified by a gain of 283to obtain the desired torque.

C. Experimental Methods

Experiments were conducted with one healthy subject(30 yrs, 56 kg, 1.65 m tall, female), who walked on a treadmillat 1.25 m·s-1 with a self-paced step period of 1.08 ± 0.06 swhile wearing the exoskeleton on one leg.

Before collecting data, we tuned parameters for each combi-nation of high- and low-level controller as the subject walkedwith the exoskeleton. High-level control parameters for H1-H4 were selected so as to result in peak desired torques ofapproximately 45 N·m. Low-level control parameters listed in

Table I were systematically tuned with the aim of minimizingtorque error. During tuning, very similar optimal low-level con-trol parameters were found across high-level controllers. Thesame values were therefore used for all high-level controllers.For model-based compensation, the value of R̃ was basedon measurements and K̃c was determined based on measuredlever arm and the manufacturer-specified stiffness of the seriesspring.

For each high-level controller, all low-level controllers weretested on the same day, without removal of the exoskeletonbetween trials. For each combination of low- and high-levelcontroller, data for one hundred steady-state steps were col-lected. Root mean squared torque error both for the set of allsteady-state steps and for the average step, which was obtainedby averaging the desired and actual trajectories of the onehundred steps in time, were then calculated.

TABLE ILOW-LEVEL TORQUE CONTROL PARAMETER VALUES

Param. Value Param. Value Param. ValueKp 0.093 R̃ 2.90 KL 0.0077Kd 0.010 K̃c 195 N·m·rad-1 D 0.022 sKmax 0.15 Ks 0.005 β 1Kpec 0.046 λ 0.077 µ 1Ki 7.7e-5 L 1.0e-9 T 0.050 shτ 11.3 N·m hk 0.039

III. RESULTS

The best torque tracking performance was observed withthe combination of feedback control and iterative learning, i.e.,PD+LRN or LRN+PD, for all high-level controllers, both inreal-time and for the average step. Between the two, PD+LRNshowed lower errors before convergence. Depending on high-level conditions, the real-time torque errors with PD+LRNwere 38%-84% lower than with PD (t-test, p < 1.9·10-34), andaverage-step torque errors were 91%-97% lower. Other addi-tions to feedback control showed minor performance effects,except that model-based compensation increased torque error.While providing low errors for average tracking, pure iterativelearning resulted in high real-time errors. For the EMG-basedcontroller, torque tracking errors and variability were generallyhigher for all torque controllers.

Some interactions between high- and low-level torque con-trollers were observed. Pure feedback control outperformedpure iterative learning control for Angle and EMG based high-level conditions, while an opposite trend was seen in Timeand NMM conditions. For the the Time-based controller, poortracking at the onset of desired torque, including a delay andovershoot, was observed for all controllers without a learningcomponent. Adding iterative learning to PD resulted in thegreatest improvement in performance for the Time basedcondition. A minor improvement in performance over pure PDwas seen with an additional integral term (PID) for Time andAngle based conditions. With Time-based high-level control,passivity (PAS) and previous-error compensation (PD+PEC)also showed a small benefit.

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TIME ANGLE NMM EMG

PD

PD

+E

DG

PD

+P

EC

PID

PD

+M

PA

S

LR

N

LR

N+

PD

PD

+L

RN

RM

S-E

AV

G (

N. m

)R

MS

-E (

N. m

)

PD

PD

+E

DG

PD

+P

EC

PID

PD

+M

PA

S

LR

N

LR

N+

PD

PD

+L

RN

PD

PD

+E

DG

PD

+P

EC

PID

PD

+M

PA

S

LR

N

LR

N+

PD

PD

+L

RN

PD

PD

+E

DG

PD

+P

EC

PID

PD

+M

PA

S

LR

N

LR

N+

PD

PD

+L

RN

0

6

12

2.7

1

4.1

9

3.5

6

2.8

4

5.5

3.6

0.3

59

0.4

07

0.2

24

0

6

12

3.8

4 ±

0.8

2

5.7

5 ±

0.7

3

4.7

3 ±

0.6

7

3.9

9 ±

0.7

2

6.3

±

0.8

5

4.5

4 ±

0.6

4

4.5

2 ±

1.7

2.1

±

0.7

3

2.1

4 ±

0.7

7

0

6

12

1.3

1

2.7

4

1.1

9

1.0

6

5.5

5

1.1

9

0.1

39

0.1

87

0.1

13

0

6

12

1.6

1 ±

0.1

6

3.1

2 ±

0.1

4

1.6

1 ±

0.1

5

1.5

±

0.1

5

5.8

9 ±

0.2

8

1.6

3 ±

0.1

8

2.1

3 ±

1.1

0.9

07

±

0.2

4

0.9

86

±

0.2

3

0

6

12

3.5

3

4.0

1

3.1

2

2.9

8.1

6

3.3

5

0.2

23

0.2

45

0.0

99

4

0

6

12

1.7

6

3.2

3

1.9

7

1.8

6

7.2

1

1.9

7

0.2

71

0.1

85

0.1

19

0

6

12

3.6

7 ±

0.2

6

4.2

7 ±

0.4

5

3.3

±

0.2

5

3.0

6 ±

0.3

2

8.4

7 ±

0.3

5

3.4

7 ±

0.3

1

1.0

4 ±

0.4

8

0.7

38

±

0.1

8

0.5

73

±

0.1

8

0

6

12

2.1

6 ±

0.1

7

3.7

3 ±

0.2

4

2.4

±

0.2

9

2.3

2 ±

0.2

1

7.3

8 ±

0.1

7

2.4

1 ±

0.2

9

1.2

3 ±

0.4

7

0.6

89

±

0.2

1

0.9

34

±

0.3

2

Fig. 5. Step-wise root-mean-squared torque errors averaged over all strides (RMS-E), and root-mean-squared torque errors for an average stride (RMS-EAVG) generated by overlapping all strides in time, for all high- and low-level control combinations

To

rqu

e (

N. m

)

TIME

0 0.25 0.5 0.75

25

50

Time (s)

ANGLE

0 0.25 0.5 0.75

25

50

Time (s)

NMM

0 0.25 0.5 0.75

25

50

Time (s)

EMG

0 0.25 0.5 0.75

25

50

Time (s)Average Step Desired TorqueDesired Torque

Average Step Measured TorqueMeasured Torque

Time=0 Heel Strike

Toe Off

Fig. 6. Overlapped trajectories of the desired and measured torques in time for all high level controllers with proportional control with damping injectioncompensated by iterative learning (PD+LRN)

Means and standard deviations of step-wise root-mean-squared torque error (RMS-E) and average-step root-mean-squared error (RMS-E AVG) are shown in Fig. 5. Error valuesfor PD+LRN and their percentage of the peak desired torque,τmax, for the average step are given in Table II. Overlappeddesired and measured torque trajectories for one hundred stepswith PD+LRN are shown in Fig. 6. The high variations oftorques for Angle- NMM- and EMG-based high level con-trollers are the result of step-to-step gait variation of the subject.PD+LRN with Angle-based desired torque also showed con-sistent performance for higher torque on two different devices(peak torques of 80–86 N·m) with a taller male subject in laterexperiments [22].

TABLE IITRACKING ERRORS WITH PD+LRN TORQUE CONTROL

RMS-E %τmax RMS-E AVG %τmax

Time 0.57 ± 0.18 N·m 1.3% 0.10 N·m 0.2%Angle 0.99 ± 0.23 N·m 2.5% 0.11 N·m 0.3%NMM 0.93 ± 0.32 N·m 2.3% 0.12 N·m 0.3%EMG 2.14 ± 0.77 N·m 5.9% 0.22 N·m 0.6%

IV. DISCUSSION

We evaluated the performance of nine prominent torquecontrollers by experiments on a tethered ankle exoskeleton,with series-elastic actuation, during human walking, with fourhigh-level controllers. Model-free proportional control withdamping injection, compensated by iterative learning, resultedin the lowest torque errors for all high-level controllers, both inreal-time and for the average step. This approach is analogousto the classical proportional-integral-derivative control; theproportional term provides basic tracking, iterative learningeliminates steady-state cyclic errors, and damping injectionprovides stability. We thus label the method as proportional-learning-damping control.

Few studies have compared the torque tracking performanceof various controllers in practical conditions for exoskeletonsand active orthoses. Few quantitative reports on torque controlof lower-limb exoskeletons are available, and these mostlyconcern benchtop tests. These tests usually do not reflect theunknown, complex and time-varying dynamics of human-robotinteractions, which define the biggest challenge in exoskeletontorque control. Little data and analysis have been provided,

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which makes interpretation of the results difficult. From theinformation available, proportional-learning-damping controlhas demonstrated better performance than existing approaches.

Some interactions between high- and low-level controllerswere observed. Iterative learning led to a bigger improvementin torque tracking for the Time-based high-level controller,presumably because desired motor positions were also learnedin time. Therefore, it might be that for Angle-based desiredtorque, iterative learning elements could be more effective ifthey were performed based on joint angle. When PD controlwas compensated by an integral term (PID), previous-errorcompensation (PD+PEC), orpassivity-based adaptation (PAS),torque tracking was slightly improved for the Time-based con-dition, which suggested that the model-free continuous-timeintegration elements in torque controllers may be beneficialwhen the desired torque is consistent in time. Error-dependentgains (PD+EDG) did not provide benefits and may be moresuited for motion based control in rehabilitation.

While showing promise in simulation and theory, model-based control elements generally worsened or had no effecton control performance in our experiments. Sensitivity tomodeling accuracy seems to be a fundamental issue. Thepartially model-based PAS controller showed a slight benefitin some conditions due to its adaptive nature, but the effect wasnot consistent.

Comparisons across high-level controllers were difficult tomake for the same low-level control due to un-normalizedtracking difficulty. Multiple values for high-level parameterswere not tested in this study, which is an area for future work.

Changes in the profiles of desired torque and joint kinematicsacross low-level controllers for the same high-level conditionreveal an interaction effect. For example, more variability indesired torquewasobservewithNMM-based thanAngle-basedassistance when using PD, but an opposite trend was seen withLRN.Thisseemstobedue to thecomplex,multi-time-scale,dy-namic interactions between continuous torque control, within-step human variations, the high-level controller, and humanadaptation over multiple steps. These effects may be importantfor selecting and tuning exoskeleton torque controllers.

Hardware, series elasticity in particular, also interacted withtorque control performance. The interactions between serieselasticity, torque control gains and high-level control objectivesshould be investigated in the future.

V. CONCLUSIONS

A systematic comparison of exoskeleton torque controllersunder walking conditions was conducted, demonstrating thatproportional control with damping injection compensated byiterative learning had better torque tracking performance thanany other methods tested or previously demonstrated. Im-plementation of this proportional-learning-damping controllerwas straightforward, requiring sequential tuning of only fourparameters. Our results suggest that this approach can beapplied to multiple torque-controlled lower-limb exoskeletonsused in cyclic processes like locomotion. There remains arich area for future research on complex interactions between

exoskeleton hardware, torque control, assistance control, taskgoals and human behavior.

VI. ACKNOWLEDGEMENTS

The authors thank Rachel Jackson and Kirby Witte forassistance with hardware maintenance and improvement.

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