First Implementation Results on FAT based AdaptiveControl for a Lower Extremity Rehabilitation Device

Jinfu Li, Student Member, IEEE, Bingquan Shen, Fengjun Bai, Chee-Meng Chew, Member, IEEEand Chee Leong Teo

Department of Mechanical EngineeringNational University of Singapore

21 Lower Kent Ridge Road, Singapore 119077li.jinfu@nus.edu.sg

Abstract—Gait restoration after stroke is a major concern ofneurological rehabilitation. In this paper, a recently developedwearable lower extremity rehabilitation device is introduced, andan adaptive control strategy based on Function ApproximationTechniques (FAT) is designed to aid stroke patients who arein the early phase of rehabilitation or severely affected. Thedevice adopts an anthropomorphic structure actuated on hipand knee joint level in sagittal plane. Frameless DC motorwith high gear-ratio harmonic drive is used as actuator. Fourierseries fitting method is used to obtain the desired hip and kneereference trajectory. This control algorithm is then implementedin the device with friction compensation to track the desired gaittrajectory. Implementation results for a healthy subject show thatgood tracking performance can be achieved, and actuator toquesare within a reasonable range. This FAT based adaptive controlalgorithm could potentially be used for stroke patients as well.

Index Terms—Lower extremity rehabilitation device, FATbased adaptive control, passive gait training

I. INTRODUCTION

Stroke is the third most frequent cause of death and

the leading cause of permanent disability in the USA and

Europe [1]. Neurological impairment after stroke frequently

causes hemiparesis or partial paralysis of one side of the

body, which affects the patient’s ability to perform activities

of daily living (ADL). Physical rehabilitation training therapies

are usually adopted to improve the lost movement functions

of stoke patients.

In the past tens of years, manually assisted treadmill training

with body weight support system (BWSS) has become a

regular therapy for gait rehabilitation of stroke patients [2]–

[4]. However, this conventional training requires a team of

three or more therapists together to guide the patient’s legs

on predetermined gait paths and stabilize the patient’s pelvis.

The quality of this treadmill training largely depends on

therapists’ experience and judgment, which can vary a lot

among therapists. Moreover, the training sessions are usually

short (20-30 minutes each session) due to therapists’ muscle

fatigue and back pain, and patient’s training progress and

recovery cannot be recorded. Therefore, as alternatives, lots

of robotic gait rehabilitation devices have been developed to

overcome the above shortcomings in recent years. They deliver

well controlled repetitive and prolonged training sessions for

hip, knee, ankle or all of them.

Currently, existing lower extremity rehabilitation devices

can be roughly classified into two groups: treadmill gait

trainers and overground wearable gait trainers [5]. Treadmill

gait trainers still use the treadmill and BWSS, but they replace

the therapists with robotic lower extremity exoskeletons. Three

commercial systems have already been available: Lokomat

(Hocoma, Switzerland) [6], LokoHelp (LocoHelp Group, Ger-

many) [7], and AutoAmbulator (Motorika, USA) [8]. Other

such robotic systems are still at a research state or under

clinical testing, such as Active Leg Exoskeleton (ALEX) [9]

and LOPES (Lower-extremity Powered ExoSkeleton) [10].

These systems are restricted to be used in hospitals instead

of homes because they are too expensive, bulky and not

portable. Overground wearable gait trainers, on the other hand,

are portable robotic lower extremity exoskeletons without

a treadmill, which can be taken home to assist with gait

training at home. Such commercialized systems are like HAL

(Cyberdyne, Japan) [11], ReWalk (Argo Medical, Israel) [12],

and eLEGS (Berkeley Bionics, USA) [13].

From the control aspect, for different groups of patients,

different control strategies must apply. Even though more

and more researches focus on developing patient-cooperative

control strategies [14] such as active impedance control [15],

assist-as-needed control [16], or electromyography (EMG)-

based feedback control [17]–[19], these control strategies are

actually not quite suitable for stroke patients who are in the

early phase of rehabilitation or severely affected because their

muscles or EMG signals are too weak to control the device.

Therefore, the passive gait training is still used for their

rehabilitation. Actually, most commercialized rehabilitation

devices adopt this passive position-controlled training. In the

other accepted conference paper [20], a FAT based adaptive

control scheme first proposed by Huang and Chen [21], [22]

has been used to demonstrate its feasibility for lower extremity

passive rehabilitation training purpose via Matlab simulations.

In this paper, we would implement this FAT based adaptive

controller to the lower extremity rehabilitation device and

demonstrate its effectiveness via a healthy subject experiment.

This paper is organized as follows. Section II briefly intro-

duces a newly developed wearable lower extremity rehabilita-

tion device, and presents its dynamics model. In section III,

hip and knee reference trajectories are obtained, the FAT

based adaptive controller is then summarized, and friction

compensation for harmonic driver actuator is presented in

detail. Then in section IV, this FAT based adaptive control

scheme with friction compensation is implemented in the

device and preliminary results from a healthy subject are

obtained. Finally, conclusions and future works are outlined

in section V.

II. HARDWARE DESIGN AND DYNAMICS MODELLING

A. Hardware Design

The lower extremity rehabilitation device, as shown in

Fig. 1, was designed to aid in the flexion and extension motion

of the wearer’s hip and knee joint. To fit a wide range of

wearers, the device consists of an adjustable anthropomorphic

frame based on the anthropometrical data provided in [23],

with actuator module attached at each joint. Orthotic cuffs

are used as the interface between the device frame and the

wearer. The actuator module is powered by a frameless direct

drive high torque DC motor with a harmonic drive at a 50:1

gear ratio, which could deliver up to 50 Nm of maximum

momentary torque and a repeated torque of 35 Nm. The

maximum output speed can reach to 15.3 rad/s. Optical

incremental encoder at 1000 counts/rev is equipped at the

pre-reduction stage of each actuator module to measure the

hip and knee angle. Ground reaction force (GRF) sensors and

EMG sensors are also incorporated for further use. To ensure

the safety, the range of motion of each joint is limited to be

slightly smaller than the normal range of motion for normal

human for safety reasons (Hip:-15◦-130◦; Knee:0◦-130◦).

Fig. 1. Lower extremity rehabilitation device

A real-time embedded controller (NI sbRIO9612) which

consists of a real-time processor, a user-reconfigurable field-

programmable gate array (FPGA), and analog and digital I/O is

used to do signal processing and low level motor control. Desk-

top computer can communicate with the controller via network

cable for high level control and monitoring. The actuator motor

is controlled by a digital servo driver. CAN communication at

1Mbits/s is implemented between the embedded controller and

the digital servo driver. All the electronics can be fitted into a

small backpack for portability. The whole system schematics

is shown in Fig. 2.

CAN Bus

Real-time controller Single-Board RIO

Power Supplies (Battery, power management)

Motor Driver

EMG sensor, GRF sensor, ……

Desktop Computer

Motor Motor

Signal Processing and Control

Network cable

Motor Driver

Fig. 2. The whole system schematics

B. Dynamics Modelling

The above rehabilitation device is hip and knee actuated on

one side of the body, and it is assumed to be fixed perfectly

with human thigh and shank. The human lower limb and

the device are considered as a whole system, and human

joint torques are seen as external torques to the system. The

combined dynamics of rehabilitation device and human lower

limb is given by

D(θ)θ+C(θ, θ)θ+G(θ) = τ+ τh (1)

where θ, θ, and θ are vectors of generalized position, velocity

and acceleration, respectively. D(θ) is the system inertia ma-

trix, C(θ, θ)θ is a vector of centrifugal and Coriolis torques,

and G(θ) is the vector of gravitational torques. τ is the torque

vector applied by robotic rehabilitation device, and the τhrepresents the torque vector provided by hip and knee of

human subject.

We also assume that the wearer’s torso is suspended to

perform passive gait training, as shown in Fig. 3. According to

Steiners’ Theorem, masses can be concentrated at the center

of the link, and denote the equivalent masses as m1 and m2.

The length of the links are L1 and L2 respectively. D, C and

G matrices are functions of m1, m2, L1 and L2.

III. FAT BASED ADAPTIVE CONTROL ALGORITHM

A. Gait Trajectory

Implementing most control strategies in the rehabilitation

devices often requires a desired trajectory to be specified.

In this work, the normal hip and knee gait trajectories from

healthy subjects are provided by reference [24]. One cycle of

hip or knee gait trajectory is approximated by fifteen terms

X0

Knee

121 L

2m

1m

1L

2L22

1 L

Hip

1�

2�

Y0

X1

Y1

Fig. 3. A simplified two link model

of Fourier series in (2), where a0, ak, bk and w (k = 1 · · ·7)

are fitting parameters given by Matlab ( Table I ), x is the gait

cycle, and θhip/knee is the gait angle in degree. The good fitting

results are shown as follows in Fig. 4.

θhip/knee(x) = a0 +7

∑k=1

ak cos(kxw)+7

∑k=1

bk sin(kxw) (2)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−10

0

10

20

30

40

50

60

70

Gait Cycle

Hip

and

Kne

e A

ngle

(deg

)

Knee

Hip

Fig. 4. Normal gait trajectory fitting results: normal hip and knee trajectoriesare plotted in red dashed lines, and fitting hip and knee trajectories are plottedin blue solid lines

In order to fit the trajectories to various wearers and change

the gait period as well, several terms of parameters are

incorporated to yield the final desired trajectories θd in (3),

where A is amplitude scaling, B is amplitude offset, and T is

gait period. These parameters can be adjusted by users. The

obtained trajectories as well as their first and second order

derivatives are used as reference trajectories in the realtime

implementation in section IV.

θd(t) = Aθhip/knee(tT)+B (3)

TABLE IFOURIER SERIES FITTING RESULTS

Fitting Parameters a0 a1 b1 a2 b2 a3

Hip 17.63 20.16 -3.356 -3.09 -1.422 0.02337

Knee 25.59 -3.313 -18.79 -12.84 6.821 -0.3184

Fitting Parameters b3 a4 b4 a5 b5 a6

Hip 1.325 -0.1398 -0.1995 0.02123 0.1208 0.09569

Knee 3.738 -0.8908 0.3473 -0.5027 0.422 -0.1007

Fitting Parameters b6 a7 b7 wHip 0.05315 -0.09582 -0.07109 6.326

Knee 0.09104 0.05284 -0.02913 6.293

B. FAT based Adaptive Controller

Since the wearers considered are those stroke patients who

are in early phase of rehabilitation or severely affected, we

assume they are completely passive. The dynamics model (1)

can be further simplified as

D(θ)θ+C(θ, θ)θ+G(θ) = τ (4)

The FAT based adaptive controller is summarized in the fol-

lowing. Details of this controller development can be referred

in [20].

The FAT controller is given as

τ = W TD ZDv+W T

C ZCv+W TG ZG −Kds (5)

where the desired gait trajectory vector obtained from section

III-A is denoted as θd , tracking error as e = θ−θd , s = e+Λe,

v = θd −Λe, and Λ = diag(λ1,λ2) with λi > 0 (i = 1,2). WD,

WC and WG are weighting matrices, and ZD, ZC and ZG are

matrices of basis functions.

The update laws can be chosen as

˙WD =−Q−1D ZDvT

s˙WC =−Q−1

C ZCvTs

˙WG =−Q−1G ZGsT

(6)

where vTs = svT , vT

s = svT , QD, QC and QG are positive definite

weighting gain matrices.

Two important conclusions are also summarized here:

• Tracking errors e converge to zeros asymptotically.

• Estimates D, C and G are bounded, and their convergence

depends on the persistent excitation condition of input.

C. Friction Compensation

In order to obtain high joint torque, frameless direct drive

DC motor with high gear-ratio harmonic drive is used as

actuator in our lower extremity rehabilitation device. However,

this kind of actuator introduces high level of internal friction,

which could greatly decrease the back-drivability under free

motion and affect the controller performance. Therefore, fric-

tion compensation for harmonic drive actuator is needed before

we implement the control algorithm.

In the actuator design, no output torque sensors or shaft

encoders are used, which makes the friction compensation

more complicated. Reference [25] provides a method of fric-

tion compensation for harmonic drive servo actuator in the

absence of output torque measurements and shaft encoder data,

and nearly complete friction compensation can be archived.

The same friction compensation algorithm is employed and

similar results are obtained. The exponential friction model

(7) is chosen as the friction model

τ f riction = (α0 +α1 exp−(θ/vs)2)sgn θ+α2θ (7)

where θ is the rotational velocity of the actuator, and α0,α1,α2

and vs are parameters determined from the fitting results. Fig. 5

shows the typical friction torque data collected from knee

actuator as a function of its rotational velocity. Mean measured

torque values are obtained from multiple experiments and then

used to do the curve fitting.

Fig. 5. Friction toque in one actuator as function of its rotational velocity:blue line shows the approximated friction model

In addition, a modification has to be made to fiction-velocity

map. Because the map shown in Fig. 5 has an infinite slope at

zero velocity, it is very sensitive to the small deformation of the

motor and measurement velocity noise, which could result in

chattering problems. Therefore, the slope is decreased by mul-

tiplying each side of the map by (1−exp(−|θ|ks)) where ks is

a factor used to adjust the slope. Decreasing the slope would

reduce the performance of friction compensation. Therefore, a

compromise between friction compensation performance and

suppression of chattering is made to determine a proper ks. The

final fitting parameters for the exponential friction model are

shown in Table II. After the friction model is obtained, then it

can be implemented using the feedback friction compensation

for the actuator, as shown in Fig. 6.

TABLE IIFITTING PARAMETERS FOR EXPONENTIAL FRICTION MODEL

Parameter Value for positive part Value for negative part

α0 0.8449 0.8440

α1 0.2309 0.2349

α2 0.3774 0.4327

vs 0.0429 0.0427

ks 300 300

dtd

�

��

friction�

� ��

total�

Fig. 6. Feedback friction compensation scheme

IV. IMPLEMENTATION AND RESULTS

The whole implementation diagram of this FAT based

adaptive control scheme with friction compensation is shown

in Fig. 7. No robot model parameters, acceleration feedback

or regressor matrix computation are needed for the controller

and adaptive update law, which greatly simplifies its design

and implementation. Then this control scheme is implemented

in the sbRIO embedded controller via Labview programming.

)(ˆ �D

),(ˆ �� �C

)(ˆ �G

��

�

�

K

�

�

d���

d��

d�

v�e��

e�

ve�

e ��

� �

��

s

�

�����

��

�

Fig. 7. FAT based adaptive control scheme

One healthy subject wears the lower extremity rehabilitation

device and walks on a treadmill with speed 0.8 (km/h) to

do experiment. The ‘affected’ leg attached with the device is

required not to exert any hip and knee torques during walking

so that the subject can be regarded as a passive wearer like

stroke patients. The reference trajectories described in (3) is

selected as A = 1, B = 0, and T = 3 (s). The control loop

rate is set to be 200 (Hz). The controller in (5) is applied

with the gain matrices Kd = diag(5,5) and Λ = diag(20,10).The eleven terms of Fourier series with period time 5 (s)are selected as the basis functions for approximation, and

initial weighting matrices are assigned to be zero matrices.

The weighting gain matrices in the adaptive update law (6) are

selected as Q−1D = 10−4I44, Q−1

C = 10−4I44, and Q−1G = 10−4I22.

The actuator saturation torques are set to be 25 Nm. The

experiment results are shown from Fig. 8 to Fig.10.

Fig. 8 shows the tracking performance of hip and knee gait

trajectories. As can be seen, the hip and knee can track the

reference trajectories precisely with tolerable errors. Actually

for rehabilitation robots, perfect tracking control is not desired

as for industry robots, because it might too rigid to threat

the wearer’s safety. In addition, no unwanted overshoots or

oscillations are observed. Fig. 9 shows the hip and knee

actuator output torques. Both actuator torques are below the

preset saturation torque 25 Nm. Additionally, we can observe

that hip actuator needs to provide higher torque. Lastly, Fig.

10 shows the parameter estimation performance for D, Cand G matrices using function approximation. They are all

bounded as desired. All the results above imply that this

FAT based adaptive control algorithm can be used for passive

rehabilitation training purpose.

0 1 2 3 4 5 6 7 8 9 10−10

0

10

20

30

40

50

60

70

Time (sec)

Hip

and

Kne

e A

ngle

(deg

)

Hip ReferenceHip TrackingKnee ReferenceKnee Tracking

Hip

Knee

Fig. 8. Tracking performance for hip and knee joint: reference trajectoriesare plotted in solid lines, and tracking trajectories are plotted in dashed lines

0 1 2 3 4 5 6 7 8 9 10−15

−10

−5

0

5

10

15

20

Time (sec)

Join

t Act

uato

r Tor

ques

(Nm

)

Hip Actuator TorqueKnee Actuator Torque

Fig. 9. Output torques of hip and knee actuator

V. CONCLUSIONS AND FUTURE WORKS

This paper briefly presents a newly developed wearable

lower extremity rehabilitation device. The FAT based adaptive

control strategy is implemented to control this device for

passive rehabilitation purpose. The effectiveness of this control

algorithm with friction compensation is verified by the tracking

performance of hip and knee gait trajectories of the device

with a healthy subject. The advantage of this control is that

it does not need acceleration feedback and regressor matrix

0 1 2 3 4 5 6 7 8 9 10−0.02

0

0.02

0.04

0.06

D E

stim

ates

0 1 2 3 4 5 6 7 8 9 10−0.01

0

0.01

0.02

0.03

C E

stim

ates

0 1 2 3 4 5 6 7 8 9 10−5

0

5x 10−3

Time (sec)

G E

stim

ates

D(11) D(12) D(21) D(22)

C(11) C(12) C(21) C(22)

G(11) G(21)

Fig. 10. FAT adaptive gains for D, C and G matrices

computation. This is the first time to implement this FAT based

adaptive control algorithm for lower extremity rehabilitation.

Future works concern the incorporation of compliance be-

tween the wearer and the device into this control algorithm.

Patient experiments as well as evaluation protocol for stroke

patients are also needed to be taken into consideration in the

future.

ACKNOWLEDGMENT

This work is under the project “Novel Rehabilitation Device

for Lower Extremities”. We acknowledge the financial support

from the Singapore Ministry of Education (MOE) Academic

Research Fund (AcRF) (Grant No.: R-265-000-419-112).

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