Abstract—In recent years, robot-assisted rehabilitation

systems have become an active research area to quantitatively

monitor and adapt to patient progress, and to ensure

consistency during the rehabilitation. In this work, an

exoskeleton type robot-assisted rehabilitation system called

RehabRoby is developed for rehabilitation purposes. An

admittance control with inner robust position control loop has

been used to control the robot-assisted rehabilitation system

RehabRoby. Real-time experiments are performed to evaluate

the efficacy of the proposed admittance control with inner

robust position control loop.

Keywords—Robot-assisted rehabilitation system,admittance

control with inner robust position control, exoskeleton robot

I. INTRODUCTION

here are over 650 million people around the world with

disabilities. Although it is accepted as 10% of the whole

world population, it is 15.7% in Europe, 12% in USA

[1] and 12.29% in Turkey [1]. Physical disability, which

occurs by birth or acquired during the life span of the person

due to the diseases or a trauma to the central nervous system

or musculoskeletal system, affects the functionality of

people. The physical therapy and rehabilitation programs are

applied to the people with disability to increase their joint

range, strength, power, flexibility, coordination and agility of

the person to improve their functional capacity as well as

third level of independence [2], [3]. In recent years, robot-

assisted rehabilitation systems have become an active

research area to quantitatively monitor and adapt to patient

progress, and to ensure consistency during the rehabilitation

[4]-[13].

Robot-assisted systems are mostly utilized in stroke

rehabilitation, but they can also be considered as a treatment

modality after the orthopedic and other neurologic

conditions. End-effector based such as MIT-MANUS [4],

MIME [5] and GENTLE/S [6] or exoskeleton type robots

such as ARMin [7]-[9], T-WREX [10], Pneu-WREX [11], L-

Exos [12], and Selford Rehabilitation Exoskeleton [13] have

been previously developed to provide assistance to patients

during the execution of upper-extremity rehabilitation

exercises. We have developed an exoskeleton type upper-

This work was supported by the Support Programme for Scientific and

Technological Research Projects (TUBITAK-3501) under Grant 108E190. F. Ozkul is with the Electrical and Electronics Engineering Department,

Yeditepe University, Istanbul, TURKEY, (fatihozkul85@gmail.com).

D. Erol Barkana is with the Electrical and Electronics Engineering Department, Yeditepe University, Istanbul, TURKEY, (corresponding

author, duygunerol@yeditepe.edu.tr).

extremity robot-assisted rehabilitation system called

RehabRoby.

Control of a robot-assisted rehabilitation system in a

desired and safe manner is an important issue during the

execution of the therapies. Previously, impedance controller,

position and admittance control have been used to control

robot-assisted rehabilitation systems. There is a human-robot

interaction in the robot-assisted rehabilitation systems, which

is an external effect that can cause changes in the dynamics

of the robotic systems. The changes in the dynamics of the

rehabilitation robotics may result in instability, which indeed

may cause unsafe situations for patients during the execution

of the rehabilitation task. Furthermore, robot-assisted

rehabilitation systems, especially exoskeleton types have

complex dynamics. Thus, there is a need to design a

controller for RehabRoby that compensates changes in the

dynamics. A controller, which is independent of dynamic

model of robot-assisted rehabilitation system, may provide a

solution to this problem [14]. Thus, in this work admittance

control with inner robust position control loop has been used

to control RehabRoby in a desired manner.

This paper describes the robot-assisted rehabilitation

system RehabRoby in Section II. Admittance control with

inner robust position control loop details are given in

Section III. Experiments that are used to evaluate the

admittance control with inner robust position control are

presented in Section IV. Discussion of the study and

possible directions for future study are given in Section V.

II. REHABROBY

RehabRoby has been designed to provide extension,

flexion, abduction, adduction, rotation, pronation and

supination upper-extremity movements and also combination

of these movements for activities of daily living (Fig. 1).

RehabRoby can provide horizontal abduction/adduction of

shoulder rotation (θ1), shoulder flexion/extension elevation

(θ2), internal and external rotation of shoulder (θ3), elbow

flexion/extension (θ4), lower arm elbow pronation/supination

(θ5) and wrist flexion/extension (θ6).

The placements of the shoulder and elbow joints in

RehabRoby are similar to ARMin III [7] except the

ergonomic design of the vertical displacement of the

glenohumeral (GH) joint in ARMin III has not been

considered in design of RehabRoby. RehabRoby has been

designed in such a way that it can be easily adjustable for

people with different arm lengths. Anthropometric

approaches have been used during the design phase of

RehabRoby. The human arm lengths have been selected as

the basis for the link lengths of the RehabRoby. The values

Design of an Admittance Control with Inner Robust Position

Control for a Robot-Assisted Rehabilitation System RehabRoby

Fatih Ozkul and Duygun Erol Barkana

T

2011 IEEE/ASME International Conference onAdvanced Intelligent Mechatronics (AIM2011)Budapest, Hungary, July 3-7, 2011

978-1-4577-0839-8/11/$26.00 ©2011 IEEE 104

include the measurements of the arm lengths of 2100 people

in 14 cities in Turkey. Additionally, RehabRoby can be used

for both right and left arm rehabilitation and can be translated

from right arm use to left arm use.

Range of motion (ROM), joint torques, velocities and

accelerations for RehabRoby have been determined using the

measurements of the movements of a healthy subject during

two activities of daily living tasks [15][16]. There is a

coupling between flexion/extension and abduction/adduction

of shoulder. The position of the horizontal shoulder rotation

angle determines the separation of the shoulder movements.

When horizontal shoulder rotation angle is 00, then shoulder

flexion/extension elevation is responsible for the

flexion/extension of shoulder, and when horizontal shoulder

rotation angle is 900, then shoulder flexion/extension

elevation is responsible for the abduction/adduction of

shoulder.

Note that there is a gravity effect and it will be not easy

for a subject to flex his/her shoulder during the execution of

the task. Thus, RehabRoby has been integrated with a

counterweight mechanism, which will reduce the gravity

effect. It will be easy for a subject to flex his/her shoulder

with this counterweight system (Fig.1).

Fig. 1. Robot-Assisted Rehabilitation System RehabRoby

An arm splint has been designed and attached to

RehabRoby (Fig. 1). It has humeral and forearm

thermoplastic supports with velcro straps and a single axis

free elbow joint. A thermoplastic inner layer covered by soft

material (plastazote) is used due to the differences in the size

of the subjects’ arms. Thus, the total contact between the arm

and the splint can be achieved to eliminate loss of movement

during the execution of the task. Kistler model press force

sensors, which have quite small sizes, are selected to measure

contact forces between the subject and RehabRoby. The

force sensor is placed in the inner surface of the

thermoplastic molded plate attached dorsally to forearm

splint via velcro straps.

RehabRoby has been interfaced with Matlab

Simulink/Realtime Workshop to allow fast and easy system

development. Humusoft Mf624 model data acquisition board

is selected to provide real time communication between the

computer and other electrical hardware. Humusoft Mf624

data acquisition board is compatible with Real Time

Windows Target toolbox of MATLAB/Simulink. Digital

incremental encoders are coupled with Maxon models of

brushed DC motors for joint position measurement. Five of

the six encoders have resolutions of 500counts/turn and one

of them has a resolution of 1000 counts/turn. Encoder data of

motors is received through a Humusoft Mf624 with a 500 Hz

sampling rate. Analog reference current values are converted

to digital ones, and then transmitted to the drivers using

RS232 serial bus with a baud rate of 115200 using

Programmable Interface Controller (PIC) microcontrollers.

The current reference values of motors are sent to the

microcontroller circuits using the analog outputs of the

Humusoft Mf624 card with the same sample rate.

Microcontroller circuits are used because four of the six

motor drivers of RehabRoby have no analog reference inputs.

Analog to digital conversion and serial transmission are

completed within 2 milliseconds. A 19’’ LCD screen is

positioned in front of the subject at a distance of about 1m to

display the reference rehabilitation task trajectory and

subject’s actual movement during the task execution. The

force values measured from the force sensors are recorded

using the Humusoft Mf624data acquisition card with a

sampling rate of 500Hz. The joint torque corresponding to

applied forces by the subject is calculated by multiplying the

force with the perpendicular distance between the force

contact point and the joint axis.

Ensuring safety of the subject is a very important issue

when designing a robot-assisted rehabilitation system. Thus,

incase of emergency situations, the physiotherapist can press

an emergency stop button to stop the RehabRoby. The motor

drivers of RehabRoby can be disabled separately or together

by pressing the driver enable/disable buttons without

disconnecting the energy of the robotic system in any case of

emergency situations. The power of the system is supported

with uninterruptible power supply, thus, there is no power

loss in the system, and RehabRoby will not collapse at any

time. Additionally, rotation angle and angular velocities of

each joint of RehabRoby are monitored by controller.

III. ADMITTANCE CONTROL WITH INNER ROBUST

POSITION CONTROL LOOP

In this work, admittance control with inner robust

position control loop is used to provide necessary motion to

RehabRoby so patients can complete the rehabilitation tasks

in a desired manner (Fig. 2). Note that RehabRoby has

complex and uncertain inner dynamics and it is sensitive to

external forces during the human-robot interaction, a simple

Proportional-Integral-Derivative (PID) or model based

position control technique may not be enough to complete the

105

tracking in a desired performance. Thus, a robust position

controller has been used in the inner loop of the admittance

controller. The effects of the parametric uncertainties in the

dynamic model and the external additive disturbances are

compensated with an equivalent disturbance estimator in the

robust position controller.

Various methods have been previously used to estimate

the disturbance in the position control of robotic systems

such as adaptive hierarchical fuzzy algorithm [17], model

based disturbance attenuation [18]. In this work, we have

used discrete Kalman filter based disturbance estimator [19],

[20], which is a commonly known and successful technique

used to process noisy discrete measurements. Additionally,

discrete linear Kalman filter based disturbance estimator

estimates the unknown states and parameters in the dynamic

model in an accurate manner. To our knowledge admittance

control with inner robust position control loop has not been

used for control of robot-assisted rehabilitation systems

before.

The general structure of the proposed low-level controller

for RehabRoby is shown in Fig. 2. The force that is applied

by the subject during the execution of the task is measured

using the force sensor and this value is then converted to

torque using Jacobian matrix. The torque value is then passed

through an admittance filter [21], which is used to define

characteristics of the motion of the RehabRoby against the

applied forces, to generate the reference motion for the robust

position controller. The reference motion is then tracked with

a robust position control which consists of a linear Kalman

filter based disturbance estimator [21].

Fig. 2. Block Diagram of Controller of RehabRoby

Admittance controller is added as a new control loop

around the robust position controller (Fig. 2). An admittance

function is used to represent the relationship between the

applied torque and corresponding joint angle of RehabRoby

using the following equation:

(1)

where, represents the applied torque, , and

represent the desired inertia, desired viscosity and desired

stiffness matrices respectively. , and are reference

joint angle, reference angular velocity and reference angular

acceleration respectively. Eqn.1 can be represented in

frequency domain as:

( ) ( ) (2)

It is possible to generate reference motion by assigning

the desired values to the parameters , and in the

admittance filter considering the desired motion

characteristics. The robust position controller in the inner

loop is responsible to track the desired motion.

State feedback technique with two feedforward

compensation term is used in the robust position control of

RehabRoby. One of the feedforward terms is used to

compensate the modeled RehabRoby dynamics and the other

term is used to eliminate time-varying equivalent

disturbances coming from the unmodelled RehabRoby

dynamics and unknown external effects. The disturbances are

estimated with a recursive algorithm which uses discrete

linear Kalman filter (LKF) method [21]. Remember the

general dynamic equation of robotic systems is given in joint

space as:

( ) ( ) ( ) ( ) (3)

where is the 6x1 joint torque vector, ( ) is the 6x6

manipulator inertia tensor, , and are the 6x1 joint

position, velocity and acceleration vectors, ( ), ( ) and

( ) are 6x1 Coriolis and centrifugal, friction and gravity

force vectors, respectively. is the 6x1 torque vector that

occurs due to the unknown external effects. The inertia tensor

( ) can be expressed as follows:

( ) ( ) (4)

where the constant diagonal terms of the manipulator inertia

tensor ( ) are represented as ( )

n=1,2…,6, and the rest of the terms of the ( ) are given in

( ). The friction term ( ) is also expressed as:

( ) ( ) (5)

where is the 6x1 viscous-friction coefficient vector. An

equivalent disturbance vector (6x1), which includes

Coriolis, centrifugal and gravity forces, parameter variations

in inertia tensor and friction terms, and unknown external

effects, is defined as:

( ) ( ) ( ) ( ) (6)

Eqn.6 is substituted in Eqn.3 and the dynamic equation of

RehabRoby is obtained as . The relationship

between joint torque and the current reference of the actuator

is taken as , where is nominal value of the

motor torque constant, is the gear ratio of the actuator and

is the current reference. includes both variations of the

motor torque constant with respect to its nominal value, ,

and the variations of the motor current value with respect to

the current reference value, . Thus the total equivalent

disturbance is calculated as . The acceleration

that will be used to calculate the can be found using

( ) , where is 6x6 diagonal matrix that is

calculated by multiplication of and .

The pole placement with state feedback method is used in

the position control of RehabRoby. Let’s define state space

model of the ith joint of RehabRoby as follows:

( ) ( ) ( ) ( )

( ) ( ) ( ) (7)

where ( ) ( ) ( ) is the 2x1 state vector, ( ) ( ) is

the control input (motor current reference), ( ) ( ) is the

equivalent disturbance, ( ) ( ) measured output and ( )

is the measurement noise. is 2x2 system matrix, is 2x1

106

control input matrix, is 2x1 disturbance matrix and is

1x2 output matrix as:

[

], [

], [

], (8)

The control input ( ) is selected as ( ) ( )

( ) where ( ) ( ) ( ) ( ). is 1x2 state

feedback gain matrix which is described by

[ ] where and are proportional and derivative gains,

respectively. ( ) is the reference position for ith

joint. ( ) is

the compensating current signal to eliminate the equivalent

disturbance, which is calculated using ( ) ( ) , where

( ) is the estimated value of the equivalent disturbance.

( ) is the other feedforward compensating signal which is

calculated using ( ) ( ) ( ) (( ) ) ( )

Eqn. 7 with state feedback becomes as:

( ) ( ) ( ) ( ) ( ) (9)

The characteristic equation of the system defined in Eqn.

(9) can be represented as (( ) ) ( )

, where ( ) √ is the damping ratio

and √( ) is the natural frequency of the system.

The characteristic time constant of the system is found using

( ) The control gains and for the state

feedback control are calculated by assigning desired values to

the , and parameters.

The equivalent disturbance ( ) is estimated using a

recursive algorithm which is based on the linear Kalman

filter design. The state space model given in Eqn. 9 is

extended by including the estimated equivalent disturbance

as a new state variable. The extended model is still linear and

time-invariant because equivalent disturbance is independent

from the state variables [22]. The linear Kalman filter

algorithm used in the estimation of the equivalent

disturbances is defined in discrete state space. The discrete

state space model of the ith joint of RehabRoby is described

as the following equation where

( ) ( ) ( ) ( ) and ( ) ( ) ( ) ( ).

( ) ( ) ( ) ( )

( ) ( ) ( ) (10)

( [

])

and is the sampling time, which is selected

smaller than the characteristic time constant . The states at

time (k) are predicted using the states estimated at time (k-1)

in the discrete linear Kalman filter algorithm as:

( ) ( ) ( ) (11)

where ( ) is the priori estimate of the state vector at time

(k). 3x3 covariance matrix of the estimation errors for the ith

joint, ( ) and its priori estimate value are calculated using

( ) ( )

, where is the 3x3 covariance

matrix of the model errors. Estimation of the states is updated

using ( ) ( ) ( ( )

( )). is 3x1 Kalman gain

matrix that minimizes the estimation errors using

( )

( ( )

)

and is the covariance scalar of

the measurement error. Covariance matrix of the estimation

errors ( ) is updated using ( ) ( ) ( ). Note that

the initial values of ( ) and

( ) are required in the

discrete linear Kalman filter algorithm. The block diagram of

the state feedback control with equivalent disturbance

estimation based on linear Kalman filter is shown in Fig.3.

Remember that asymptotic stability of the linear Kalman

depends on controllability and observability of the robotic

system and bounded A, Q and R matrices [23]. Thus, Qi and

Ri are selected as constant matrices and diagonal since the

measurement and model noises are considered as stationary

random processes.

IV. RESULTS

The admittance control with inner robust position control

loop had been evaluated with real-time experiments. The

performance of the robust position controller with and

without disturbance had been evaluated with two

experiments.

Initially, exact values of the matrix, which contains the

mean values of the inertia tensors correspond to the each

joint of RehabRoby, had been calculated experimentally

(Table I). Viscous friction coefficients had been taken from

the datasheets of the motors. The effects of the mechanical

parts of RehabRoby on viscous friction had been ignored

and considered as disturbance. The values of for each

joint had been calculated by multiplying the torque constant

and gear ratio of the corresponding joint (Table I). The

damping ratio ( ) and the time constant had been selected as

√ ⁄ and 0.4 seconds, respectively. The measurement noise

was small because of the high resolution digital encoders,

thus the measurement error covariance had been selected

as 10-6

. The uncertainties and parameter variations in the

RehabRoby were compensated by the estimated equivalent

disturbance. Thus, the model error variance of the equivalent

disturbance signal had high values where the model error

variances of the position and the velocity values were low.

The model error covariance matrix had been selected as

( ) and the initial values of ( ) and

( ) were taken as zero for each axis of RehabRoby.

107

Fig. 3. Robust Position Controller with Disturbance Estimator

TABLE I: THE PARAMETERS OF THE DYNAMIC MODEL OF REHABROBY

AND ROBUST POSITION CONTROLLER

(kgm2) 17 10 48 2 30 1

(Nms/rad)) 0.014 0.038 0.003 0.014 0.0014 0.0011

(Nm/A) 3.96 2.77 16.07 1.98 16.7120 2.59

(A/rad) 53.68 45.14 37.36 12.63 22.4457 4.8277

(As/rad) 21.46 18.037 14.94 5.044 8.9755 1.9301

In the first experiment, the discrete linear Kalman filter

based disturbance estimator had not been used and the

control of the RehabRoby had been performed using state

feedback technique and the feedforward signal that

compensated the affects of the modeled joint dynamics.

Then, in the second experiment the disturbance estimator

had been added into the robust position controller.

RehabRoby had flexed the elbow joint (Theta-4 (θ4)) to 900

in 10 seconds and the subject was asked to stay passive

during this motion. Minimum jerk trajectory method had

been used to define a smooth reference trajectory for this

motion. Sinusoidal disturbance signal with amplitude of 0.75

and frequency of 2 Hz was added to the current reference

input, which simulated a situation that might happen during

a human robot interaction. The results of the robust position

controller with and without disturbance had been shown in

Fig. 4 and Fig. 5, respectively. When discrete linear Kalman

filter based disturbance estimator had not been used, then the

tracking error had reached about 140

because modeled

RehabRoby did not include the parameter variations, non-

linear effects of the robotic system, and the disturbances that

came from the external sources. The state feedback and

feedforward compensation signals obtained considering the

modeled RehabRoby were not enough for successful

trajectory tracking (Fig. 4). On the other hand, when discrete

linear Kalman filter based disturbance estimator estimated

the disturbances, the maximum error reduced to about 0.70

(Fig. 5). The equivalent disturbance signal estimated using

discrete linear Kalman filter had compensated the effects of

the unmodelled parameter variations, nonlinear terms and

unexpected external forces. Therefore, it is very important to

design a robust position controller with disturbance

estimator for a robot-assisted rehabilitation system to

complete the task in a safe and desired manner.

Fig. 4. Evaluation of Robust Position Controller without Disturbance

Estimator

Fig. 5. Evaluation of Robust Position Controller with Disturbance Estimator

0 5 10 15-90

-60

-30

0

Time (sec)

Th

eta-

4 (

deg

)

0 5 10 15

-10

-5

0

Time (sec)

Th

eta-

4 E

rro

r (d

eg)

Desired Actual

0 5 10 15

-90

-60

-30

0

Time (sec)

Thet

a-4 (

deg

)

0 5 10 15

-0.5

0

0.5

Time (sec)

Thet

a-4 E

rror

(deg

)

0 5 10 15-6

-4

-2

0

2

Time (sec)

Est

imat

ed D

istu

rban

ce

(Nm

)

Desired Actual

108

V. DISCUSSION AND CONCLUSION

We have developed an exoskeleton type upper-extremity

robot-assisted rehabilitation system called RehabRoby.

RehabRoby is adaptable for patients with different gender.

Additionally RehabRoby can be adjusted easily for people

with different arm lengths. Furthermore, RehabRoby can be

used for both right and left arm.

Admittance control with inner robust position control

loop has been used to provide necessary motion to

RehabRoby to complete the rehabilitation task in a desired

manner. The level of resistance that will be applied by

RehabRoby can be varied using admittance control

considering patient’s movement capability. Admittance

controller has been integrated with a robust position

controller which consists of a linear discrete Kalman filter.

The effects of the parameter variations and nonlinearities in

the inherent dynamic model of RehabRoby and also the

external forces that may happen during the human-robot

interaction are compensated with the equivalent disturbance

estimated with a recursive algorithm based on Kalman filter.

Note that admittance control with inner robust position

control loop does not need an exact knowledge of

RehabRoby’s dynamic model, thus the computation effort of

the control algorithm has been minimized. The evaluation of

the proposed robust position controller has shown that

discrete linear Kalman filter based disturbance estimator can

compensate the effects of the uncertainties in the dynamic

model and external disturbances that might happen during

human-robot interaction. As seen from the results the error

decreased from 140 to 0.5

0 when the disturbance estimator

was included in the closed loop control system.

As a future work, the robust position controller

performance will be improved using adaptive Kalman filter

which will adjust the admittance parameters of RehabRoby

for each subject.

ACKNOWLEDGEMENT

We gratefully acknowledge the help of Dr. Serap İnal and

Dr. Sule Badilli Demirbas who are in Physiotherapy and

Rehabilitation Department in Yeditepe University.

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