Journal of Medical and Biological Engineering, 34(3): 284-292 284

Guidance-control-based Exoskeleton Rehabilitation Robot for

Upper Limbs: Application to Circle Drawing for

Physiotherapy and Training

Wei-Wen Wang1 Bing-Chun Tsai1 Li-Chun Hsu1 Li-Chen Fu1,2,* Jin-Shin Lai3,4

1Department of Electrical Engineering, National Taiwan University, Taipei 106, Taiwan, ROC 2Department of Computer Science and Information Engineering, National Taiwan University, Taipei 106, Taiwan, ROC

3Department of Physical Medicine and Rehabilitation, National Taiwan University, Taipei 106, Taiwan, ROC 4Department of Physical Medicine and Rehabilitation, National Taiwan University Hospital, Taipei 106, Taiwan, ROC

Received 22 Aug 2013; Accepted 5 Feb 2014; doi: 10.5405/jmbe.1663

Abstract

Cerebral vascular disease is the leading cause of functional disability among adults. Approximately half of all

stroke survivors continue to suffer from severe neurological deficits and hemiparesis in the upper extremities as well as

many secondary complications due to immobilization. Robotics can provide highly intensive intervention in stroke

rehabilitation as well as an objective means of measuring patient progress. This study designs an upper limb

rehabilitation (Rehab) robot with multiple degrees of freedom. This design provides a wider range of motion in

3-dimentional space than that provided by an existing endpoint-fixation system. In addition, unlike cable suspension

systems that lack biofeedback, the sensors incorporated into the proposed design can be used to detect the voluntary

force produced by the stroke patient. The Rehab robot features an exoskeleton-type design with in-built redundancy, a

guidance control system, and force feedback using an electromyographic trigger. Three rehabilitation modes can be

selected by physical therapists according to the severity of the patient’s upper-limb impairment: passive, active, and

guidance. Guidance mode assists patients in motor training, with programs such as drawing circles, which involves

complex movements that require coordination between the shoulder and elbow joints. Such skills are ideally suited to

relearning functional tasks following a stroke. Physical experiments were conducted in this pilot study to evaluate the

performance of the Rehab robot. The results indicate that the robot could be effective. Guidance mode achieves the

desired guidance functions, informing the subject of the pose required to complete the task as well as enabling them to

reduce unnecessary muscle use.

Keywords: Rehabilitation, Exoskeleton, Kinematics, Robot-assisted therapy

1. Introduction

Most stroke patients suffer from motor dysfunction and

approximately half of all stroke survivors continue to suffer

from severe neurological deficits and hemiparesis in the upper

extremities (UEs) [1]. Many secondary complications due to

immobilization may also occur, including joint contracture,

muscle atrophy, and shoulder-hand syndrome. To prevent such

complications and regain functional motor capabilities in the

UEs, several studies have focused on the development of more

effective rehabilitation techniques for stroke patients.

Traditional rehabilitation is still limited by a number of issues.

For example, one-on-one treatment is labor-intensive and

* Corresponding author: Li-Chen Fu

Tel: +886-2-23622209; Fax: +886-2-23657887

E-mail: lichen@ntu.edu.tw

experience-dependent. Furthermore, the subjectivity involved

in most clinical scales hinders the precise quantification of

improvement following rehabilitative intervention.

As a result, interest in the use of robotic therapy for

rehabilitation is increasing [2-5]. Robotics can provide highly

intensive intervention in stroke rehabilitation as well as an

objective means of measuring patient progress. In addition, the

use of a human-computer interface enables a robot to optimize

the movement patterns required for patients with UE paresis.

Lo et al. (2010) studied the effectiveness of robot-assisted

therapy in reducing motor impairment in arms affected by

stroke [4]. They found that the robot-assisted therapy did not

significantly improve motor function over a period of 12

weeks; however, improvements in motor capability and motor-

task performance were observed after 36 weeks.

Three primary types of robot are used to contact or

interact with stroke patients. The first type is an endpoint-

fixation system, such as PHANTOM [6] or MIT-Manus [2],

J. Med. Biol. Eng., Vol. 34 No. 3 2014 285

which fixes the distal portion of the UEs of patients in order to

guide the desired movements. This enables stroke patients to

execute tasks using only forearm support. The second type is a

cable suspension system, such as the Freebal gravity

compensation system [7]. This type of system provides

antigravity support for the UEs during rehabilitation. The third

type is an exoskeleton arm system, such as ARMin [8,9],

ULERD [10], and MAHI [11].

The proposed rehabilitation (Rehab) robot is an

exoskeleton designed specifically for UE rehabilitation. This

design provides a wider range of motion (ROM) in 3-

dimentional space than that provided by an endpoint-fixation

system. In addition, unlike cable suspension systems that lack

biofeedback, the sensors incorporated into the proposed design

can be used to detect the voluntary force produced by the stroke

patient for further analysis.

The proposed Rehab robot has three key elements: a

redundant design combined with selective inverse kinematics

(IK) solutions, a guidance control system, and an

electromyographic (EMG) trigger. The redundant design refers

to additional joints beyond those found in a normal human

upper limb. The IK problem arises from the redundant design;

therefore, this study investigated the geometrical relationship

between the robot arm and the human arm and devised an

effective IK solution. The guidance control system was designed

for stroke patients with mild-to-moderate UE impairment to

ensure correct joint movements. An EMG trigger modified from

MIT-Manus [12] and a proportional-integral-derivative (PID)

controller and an impedance controller, which are commonly

found in Rehab robots [13-15], are also included.

One important application of the proposed Rehab robot is

circle drawing. It is a training program that executes the

coordinated movements using the paretic arm. Virtual reality

environments and games have been developed and combined

with Rehab robots to facilitate long-term training and increase

movement in therapy [16,17]. Miyoshi et al. (2010) pointed out

that drawing a circle requires complex movements and the

coordination of multiple muscular co-contractions as well as

eccentric activity [18] in the medial/lateral and forward/

backward directions. Ju et al. (2005) used a robot to guide the

upper limbs of subjects in linear and circular movements [19].

Based on previous works [18,19], the complex circle-drawing

movement should enhance the coordination and motoring of

shoulder flexion/extension. Motions that mimic circle drawing

in the vertical plane are common in daily life, such as turning a

steering wheel or cleaning windows. The shoulder wheel has

been used for training this kind of motion. In addition, a

considerable relationship has been reported between the

activation of the motor cortex and the copying of visual

representations of particular geometrical shapes [20].

2. Materials and methods

2.1 Rehabilitation modes of Rehab robot

The rehabilitation mode of the proposed Rehab robot can

be divided into three types: passive, active, and guidance.

These modes are similar to those used in traditional programs

for the rehabilitation of stroke patients.

As with passive ROM exercises, the passive mode of the

Rehab robot provides an external force to stroke patients with

severe motor impairment. In this setting, force is provided

entirely by the Rehab robot to help execute the rehabilitation

movements designed by physical therapists. Active mode is

used for stroke patients with mild UE impairment, such that

patients can move their arm freely. Motion tracking by sensors

in the Rehab robot is used for analysis. Finally, in guidance

mode, the joint movements of patients are guided using force

feedback with an EMG trigger. For example, the affected arm

of patients can be drawn back to a plane by the motion tracking

system if it tends to deviate from the plane.

2.2 Kinematics model of human upper limbs

Generally speaking, the shoulder joint complex has 3

degrees of freedom (DOFs) in its movement, 2 DOFs at the

elbow joint, and 2 DOFs at the wrist joint. Table 1 summarizes

the normal ROM of a human.

Table 1. Movements and limitations of human upper limbs.

Movement Range of motion

Shoulder flexion/extension 0-180°/0-60°

Shoulder abduction/adduction 0-180°/0-70° Shoulder external/internal rotation 0-34°/0-97°

Elbow flexion/extension 0-150°/0-0° Forearm pronation/supination 0-90°/0-90°

Wrist flexion/extension 0-80°/0-70°

Wrist lateral/medial deviation 0-30°/0-20°

2.3 Design of mechanical structure

The proposed exoskeleton robot arm is equipped with

more joints than those in a human arm in order to increase the

ROM to make the robot suitable for most patients. The

exoskeleton is a 9-DOF mechanical manipulator, including 6

DOFs at the shoulder joint complex, 2 DOFs at the elbow joint,

and 1 DOF at the wrist joint, as shown in Fig. 1(a). Mechanical

joints 1 through 6 of the Rehab robot are used to accommodate

motions which originate in the shoulder area; mechanical joint

7 accommodates motions in the human elbow joint

(flexion/extension); mechanical joint 9 accommodates motion

in the human forearm joint (pronation/supination); the

remaining mechanical joints accommodate motions produced

by the human wrist joint. To ensure that the robot can adapt to a

variety of patients, the mechanism for the upper arm can be

adjusted between 26 and 34 cm, while the forearm can be

adjusted between 24 and 30 cm.

(a) (b)

Figure 1. (a) Photograph and (b) simplified schematic diagram of

proposed Rehab robot.

Rehabilitation Robot for Upper Limbs 286

2.4 Sensors

The proposed sensor system includes a potentiometer and

a motor encoder for each joint, as well as EMG and force

sensors for the upper limbs of the patient. The Rehab robot is

also equipped with 4 force sensors mounted at the connections

between the robot arm and the human arm, as shown in

Fig. 1(a). Each of these sensors was realized using a pair of

strain gauges to measure the interaction force between the

patient and robot. The force of the upper arm is measured by

two force sensors which monitor shoulder flexion/extension

and horizontal adduction/abduction. Elbow flexion/extension

with shoulder rotation yields an interaction force measured

from the forearm.

2.5 Safety issues

A safety system is implemented to determine which parts

of the Rehab robot may be broken or have failed. The system

includes two parts: a dual-position sensor system that obtains

two kinds of position information that validate each other and a

hand button to control the motion state by allowing state

jumping in order to prevent potential injury. An emergency

button is provided to avoid some critical circumstances that

may occur. Besides what we have just mentioned so far, our

method also asks part of the device deemed for safety guard

must be automatic in order to ensure that the system can

automatically detect the hazard before any harm could occur.

Moreover, such safety detector can prevent too frequent

artificial stop of the machine when a patient is during the

course of rehabilitation training while feeling uncomfortable,

but in fact, he can still work along with the machine well.

2.5.1 Dual-position sensor system

Although we have mentioned about the range of motion of

this rehabilitation robot previously, and have shown the design

target is to achieve the sufficient rehabilitation workspace of

the upper-limb of a human body, single failure of robot

function that may take place includes failures of components

also need to be considered during training and therapy. Given

the above-mentioned philosophy, we have to take into account

the positioning failure in particular. Here, we use the

potentiometer to detect the absolute position of each robot joint;

however, the potentiometer provides an absolute measurement

but with the lower precision. On the other hand, the encoder

usually has higher precision during measurement of the

position change, but it cannot figure out the current absolute

position due to lack of initial position information. After the

system finishes the calibration, this dual potion sensor system

will work synchronously. If one of the two sensor sub-systems

fails, the system will cut off power to avoid potential harm until

the problem is removed, and then the system will be restarted.

For the up-down linear motion joint, the dual position sensing

is set up with the same strategy to determine the upper and

lower limitations of joint position.

2.5.2 Hand button for motion suspension

A hand button panel was designed for the patient’s use. It

prevents the Rehab robot from imposing harm to the patient

during the course of training. When the patient cannot

accomplish a training step due to pain, this mechanism

immediately moves the robot back to the previous step. The

break posture is recorded and given to a therapist to evaluate

the difficulties encountered during the designed course of

rehabilitation and to identify possible modification of the

rehabilitation program later on.

2.5.3 Emergency button

The robot arm uses AC 110 V for power. Two emergency

buttons can be used to cut off the power system immediately.

One is a manual control and the other is for the pedal break.

When the power is shut down, it is critical for the robot arm not

to fall quickly. A high-ratio reduction gear is thus used for the

transmissions and vertical joints as a lock of mechanical

structure.

2.6 Inverse kinematics of Rehab robot

This section explores all feasible motions of the

exoskeleton-type Rehab robot arm through the study of IK

solutions. A simplified schematic diagram of the robot structure

is presented in Fig. 1(b), in which a total of 12 coordinate

frames are assigned to the base and appropriate locations on the

11 joint axes using Denavit-Hartenberg (D-H) notation. The

origins of coordinate frames are referred to as “joint pivots” for

convenience. Note that joint V1 (z8) and joint V2 (zV1) are

stationary; hence, the associated rotation angles V1 and V2 are

constant, leading to a U-shaped link which connects the arm at

the origin of the coordinate frame {XYZ7} to the handle for

grasping at the origin of the coordinate frame {XYZ9}.

Notations d1 (with sliding joint) and 2 to 9 (with revolute

joints) are treated as variables corresponding to various joint

motions. The associated D-H parameters are listed in Table 2.

Table 2. Denavit-Hartenberg parameters of Rehab robot.

Joint d (cm) a (cm) (rad.) Home

(rad.)

1 0 d1 0 0 π/2 2 2

0 a2 0 0

3 3 0 a3 0 0

4 4 0 a4 -π/2 0

5 5 0 0 -π/2 -π/2

6 6 d6 0 π/2 0

7 7 0 a7 0 π/2

8 8 0 a8 π/2 0

V1 V1 0 aV1 0 π/2

V2 V2 0 0 -π/2 0

9 9 d9 0 0 0

The parallel motion principle is generally employed when

the relationship between the exoskeleton robot arm and the

human arm is sought, which in turn helps solving IK solutions

of the robot arm. In short, the problem is simplified by finding

only the solutions to which both the Rehab robot and the

human arm will conform since the robot is exoskeleton-type.

The position trajectories of the essential joint pivots of the

Rehab robot are first determined by basing these trajectories on

J. Med. Biol. Eng., Vol. 34 No. 3 2014 287

those found in various joints of the human arm. More

specifically, the positions of the three joint pivots of the robot

arm which respectively correspond to the human shoulder joint,

elbow joint, and wrist joint are found. This facilitates solving

the pose of the Rehab robot using geometry information

associated with these three joint pivot positions.

Suppose that the positions of the human shoulder joint Ohs,

elbow joint Ohe, and wrist joint Ohw, as well as the length of

upper arm lhse, the length of forearm lhew, and the parallel

distance lhr between the Rehab robot and the human arm are

known. Denote the pivots of joints 1 to 9 of the robot arm as O1

to O9, and rename the pivots of joints 5, 7, and 8 as robot

shoulder joint Ors( = O5), elbow joint Ore( = O7), and wrist joint

Orw( = O8), respectively. In accordance with the formerly

mentioned principle, the latter three robot joint pivots should

correspond to joints Ohs, Ohe, and Ohw of the human arm,

respectively. If the lengths of the upper arm and the forearm of

the robot are denoted as lrse( = d6) and lrew( = a7), respectively,

the relationship between the human arm and the Rehab robot

can be characterized as shown in Fig. 1. The mentioned IK

calculations are presented in greater detail in our previous

paper [21].

2.7 Control system

Figure 2 presents the control system for the four

rehabilitation modes. The control system comprises an

impedance controller, an EMG trigger, and a guidance

controller. The impedance controller is a torque controller that

minimizes the torque/force interaction between the Rehab robot

and the human arm as much as possible, thereby enabling the

Rehab robot to follow human volition in its movement. The

EMG trigger is used to check whether the human muscles have

contracted. Finally, the guidance controller provides the local

target of the human pose based on the current pose and hand

position (or pose) of the target. Passive mode is executed using

zero gain in the impedance controller and 100% gain in the

guidance controller, whereas active mode is executed using

positive gain in the impedance controller and zero gain in the

guidance controller. Guidance mode is executed using positive

gain in the impedance controller and 10%~90% gain in the

guidance controller.

Figure 2. Diagram of control system.

2.7.1 Impedance controller

Geometry is first used to examine the relationship between

force sensing and various motions of the human arm. Figure 3

shows the relationship between the exerted forces due to

movement of the upper arm and shoulder, which

mathematically can be expressed in terms of the equivalent

shoulder torques:

hs1 = ru sin(hs2 +

F1 coshs3 + F2 sinhs3)

sin(hs2 +

coshs3(F3lu + F3rf cos(he

)))

+ sinhs3 F4 rf + lu cos(he

)

F3rf cos(hs2 +

) sin(he

) (1)

hs2 = F4 coshs3(rf + cos(he

) lu)

F3sinhs3 (lu + cos(he

) rf

+ ru(F2 coshs3 F1 sinhs3) (Gu (hs2) (2)

(a) (b) (c)

Figure 3. Forces (F1~F4) sensed from upper arm and forearm. (a) Front,

(b) right, and (c) top views.

Similarly, the exerted forces due to movement of the

forearm result in the corresponding equivalent shoulder and

elbow torques are mathematically expressed as follows:

hs3 = F3．rf ．sin (he

) Gf (hs2,hs3,he) (3)

he = F4．rf Gf (hs2,hs3,he) (4)

In the above equations, the variables are defined as:

hs1 represents equivalent shoulder torque causing the

exoskeleton to move under shoulder abduction/ adduction;

hs2 represents equivalent shoulder torque causing the

exoskeleton to move under shoulder flexion/extension;

hs3 represents equivalent shoulder torque causing the

exoskeleton to move under shoulder rotation;

he represents equivalent elbow torque causing the exoskeleton

to move for elbow flexion/extension;

ru represents the distance between the shoulder and force

sensor;

rf represents the distance between the elbow and force sensor of

forearm;

lu represents the distance between the shoulder and elbow;

hs1 represents the angle of shoulder abduction/adduction;

hs2 represents the angle of shoulder flexion/extension;

hs3 represents the angle of shoulder rotation;

he represents angle of elbow flexion/extension;

F1, F2 represent the forces sensed from the upper arm;

F3, F4 represent the forces sensed from the forearm;

Gu(hs2) represents the influence of gravity on the upper arm;

Gf/hs2/hs3/he represents the influence of gravity on the

forearm.

Rehabilitation Robot for Upper Limbs 288

Impedance control is used to imitate mechanical

impedance between the pose and torque of the human upper

limb. The general form is:

( ) ( ) ( )m d m d m dM B K (5)

where:

hs1 hs2 hs3 he] is vector of equivalent torques based on

Eqs. (1) to (4);

hs1 hs2 hs3 he] is the current pose of the human upper

limb, where hs1, hs2, hs3, and he are as previously

defined;

d is the desired pose of the human upper limb;

Mm, Bm, and Km are inertia, damping, and stiffness matrices,

respectively.

Since the motion of the Rehab robot for stroke patients is

typically slow, the inertia and velocity effects are relatively

small, and in most cases can be ignored. Therefore, for

simplicity, it is assumed below that the imitated inertia Mm and

damping Bm of the mechanical impedance are zero. Under these

assumptions, Eq. (5) can be simplified as follows:

d + Km-1 = + (6)

qd q q Lr-1Lh( Jr

-1(q) Jh(· (7)

where:

= Km-1 is the compensated pose of the human upper limb;

x=Lh() is the direct kinematics model of the human upper

limb;

q= Lr-1(x) is the IK model of the Rehab robot;

Jh( is the Jacobian matrix of the human upper limb such that

x = Jh(·;

Jr-1(q)

is the inverse Jacobian matrix of the Rehab robot such

that q = Jr-1(q·x.

2.7.2 Force feedback system with EMG trigger

EMG sensors are an efficient way to record and evaluate

electrical activities in skeletal muscles. Many studies have

shown that the mechanical force exerted during muscle

contractions is directly related to EMG amplitude [22]. Stroke

patients with paretic upper limbs are unable to execute

functional tasks independently; thus, a Rehab robot is often

required to provide assistance for the completion of tasks. In

this study, the Rehab robot incorporates a force feedback

system with an EMG trigger.

EMG equipment is used to detect the weak EMG signals

produced by stroke patients. The force sensor is a transducer

that converts a mechanical input force into electrical output

signals. Therefore, comparing EMG signals and electrical

signals from the mechanical force sensors enables the proposed

system to identify muscular contractions. The Rehab robot then

assists the patient with appropriate external force to complete

the designated task. The system is detailed as follows:

(1) EMG pre-processing: EMG signals mch(t) are recorded

using a band-pass filter from 20 Hz to 450 Hz. Myoelectric

activity Ech(t) is defined as follows:

2( ) ( )t

ch cht TE t m t dt

(8)

where ch = 1, 2, …, 8 indicates the specific muscle.

(2) Triggered signal: Threshold Tch is determined

according to the myoelectric activity of the relaxed muscle. The

triggered signal is defined as follows:

1, ( )( )

0,

ch chch

if E t TTC t

otherwise

(9)

The control strategy (6) is then modified to reflect the

incorporation of the EMG trigger:

d t (t) TCch t·

K (10)

2.7.3 Guidance controller

The IK of the Rehab robot described in Section 2 does not

consider the problem of redundancy if the desired pose of a

human arm is known. However, we cannot determine which

pose is appropriate if we only know the target position of the

human hand in daily life. A previous study [23] proposed an

optimal feedback control system to minimize movement in

order to address the issue of redundancy. Thus, this study

adopts a straightforward geometric method to resolve this

challenge.

As outlined in [24], when a healthy human subject moves

their hand from one point to another, the trajectory of the hand

tends to follow the dotted line shown in Fig. 4. In other words,

the dotted line in Fig. 4 can be used to identify the various

reference positions of the human wrist. The explicit formula is:

Xhwr = Xhw + KG· (Xhwt Xhw) (11)

where:

Xhwr = [xhwr yhwr zhwr]

is the reference position of the wrist;

Xhwt = [xhwt yhwt zhwt] is the target position of the wrist;

Xhw = [xhw yhw zhw] is the current position of the wrist;

KG represents guidance gain.

Figure 4. Two desired paths: line and circle. This figure shows the

relationship between the reference pose, current pose, and

desired path.

The position of the elbow is crucial in determining the

complete reference pose of an upper limb; however, solutions

related to the elbow suffer from the problem of redundancy (as

shown in Fig. 4). Based on a minimum movement policy, this

study finds the reference elbow position with the minimum

distance from the current elbow position. Thus, all solutions to

the elbow reference position are found when the shoulder and

reference wrist positions (referring to Fig. 5(a)) are known. In

J. Med. Biol. Eng., Vol. 34 No. 3 2014 289

(a) (b)

Figure 5. Two spherical surfaces. The center of the first spherical

surface is the position of shoulder Xhs and the radius is the

length of the upper arm lhes. The center and radius of the

second spherical surface are the reference position of wrist

Xhwr and the length of forearm lhew, respectively. The double

line represents the solutions for the position of the elbow,

comprising two spherical surfaces. (a) The solution is a circle

whose radius and center are respectively r and P. (b)

Relationship between circle C, current elbow position Xhe, and

projection Q.

other words, once the shoulder position is known, it is clear that

elbow position Xher = [xher yher zher]

sits on the spherical

surface:

Xher Xhs = lhes (12)

where Xhs = [0 0 0] is the shoulder position and lhes

denotes the distance between the shoulder and the elbow. Next,

given this wrist position, the elbow position Xher is situated on

the spherical surface:

Xher Xhwr lhew (13)

where hewl represents the distance between the elbow and the

wrist. Now, all possible reference elbow positions which lie on

a circle that intersects the spheres from (12) and (13) and are

located within a plane referred to as the E-plane can be found.

The solution circle of all possible Xher satisfies the following

plane (E-plane) equation:

(Xhwr Xhs)T(Xher Xhs)

2 XhwrTXher

2 (14)

where = lhsw2 + lhes

2 lhew2 with lhsw = Xhwr Xhs. Using Eq.

(14), the plane in space can be rewritten as follows:

xhwr xher yhwr yher zhwr zher

2 (15)

The normal vector of plane (15) is the vector of the reference

position of the wrist:

Xhwr xhwr yhwr zhwr

Next, center P and radius r of the circle, representing all

possible elbow reference solutions, are found. By employing

the law of cosine given all edge lengths of the triangle

XherXhwr Xhs, the following is obtained:

P = Xh Xhwr Xhs

Xhwr Xhs ·lhes ·cos (16)

r lhes ·sin (17)

where

2 2 21cos ( )

2

hsw hes hewhwr hs her

hes hsw

l l lX X X

l l .

All possible elbow reference positions comprise a circle;

therefore, redundancy in the solution remains. To compensate

for this issue, an additional constraint is imposed to maintain

the distance between the candidate elbow solution and the

current position of the human elbow minimum. According to

Fig. 5(b), the distance between the current elbow position Xhe

and the solution circle is:

D hdisQ,C (18)

where h is the distance between the current elbow position; the

E-plane is derived from Eq. (15); and Q is the projection of the

current elbow position onto the E-plane (15). Q is calculated

according to the current position of wrist Xhe following the

direction of the normal vector Xhwr /Xhwr of the E-plane. This

allows us to move the distance between the E-plane and the

current position of wrist dis(E-plane, Xhe). The value of Q is

defined as follows:

Q = Xhe dis(E-plane, Xhe) ·Xhwr

Xhwr

= Xhe xhwr xhe+ yhwr yhe+ zhwr zhe

Xhwr ·

Xhwr

Xhwr (19)

Additionally, C is an arbitrarily position on the solution circle.

Because h is a constant, the amplitude of distance D is

determined by dis(Q,C) regardless of where C is positioned on

the circle. Thus, the minimum dis(Q,C) can be found if C is

selected as the intersection of the line connecting the center of

circle P and projection Q (as shown in Fig. 5(b)). Thus, the

reference elbow position leading to the minimum movement

can be expressed as:

arg min | |her heC

Q PX X C P r

Q P

(20)

Thus far, all of the reference elbow locations have been

determined point-wise, but this is insufficient to constrain or

guide patients through a desired target path for the hand. A

method capable of guiding the patient to return their hand to the

desired path when the hand deviates from that path is thus

proposed. The method is suggested by Fig. 4, which illustrates

two desired paths: a linear path and a circular path in free space.

In this method, the system controller first chooses the best

direction for the wrist to return to the desired path. The

controller then determines the optimal reference elbow pose

according to the previous strategy in order to guide the patient

to complete the wrist movement successfully.

3. Results

Drawing circles in the frontal plane is a training program

in which the rehabilitation mode (passive, active, or guidance)

can be selected. The experiments conducted in this work were

approved by the Institutional Review Board of National Taiwan

University Hospital.

Prior to initiating circle drawing, the Rehab robot must be

calibrated. The shoulder and elbow joints of the Rehab robot

are set to initial positions and the lengths of the Rehab robot

upper arm and forearm are adjusted. The subject sits with their

Rehabilitation Robot for Upper Limbs 290

upper arm and forearm attached to the support base,

immobilized by straps. The hand of the subject grasps the

handle. Surface EMG electrodes are then attached to the skin

surface of the subject, namely at the deltoid muscle (anterior,

middle, and posterior), the bicep brachii muscle, and the tricep

brachii muscle. These muscles are responsible for shoulder

flexion/extension, abduction, and elbow flexion/extension. The

EMG noise level is set at the threshold value during the resting

state. During the experiment, an EMG amplitude which

exceeded this threshold value indicated muscle activation.

Following setup, the task of circle drawing is executed

with visual feedback from the computer screen in each mode.

Up to shoulder level, the diameter of the target circle can

be adjusted from 0 to 30 cm in the clockwise direction. The

distance between the circle center and the acromion of the right

shoulder is approximately 30 cm. The speed of circle drawing

can also be adjusted (30 to 60 seconds per circle). The subject

follows the circle track shown on the computer in front of

them.

Different designs can be substituted depending on the

needs of individual patients. A training program which involves

circle drawing in the frontal plane is suitable for stroke patients

who have adequate ROM in their right upper limbs (i.e., the

flexion ROM of the right shoulder joint is over 90°, and the

extension ROM of the right elbow joint is not limited). The

ROM and muscle strength of the shoulder joint play important

roles in executing daily activities and also emphasize

movement of the shoulder complex.

Two healthy subjects from the Rehab robot design group

(male, ages = 24 and 25 years) participated in the circle

drawing experiment. In the experiment, the subjects drew

circles 24 cm in diameter. Motion speed was set sufficiently

slow (60 seconds per circle) to ensure stability in the movement.

The three rehabilitation modes were used in sequence.

Experimental data were recorded for further analysis.

Figure 6 shows the trajectory of the wrist in the xz and yz

planes under the three modes. Errors in wrist trajectory are

shown in Fig. 7. The angle of the upper limb and the force of

the joint under the three modes are shown in Figs. 8 and 9,

respectively. Table 3 presents the trajectory error of each joint

using the Rehab robot in passive mode.

4. Discussion

The trajectory error for every joint of the Rehab robot is

bound by a small value in passive mode. The trajectory of the

wrist tries to follow the circle path (shown in Figs. 6 and 7). It

appears that the PID controller provides better tracking results

in the experiment when the system is set to passive mode.

Figures 6(b) and 6(c) clearly show that the circular

trajectory in active mode is not as smooth as that of guidance

mode. This is because moving the wrist along a pre-defined

path according to a low resolution screen is not particularly

easy for patients. Specifically, the depth value (y axis) of the

wrist appears to drift a great deal in active mode (as shown in

Fig. 6(b)). However, this defect is overcome in guidance mode

(as shown in Fig. 6(c)), which demonstrates that this mode can

effectively guide or limit the trajectory of the human wrist.

Comparing the trajectory errors of the wrist under guidance

mode and active mode, the former is obviously reduced,

particularly in the y axis (as shown in Figs. 7(b) and 7(c)).

(a)

(b)

(c)

Figure 6. Trajectory of human wrist in xz and yz planes for subject 1 in

(a) passive, (b) active, and (c) guidance modes.

(a)

(b)

(c)

Figure 7. Error trajectory in position of human wrist in (a) passive

(subject 1), (b) active (subjects 1 and 2), and (c) guidance

modes (subjects 1 and 2).

J. Med. Biol. Eng., Vol. 34 No. 3 2014 291

(a)

(b)

(c)

Figure 8. Angle of upper limb versus time in (a) passive (subject 1), (b)

active (subjects 1 and 2), and (c) guidance modes (subjects 1

and 2).

(a)

(b)

(c)

Figure 9. Internal force between human upper limb and Rehab robot in

(a) passive (subject 1), (b) active (subjects 1 and 2), and (c)

guidance modes (subjects 1 and 2).

Table 3. Trajectory error of each Rehab robot joint in passive mode.

Axis Root mean square of error (rad) Range of error

1 0.0824 (cm) -0.0784~0.1673 (cm)

2 0.0022 (rad) -0.0047~0.0041 (rad) 3 0.0032 (rad) -0.0083~0.0048 (rad)

4 0.0010 (rad) -0.0144~0.0222 (rad) 5 0.0224 (rad) -0.0333~0.0322 (rad)

6 0.0137 (rad) -0.0237~0.0251 (rad)

7 0.0049 (rad) -0.0072~0.0073 (rad) 8 0.0000 (rad) -0.0000~0.0000 (rad)

9 0.0000 (rad) -0.000~0.0000 (rad)

Figure 8 illustrates that the tendencies of the shoulder and

elbow flexion are similar; however, the tendencies of shoulder

abduction and internal rotation differ among the three modes.

This may be attributed to the different strategies used to resolve

redundancy. The strategy in passive mode is to adopt minimal

elbow movement, whereas that in active mode is to give control

to the subject. In contrast, the strategy in guidance mode is

based on the trajectory error of the wrist in which 1) minimal

elbow movement is selected if the trajectory error of the wrist

is too high; 2) the subject is given control if the trajectory error

of the wrist is sufficiently small; 3) or a mix of 1) and 2) if the

trajectory error is moderate. In the second case, the control

system of the Rehab robot will not intervene, thereby allowing

the subject to continuously control their upper limb provided

that the wrist position does not deviate too far from the circle

path (as shown in Figs. 8(a) and 8(b)).

In passive mode, the subject does not provide any force to

the Rehab robot; therefore, the force sensors sense only the

gravity affecting the upper limb. In practical terms, the force

value is not smooth (Fig. 9) because the Rehab robot is not a

completely rigid body. Active and guidance modes also

experience the same problem, but the control system

incorporating the EMG trigger is able to filter out some of the

structural oscillations. Generally, EMG signals reflect the

volition of the subject. In Figs. 6(c) and 7(a), the subject’s

elbow is constantly working (biceps and triceps) because the

subject is trying to control the depth (y axis) value of the wrist

by manipulating their elbow joint. It is worth mentioning that

the amplitude of the EMG signal in guidance mode is smaller

than that in active mode, which implies that the subject is able

to control their wrist to trace the circular path more easily. To

summarize, guidance mode achieves the desired guidance

function, informing the subject of the pose required to complete

the task as well as enabling them to reduce unnecessary muscle

use.

5. Conclusion

This study proposed a Rehab robot that can detect

voluntary movements using force sensors. The robot includes a

redundant design combined with IK solutions, a guidance

control system, and force feedback with an EMG trigger. The

rehabilitation modes (passive, active, and guidance) of this

Rehab robot are similar to techniques used in traditional

rehabilitation training programs. The circle drawing exercise

was used to demonstrate coordination training of multiple

muscles and joints. Circle drawing with a robot also emulates

the concept of motor learning, which emphasizes intensity and

Rehabilitation Robot for Upper Limbs 292

task-specificity to enable effective motor recovery following a

stroke. It has also been reported that circle drawing is

associated with cognitive effort. In other words, relearning

motor control promotes the formation of internal models.

Acknowledgments

This research was sponsored by the National Science

Council, Taiwan, under grants NSC 96-2218-E-002-008 and

NSC 100-2321-B-002-076, National Taiwan University,

Taiwan, under grant NTU-CESRP-103R7617, and National

Taiwan University Hospital, Taiwan, under grant NTUH99P08.

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