Abstract—The idea of using robots to assist a therapist with a

rehabilitation exercise has led to the development of several

rehabilitation robotic devices. The scope of robotic devices in

rehabilitation is rapidly advancing based on the developments

in robotics, haptic interfaces and virtual reality. GENTLE/S

was a rehabilitation system that utilized haptic and virtual

reality technologies to deliver challenging and meaningful

therapies to upper limb impaired stroke subjects. The current

research is working towards designing the GENTLE/A system

with a better adaptive human-robot interface. This paper

presents the results from an exploratory study conducted with

twenty healthy subjects. The aim of the study was to identify

the contribution by subject/robot during different human-robot

interaction modes. Our results show that it is possible to

identify the leading or lagging role of a subject during a

human-robot interaction session where a reference trajectory is

used to drive the arm along a path. The final goal is to use these

observations to probe various ways in which the adaptability of

the GENTLE/A system can be improved as a therapeutic device

and an assessment tool.

Keywords- stroke rehabilitation, robotic therapy, adaptable

system, lead-lag interactive behaviour

I. INTRODUCTION

Stroke [1] is a major cause of chronic impaired arm

function and may affect many activities of daily living.

Restoration of motor function has been a key objective of

stroke rehabilitation. The use of robotic devices for

rehabilitation purposes is a relatively new field within the

area of robotics in health care and emerged from the concept

of using robots to assist people with disabilities. The focus

of our research is robotic assistance in stroke rehabilitation.

Research on robotic assistance in stroke rehabilitation is

rapidly advancing based on the recent developments in

robotics, haptic interfaces and virtual reality.

The basis of all stroke rehabilitation is the assumption that

patients can re-gain lost motor skills by re-learning and

practice. Studies suggest that retention of motor learning is

best accomplished with variable training schedules and, for

optimal results, rehabilitation techniques need to be geared

toward patients’ specific motor deficits [2]. Robot-assisted

therapy facilitates individualized training exercises for

patients where the patients can train independently and also

has the scope of offering ‘Tele-rehabilitation’.

The work being carried out in this research is based on the

GENTLE/S [3]-[5] rehabilitation system. GENTLE/S

Manuscript received January 31, 2012.

Radhika Chemuturi, Farshid Amirabdollahian and Kerstin Dautenhahn

are with Adaptive Systems Research Group, Science and Technology

Research Institute, University of Hertfordshire, Hatfield, AL10 9AB, UK Contact author: Radhika Chemuturi (e-mail: r.chemuturi1@herts.ac.uk)

utilised haptic and virtual reality technologies to deliver

challenging and meaningful therapies to upper limb impaired

stroke subjects. The clinical trial results with the GENTLE/S

[6], [7] system and other systematic reviews [8]-[10] in the

area of rehabilitation robotics bring out the need for robotic

therapy to be highly 'adaptable' according to the specific

needs and performance of the patient. Research [11], [12]

also highlights the opportunity for using robotic technology

to quantitatively 'assess' the underlying recovery process.

The current research is therefore working towards designing

the GENTLE/A rehabilitation system that can provide

individualised adaptability and assessment during stroke

rehabilitation.

Our approach to make the system adaptable is based on

studying the contribution by the subject or the robot during

different specifically designed human-robot interaction

modes of the system. We use the term ‘leading’ for cases

where the position of the subject’s arm is further on the

desired path when compared to the reference position. The

term ‘lagging’ refers to cases where the position of the

subject’s arm follows the positions given by the reference

trajectory. Our experiment aimed to investigate whether it is

possible to reliably identify the role of the subject during an

interaction session where this role is a known condition.

The HapticMaster (HM) robot (Moog BV [14]), the main

component of the GENTLE/A system, was programmed to

implement the minimum jerk trajectory (MJT) model. This

was one of the models used to create smooth and human-like

trajectories [13], [16]. Similar to its earlier incarnations, the

GENTLE/A system uses this model to create a reference

trajectory between two points in the work space. Different

modes were designed in the system to allow the robot or the

subject to take charge of the movement. Data was recorded

in both the situations, i.e. when the robot led the movement

while the subject remained passive as well as when the

subject took the lead by overtaking the robot. Although the

MJT was used as a reference trajectory for pulling or

tracking the subject's hand, any other human arm trajectory

model can be used in a similar way as presented in the

following sections.

In a preliminary experiment [15], we investigated whether

just the error from the reference position could be used to

detect the leading/lagging role of the subject. This was

performed on two settings: single-axis as well as planar

point-to-point reaching movements. The results obtained

showed that it was possible to identify whether the robot, or

the subject were leading the interaction modelled by the

MJT, but the sign of the error depended on moving away or

Impact of lead-lag contributions of subject on adaptability of the

GENTLE/A system: an exploratory study

Radhika Chemuturi, Farshid Amirabdollahian, Member, IEEE,

and Kerstin Dautenhahn, Member, IEEE

The Fourth IEEE RAS/EMBS International Conferenceon Biomedical Robotics and BiomechatronicsRoma, Italy. June 24-27, 2012

978-1-4577-1198-5/12/$26.00 ©2012 IEEE 1404

towards the reference coordinates. Next we investigated

whether a 3-dimensional movement (movement with

components on each of the three axes X, Y and Z) would

result in similar effects when a person purposely lags or

leads in performing a trajectory segment. This paper presents

the results obtained from a second study formulated to

answer this question.

II. METHODS

A. Experimental Set-up

The GENTLE/A experimental set-up used the hardware

and software components of the GENTLE/S rehabilitation

system [5] with some specific modifications. The

HapticMaster robot with its gimbal attachment formed the

vital component of the GENTLE/A system. The 24” wide

LCD screen for display stands on a rotary arm, which can be

turned from one side to the other side of the exercise table

and thus can be adjusted based on the dominant side of the

subject. Due to the participation of healthy volunteers, the

overhead frame support mechanism, elbow orthosis and

magnetic wrist attachment of the GENTLE/S system were

excluded.

Figure 1. The GENTLE/A experimental set-up

The current setting uses Window 7 (64 bit) and programmed

using Visual Studio 2009, with the C++ programming

language. Data during interaction was captured using

comma de-limited files. The graphical user interface was

programmed under OpenGL. The HapticMaster robot was

programmed to operate in two modes:

Passive Mode: The subject remained passive holding the

gimbal while the robot executed the movement from

source to target in its workspace. During this mode, the

subject’s arm was moved along the predefined reference

trajectory using a 2nd

order spring-damper system and a set

duration.

Active-Assisted Mode: The subject had to initiate the

activity, and the robot assisted the subject for the rest of

the activity. Thus in this mode, the subject and the robot

worked in collaboration to reach the target. The active-

assisted mode also utilised the set duration to propel the

arm along the predefined trajectory.

The new design of the Virtual Reality (VR) environment

allowed the experimenter to insert the target points that were

displayed as numbered spheres in green and rendered a pipe

(presented as a cylinder graphically) connecting these points

(Fig. 2). This connector pipe acted as a guide to the desired

straight-line path between the source and the target points.

The end-effector position was displayed as a small yellow

ball moving in the workspace of the robot. The subject could

initiate and execute movement between targets in the active-

assisted mode while in the passive mode the robot cycled by

itself through these defined points. The movement between a

source and a target point was termed as a ‘segment’ and a

duration of 4 seconds was set to execute each segment. All

numbered points were visited sequentially, ending with a

segment connecting the last pair (points 5 and 6 in Figure 2).

When the subject was due to start the movement from the

source of a segment, the target point glowed in pink and

once the subject reached the target point, it turned green

becoming the source for the next segment and the target for

the subsequent segment glowed in pink and so on. The

progress along the desired MJT path for the segment was

displayed as a grey cylinder and the actual path achieved by

the subject was displayed as a red cylinder. The angular

deviation from the desired path was calculated as θ and

when θ>10˚, a green arrow was displayed informing the

subject of the direction in which movement was deviating.

The break between one segment to the next was

characterized by a delay of 3 seconds when the target point

for the next segment gradually grew in size and popped (like

a balloon), serving as both an audio and a visual cue for the

subject to start the movement towards the target.

Figure 2. VR environment showing the execution of Segment-2,

target point in pink, progressing grey and red cylinders and

deviating green arrow. Points 1, 3 and 5 were located closer to the

subject’s body and points 2 and 4 were located farther away from

the subject’s body.

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B. Experimental Protocol

The protocol for the experiment was approved by the

ethics committee at University of Hertfordshire. All

participants provided informed consent prior to the

experiment. Twenty healthy volunteers took part in the

experiment aged between 23 and 60 (mean 36.9±11.3

standard deviation) and including 15 male and 5 female

subjects. The experiment was conducted in two phases:

Training Phase: The subject was instructed to hold the

ring (gimbal) attached to the end of the robotic arm and

move the ring along the guiding pipe joining the target

points shown on the screen. The subject was encouraged to

understand the operation of the system and was advised to

try the passive and the active-assisted modes at least once to

become familiar with the experimental procedure.

Actual Performance Phase: Once the subject was familiar

and comfortable with the activity, the actual performance

phase was executed. In order to create a situation where the

subject purposely led the activity, the active-assisted mode

was executed twice. The first run was termed Active

Assisted-1 (AA1) where the subject was instructed to initiate

the movement at the source point and then allow the robot to

take charge of the movement until the target point was

reached. The second run was termed Active Assisted-2

(AA2) and the subject was asked to execute the entire

movement from source to target points while trying to

overtake the robot using the virtual representation of the

grey and red cylinders. Thus the actual performance phase

involved executing the passive and two runs of the active-

assisted modes in that order.

A fixed set of points was used during the experiments

with all participants. The movement started at point 1,

progressed sequentially, and ended at point 6 during each

mode. The path with source at point 1 and target at point 2

was coded as segment-1 and so on. Data was recorded

during the interaction sessions, including Cartesian

positions, velocities and forces exerted at the robotic end-

effector.

The fixed set of points used was obtained from the

GENTLE/S database. The idea of using the same set of

points during this experiment was to facilitate the

comparison of results with stroke subjects with that of

healthy subjects in future.

III. RESULTS AND ANALYSIS

The data recorded from the ‘actual performance phase’

was used for data analysis purposes. Fig. 3 shows the

organisation of the raw data for analysis.

A. Parameters

Tau ( :

Parameter, τ, was calculated using the sample time (t), time

at the start and time at the end of each

trajectory segment:

This was a parameter of convenience used to map the

exercise time to a parameter between -1 and 1, which

allowed for considering all trajectories using the same

temporal window and also provided a chance to look at the

trajectory symmetry.

Figure 3. Organisation of raw data for analysis

parameter:

Cartesian positions, velocities and forces were sampled at a

time interval of 50 milliseconds. The line joining the source

point to the current position achieved by the subject was

termed ‘actual vector’ and the line joining the source point

to the reference MJT position that the robot was

programmed to follow was termed ‘MJT vector’.

Figure 4. Representation of the ‘Guiding’ and the ‘Actual’ vectors

and derivation of Effort and Error components

(

| || |)

Fig. 4 and the equations below the figure show the

derivation of Effort and Error components of the actual

vector. , derived by projecting the actual vector

12

tend tstart

t tend where

1 1

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onto the guiding vector (line joining the source and target

points) and , derived as the extent by which the

actual vector was deviating from the guiding vector.

and were similarly calculated using

the MJT vector and the guiding vector. Analysis of Error

calculations was left for future work. In order to compare the

progress achieved by the robot and the subject a new

parameter was calculated as follows:

(1)

B. Tau ( versus (Segment-specific analysis)

The passive mode was considered for testing the lagging

performance of the subject. The subjects were instructed to

remain passive and follow the robot which executed the

entire movement from the source point to the target point of

various segments. As a consequence of using second order

virtual spring-damper to propel the arm along the path (as

shown in [13]), the actual trajectory achieved by the subject

lags the MJT trajectory when the subject purposely remains

passive and hence according to (1), the parameter

during the passive mode always remains positive. Similarly

the subject was asked to overtake the robot during the AA2

mode and hence this mode was considered for testing the

leading performance of the subject. The actual trajectory

leads the MJT in the AA2 mode and according to (1), the

parameter remains negative. Therefore the

hypothesis for our data analysis was whether it is possible to

use the sign for the in order to identify subject’s

leading or lagging role.

Subject’s role Testing condition

Lagging

Leading

Our first step of data analysis was to check the spread of

the parameter during each segment performed

under different modes. Segment wise graphs of tau vs

were plotted with each plot showing a different

patterned- coloured line for different modes (Passive, AA1

and AA2). Fig. 5 shows the plots for SubID=15 during

various segments. Similar results were observed for other

subjects.

Fig. 5(a) shows that was satisfied for

all the five segments, while was satisfied

during segments 3 and 5 and the major part of segment-1,

but during segments 2 and 4, showed a varying

pattern as tau progressed from -1 to 1. To explore this

further, we computed the summation of

samples for each segment that could indicate if

remained negative for major part of the segment. Therefore

the new testing condition for leading performance of the

subject was formed as below,

Leading role ∑

Where n is the number of samples recorded during a

trajectory segment.

Figure 5(a). Segment specific plots of Tau (τ) vs ∆Effort during

different modes for SubID=15

Figure 5(b). Segment specific plots of Tau (τ) vs Velocity during

different modes for SubID=15

The number of subjects (out of 20 participating subjects)

satisfying the leading performance condition during various

segments of the AA2 mode can be summarized as: Segment-

1 (13/20), Segement-2 (8/20), Segment-3 (13/20), Segment-

4 (5/20) and Segment-5 (10/20). These identified a visible

difference between segments 1, 3 and 5 versus segments 2

and 4. To examine if this difference was dependent on the

length of the segment, we conducted a correlation test

between magnitude of segments (summarized in a table at

-1 -0.5 0 0.5 1-0.1

-0.05

0

0.05

0.1Segment-1

E

ffort

(m

)

-1 -0.5 0 0.5 1-0.1

-0.05

0

0.05

0.1Segment-2

E

ffort

(m

)

-1 -0.5 0 0.5 1-0.1

-0.05

0

0.05

0.1Segment-3

E

ffort

(m

)

-1 -0.5 0 0.5 1-0.1

-0.05

0

0.05

0.1Segment-4

E

ffort

(m

)

-1 -0.5 0 0.5 1-0.1

-0.05

0

0.05

0.1Segment-5

E

ffort

(m

)

PassiveAA1AA2

Segment Magnitude

Segment-1 0.236205

Segment-2 0.252054

Segment-3 0.253221

Segment-4 0.238556

Segment-5 0.315249

-1 -0.5 0 0.5 10

0.05

0.1

0.15

0.2Segment- 1

Velo

city (

m/s

ec)

-1 -0.5 0 0.5 10

0.05

0.1

0.15

0.2Segment- 2

Velo

city (

m/s

ec)

-1 -0.5 0 0.5 10

0.05

0.1

0.15

0.2Segment- 3

Velo

city (

m/s

ec)

-1 -0.5 0 0.5 10

0.05

0.1

0.15

0.2Segment- 4

Velo

city (

m/s

ec)

-1 -0.5 0 0.5 10

0.05

0.1

0.15

0.2Segment- 5

Velo

city (

m/s

ec)

Passive

AA1

AA2

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the bottom right of Fig.5(a)) and the number of subjects that

managed to lead the performance during those segments, but

no significant correlations were found. The velocity plots in

Fig.5(b) show a smooth pattern during the Passive and the

AA1 modes compared to a visibly multi-peak velocity

during the AA2 mode. This indicated that subjects actively

contributed to the AA2 mode, yet did not manage to lead the

robot in achieving the task goals.

It was notable from Fig.1 and Fig.2 that segments 1, 3 and

5 were reaching segments where the movement started at a

source point located closer to the subject’s body and ended

at the target point away from the body. Segments 2 and 4

were returning segments where the movement started at a

source farther away from the subject’s body towards a target

closer to the body. Our observation here indicated that in

cases where the robot moved towards the subject’s body, the

subject played a leading role (as reflected by ) for a

smaller proportion of the time when compared to cases

where the robot moved away from the subject’s body.

C. Tau (τ) versus ∆Effort (Quadrant-specific analysis)

As discussed earlier, a large number of subjects could not

play a leading role during segments 2 and 4 of the AA2

mode when they were instructed to do so. Also, plots of

segments 1, 2 and 4 in Fig. 5 showed that the sign of did not remain constant as tau progressed from -1 to 1. A

possible cause was linked to the set duration of the

movement and whether there has been enough time allocated

to perform a segment comfortably. The segments were

therefore fragmented in to four equal quadrants (based on

tau) to carry out a closer observation of lead/lag role of the

subject during various segments of the AA2 mode. The four

quadrants were formed as follows: Quadrant-1 (Q1, ), Quadrant-2 (Q2, ), Quadrant-3

(Q3, ) and Quadrant-4 (Q4, ). The

decision to divide the segments into four equal quadrants

was solely based on the literature and the expectation of a

bell-shaped velocity profile during these segments. Our

anticipation was that if duration is an influencing parameter,

there will be a gradual reduction of subject numbers

managing to lead the robot as one progressed from Q1-Q4.

The condition for the leading role was then applied to all

four quadrants of each segment and the number of qualifying

subjects that led the interaction during that quadrant was

counted.

The results were presented by the bar chart (Fig. 6).

Reaching segments (1, 3 and 5) show similar patterns with

≥50% subjects satisfying the leading performance condition

during Q1, Q2 and Q4 and <50% during Q3. Similarity also

existed in returning segments (2 and 4) with ≥50% subjects

satisfying the leading performance condition during Q1 and

Q2 and <50% during Q3 and Q4. This showed that during

Q1 and Q2 the majority of the subjects could lead the

performance during all segments in the AA2 mode when

they were asked to do so, but the lead role was not consistent

during Q3 and Q4. It further highlighted that there is

potentially a link between the type of reaching task, its set

duration and the subject’s ability to lead during an active

assisted interaction.

Figure 6. Quadrant specific counts of subjects satisfying leading

condition in the AA2 mode during various segments. Segments

were re-ordered to allow for better comparison.

IV. DISCUSSION

During this exploratory study, the duration to execute

each segment was set to 4 seconds. Data analysis results

showed that the subjects did not always lead the robot when

they were asked to do so in the AA2 mode. When the

segment was further fragmented into quadrants, the results

showed the leading role in Q1 and Q2 and an inconsistent

role in Q3 and Q4 in majority of the cases. A likely

explanation for this behaviour is that subjects were restricted

from performing at their normal and natural pace by the pre-

set 4 seconds duration while segment lengths and arm

movement patterns varied. It could also be linked to the type

of movement (reaching away or returning towards the

subject’s body) required for executing each segment. Also,

Fig. 2 shows that reaching segments (1, 3 and 5) had a more

pronounced gravity component towards Q3 and Q4 while

returning segments (2 and 4) present the opposite (as the

arm-shoulder support gravity compensation unit was not

used during this experiment). In our next experiment we

plan to include trajectories towards and away from the body

with horizontal and vertical components, allowing us to test

whether gravity is also a contributing factor. This would also

give us an opportunity to study the influence of movement

direction on the performance of the subject.

Our findings presented in this paper further highlight the

need for adaptive interaction as it has magnified that

different movement patterns require different settings. An

interesting question here is whether a customised duration is

sufficient to pose a therapeutic challenge?

One logical approach was that the duration for performing

segments should be based on subjects’ pace in performing a

segment. In our on-going experiment we included a new

customisation phase to calculate the average reaching time

Seg-1 Seg-3 Seg-5 Seg-2 Seg-4

Q1 20 16 16 18 16

Q2 12 12 10 12 12

Q3 8 9 5 9 5

Q4 12 13 13 3 4

0

5

10

15

20

25

Co

un

t (o

ut

of

20

)

Leading role in AA2 (Quadrant-wise)

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for the participating subject and execute the rest of the

experiment based on the average reaching time for that

subject and type of movement, i.e. reaching away or

returning towards the body.

In our ongoing experiment modifications were made to

make the GENTLE/A system adaptive to a subject’s ability

to perform a segment based on observed duration values

during an ‘adaptive phase’. As ∑ is used for this

purpose, program code has been enhanced to compute the

∑ parameter for each segment as the experiment

progresses. The experiment begins with a constant value for

the duration set to execute each segment. During the AA2

mode once the execution of a segment finishes,

the duration to execute that segment in the next

cycles is altered using the following algorithm:

∑

( )

( )

∑

[ ]

The two main aims of the ongoing experiment are to test

the adaptability of the GENTLE/A system to segment

duration and to repeat the investigation on lead-lag role of

the subject interacting with the GENTLE/A system tuned to

operate with customized segment durations for that subject

on a more versatile set of points. The data recorded until this

date is showing some promising results where the duration

to execute each segment adjusts through the initial iterations

and settles down to an optimum value for each segment

displaying the characteristic of an adaptable system. This

data also shows that adaptive times vary between the

reaching away and returning towards the body durations,

further confirming the findings shown by Figure 6. We plan

to complete this experiment and present its findings in future

publications.

V. CONCLUSION

We described in this paper an approach to identify the

leading or lagging role of the subject interacting with the

system. We aim to use this information to improve the

adaptability of the GENTLE/A system by customizing the

exercise parameters, including segment duration or

increasing the assistance provided to the subject in case of

lagging performance and reducing the assistance in case of

leading performance. The results from this exploratory study

showed that vector projections of the position data achieved

by the subject when compared to the reference positions

driven using MJT could inform the lead-lag role of the

subject. The varying performance of the subjects during

different quadrants of reaching and returning trajectory

segments opened a new line of investigation into reaching

durations recorded. Studying these durations hinted further

on their links to the lagging or leading role of the subject.

Adapting the GENTLE/A system according to the

performance of the subject forms a vital part of our ongoing

experiment. Further research into exploring the potential of

average reaching times as an ‘assessment’ parameter is also

under progress.

VI. REFERENCES

[1] National Stroke Association. Available: http://www.stroke.org

[2] J. Krakauer, “Motor learning: its relevance to stroke recovery and neurorehabilitation,” J. of Current Opinion in Neurology, vol. 19, no.

1, pp. 7, 2006.

[3] F. Amirabdollahian, R. Loureiro, B. Driessen, and W. Harwin, “Error Correction Movement for Machine Assisted Stroke Rehabilitation,”

in Proc. ICORR, 2001.

[4] W. Harwin, R. Loureiro, F. Amirabdollahian, M. Taylor, G. Johnson,

E. Stokes, S. Coote, M. Topping, C. Colin, and S. Tamparis, “The

GENTLE/S Project: A New Method of Delivering Neuro-

Rehabilitation,” in Proc. AAATE, 2001, pp. 36-41. [5] R. Loureiro, F. Amirabdollahian, M. Topping, B. Driessen, and W.

Harwin, “Upper Limb Robot Mediated Stroke Therapy-GENTLE/s

Approach,” J. of Autonomous Robots, vol. 15, no. 1, pp. 35-51, 2003. [6] S. Coote, E. Stokes, B. Murphy, and W. Harwin, “The effect of

GENTLE/S robot-mediated therapy on upper extremity dysfunction

post stroke,” in Proc. ICORR, 2003. [7] F. Amirabdollahian, R. Loureiro, E. Gradweli, C. Colin, W. Harwin,

and G. Johnson, “Multivariate Analysis of the Fugl-Meyer Outcome

Measures Assessing the Effectiveness of the GENTLE/S Robot-Mediated Stroke Therapy,” J. of NeuroEngg & Rehabil, vol. 4, no. 4,

2007.

[8] G. Kwakkel, B. Kollen, and H. Krebs, “Effects of Robot-Assisted Therapy on Upper Limb Recovery After Stroke: A Systematic

Review,” J. of Neurorehabil Neural Repair, vol. 22, no. 2, pp. 111-

121, 2008.

[9] J. Mehrholz, T. Platz, J. Kugler, and M. Pohl, “Electromechanical

and robot-assisted arm training for improving arm function and

activities of daily living after stroke (Review),” J. of Stroke, vol. 40, no. 5, 2009.

[10] G. Prange, M. Jannink, C. Groothuis-Oudshoorn, H. Hermens, and

M. IJzerman, “Systematic review of the effect of robot-aided therapy on recovery of the hemiparetic arm after stroke,” J. of Rehabil Res

Dev, vol. 43, no. 2, pp. 171-184, 2006.

[11] D. Reinkensmeyer, L. Kahn, M. Averbuch, A. McKenna-Cole, B. Schmit, and W. Z. Rymer, “Understanding and treating arm

movement after chronic brain injury: progress with the ARM Guide,”

J. of Rehabil Res Dev, vol. 37, no. 6, pp. 653-662, 2000. [12] L. Kahn, P.Lum, W. Rymer, and D. Reinkensmeyer, “Robot-assisted

movement training for the stroke-impaired arm: Does it matter what the robot does?,” J. of Rehabil Res Dev, vol. 43, no. 5, pp. 619-630,

2006.

[13] F. Amirabdollahian, R. Loureiro, and W. Harwin, “Minimum Jerk Trajectory Control for Rehabilitation and Haptic Applications,” in

Proc. ICRA, 2002, pp. 3380-3385.

[14] R. V. d. Linde, and P. Lammertse, “HapticMaster –a generic force controlled robot for human interaction,” Industrial Robot: An

International Journal, vol. 30, no. 6, pp. 515-524, 2003.

[15] R. Chemuturi, F. Amirabdollahian, and K. Dautenhahn, “A Study to understand lead-lag performance of Subject vs Rehabilitation

system,” in Proc. Augmented Human, 2012.

[16] E. Bizzi, N. Accornero, W. Chapel and N. Hogan, "Posture Control and Trajectory Formation during arm movement," J. of

Neuroscience, vol.4, no.11, pp.2738-2744, 1984.

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