1) The document proposes an adaptive weight support method for shoulder flexion during robot-assisted arm therapy for stroke and spinal cord injured patients. 2) An inverse static model of the cable-driven robotic system and passive human arm is used to estimate the rope forces needed to flex the arm and compensate a given percentage of the arm weight. 3) Experiments with two spinal cord injured patients show that the adaptive weight support approach achieved a desired larger range of motion compared to conventional constant rope forces.

1. Adaptive Arm Weight Support using a Cable-Driven Robotic System
Sven Knuth, Arne Passon, Frank D¨ahne, Andreas Niedeggen, Ingo Schmehl and Thomas Schauer
Abstract— Many stroke and spinal cord injured (SCI) pa-
tients suffer from a paretic arm movement, which can be
characterized by a limited shoulder flexion. We consider a
possibility to assist the patient in slow arbitrary arm flexions
within a large range of motion. To address this issue, we propose
a shoulder flexion dependent weight support during robot-
assisted therapy of the upper limb. Inverse static models of the
cable-driven robotics and the passive human arm are used to
estimate the required forces at the ropes to flex the upper arm
in order to compensate a given percentage of the arm weight.
Our results show that conventional constant rope forces during
a therapy may produce an over- or undercompensated weight
support, whereas the proposed adaptive approach achieves a
desired larger range of motion.
I. INTRODUCTION
Robotic devices play a central role in the treatment of
stroke and spinal cord injured patients. Current developments
of arm rehabilitation robotics mostly use two strategies to
support the arm lifting of patients. They either compen-
sate deviations from prescribed motion sequences, which
preclude arbitrary movements, or they assist with manually
selected constant forces, which can lead to an over- or
undercompensated weight support, see e.g. [1], [2]. This
contribution proposes and investigates a method without the
two mentioned possible disadvantages to adaptively support
the shoulder flexion during robot-assisted arm therapy. To
evaluate the developed approach, we used the cable-driven
arm rehabilitation robot DIEGO (Tyromotion GmbH, Aus-
tria) and performed experiments with two SCI patients.
II. METHODS
A. Rehabilitation robot
The cable-driven robotic system DIEGO was used to
evaluate the proposed adaptive weight support. Two ropes
of the robotics are attached on the forearm, where one is
connected next to the elbow joint and the other next to
the wrist joint. Forces are applied at these ropes to realize
the weight support. The vectors TW and TE as shown
in Fig. 1, determine the directions and magnitudes of the
applied forces. The directions depend on the current upper
limb position related to the actuators, which are located
above the user. Estimations of the shoulder, elbow and wrist
The work was conducted within the research project BeMobil, which
is supported by the German Federal Ministry of Education and Research
(BMBF) (FKZ16SV7069K).
S. Knuth, A. Passon and T. Schauer are with the Control Systems Group
at the Technische Universit¨at Berlin, Berlin, Germany.
F. D¨ahne and I. Schmehl are with the Clinic for Neurology, Stroke Unit
and Early Rehabilitation at the Unfallkrankenhaus Berlin, Berlin, Germany.
A. Niedeggen is with the Spinal Cord Injury Center at the Unfallkranken-
haus Berlin, Berlin, Germany.
positions are provided by the robotic system depending on
the measured cable extensions and deflections.
B. Arm model
z
y
τuser
vu
vf
θC
f
θu
Fgu
Fgf
TE TW
Fig. 1. Static model of the upper limb with the arm segment vectors vf
and vu, the gravitational forces Fgu and Fgf , the flexion angles θC
f and
θu, the rope tension vectors TW and TE, and the torque τuser which is
contributed by the user.
A simple static arm model with two segments describes
the upper limb within a vertical plane, see Fig. 1. Thus, the
model is restricted to sagittal plane motions as flexion and
extension of the shoulder and elbow joint. A quasi stationary
state is assumed due to slow movements of the patients. The
vector vu describes the upper arm segment and the forearm
segment is given by the vector vf . The forearm’s flexion
θC
f is assumed to be almost horizontal to the ground to
achieve a simplified weight support method. Consequently,
the shoulder flexion angle θu completely determines the arm
position. The torque τuser is applied by the user and can not
be measured directly. The static arm model is described by
two configurations. In the first configuration with θu as input
and the gravitational torque τg as output, no weight support
is provided by the robotic system. Thus, it is possible to
determine τg due to the gravitational forces Fgu and Fgf
which is required to hold the arm at the current θu as
τg = gh(θu) = − ex
1
2
vu(θu) × Fgu
+
vu(θu) +
1
2
vf (θu) × Fgf
, (1)
where ex is the unit vector in the direction of the x-axis
of the coordinate system shown in Fig. 1. In the second
configuration with the input θu and the torque generated by
the robotic system (τr) as output, no gravitational forces are

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Fig. 3. Experimental results. The patient had to follow a given reference trajectory θref
u . The observed flexion angle θu and the adjusted rope tension
uTE
are shown. Periods with adaptive and constant support are highlighted by white and gray background, respectively.
assumed to determine the torque at the shoulder:
τr = ex vu(θu) × TE(θu)+
(vu(θu) + vf (θu)) × TW(θu) . (2)
The torque contributed by the user can now be estimated by
τuser = τg − τr.
C. Control System
Shoulder / ArmRobotics
τr
gh(θu)/sD(θu)
y = θu
s%
uTE
flexion-feedback
τuser
Fig. 2. The interaction between the robotics, which provides the torque
τr, and the user, who provide the torque τuser, can be described as a SISO
system with the required force magnitude uTE
as input and the resulting
shoulder flexion θu as output. The developed flexion-feedback is given by
the inverse static model gh(θu)/sD(θu) and the scale factor s%.
Using the static arm model, we can manipulate the weight
support such that it fully compensates the shoulder flexion
dependent gravitional torque τg by setting
τr = τg. (3)
From experience, we achieved an almost horizontal forearm’s
flexion by choosing TW 2 proportional to TE 2, where
.. 2 denotes the Euclidean norm. Thus, equation (2) can be
factorized as
τr = TE 2 sD(θu). (4)
With the gravitational torque (1) and the torque due to the
robotics (4), equation (3) can be solved to derive the elbow
rope tension for 100 % weight support by
TE 2 = gh(θu)/sD(θu). (5)
Taking into account, that the patient can contribute an amount
of the required torque τg, we can scale the provided torque
τr with a patient dependent factor s% ∈ [0, 1] to realize an
appropriate level of support. Consequently, we obtain the
required elbow rope tension by
uTE
= s% TE 2 = s% gh(θu)/sD(θu). (6)
The resulting flexion-feedback is illustrated in Fig. 2.
III. RESULTS
We performed experiments with two SCI subjects (injury
levels C4-complete and C1-incomplete), who signed the
consent information by the ethics committee of the Berlin
Chamber of Physicians. The trials were divided into two
steps. First, the relaxed and passive human arm was gradually
lifted by the robotics from around 45◦
until 90◦
. We used the
recorded data for a nonlinear-least-square optimization with
the elbow rope tension uTE
as input and θu as output to
estimate the arm segment lengths and masses. In the second
step, the patient performed a movement with a repetitive
pattern. The pattern included three different shoulder flexion
levels θref
u , where the patient has to hold the arm for ten
seconds. The patient received either an adaptive or constant
support during each pattern. The therapist chose a constant
support for the patient, which provided the largest range of
motion between 45◦
and 90◦
. For the adaptive support, the
scale factor s% was chosen in such a way that the before
selected constant force was generated by (6) in the middle
of the flexion range at 65◦
.
The experimental results in Fig. 3 show that the movement
range could only be slightly extended by approx. 10◦
for one
patient when using the adaptive support in comparison to a
constant support. For the other, less impaired patient (injury
level C4-complete) no difference was found.
IV. DISCUSSION AND CONCLUSION
The results show that an adaptive weight support is fea-
sible avoiding over- and undercompensation. The movement
range extension depends on the impairment of the patient.
We expect that more severe impaired patients will benefit
more from the presented approach.
Additional experiments are planned to evaluate the effec-
tiveness also for stroke patients and more SCI patients. In
the future, we want to extend the model to three dimensions
and dynamic movements.
REFERENCES
[1] L. Marchal-Crespo and D. J. Reinkensmeyer, “Review of control strate-
gies for robotic movement training after neurologic injury,” Journal of
NeuroEngineering and Rehabilitation, vol. 6, no. 1, pp. 20+, 2009.
[2] G. Rosati, P. Gallina, and S. Masiero, “Design, implementation and
clinical tests of a wire-based robot for neurorehabilitation.” IEEE
transactions on neural systems and rehabilitation engineering : a
publication of the IEEE Engineering in Medicine and Biology Society,
vol. 15, no. 4, pp. 560–9, 2007.