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On the Relationship Between Human Motor Control Performance and Kinematic Synergies in Upper Limb Prosthetics

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Current prosthesis command interfaces only allow for a single degree of freedom to be commanded at a time, making coordinated motion difficult to achieve. Thus it becomes crucial to develop methods that complement these interfaces to allow for intuitive coordinated arm motion. Kinematic synergies have been shown as an alternate method where the motion of the prosthetic device is coordinated with that of the residual limb. In this paper, the mapping between the parameters of a kinematic synergy model and a measure of task performance is established experimentally in order to test the applicability of online optimization methods for the identification of synergies. To achieve this, a cost function that captures the objective of the reaching task and a linear kinematic synergy model were chosen. A human experiment was developed in a Virtual Reality (VR) platform in order to determine the synergy-performance relationship. The experiments were performed on 10 able-bodied subjects. The relationship observed between the synergy parameter and the reaching task cost function suggests existing online optimization methods may be applicable.
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On the Relationship Between Human Motor Control Performance and
Kinematic Synergies in Upper Limb Prosthetics
Ricardo Garcia-Rosas, Denny Oetomo, Chris Manzie, Ying Tan, and Peter Choong
Abstract Current prosthesis command interfaces only allow
for a single degree of freedom to be commanded at a time,
making coordinated motion difficult to achieve. Thus it becomes
crucial to develop methods that complement these interfaces to
allow for intuitive coordinated arm motion. Kinematic synergies
have been shown as an alternate method where the motion of
the prosthetic device is coordinated with that of the residual
limb. In this paper, the mapping between the parameters of a
kinematic synergy model and a measure of task performance is
established experimentally in order to test the applicability of
online optimization methods for the identification of synergies.
To achieve this, a cost function that captures the objective of
the reaching task and a linear kinematic synergy model were
chosen. A human experiment was developed in a Virtual Reality
(VR) platform in order to determine the synergy-performance
relationship. The experiments were performed on 10 able-
bodied subjects. The relationship observed between the synergy
parameter and the reaching task cost function suggests existing
online optimization methods may be applicable.
I. INTRODUCTION
The command interfaces available to current robotic pros-
thetic arms usually include a combination of proportional
surface electromyography (sEMG) sensors and buttons or
smartphone applications. However, these interfaces only al-
low for continuous control of a single degree of freedom
(DOF). Given this difference between prosthesis DOF and
interface signals, complex coordinated motion of the whole
human-prosthesis arm is unavailable to their users. These
difficulties and complexity have been linked to device aban-
donment [1]. Thus it is important to develop methods that
can complement sEMG and allow for intuitive coordinated
arm motion in prosthetics.
One of such methods is based on the theory of muscle
synergies, which states that muscles are grouped by the
Central Nervous System (CNS) in order to regulate complex
coordinated motion in a simplified manner [2]. Similarly,
synergies can represent the relationships between the DOF
of a limb; these are known as kinematic synergies [3].
Kinematic synergies have been proposed as an alternate
method to sEMG for providing commands to a prosthetic
arm [4], allowing prosthesis users to perform coordinated
arm motion. Given that fine motion of the residual limb is
typically still available to amputees, synergistic prosthesis
interfaces may provide an advantage over purely sEMG
interfaces where fine regulation of the signals is difficult.
This project is partially funded by the Valma Angliss Trust and Defence
Science Technology Group CERA program.
R. Garcia-Rosas, D. Oetomo, C. Manzie and Y. Tan are with the
School of Electrical, Mechanical and Infrastructure Engineering, and P.
Choong with the Department of Surgery, The University of Melbourne,
VIC 3010, Australia. ricardog@student.unimelb.edu.au;
{doetomo,manziec,yingt,pchoong}@unimelb.edu.au.
Current synergistic approaches to prosthesis arm motion
regulation utilize Artificial Neural Networks (ANNs), where
an ANN is used to coordinate motion of the residual and
prosthetic limb [4], [5]. In order to determine their relation-
ship, the ANN is trained using machine learning methods
with reaching motion data-sets gathered from able-bodied
subjects [5]. While these methods have shown promising
results, the ANNs have been observed to be sensitive to
individual variation. This may produce a challenge for gen-
eralizing the approach to subjects outside the training set [5].
Retraining of the ANN for an amputee may not be possible
as training data requires full reaching motion [4], [5]. While
these methods identify averaged synergies for the training
group, it has been shown that optimal synergies can vary
across individuals [6]. Furthermore, natural motion in am-
putees can vary significantly from that of able-bodied people
due to the changes in the limb dynamics and constraints as
a result of the amputation.
A method for identifying the optimal synergies for a given
individual has the potential to allow the algorithms to adapt
to their users and their changes in behavior. This need has
been explicitly identified in pre-clinical studies with syner-
gistic prostheses [7], motivating the consideration of online
optimization methods, such as Extremum Seeking (ES) [8],
in order to identify such synergies. A feasibility study with
such technique was performed by the authors [9], where
appropriate assumptions on human motor control dynamics
were needed, such as the existence of a local extremum in the
input/output map of interest [10, Assumption 2]; which is a
common requirement for gradient based online optimization
methods. It is established in the literature that human motor
control strategy converges to a particular trajectory of task
execution when the task is learned (e.g. [11]). What the
present study seeks to establish is that given a range of
possible kinematic synergies, when all the synergies are
learned by the human (rather than focusing on a single
synergy), there exists one where the performance of the task
is better, by a specified measure, than with other synergies.
In this paper, the relationship between the parameters of a
synergy model and a measure of task performance (or cost)
is established experimentally in order to test the applicability
of online optimization methods for the identification of
synergies. To achieve this, a cost function that captures
the objective of the reaching task and a linear kinematic
synergy model were chosen without loss of generalization
to other approaches that are linear in their parametrization.
A human experiment to determine the synergy-performance
relationship for a set of synergies was developed in a Virtual
Reality (VR) platform. The experiment was performed on 10
able-bodied subjects. The Institution’s Ethical Review Board
approved all experimental procedures involving humans.
II. METHODOLOGY
A. Model of kinematic synergy
There exist multiple approaches to represent muscle and
kinematic synergies, both non-model [5] and model based
[12]. Given that the focus of this work is on finding the
relationship between synergies and task performance rather
than the choice of synergies, a shoulder-elbow linear synergy
model was chosen. Linear synergies have been observed
to occur between the shoulder and elbow during reaching
motion [13]. Furthermore, they have been used to model
upper limb muscle synergies and their linear combination
can produce complex motion as observed in [12]. In the case
of kinematic synergies, the velocities of the DOF of the limb
are the ones being coordinated [5].
Let the residual limb joint velocities ˙
qr, in this case the
shoulder, be given by ˙
qr=˙qfle ˙qabd ˙qrotT, where ˙qf le,
˙qabd,˙qrot are scalar and represent shoulder flexion/extension,
abduction/adduction, and humeral rotation respectively. Sim-
ilarly, let prosthesis joint velocities ˙
qp, in this case the elbow,
be given by ˙
qp= ˙qelb, where the scalar ˙qelb represents
elbow flexion/extension. Then, a linear kinematic synergy
is given by ˙
qp=θ˙
qr, where θrepresents the synergy
parameters and is restricted to a compact set Θwhich
includes the physically feasible parameters. Then the desired
elbow velocity provided by the synergy can be used to
generate a reference for the prosthesis controller as is shown
in Figure 1, where the controller is a predetermined feedback
controller. Experimentally identifying the optimal parameters
θfor a group of individuals and the relationship of θto task
performance will be the main objective of this work.
Fig. 1. Synergistic prosthetic elbow block diagram.
B. Reaching task characterization
A widely accepted method for modelling trajectory plan-
ning and generation in the CNS is to characterize motor
control performance with a cost function which is opti-
mized to determine the desired hand trajectory. Multiple cost
function based motion characteristics have been proposed
in the literature such as tracking error, torque-change, and
hand jerk [14]. Given the application and experimental
hardware setting, tracking and hand jerk are more feasible
for measurement than other methods.
Therefore, the cost function that characterizes motor con-
trol performance of a reaching task can be described by
J(θ) =
M
X
j=1
αjψj(θ),(1)
where M > 0is the number of motion characteristics
in the cost function, αj>0the weight given to each
characteristic, and the positive function ψj(·)represents a
motion characteristic. In this work two motion characteristics
were considered: ψ1(·)the tracking error, and ψ2(·)hand
jerk, which are given by
ψ1=kpi(Ti
f,θ)¯pfk2, ψ2=ZTi
f
To
k...
pi(t, θ)k2dt, (2)
where irepresents an iteration of the task, Tois the start
time of the motion, which is constant across all iterations,
and Ti
f>0is the motion end time which can vary across
iterations. Moreover, it has toToTi
ftf,max .
C. Experiment description and protocol
Subjects performed a center-out forward reaching task
from a seated position while using a virtual synergistic
prosthetic elbow. The start and end positions were constant
throughout the experiment and were shown in the VR
environment as presented in Figure 2.B. The scalar parameter
θchosen for the experiment was the one related to shoulder
flexion/extension ˙qfle , and 10 different values were explored.
In order to be able to observe the mapping between Synergy
and Performance, it was necessary to isolate the transient
behavior due to task learning. Thus subjects repeated the
reaching task for each value until it was deemed as learned.
Learning of the task was determined by the variability of
the trajectory followed by the hand, with the successfully
learned task condition being reaching a variability radius
under p= 2cm. This condition was determined by fol-
lowing studies that demonstrated that as humans learn a
hand reaching task, the variability of hand trajectories is
reduced [15]. The p= 2cm radius was chosen by testing
the reaching capabilities of able-bodied people, hardware
tracking precision, and additional tolerance to account for
the virtual prosthesis.
Trajectory variability was determined by sampling hand
trajectory and evaluating it at fixed time steps. Trajectory
mean and standard deviation was calculated for a sliding
window of 10 task repetitions at each sampling time step.
This was used to generate a spheroid centered at the mean
hand position with radius given by the standard deviation.
The set of spheroids represents the mean trajectory and
standard deviation [16]. The learning condition is achieved
when the radius of all spheroids is smaller or equal to p.
The experiment was performed on 10 able-bodied subjects
(A-J). The forward reaching task was repeated a minimum
of 10 times and maximum of 50 times for each parameter to
be analyzed, with successful learning triggering a parameter
change. The parameter values for each subject were manually
determined by the experimenter in order to explore the
regions of the parameter space best suited to each subject,
with the first three values being predetermined to 1.5,1.1,
and 1.9, in the respective order. Subsequent values were
chosen by alternating between the extremes of the identified
search region in order to minimize skill transfer between
synergy values. Cost functions (ψ1,ψ2) were normalized to
be within the same range (0-1) and equal weights were given
to them (α1=α2= 1). Each reaching motion had a time
limit of 3 seconds. Sessions were separated in five blocks:
1) Hardware calibration (5 minutes).
2) VR training (2 minutes).
Fig. 2. Experiment platform set-up: A) Subject position and sensor placing. B) Subject in virtual environment. C) Subject and VR views.
3) Experiment task block 1 (25 minutes).
4) VR rest (5 minutes).
5) Experiment task block 2 (25 minutes).
During hardware calibration, the sensor and virtual upper
arm were calibrated such that the virtual upper arm matched
the dimensions and motion of the subject’s upper arm. Sub-
jects were allowed to rest for 1 minute every 50 repetitions in
order to minimize upper arm fatigue. A longer rest was given
in between experiment blocks, where subjects removed the
VR headset in order to minimize VR fatigue. The procedure
was approved by the Institution’s Ethical Review Board
under project number 1750711.1.
D. Hardware set-up and data gathering
The VR experiment platform was developed on an Oculus
Rift headset with the application developed in Unity3D. The
experiment was run on an Intel Core i7-7700HQ processor at
3.8GHz, with 16GB RAM, and an NVIDIA GeForce GTX
1070 video card with 8GB GDDR5. The Oculus Rift set-up
included 3 tracking sensors, two placed in the front corners
of the room and one in a back corner, and one Oculus Touch
controller. Virtual residual limb motion was determined by
a Touch controller attached to the subject’s dominant upper
arm as shown in Figure 2.A. Motion of the lower arm had no
effect on the motion of the virtual arm. Data gathering and
VR update was performed at 90Hz. The subject’s shoulder
rotation and angular velocity in 3 DOF, the rotation and
angular velocity of the virtual prosthetic elbow, and hand
position and velocity in 3D space were gathered.
III. RESULTS AND DISCUSSION
Subjects were able to maintain a consistent level of
trajectory variability across iterations, converging asymptot-
ically to the desired threshold (p) as learning occurred,
as has been observed with performance in other works [11].
Representative results of this are shown in Figure 3.A, where
variability across iterations for subject E is presented. The
sudden increases in variability are due to a change of θvalue,
which has been previously observed in humans when sub-
jected to changing system dynamics [17]. In a few subjects
where slower learning rate was observed, convergence to the
desired level of trajectory variability pwas not achieved
within the allotted number of iterations in the experiment.
In these cases, variability was observed to increase towards
the last iterations as can be seen in Figure 3.B. This may be
attributed to fatigue due to the larger number of repetitions
performed during the experiment. These results suggests that
the chosen learning condition should be able to accommodate
for individual capabilities, learning rates and performance
variation throughout the use of the device to properly isolate
the transient behavior caused by human learning dynamics.
0 20 40 60 80 100 120 140
Iteration
0.02
0.03
0.04
0.05
0.06
0.07 A)
Trajectory variability
Threshold ( p)
New value introduced
280 300 320 340
0.02
0.03
0.04
0.05
0.06
0.07 B)
Fig. 3. A) Subject E (whole experiment) and B) Subject F (last two θ
values) trajectory variability across task iterations.
Figure 4 presents the relationship between the proposed
cost function (J) in Equation (1) and the synergy parameter
values (θ) for all able-bodied subjects (A-J), where the last 10
iterations per value (as per the learning condition presented
in Section II-C) were used to generate the box and whiskers
plots. It was observed that the performance range (J)differs
across individuals, and that the minimum cost (J) was
observed at different synergy parameter values (θ) for
different subjects. This highlights both individual variability
in performance (J)and in synergies (θ). Furthermore, when
the average best synergy across all subjects (θ
µ= 1.7) is
considered and performance evaluated, it can be observed
that for some subjects performance would be significantly
impaired, e.g. by 32% for subject D and 66% for subject I.
This highlights the significance of finding the best synergy
for each individual.
The purpose of this work aimed to observe a unique mini-
mum in the Performance/Synergy J(θ)map for each person.
Due to the relatively low number of subjects, a statistically
significant quadratic map was not obtained. However, it can
be observed in the subjects that achieved lower variability,
see Figure 4.A-B and D-E, that there is a trend towards
exhibiting a unique minimum as the task is learned; since
lower variability can be attributed to learning of a task [15].
This difference in learning of the task across subjects may
be attributed to the different learning rates across individuals
[11]. Such that the individuals that were able to learn the task
1 1.5 1.7 2 2.5
0.1
0.15
0.2
0.25
0.3
0.35
0.4 B)
1 1.5 1.7 2 2.5
0.06
0.07
0.08
0.09
0.1
0.11
0.12
0.13 A)
1 1.5 1.7 2 2.5
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.26
0.28 C)
1 1.5 1.7 2 2.5
0.07
0.08
0.09
0.1
0.11
0.12
0.13
0.14
0.15
0.16 E)
1 1.5 1.7 2 2.5
0.05
0.1
0.15
0.2
0.25
0.3 F)
1 1.5 1.7 2 2.5
0
0.1
0.2
0.3
0.4
0.5
0.6 G)
1 1.5 1.7 2 2.5
0.05
0.1
0.15
0.2
0.25
0.3
0.35 H)
1 1.5 1.7 2 2.5
0.06
0.07
0.08
0.09
0.1
0.11
0.12
0.13
0.14
0.15 I)
1 1.5 1.7 2 2.5
0.05
0.06
0.07
0.08
0.09
0.1
0.11
0.12
0.13 J)
1 1.5 1.7 2 2.5
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.26
0.28 D)
* = 1.6
J* = 0.112
* = 1.7
J* = 0.081
* = 2.1
J* = 0.107
* = 1.5
J* = 0.112
* = 1.7
J* = 0.077
* = 1.4
J* = 0.109
* = 1.8
J* = 0.188
* = 1.6
J* = 0.108
* = 1.5
J* = 0.077
* = 1.9
J* = 0.066
Fig. 4. Performance vs Synergy (J(θ)) relationship box and whisker plot results for all able-bodied subjects (A-J). The x-axis represents the synergy
parameter values and the y-axis the cost. Circles represent the mean cost and lines the standard deviation.
within the allocated iterations show a result more reflective
of a quadratic map (e.g. A-B, D-E). This may suggest that
when the task is yet to be “learned”, the J(θ)map is
unreliable for the proposed purposes. On the other hand, as
the task is learned and trajectories become more consistent,
the map shows properties desirable for online optimization
algorithms, such as a local unique extremum.
IV. CONCLUSION
An experiment to determine the relationship between
the parameters of a linear synergy (θ) and a measure of
motor control performance (J) that characterizes a reaching
task was presented. This experiment extended from typical
experiments on human motor control by the exploration
and learning of different motion settings, in the form of
synergy parameters, rather than the learning of a single one.
It was observed that values of the cost function differ across
individuals, and that the minimum cost was observed for
different synergy parameter values for different subjects.
This highlights individual variability in performance, but
also in synergies. While a statistically significant quadratic
map was not obtained, it was observed that there is a
trend towards exhibiting a unique minimum as the task is
learned. This observation suggests that as the task is learned,
the map obtained from the experiment shows properties
desirable for online optimization algorithms. This highlights
the importance of developing a design framework that can
determine successful learning of the task while accounting
for individual capabilities, learning rate and filtering external
disturbances. Future work will investigate the implementa-
tion of the identification algorithm in the VR experimental
platform, to develop a method for triggering algorithm that
can update based on the learning condition, and to conduct an
experiment to demonstrate the performance of the algorithm.
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... regulating the movement of an elbow prosthesis as a function of the movement of the shoulder joint (residual limb) in a transhumeral amputation. However, the kinematic synergies investigated in the literature to date have been found to be dependent on individual motor behaviour and the task, making them difficult to generalise and implement practically [5], [6], [7], [8]. ...
... Therefore, this relationship is dependent on the initial limb position and the task used to calibrate the synergy. Both types of synergies require extensive calibration, and have been found to be dependent on individual motor behaviour and the task to be performed [4], [5], [6], [7], [9]. While recent results have demonstrated that differential kinematic synergies can be personalised to their user during task execution [8], a library of task-specific and individually personalised synergies would be needed to provide the large range of movements required by ADLs [12]. ...
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