Low-Dimensional Motor Control Representations in Throwing Motions

Abstract

In this study we identified a low-dimensional representation of control mechanisms in throwing motions from a variety of subjects and target distances. The control representation was identified at the kinematic level in task and joint spaces respectively, and at the muscle activation level using the theory of muscle synergies. Representative features of throwing motions in all of these spaces were chosen to be investigated. Features were extracted using factorization and clustering techniques from the muscle data of unexperienced subjects (with different morphologies and physical conditions) during a series of throwing tasks. Two synergy extraction methods were tested to assess their consistency. For the task features, the degrees of freedom (DoF) and the muscles under study, the results can be summarized as: 1) a control representation across subjects consisting of only two synergies at the activation level and of representative features in the task and joint spaces, 2) a reduction of control redundancy (since the number of synergies are less than the number of actions to be controlled), 3) links between the synergies triggering intensity and the throwing distance, and finally 4) consistency of the extraction methods. Such results are useful to better represent mechanisms hidden behind such dynamical motions, and could offer a promising control representation for synthesizing motions with muscle-driven characters.

Full text

Research Article
Low-Dimensional Motor Control Representations in
Throwing Motions
Ana Lucia Cruz Ruiz,
1,2
Charles Pontonnier,
1,2,3
and Georges Dumont
1,2
1
INRIA/IRISA/M2S MimeTIC, Rennes, France
2
Ecole Normale Supérieure de Rennes, Univ Rennes, Rennes, France
3
Ecoles de Saint-Cyr Coëtquidan, Guer, France
Correspondence should be addressed to Georges Dumont; georges.dumont@ens-rennes.fr
Received 18 July 2017; Revised 9 October 2017; Accepted 29 October 2017; Published 31 December 2017
Academic Editor: Stefano Rossi
Copyright © 2017 Ana Lucia Cruz Ruiz et al. This is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is
properly cited.
In this study, we identified a low-dimensional representation of control mechanisms in throwing motions from a variety of subjects
and target distances. The control representation was identified at the kinematic level in task and joint spaces, respectively, and at the
muscle activation level using the theory of muscle synergies. Representative features of throwing motions in all of these spaces were
chosen to be investigated. Features were extracted using factorization and clustering techniques from the muscle data of
unexperienced subjects (with different morphologies and physical conditions) during a series of throwing tasks. Two synergy
extraction methods were tested to assess their consistency. For the task features, the degrees of freedom (DoF), and the muscles
under study, the results can be summarized as (1) a control representation across subjects consisting of only two synergies at the
activation level and of representative features in the task and joint spaces, (2) a reduction of control redundancy (since the
number of synergies are less than the number of actions to be controlled), (3) links between the synergies triggering intensity
and the throwing distance, and finally (4) consistency of the extraction methods. Such results are useful to better represent
mechanisms hidden behind such dynamical motions and could offer a promising control representation for synthesizing
motions with muscle-driven characters.
1. Introduction
Understanding how humans control motion is an important
aspect in a variety of fields, ranging from neuroscience to
robotics and animation [1]. Several theories have been pro-
posed which aim at unveiling the efficient and powerful
mechanisms behind human motion generation. In neurosci-
ence and biomechanics, some of the objectives of identifying
such mechanisms are to validate an existing motor control
theory, to diagnose and treat pathologies, or to enhance ath-
letic performance. In animation and robotics, identifying
such mechanisms is the key to enhance the realism and effi-
ciency of the motions in virtual humans and robots, since it
would allow the development of more realistic motion
controllers, reflecting a global control of motion [2]. More
realistic motions imply a higher degree of similarity to
humans, at the visual, kinematic, and dynamic level.
Our motivation lies in the domains of neuroscience and
animation. In the animation field, characters with more
detailed actuators (or muscles) are starting to be used for
motion synthesis. The use of muscle-based characters entails
several advantages such as smoother torque generation [3],
more realistic responses to perturbations [4, 5], and an ease
to simulate pathologies and fatigue [6, 7]. However, the use
of muscles complicates the control problem by augmenting
nonlinearity and redundancy, as at least two muscles are
necessary to actuate each degree of freedom [8]. Further-
more, computationally expensive optimization-based solu-
tions, which are unlikely to represent how humans control
motions, are used to compute a high number of control signals.
Thus, it is necessary to define compact control schemes
reducing the complexity of the control for such applications.
Neuroscience provides several interesting ways to circum-
vent this issue, such as the theory of muscle synergies [1, 9],
Hindawi
Applied Bionics and Biomechanics
Volume 2017, Article ID 3050917, 19 pages
https://doi.org/10.1155/2017/3050917

that tries to reduce redundancy by identifying a simple and
generic control representation of given tasks. This theory is
based on an interesting hypothesis of how redundancy is
handled by the central nervous system (CNS): it assumes
the existence of links between the ensemble of muscle control
signals during the performance of a task, which reduces
redundancy. Thus, through synergies, the muscles are
controlled as groups and not individually. There is support
for a neural organization of these synergies [10, 11] while
remaining an open question [12, 13]. Even if the interpreta-
tion of the low dimensionality revealed by decomposition
methods is subject to debate [14, 15], these methods allow
the creation of a compact and low dimensional control
representation based on experimental data for simple and
complex motions. Indeed, electromyography (EMG) signal-
processing strategies (principal components analysis, non-
negative matrix factorization) are able to extract compact
features from EMG signals, even if these extracted synergies
may be a consequence of a more complex mechanism
[16, 17]. Many studies have extracted synergies during a
variety of simple upper body human motions (such as
pointing and reaching [18, 19]). However, to the authors’
knowledge, only few studies have dealt with complex,
unconstrained (or free), and dynamic motion [20, 21], and
among them, overhead throwing is interesting to analyze
through this theory.
An overhead throwing motion consists of launching an
object forward and above the shoulder by using one arm.
This is the type of motion with which humans can throw
with speed and accuracy [22]. Unlike simple manipulation
tasks such as reaching, lifting, pulling, and pushing, this task
is more complex, requiring a higher coordination, accuracy,
and skill. Thus, it is a highly redundant and nonlinear task,
which involves a dynamic manipulation [23]. It is highly
redundant because there exists an infinite number of solu-
tions or movements that achieve the same target hit. It is
highly nonlinear due to the fact that positions and velocities
are coupled and that in order to hit the desired target, at
the moment of ball release, the hand velocity, position, and
the object’s time of flight should satisfy the parabolic projec-
tile equation. Finally, it is also dynamic because of the high
accelerations and momentum at certain motion phases.
Thus, the aim of this work is to identify a compact represen-
tation of the control mechanism behind overhead throwing
motions in order to (1) validate a control representation
extraction methodology and (2) produce a low-dimensional
control representation which could later be exploited to syn-
thesize throwing motions in animation. Such representations
could later be extracted from other types of throwing
motions (such as sidehand and underhand throws) and sim-
pler arm motions such as pointing, to feed a controller library
that may produce a variety of motions from these compact
representations [24].
The generic representation should contain a reduced set
of control variables (less than the number of joint actions
in study). It should also encode important temporal and spa-
tial control trends, invariant over a variety of morphologies.
Finally, it should show some of the links between these con-
trol variables and task space goals or features, that has to be
used as controller inputs in motion synthesis tools. One of
our previous work [25] has shown that the control strategy
could be represented as synergies during throwing motions.
However, this analysis comprehended solely the activation
space and a unique subject. In this paper, we propose to
extend this analysis by extracting control strategies from a
variety of subjects and by analyzing their relationships with
kinematic goals.
For this purpose, we present an analysis to identify
generic representations of control strategies starting at the
task space level, joint space level, and until finally reaching
the activation (or actuation) space level, where we extract
the synergies or basis control functions. First, the experimen-
tal setup used to extract the motion and muscle data is pre-
sented. Next, the control variables or features at the task,
joint and activation spaces are defined. This is then followed
by a detailed explanation of the methods used to extract the
control representation, which encompass clustering and
matrix factorization techniques. Two methods were used to
extract the muscle synergies and the consistency of their
results is assessed. Finally, the generic control strategies rep-
resentations are illustrated and explained. Results show the
existence of a generic control representation at the activation
level for a variety of morphologies during throwing tasks, and
its relationship with task space goals and features. Our new
model could be later used to control a larger variety of
characters and a larger family of motions involving similar
task space goals.
2. Materials and Methods
2.1. Experimental Setup
2.1.1. Subjects. Ten healthy men (age 29.8 ±5.6 years old;
weight 72.4 ±9.9 kg; height 1.77 ±0.07 m) volunteered for
the experiments. The subjects were all right handed and all
except one (subject 3) had never suffered injuries in the right
arm. Furthermore, none of the participants were profes-
sional athletes, and they all had different physical conditions
(with a mean number of hours of sport activity per week of
3.85 ±3.07). Each subject provided a written informed
consent form before participation. The experimentation was
conducted in accordance with the Declaration of Helsinki
(1964). The study was approved by the ethics committee of
the M2S laboratory of University of Rennes 2.
2.1.2. Task. A series of experiments were conducted where
the task consisted of a right-hand overhead throw to a static
target placed at different distances from a fixed throwing site.
The target was placed at 2 m, 4 m, and 7 m along a straight
line from the throwing site. The target was a hole of diameter
0.7 m placed at 1.5 m from the ground. The ball was a stan-
dard American football ball, 0.28 m long and 0.15 m large,
weighing 0.4 kg. Before beginning the experiments, the sub-
jects underwent a short training where they practiced long
distance throws for 5 to 10 minutes. Once the training was
finished, the experiments began. During these experiments,
the throwing order was randomized (to reduce learning
effects) and for each distance the subjects performed 6 throws
2 Applied Bionics and Biomechanics

for a total of 18 throws. A description of the motion and the
experimental setup are featured in Figures 1 and 2. The over-
head throw is composed of four main stages [26]: starting
position, cocking, acceleration, and release and follow-
through. In the starting position, the thrower positions his
body sideways with respect to the intended target. The
cocking phase consists of the motion between the starting
position until maximum external rotation is reached before
the ball starts to move forward. The acceleration begins as
the ball is moved forward and finishes when the ball is
released. This phase is known as the explosive phase since
the velocity of the ball changes from zero to its maximum
in a short time period. Finally, the release and follow-
through phase consists in a deceleration of the throwing
arm once the ball is released.
For each throw, the subject stood in starting position
(see Figure 1). Recording began (onset) when a motion of
the hand was detected (threshold at 0.05 m/s) and ended
when the ball was released (offset).
2.1.3. Data Acquisition and Processing. During the throwing
task, the activity of several muscles of the right arm and body
kinematics were recorded. For this study, we focused on
studying 4 degrees of freedom (DoF) and 6 muscles. The
segmental interaction principle states that energy can be
transferred between segments, and in both simultaneous
and sequentially coordinated movements, energy is trans-
ferred through the linked segment system of the body [28].
However, studies have shown that unlike baseball throwing,
in football throwing (or passing), the rotations or contribu-
tions of the legs, pelvis, and upper torso are limited [29].
Thus, we decided to first focus on the arm’s kinematic chain
(beginning at the glenohumeral joint) and on the degrees of
freedom with the highest contribution to throwing per
segment. These degrees of freedom were the shoulder
internal/external rotation and shoulder, elbow, and wrist
flexion/extension. The shoulder internal/external rotation
and elbow flexion/extension were specially selected due to
the fact that they are the major upper limb actions during
throwing [23], mainly during the acceleration phase [30].
Next, we selected a set of muscles which contained (1) at
least an agonist and antagonist muscle per each DoF under
study, (2) muscles with important contributions during
throwing [31, 32], and (3) muscles which could be reached
by surface EMG electrodes [33]. Thus, the recorded muscles
were the deltoid posterior and anterior, the biceps, the triceps
long, and the wrist extensors (extensor digitorium, extensor
carpi radialis and ulnaris) and flexors (flexor digitorium,
flexor carpi radialis and ulnaris), which were recorded as
a group.
The muscle activity was collected using wireless surface
EMG electrodes (Cometa Waveplus EMG system) and
well-known electrode placement protocols [33, 34]. This
activity was then processed using a standard protocol [35]:
the EMGs were amplified (gain 1000), digitized (1 kHz),
band-pass filtered (10–450 Hz, 4th order Butterworth filter
with no phase shift), rectified, and low-pass filtered (6 Hz,
4th order Butterworth filter with no phase shift [36]). Addi-
tionally, electrocardiogram (ECG) artifacts were removed
using an ICA-based filtering procedure [37]. Motion was
captured using a Vicon system (16 cameras, 100 Hz sampling
rate) and reflective markers. The markers were placed on
bony landmarks (49 markers) as recommended by the Inter-
national Society of Biomechanics (ISB) [38–41], around the
target (6 markers), and on the ball (9 markers) (Figure 3).
Each of the marker trajectories was low-pass filtered (10 Hz,
4th order Butterworth low-pass filter with no phase shift).
2.2. Control Features. The throwing motions can be charac-
terized at three different levels: in the task space, in the joint
space, and in the activation space (muscular space). The
following sections aim at characterizing the motion at each
of these levels through the definition of a set of kinematic
and muscular features.
2.2.1. Task Space Features. Overhead throwing motions are
horizontal projectile motions which are determined by three
factors: velocity of release, height of release, and angle of
release [42]. Based on this observation, a set of task space fea-
tures was defined and analyzed across task space conditions.
These task features were the hand velocity of release and the
hand release height which was normalized by the subject’s
height, as shown in Figure 4. The angle of release was not
considered due to its difficult estimation caused by marker
occlusion—some of the markers of the arm were lost at the
time of release of the ball, and the release angle computation
was very sensitive to the methods used to reconstruct missing
trajectories of the markers. Nevertheless, studies have shown
that the most important parameter when determining the
range of throwing is the release speed [43, 44]. This is also
evidenced by the equations of projectile motion, which show
that the range is roughly proportional to the square of the
release speed.
Figure 1: Overhead throwing motion. Example of an overhead
throwing motion to a 4 m target (bone graphics issued from [27]).
Representative posture of each phase of the motion is shown.
2 m
rowing site
4 m
7 m
Figure 2: Experimental setup. The setup consisted of a throwing site
and a target that could be placed at 2, 4, and 7 m from the thrower.
Motion capture was done thanks to 16 cameras, and EMG
measurements were done through a wireless EMG system.
3Applied Bionics and Biomechanics

The time of release trel was computed as the instant at
which maximum hand velocity was reached, since it is
known that this event occurs almost in parallel to the ball
release in the acceleration phase. For this purpose, a reflective
marker was placed on the outer side of the hand (third meta-
carpal bone) and its position was recorded. After the deriva-
tion of this marker’s trajectory, the maximum hand velocity
or velocity at release vwas computed as follows:
v= max vxt2+vyt2+vzt2, 1
where vxt,vyt, and vztare the velocity components of
the hand marker in the global coordinates frame, as defined
in Figure 4 ( xfront, zup). The hand height at release (h)
was determined as follows and divided by the subject’s height
to allow an intersubject comparison
h=hztrel
hsbj
, 2
where hzis the hand marker’s position component along
z and hsbj is the height of the subject.
These two features were computed for each subject and
repetition. Then, they were grouped per throwing distance
(d), which could be 2 m, 4 m, or 7 m, yielding a total of six
vectors. The means and standard deviations of these vectors
were later calculated, resulting in one task feature vector for
subject j:
fT,j=v2m,j v4m,j v7m,j h2m,j h4m,j h7m,j3
2.2.2. Joint Space Features. The joint space features consisted
of the joint positions and velocities. The joints positions were
estimated from motion capture, with an inverse kinematics
method allowing the segment lengths and marker positions
to be calibrated [45]. The joint velocities where computed
by deriving the joint position trajectories. The joint space
analysis focused on the following degrees of freedom of the
throwing arm: shoulder internal/external rotation and shoul-
der, elbow, and wrist flexion/extension (q1t,q2t,q3t,
and q4t, resp.).
An average trajectory was computed for each subject,
each degree of freedom, and each throwing distance. These
trajectories were later time normalized across subjects in
order to allow the intersubject comparison in Section
2.3.1. A joint space feature vector per subject jwas con-
structed, containing the mean joint position Qdmatrices
per throwing distance:
fQ,j=Q2m,jtQ4m,jtQ7m,jt, 4
where each joint position matrix contains the average posi-
tions q t per DoF
Qd=q1t q2t q3t q4t5
2.2.3. Activation Space Features. The control done at the
muscle level is the one that interests us the most, since it is
the actuation space. This control can be described via muscle
activations. However, an activation representation is redun-
dant since there are more muscles than degrees of freedom
and each muscle needs its own activation signal. A simpler
and less redundant representation of these signals can be
achieved via muscle synergies [18, 46].
Deltoid
anterior
Deltoid
posterior
Triceps
long Biceps
Wrist
extensors
Wrist
exors
Reective
marker
(a)
Reective
marker
(b)
Figure 3: Marker and EMG placement [33, 34]. Recommendations were followed for the EMG placement, whereas reflective markers were
placed following the ISB recommendations with small adjustments [38–41].
Figure 4: Subject at release time and corresponding task space
features. The features consist of the hand release height and the
hand velocity of release. Marker occlusion prevented the definition
of the angle of release as a reliable feature.
4 Applied Bionics and Biomechanics

One way to represent such synergies is via the time-
invariant synergy model [8, 25]. In this model, a synergy wi
is defined as a M×1vector of coefficients, specifying the rel-
ative activation level of M-muscles. Each synergy is paired
with a time-varying combination coefficient vector cit
1×T, which determines its temporal evolution. A set of
N-synergies can be linearly combined to generate M-muscle
activation patterns At:
At =WC t=w1w2…wN
c1t
c2t
…
cNt
, 6
where A t is the M×Tsample matrix containing the
recorded muscle activations patterns, Wis the M×Nmuscle
synergy matrix, and Ctis the N×Tsamples combination
coefficient matrix. To separate and highlight the contribution
of each synergy wiand its coefficient citto the muscle acti-
vation patterns, the previous equation can also be written as
At =〠
N
i=1
wicit7
Based on this model, the time-invariant activation space
feature fAwas defined as the matrix W, and the time-
variant activation space feature fAttwas defined as the
matrix Ct:
fA=W,
fAtt=Ct,
8
where
Ct=C2m tC4m tC7m t9
Each submatrix Cdtis of dimensions N×Td, where Td
is the total number of samples contained in the throws to
distance d.
In our case, this model was used in two methods (see
Section 2.3.2). Their results were compared to test their
robustness and consistency. The first method consisted of
extracting a synergy model (W,Ct) per subject, and the
second method consisted of extracting one synergy model
representative of all subjects. Thus, in the first case, a variety
of Wmatrices were generated representing each subject’s
throw, and in the second case, a single Wmatrix was gener-
ated representing all subjects and throws.
For both models, the combination coefficient matrix Ct
encoded the temporal evolution of the synergies during each
throw. These coefficients will be further described in terms of
(1) their shapes, (2) how their energy changes with throwing
distance, and (3) their triggering order. In general, the aver-
age image of the energy Eci,dof each combination coefficient
ci,dcontained in matrix Cdtwas computed as follows:
Eci,d=〠Td
s=1 ci,dts
2
n,10
where nis the number of trials per throwing distance and
tsthe current time sample.
2.3. Control Representation Extraction. Once the features to
analyze were defined at each level (task, joint, and activation
spaces) and for each subject j, control representations based
on these features were extracted. The objective of such an
extraction was to verify if a generic control representation
existed for overhead throwing across subjects. Such repre-
sentations are denoted by an index All, which generalizes
the subject feature vectors (j) of the previous sections to
all participants.
The identification of these representations was made
through clustering algorithms for the time-invariant
features and averaging and cross-correlation for the time-
variant features.
Clustering is a technique that consists of the assign-
ment of features into groups or subsets based on similar-
ity criteria. In the next sections, we will see that the
existence of a generic representation in each space will
depend on the number of clusters or groups found with
these techniques.
The first step before using the clustering algorithms is
feature scaling. This preprocessing step is necessary due
to the fact that clustering algorithms use distances to
classify features. Thus, features should be standardized such
that they have contributions of equal importance in the
distance measurements.
Two different types of clustering algorithms were used to
extract control representations from the time-invariant
features: a centroid-based clustering (k-means) algorithm
and a connectivity-based clustering algorithm (hierarchical
clustering). These two algorithms were used in order to verify
if different techniques yielded similar control representa-
tions. Furthermore, the specific interest in using hierarchical
clustering was to verify if the chosen number of clusters of
the k-means algorithm matched the natural divisions in
the data.
K-means clustering is an iterative algorithm for data
partitioning that assigns or classifies features into one of
kclusters defined by centroids. The main steps of the
algorithm are the following, given k: (1) select kinitial
cluster centroids, (2) compute the distances between each
feature to each cluster centroid, (3) assign the features to
the cluster with the closest centroid all at once (phase 1),
and individually reassign points if it reduces the sum of
distances (phase 2), (4) obtain new centroids by averaging
the features in each cluster, and (5) repeat steps 2–4 until
the assignments do not change or the iterations reach their
maximum. The k-means++ algorithm in MATLAB was
used with a squared Euclidean norm to compute distances.
The advantage of this algorithm is that it uses the heuristic
in [47] to find centroid seeds for k-means clustering. This
induces a faster convergence to higher quality solutions or
to a lower sum-of-squares point-to-cluster centroid dis-
tances (within each cluster). Finally, in order to assess
5Applied Bionics and Biomechanics

the k-means clustering quality, an indicator called cluster
silhouette was computed [48, 49]. This indicator enables
us to distinguish clear-cut clusters from weak ones. It
measures how similar the features are to features in their
own cluster, when compared to features in other clusters,
and is computed as follows:
Sil =
bj−gj
max bj,gj
, 11
where gjis the average distance from the jth feature to the
other features in the same cluster as jand bjis the minimum
average distance from the jth point to points in a different
cluster, minimized over clusters. The silhouette value can
range from −1 to 1. By averaging the silhouette values of each
feature in the cluster, an average silhouette Sil can be
obtained for the entire cluster. A subjective interpretation
for this value was proposed by the authors of [49] to assess
the clustering quality, as shown in Table 1.
This interpretation was used to select with which num-
ber kof clusters the data was well separated Sil ≥0 71 or
if no separations could be made, in which case only a single
cluster exists.
To complete this assessment, hierarchical clustering was
also used to partition the feature space into groups. Hierarchi-
cal clustering is an algorithm for cluster analysis that aims at
grouping features at different levels using a cluster tree or
dendrogram. In agglomerative hierarchical clustering, each
feature starts in its own cluster; these clusters are then
combined via a metric and a linkage criterion. The metric
defines a distance between pairs of features, and the linkage
criterion defines the distance between sets by computing the
pairwise distances between features. An advantage of this
strategy is that it does not need an initial indication of the
number of clusters, and therefore, it reveals the natural divi-
sions in the data. For its implementation, the hierarchical
algorithm tools in MATLAB were used with the Euclidean
distance as metric and an unweighted average distance
(Euclidean) for the linkage.
The following sections present how these methods and
the synergy extractions [9] were used to extract control
representations across subjects.
2.3.1. Task and Joint Space Control Representation Extraction.
First, we determined if a common representation existed
across subjects in task space. Thus, the feature vectors fT,jin
(3) were first standardized and then given as inputs to the
clustering algorithms. First, the k-means algorithm was
applied by varying the number of clusters and checking how
well the clusters were separated thanks to the clusters’silhou-
ette values. In this space, since each subject is characterized by
a single vector, we expect a common representation to exist
when k=1. In other words, when the features are so similar,
that well-separated clusters cannot be formed. If this was the
case, then, the common strategy was defined by averaging
the task feature vectors across subjects:
fT,All =v2m,All v4m,All v7m,All h2m,All h4m,All h7m,All
12
To further verify the results of k-means, hierarchical
clustering was then applied. This algorithm does not need
an initial estimate of the desired number of clusters; thus, it
was used in order to determine if the natural cluster divisions
of the data agreed with the results provided by k-means. In
other words, if no natural cluster divisions were found and
a common task control strategy across subjects existed.
Finally, a Wilcoxon rank sum test was performed on the
features across subjects to detect significant changes in their
values with regard to the throwing distance (confidence level
below 0.05).
At the joint space level, the features fQ,jused to represent
the motion are all time varying (average joint positions per
subject). Therefore, cross-correlation was used to evaluate
the similarity of the joint trajectories and velocities across
subjects and throwing distances. A high correlation signified
that the joint trajectories or velocities were similar among
subjects. Low correlations signified very low kinematic simi-
larities. The common joint space strategy was then defined by
averaging the joint trajectories and velocities across subjects:
fQ,All =Q2m,All t Q4m,All t Q7m,All t13
2.3.2. Activation Space Control Representation Extraction.
The synergies and their combination coefficients (Section
2.2.3) were extracted via a NMF (nonnegative matrix factor-
ization) [50] algorithm. This algorithm decomposes a non-
negative matrix into a nonnegative linear combination of
basis vectors, by solving the following optimization problem:
minimize
W,C
1
2At −WC t 2
F,
subject to W,Ct ≥0
14
When applying this algorithm, the synergy model
order or number of synergies to extract should be defined.
To do this, we used two criteria. The first criteria con-
sisted of choosing a number of synergies Nless than the
number of recorded muscles M=6 in order to obtain a
lower dimensional control representation. The second cri-
teria attempted to preserve a good quality in the recon-
struction of the original activations. Therefore, a criterion
based on the average coefficient of determination r2
between the original and reconstructed muscle patterns
[9, 18] was used. This criterion states that the chosen
Table 1: Assessment of k-means clustering quality [49].
Subjective interpretation of the average silhouette value
Sil Proposed interpretation
0.71–1.00 A strong structure has been found
0.51–0.70 A reasonable structure has been found
0.25–0.50 The structure is weak and could be artificial,
try additional methods on data set
≤0.25 No substantial structure has been found
6 Applied Bionics and Biomechanics

number of synergies should correspond to the sharpest
change in the slope of the r2curve (as in the submitted
version within the results). This change in slope is inter-
preted as the point separating “structured”from noise-
dependent variability. After this point, additional synergies
start to capture only the small residual noise-dependent
variability; therefore, this can be used to define the mini-
mum number of synergies that capture the task-related
features [46, 51, 52]. We highlight the fact that these cri-
teria guarantee that the number of control variables Nwill
be less than the number of muscles or actuators; however,
there is no guarantee that they will be less than the num-
ber of DoF. This is a possible added value of a representa-
tion through synergies. The NMF algorithm used was the
one developed in [53] and the update rule used was the
nonnegative least squares one.
We employed two methods for identifying a representa-
tive synergy (or time-invariant features) using this extraction
algorithm. The first is based on k-means [54] and hierarchical
clustering, and the second one is based on the identification
procedure in [9]. The comparison of the results extracted
from both methods was useful to test the consistency and
robustness of these extraction methodologies.
The first method consisted of 3 stages: (1) extraction of
individual subject synergy models, (2) standardization of wi
vectors, and (3) application of k-means and hierarchical
clustering algorithms. In the first stage matrix, At(6
muscles ×3600 samples) was constructed by concatenating
the activation signals for all the trials of individual subjects.
This method enabled us to take into account intrasubject
variability in the synergy extraction. The concatenated
signals were normalized by their maximal value to obtain
activations framed between 0 and 1. Next, NMF was applied
on this matrix to obtain one N-synergy model (W,Ct) per
subject. Once a model was obtained for each subject, the
synergy matrices Wwere standardized for their use in the
clustering algorithms. Essentially, each synergy wiof each
subject was a feature vector containing the relative activation
levels of the muscles. These vectors were treated individually
and without specifying their correspondence to a specific
subject. They were used to create a synergy pool on which
k-means and hierarchical clustering were applied in order
to identify common features among this synergy pool. The
k-means algorithm was applied first while varying the num-
ber of clusters k. We expected a unique strategy to exist when
k=N, in other words when the number of clusters is equal to
the number of synergies extracted for each subject. If this was
the case, then the centroids of these clusters represented the
mean synergy vectors or the representative activation control
representation for all subjects through method I WI,All .
(a) Mean release: hand velocity (b) Mean release: hand0 height/subject height
Figure 5: Task space features per subject and throwing distance. Both hand release velocity and release height increased with the throwing
distance for all the subjects.
Figure 6: Task space cluster separation quality using k-means. Strongly separated clusters Sil ≥0 71 containing a similar number of subjects
cannot be found. A single cluster exists across subjects.
Figure 7: Task space cluster separation using hierarchical clustering.
In this case, the clusters are not well separated.
7Applied Bionics and Biomechanics

fA,All =WI,All 15
Finally, hierarchical clustering was applied. This
algorithm was used in order to determine if the natural
cluster divisions of the data corresponded to the number
of k-means centroids.
The second synergy extraction method consisted in the
direct identification of a common activation control strategy
for all subjects, based on [9]. In this method, the NMF
algorithm was applied on a matrix At(6 muscles ×36,000
samples), constructed by concatenating the activation signals
for all trials of all subjects. Therefore, by applying NMF
on this pool of EMG signals, one common synergy model
WII,All was found for all subjects.
fA,All =WII,All 16
However, the coefficients CII tin this method encoded
how much and when each synergy was triggered for each
repetition and subject. Therefore, to identify a common
time-varying control representation for all subjects and repeti-
tions CII,All t, averaging and correlation computation were
used. First, the mean combination coefficients per subject per
throwing distance were computed. Next, cross-correlation was
used to make comparisons across subjects at each throwing
distance. Thus, a common combination coefficient was com-
puted by making a second averaging across all subjects.
fAt,All t=CII,All t, 17
where CII,All tcontains the coefficient matrices per
throwing distance
CII,All t=CII,2m,All tCII,4m,All tCII,7m,All t
18
3. Results and Discussion
3.1. Global Considerations. The motion, as defined in the task
description above, had an average duration of 1.67 ±0.27 s
for all the throws made by all the subjects. Thus, the standard
deviation seemed sufficiently low to compare the different
throws and normalize them against time, as it has been done
for some of the processing of extraction. The subjects had a
global performance higher than 80%, meaning that the task
was quite easy to perform and reproducible from one trial
to one other. The following sections detail the representa-
tions extracted from the experimental data in the task, joint,
and activation spaces. For all the cross-correlation we
performed, the mean value of the lag was about less than
10
−15
% of the signal length, meaning that most of the
signal shapes were comparable directly. Therefore, we did
not present the lags related to cross-correlation results in
the corresponding tables.
3.2. Task Space Control Representation. The subject task
features fT,jwere collected and a representative task space
control representation fT,All was extracted as described in
Section 2.3.1. The task feature vector for each subject is
featured in Figure 5. A gradual increase in hand release veloc-
ity and height can be seen across subjects as the throwing
Figure 8: Representative task space representation for all subjects fT,All . These are the mean and standard deviation values of the features
shown in Figure 5. The global increase of both features with regard to the throwing distance is straightforward.
Table 2: Mean intersubject cross-correlation coefficient per
throwing distance.
Mean intersubject cross-correlation coefficient per throwing
distance
DoF corr2m corr4m corr7m
q10.6681 ±0.2396 0.7493 ±0.1579 0.6335 ±0.2048
q20.9684 ±0.0259 0.9494 ±0.0485 0.9403 ±0.0529
q30.9723 ±0.0207 0.9526 ±0.0316 0.9329 ±0.0394
q40.6025 ±0.2520 0.6077 ±0.2634 0.6210 ±0.1922
q10.7349 ±0.1012 0.6290 ±0.1392 0.4830 ±0.1317
q20.6878 ±0.1257 0.6374 ±0.1671 0.5588 ±0.1063
q30.8170 ±0.1036 0.8502 ±0.0880 0.7954 ±0.0840
q40.7217 ±0.1309 0.6540 ±0.2192 0.7277 ±0.1226
8 Applied Bionics and Biomechanics

distance increases. Moreover, as evidenced by the Wilcoxon
rank sum test, this increment is statistically relevant in 9/10
subjects for the hand velocity and in 7/10 subjects for the
hand height.
Next, k-means and hierarchical clustering were applied
on the feature vectors in order to determine if one sole task
space control representation existed. We expected a unique
control representation if no strong separated groups can be
found among the subject task vectors, in other words if a
single cluster exists.
k-means was first applied while varying the number of
clusters k. Figure 6 shows each cluster’s silhouette. The
average silhouette value Sil is below 0.71 (Table 1) as k
increases. At k=5, it reaches a value above this threshold
but clusters containing 1-2 subject vectors begin to be
formed. Therefore, since the k-means analysis did not dif-
ferentiate the subjects, a common representation of the
control at the task space level can be obtained from the
averaging of the task space features.
Hierarchical clustering was then applied in order to verify
if the results of the k-means clustering were consistent with
the natural division of the data. The hierarchical clustering
was only used to consider qualitative and visual informations
about data division. Figure 7 features the resulting cluster
tree. In this tree, no visually significant divisions are found.
This is shown by the fact that heights of the links at each level
are not qualitatively different from the heights of the links
below them, indicating a high closeness across groups. Fur-
thermore, with this procedure, we can see that as the number
of clusters increases, groups containing very few subject
vectors begin to be formed. Consequently, we concluded that
all subjects were presenting similar changes in the task space
features with regard to the task constraints (throwing dis-
tance). In other words, subjects increased significantly the
hand release velocity and height as the throwing distance
increased. The average task features fT,All were computed
by averaging the subject task feature vectors and it is shown
in Figure 8. Velocity increments of about 1.3 m/s and hand-
height/subject-height increments of 0.05 are seen as the
Figure 9: Representative joint space strategy for all subjects fQ,All . Computed by averaging joint features across subjects for each DoF. Solid
lines are the average values and dashed lines the standard deviation values. The joint space analysis focused on the following degrees of
freedom of the throwing arm: shoulder internal/external rotation and shoulder, elbow, and wrist flexion/extension (q1t,q2t,q3t, and
q4t, resp.). Angles are given in degrees.
Table 3: Mean intersubject and interdistance cross-correlation
coefficients. The representative joint space strategy shown in
Figure 9 was correlated across throwing distances.
Mean interdistance cross-correlation coefficients
DoF corr2m,4m,7m
q10.9171 ±0.0213
q20.9989 ±0.0005
q30.9991 ±0.0004
q40.9315 ±0.0467
9Applied Bionics and Biomechanics

distance increases by 2 to 3 m. Moreover, the range is roughly
proportional to the square of the release speed, as can also be
evidenced through the equations of projectile motion. Thus,
our results are consistent with other studies that indicate an
increase in height and speed with throwing distance and
the existence of a proportionality relationship between speed
and range [23]. This is a straightforward result that may be
mostly induced by the motion constraints (distance to throw,
motion type) and the difference of strategy between subjects
may appear in the amount of changes from one distance to
one other as it can be observed in Figure 5. However, the
averaging of the task space features as a unique representa-
tion of the control in the task space makes sense since the
trends featured in Figure 8 respect the same pattern as the
one seen for all the subjects.
3.3. Joint Space Control Representation. The subject joint
features fQ,jwere then used to determine if a common joint
space control representation fQ,All existed, as described in
Section 2.3.1. The features showed a high repeatability
across subjects at each throwing distance, regardless of
the inexperience and small differences in style of our
throwers. These kinematic similarities were quantified as
correlations among subjects and are shown in Table 2.
As the throw is performed, the motion is repeatable in
the forward direction. Thus, high correlations are seen in
the joint trajectories, especially in the shoulder q2t
and elbow q3tflexion/extension. Lower but still signif-
icant correlation is seen in the shoulder internal/external
rotation q1tand wrist flexion/extension q4t. The
differences in internal/external rotation q1tcould be
due to each subject’s throwing style, while the differences
in wrist flexion/extension q4tcould be linked to the
fact that the most distal segments have larger contribu-
tions to accuracy over speed [32, 55].
In terms of articular velocities, the motion is less repeat-
able. Nevertheless, as seen in the previous section, different
velocity control strategies in the joint space can result in a
common velocity feature in the task space across subjects.
These differences may be linked to individual differences in
the throwing strategy and cannot be used as a common
feature of the control representation in the joint space.
Finally, a representative joint space control strategy was
computed by making averages across subjects and throwing
distances for joint trajectory included as a feature. This
control representation is featured in Figure 9 and in Table 3.
Similar kinematic trends are shared across throw types. For
instance, as the throw progresses, the shoulder is internally
rotated and flexed, while the elbow is extended and the wrist
is gradually flexed. Lastly, these similarities were also reflected
in the intersubject and interdistance correlation, which
resulted in very high correlation coefficients for all DoF,
as shown in Table 3.
3.4. Activation Space Control Representation. The synergy
extraction method described in Section 2.3.2 was applied
on each of the subject’s EMG dataset while varying the
number of synergies. The objective was to identify a model
with less synergies than the number of recorded muscles
or actuators N<M, for each subject, that would guaran-
tee a good reconstruction of the original EMG signals.
Figure 10 depicts the quality of reconstruction r2for each
subject and synergy model. The sharpest change in slope
of this curve occurred at N=2 for 8 subjects and at N=3
for 2 subjects. Thus, we opted for the 2-synergy model
which allowed an average quality reconstruction of 0.7382
across subjects.
3.4.1. Synergy Model (W). Method I was applied in order to
determine a common representation of the control in the
activation space. First, the 2-synergy models were extracted
for each subject. Then, a pool containing the individual
synergies wiof all subjects was constructed, without specify-
ing if the synergies belonged to the same subject. Thus, the
pool contained 20 synergies (2 synergies per subject). Finally,
k-means clustering was applied on this pool while varying the
number of clusters k. We expected a common control repre-
sentation to exist when k=Nor when the number of clusters
is equal to the number of synergies extracted per each subject.
Figure 11 shows that indeed the best cluster separation is
achieved at k=Nor k=2, where the average silhouette value
Figure 10: Activation reconstruction quality across synergy models per subject. The NMF algorithm was applied on each of the subject’s
EMG data set while varying the number of synergies (N). The resulting curve depicts the r2values for each model.
10 Applied Bionics and Biomechanics

for both clusters is equal to 0.7181. If a higher number of
clusters or separations is found, the average silhouette values
decrease and clusters containing very few synergies are
formed. This evidences that 2 clusters are sufficient to classify
the synergies.
To further verify if the natural divisions of the data corre-
sponded to 2 groups of distinctive synergies, hierarchical
clustering was applied. This resulted in the cluster tree in
Figure 12. In this tree, we can see how the 20 synergies in
the pool are partitioned into 2 clusters as well. This is shown
by the fact that the link separating the synergy data into two
branches is inconsistent with the links below it. It indicates a
higher closeness among the synergies within each group than
across each group.
Interestingly, the individual synergies within each cluster
in the tree matched those in the clusters computed via
k-means. Thus, a mean activation control representation
WI,All for all subjects was extracted from the centroids of
the 2-cluster model obtained via k-means (Figure 6, top).
Each of these centroids or mean synergies contains the rela-
tive action levels of groups of muscles. Finally, we wanted
to demonstrate how well the synergy WI,All represented
all of the subjects’individual synergies. In order to do this,
the normalized dot product between the synergy WI,All
(centroid) and each of the subjects’2-synergy models W
(cluster points) was computed. The results showed that a
high similarity exists between these models, with a mean
normalized dot product of 0.9495 ±0.0485 for w1and
0.9170 ±0.0537 for w2.
Method II was then applied to identify the representative
synergy model directly from a pool containing the EMG
signals of all subjects. Thus, this pool contained 6 signals
(one per muscle), and each signal contained 180 concatenated
activations corresponding to each of the subjects’trials
(10 subjects, 3 throwing distances, and 6 trials per distance).
As in the individual subject synergy extractions, the number
of synergies was chosen as the number corresponding to the
sharpest change in the r2curve. This change occurred again
at N=2 synergies, where the quality of reconstruction was
of 0.6526. This slight decrease in quality of reconstruction
with respect to the individual extractions is expected since
method II attempts to reconstruct a higher number of trials
performed by different subjects simultaneously.
The resulting representative synergy WII,All is depicted in
Figure 13. Again, each synergy contains the relative activa-
tion levels of a group of muscles throughout the motion.
The first synergy w1can be seen as the agonist synergy, and
the second synergy w2can be seen as the antagonist synergy
to the motion. Therefore, w1contains a high activation of
muscles corresponding to shoulder flexion, internal rotation
(deltoid anterior), elbow extension (triceps longs), and wrist
flexion (wrist flexor group). While w2contains a high activa-
tion of muscles corresponding to elbow flexion (biceps), wrist
extension (wrist extensor group), and a very low activation of
the shoulder muscles (deltoid anterior and posterior).
Finally, the representative synergy vectors (W) com-
puted with both methods are similar, as shown by their
normalized dot products (0.9248 for w1and 0.9524 for w2).
Consequently, a common grouping and relative activation
of muscles were found for different task space conditions
and subjects during a throwing motion. This emphasizes
the consistency of the results obtained by both methods
to find a proper activation space control representation
of the motion. However, in order to define a common
control representation for throwing in the activation
space, it is also necessary to identify a representative pattern
for the time-varying part of the synergies (combination
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
1
2
Cluster number
k = 2
1
2
3
k = 3
1
2
3
4
Silhouette value
k = 4
1
2
3
4
5
k = 5
Figure 11: Cluster separation quality using k-means. Strongly separated clusters Sil > 0 71 are found at k=Nor k=2. A common activation
space control representation exists across subjects.
2 15 11 3 5 18 10 13 7 19 1 16 17 12 6 8 20 4 9 14
0.5
1
1.5
2
2.5
3
3.5
4
Individual subject synergies
Distance between clusters
Figure 12: Synergy clusters using hierarchical clustering. Natural
data divisions are found when the height of a link strongly differs
to the height of the links below it. Thus, in this case, the clusters
are well separated.
11Applied Bionics and Biomechanics

coefficients). The following section presents the results of
this analysis.
3.4.2. Combination Coefficients (C). Method II also resulted
in a set of time-varying coefficients which encoded the
triggering times and intensity for each subject and their
repetitions CII t. The average coefficients computed per sub-
ject and throwing distance are featured in Figures 14 and 15.
Repeatable trends can be seen among and across subjects.
For instance, the first coefficient c1is generally bell shaped
(as the velocity profile in ballistic movements), while the sec-
ond coefficient c2is more irregular, it has a lower amplitude,
and it tends to decrease as the throw is performed. A consid-
erable intersubject repeatability at each throwing distance is
also demonstrated by high correlation coefficients, as featured
in Table 4.
The high intra- and intersubject repeatability outlines the
existence of similar patterns of activation for each synergy
across subjects and throwing distances. Therefore, an activa-
tion space control representation CII,All twas computed by
Figure 13: Representative activation space strategy (synergies) WI,All and WII,All for all subjects. A common control representation in the
activation space was identified for the time-invariant part of the synergies (W) through method I and method II.
0 50 100
0 50 100 0 50 100 0 50 100 0 50 100 0 50 100
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Sbj3 Sbj4 Sbj5
Sbj6
Time normalized (%)
Sbj7 Sbj8 Sbj9 Sbj10
2 m
4 m
7 m
Figure 14: Average combination coefficient c1per subject and throwing distance.
12 Applied Bionics and Biomechanics

performing averages across subjects at each throwing dis-
tance. The mean coefficients per distance are depicted in
Figure 16. A high interdistance correlation is seen for both
coefficients (Table 5). Thus, these coefficients not only pre-
serve the main trends in each of the subjects’averages but
also emphasize the similarities in terms of shape across
throwing distances.
Besides a repeatability in terms of shape, the combination
coefficients exhibit discrepancies across subjects. Figure 17
shows the coefficients c1and c2from Figures 14 and 15 in
one same plot. Globally, at the beginning of the throw c2
(antagonist synergy) is activated, then, the amplitude of this
synergy is diminished, until c1(agonist synergy) is activated.
At this moment c2is activated again, and the most significant
coactivation occurs among the synergies. The same behavior
is seen on the representative activation space strategy in
Figure 16. This is consistent with the fact that ballistic move-
ments exhibit concurrent agonist and antagonist muscle acti-
vation [56]. During these motions, a first activation is needed
to accelerate the limb toward the target (c1), followed by a
second activation to decelerate and stop the movement (c2).
This sequence of bursts (from antagonist to agonist and from
agonist to antagonist) is a characteristic of the antagonist
activity in the upper extremity while throwing. Such “triad”
burst sequences have been previously identified in EMG
analysis of throwing (at the wrist and elbow muscles) [32]
and in badminton smash strokes [55].
Individual differences in combination coefficients trig-
gering can be seen between subjects, especially for c1.
This indicates that even if it is possible to find a
common representation of the control in the activation
space for time-invariant features W, the combination
coefficients Cencapsulate individual strategies and differ-
ences between subjects.
Another characteristic that was analyzed was the change
in energy across throw types. Figure 18 shows the average
energy at each throwing distance per subject, as described
in 10. The results show that the energy changes in the coeffi-
cients are linked to changes in the task space features: like the
task space features, the energy in the coefficients increases
with the throwing distance. For c1(agonist synergy), this
increment is always gradually incrementing, and it is statisti-
cally relevant for 6/10 of the subjects. This increment in the
actuation signals (or synergies) is consistent with the incre-
ment in torque magnitudes, observed during the synthesis
of throwing motions to different ranges [23].
This link between the task space and the activation space
is fundamental in order to specify muscle-based controllers
available to synthesize motions from task space goals. Indeed,
such a controller will define a control law to actuate the mus-
cle in order to achieve task space goals and the results of the
current study are helpful to design these control laws [2].
3.4.3. Activation Reconstruction. Finally, we show the quality
of EMG reconstruction using the representative synergy
model (WII,All,CII,All t) found through method II. We
finally get an overall reconstruction quality of r2= 0.6526
for the 180 concatenated muscle activations. This is reflected
through different degrees of quality reconstruction among
the subject trials. In Figures 19 and 20, examples of the acti-
vation reconstruction of a 7 m trial for different subjects are
050 100
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Sbj1 Sbj2 Sbj3 Sbj4 Sbj5
Sbj6
Time normalized (%)
Sbj7 Sbj8 Sbj9 Sbj10
2 m
4 m
7 m
Figure 15: Average combination coefficient c2per subject and throwing distance.
Table 4: Synergy coefficients mean intersubject cross-correlation
coefficient per throwing distance.
Mean intersubject cross-correlation coefficient per throwing
distance
Synergy coeff.corr2m corr4m corr7m
c10.9129 ±0.0534 0.9390 ±0.0320 0.9264 ±0.0382
c20.8761 ±0.0727 0.8615 ±0.0769 0.8702 ±0.0650
13Applied Bionics and Biomechanics

shown. In the first case, the triggering order and shape of the
reconstructed activations follow closely the recorded ones. In
the second example, the original activations contain many
small oscillations, which are not well reconstructed. These
oscillations may be noise artifacts and were therefore
excluded from the reconstruction by the reconstruction qual-
ity criteria r2, as it has been explained in the Methods section.
Moreover, considering the number of trials that are being
reconstructed simultaneously, such differences in recon-
struction accuracy were expected.
In addition, we can see (Figure 21) the reconstruction
quality per muscle with regard to the number of synergies
extracted on the global set (method II). We can see that the
results are quite consistent from one muscle to one other.
Indeed, most muscles respect the rule that the biggest change
of slope of r2appears after 2 synergies. However, the biceps
exhibit a relatively low reconstruction level with 2 synergies
and seem to have its highest change in slope at 3 synergies.
This result can be explained by the relatively low level of
activation of the biceps during the task, that may be less
well captured by the synergy extraction than the more
activated muscles like the triceps long. In a more general
manner, muscles that stabilize the motion may be less well
captured by the low-order synergies than the muscles
producing the motion.
3.5. Summary. The previous results show the existence of a
common control representation (for a subset of muscles
and DoF) in various throwing tasks, and subjects with no
particular training on throwing motions or throwing sports.
This representation was described through a set of features
in the task, joint, and activation spaces. The control represen-
tation identified in the task space consisted of increasing the
hand release height and velocity to reach longer distance
targets. These endpoint features were achieved through a
common set of joint trends, but with different velocity trends
across subjects.
In the activation space, a lower dimensional control
representation and its link with changes in the task space
features were identified. This control strategy consisted of
using only 2 synergies (an agonist and an antagonist synergy)
to represent the activation of 6 muscles of the right arm.
These synergies were triggered with the order and concur-
rency expected from ballistic movements, and their trigger-
ing intensity was linked to the desired launch distance, the
increments in velocity, and height of release. Therefore, at
the actuation level, we were able to extract a reduced control
representation (muscle synergies) linked to task conditions,
for a highly redundant, nonlinear, and dynamic motion.
Such a method, by providing a compact representation, has
the interest to depict the individual and common control
features in the way the motion is generated by each subject
and seems useful to better understand the control strategies
used. This does not prove the existence of a motor control
mechanism that would be muscle synergies. However, the
results are compatible with the notion of muscle synergies
0 50 100
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0
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0
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0
0.2
0.4
Average c1 (2 m) Average c1 (4 m) Average c1 (7 m)
Average c2 (2 m)
Time normalized (%)
Average c2 (4 m) Average c2 (7 m)
Figure 16: Representative activation space strategy (combination coefficients) CII,All tfor all subjects. A common control strategy in the
activation space was identified for the time-variant part of the synergies through method II.
Table 5: Synergy coefficients mean interdistance cross-correlation
coefficients.
Mean interdistance cross-correlation coefficients
Synergy coeff.corr2m,4m,7m
c10.9895 ±0.0035
c20.9833 ±0.0089
14 Applied Bionics and Biomechanics

organized by the nervous system to implement such
control strategies.
Moreover, the direct extraction of a single synergy model
from an experiment involving such a complex motion, and a
variety of human morphologies, skills, and task conditions, is
also a contribution. The results obtained by both methods of
synergy extraction showed encouraging results, since their
consistency and robustness was clearly established through
their comparison. The accuracy of this synergy model is
supported by studies [57] that evidence a higher performance
of matrix factorization algorithms in experimental protocols
that incorporate unconstrained tasks, a variety of conditions,
and motor variability (synergy extraction from EMG time
series data and not averages).
It is worth noting that these results span a limited set of
degrees of freedom and muscles and that the extracted syner-
gies for this task can change depending on the number and
choice of muscles [58]. They also highlight generic but basic
mechanisms needed to control an overhead throwing motion
to a specific distance. To analyze the accuracy, efficiency, or
performance of the throw, studies with additional features
at key moments and their relationship to successful target
hits are needed. These features could include task space
features, such as release angle; joint space features, such as
velocities and accelerations at release; and activation space
features that include more muscles and quantify subtle differ-
ence in the way in which the synergies are triggered across
different throws. With more features, we could expect to find
more links across task, joint, and activation spaces.
Future contributions could include repeating this analy-
sis on professional throwers (such as football players or
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0
0.2
0.4 Sbj4
0
0.5 Sbj5
0
0.5 Sbj6
0
0.5
1Sbj7
0
0.5 Sbj8
0
0.5
1Sbj9
0
0.5
1Sbj10
0
0.5
1Sbj1
0
0.2
0.4 Sbj2
0
0.5
1Sbj3
0
0.5 Sbj4
0
0.5
1Sbj5
0
0.5
1Sbj6
0
0.5
1Sbj7
Time normalized (%)
0
0.5
1Sbj8
0
0.5
1Sbj9
0
0.5 Sbj10
c1
c2
2 m
4 m
7 m
Figure 17: Triggering order and coactivation per subject and throwing distance. A repeatable triggering tendency is seen across subjects:
(1) c2triggering, (2) c1triggering, and (3) c2triggering. This sequence is consistent with the expected triggering in ballistic motions.
Sbj1 Sbj2 Sbj3 Sbj4 Sbj5 Sbj6 Sbj7 Sbj8 Sbj9 Sbj10
0247 247 247 247 247 247 247 247 247 247
247 247 247 247 247 247 247 247 247 247
50
100
150
200
0
50
100
150
200
c1
Sbj1 Sbj2 Sbj3 Sbj4 Sbj5 Sbj6 Sbj7 Sbj8 Sbj9 Sbj10
c2
Energy
rowing distance (m)
Figure 18: Combination coefficient energy per subject and throwing
distance. The energy in c1(agonist synergy) gradually increases with
throwing distance.
15Applied Bionics and Biomechanics

pitchers). We expect a higher repeatability at all levels for
trained subjects. Also, future analysis could include throws
to larger distances and the usage of balls of different masses
and sizes.
Finally, the synergies obtained in the current studies will
be applied and validated in the domain of muscle-based
character animation. For instance, the relationships between
the 2 control variables (or synergies) and well-defined task
space goals (desired release speed and height) will be
exploited to control highly redundant characters. A previous
study [8, 24] has already tested synergies on a subject-scaled
character. It would be interesting to test the generic synergies
presented in this paper on a variety of morphologies. Ulti-
mately, this application could also entail the construction of
a synergy database for animation. A database containing
synergies and their relationships with task space goals, for
a richer variety of motions (reaching, writing, or other
arm gestures), degrees of freedom, and muscles, which
could also serve as a basis to synthesize motions in
physics-based animation.
4. Conclusion
It seems that motion control can be encapsulated through
lower dimensional control representation of each task we per-
form, to achieve fast, efficient, and coordinated movements.
Synergies encode a variety of muscle information in a reduced
set of temporal and spatial signals and are thus a good candi-
date to represent the control in a compact way. Many studies
have extracted muscle synergies from EMG signals in both
upper-body and lower-body motions. Our study has found
common control features among subjects in the task, joint,
and activation spaces, especially through the extraction of
muscle synergies from a set of EMG signals, for a dynamic
0 50 100
0
0.2
0.4 DeltP
0 50 100
0
0.5
1DeltA
0 50 100
0
0.2
0.4 Bic
0 50 100
0
0.5
Normalized
TrpLg
050 100
0
0.5
1
Time normalized (%)
WrstE
0 50 100
0
0.5
1WrstF
Recorded
Reconstructed
Figure 19: Example 1: activation reconstruction using WII,All and CII,All t.
0 50 100
0
0.2
0.4
Normalized
DeltP
0 50 100
0
0.5 DeltA
0 50 100
0
0.5
1Bic
0 50 100
0
0.5 TrpLg
050 100
0
0.5
1
Time normalized (%)
WrstE
050 100
0
0.5
1WrstF
Recorded
Reconstructed
Figure 20: Example 2: activation reconstruction using WII,All and CII,All t.
16 Applied Bionics and Biomechanics

and acyclic motion. A motion which was performed by unex-
perienced subjects while following general guidelines that
allowed a free throwing motion.
We first described the throwing task and experiments
from which the control strategy was extracted. Next, we char-
acterized the motion through a set of control features in the
task, joint, and activation spaces and detailed the methods
to extract them. Finally, the results showed that with this
set of features (1) a common control representation exists
across subjects, (2) this representation significantly reduces
the redundancy in the activation space through the encapsu-
lation of the coactivated muscles in a low-dimensional repre-
sentation (2 synergies encode the actions of 6 muscles), (3)
links exist between the task and activation space features,
which were revealed by varying the throwing distance, and
(4) finally both methods of synergy extraction were able to
provide consistent and similar results and are therefore
legitimate these methods of extraction.
Lastly, since the identified control representation
comprises the use of less control signals than actuators
and DoF, it would be useful for synthesizing motions with
overactuated or muscle-based characters at a reduced
computational cost.
Conflicts of Interest
The authors declare that there is no conflict of interest
regarding the publication of this paper.
Acknowledgments
The authors wish to thank Anthony Sorel for his contribu-
tions during and after the experiments and Antoine Muller
for providing the inverse kinematics algorithm. This study
was funded by the ANR project ENTRACTE (Grant agree-
ment: ANR 13-CORD-002-01).
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