First review of the IP SKILLS FP6-IST-035005, Pisa, December 2007
Coordination and human perceptuo-motor skills
Pisa, December 2007, first SKILLS review
SKILLS, FP6-IST-035005
Julien Lagarde, Denis Mottet, & Benoît G. Bardy
University Monpellier1
Coordination in biological motion has attracted much attention from artists for
centuries, and for a little more than a century has represented a challenge for both scientists
and engineers. On various paintings the gaits of the horse were wrongly represented. Before
the age of sophisticated measurement tools for motion analysis (e.g., the early high speed
photographs of Eadward Mybridge, see Figure 1), the understanding and representation of the
organisation in time and space of multidegrees of freedom movement remained elusive if not
essentially a product of imaginative creation. Research on human skills accumulated to show
us how the body parts of the human body are coordinated to produce functionally specific
spatiotemporal patterns, such as standing, walking, reaching, jumping, or talking.
Coordination in the present approach is understood as the emergence of stable and
reproducible relationships between components (Schöner & Kelso, 1988). In many everyday
situations, in sports, or at the work place, such instances of coordinated behaviours, very
flexible yet stable, finely tuned to the environment, and energetically optimized, are not a
given but require training and learning. These very efficient coordinated actions are supported
by the acquisition of perceptuo-motor skills. Despite the achievements of scientific enquiry in
this field, the story of the understanding of these skills is far from being close.
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First review of the IP SKILLS FP6-IST-035005, Pisa, December 2007
Figure 1. First quantitative insights about the perceptuo-motor skills involved in a very complex system: the
coordination between horse and rider in a seated trot (From Eadward Muybridge, 1899).
This paper presents an overview in six short paragraphs of the current developments in
the major themes in perceptivo-motor coordination, which we think are of interest for the
understanding of skills. These themes include, by order of appearance, 1) a general definition
of what coordination stands for, 2) the question of variability in movement, 3) a presentation
of the so-called redundancy problem, 4) the most recent approaches that relates redundancy
and variability, 5) the question of the interplay between noise and dynamical stability, and
finally 6) the multi- scale study of learning.
1. Skills under the coordination patterns scope
Theories of coordination aim at understanding how individuals learn to assemble and
coordinate the very many degrees of freedom which are active in human beings, including
nervous system, body and behaviour. The focus here is predominantly on the formation of
task-specific coherent organizations of muscles, body segments, joint angles, and endeffectors, in a particular actor-environment context, but also on relations between movement
and the environment. By an effector system we understand the set of limb segments used in a
given action; the terminal or end-effector is directly related to the goal of the performed
action. Synergies (Latash et al., 2003), another name for coordinative structures with a
historical emphasis on muscular- articular links (Bernstein, 1967), are characterized by mutual
dependencies and patterned changes between kinematic variables (see Figure 2, left
illustration). Synergies were originally defined in an anatomical sense, as fixed arrangement
of agonist and antagonist muscles having similar actions at a joint. Early on, synergies were
defined as the solution of the problem of degrees of freedom in biological movement
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coordination and control, which requires the compression of the movement’s state space into
a control space of very few dimensions (Turvey, 2007). On its way the concept of synergy left
its anatomical clothes to become tailored into a functional concept, a usage of linkages among
muscles in a behavioural situation (Turvey, 2007).
Figure 2. Illustration of a multidegrees of freedom coordination in humans goal directed movement and in a
physical system.
Synergies relate to particular preferred relations among outputs of each element, which
are better seen in the averages over several realizations of a task. Such relations have been
described for a variety of tasks including vertical posture, locomotion, reaching, grasping,
speech, and finger force production, among others. Systematic relationships between effectors
can reduce the number of degrees of freedom (i) to form functional units, or patterns, (ii) to
shape patterns of motion in a dynamical system’s state variables (e.g., position and velocity),
and (iii) to shape spatiotemporal patterns of movement during skilled actions (Saltzman &
Kelso, 1987).
Many other systems in nature are characterized by a well organized cooperation
among numerous parts expressed in spatio-temporal patterns, among which some very well
understood physical systems. However, coordination in human perceptuo-motor skills differs
fundamentally from the one encountered in physics: only the former is a functional, goal
directed behaviour. Physical objects are characterized by properties while biological objects
are characterized by functions. Moreover coordination in human perceptuo-motor skills deals
with information, not only forces (Kelso, 1995; Warren, 2006). Firstly, perception and
movement are tightly intermingled in behavioural coordination, and perception is all about
information. Secondly the couplings between body parts, sensory systems, or neuronal
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populations, key to give rise and sustain coordination, are not only mechanical, but often only
informational. Indeed the task of discovering the laws underlying coordination in human
skilled behaviour is made very difficult because such a system embraces very many
components, and an activity that evolves at different spatial and temporal scales (joints,
muscles, neurons population, cells, ions channels, genes…), with local coordination taking
place at each level. However the fact that the systems of interest are goal directed is of
considerable help: goal directed systems basically tell us what their purposes are, and
accordingly enable (to some extent) to keep the essentials and get rid of the details.
Coordination patterns that one can observe in human skilled behaviour are based on
the cooperation of many sub-systems. This cooperation is made possible by the interaction of
the many degrees of freedom involved. Fortunately, patterned motor activity can be very often
described by one or few collective variables that summarises the coordination. Such collective
variables have been rigorously described close to a qualitative change (bifurcation) by use of
the adiabatic elimination procedure, according to the slaving principle which states that “longliving variables slave short-living variables” (Haken et al., 1985; Haken, 1983). In modern
non linear dynamical systems, this reduction corresponds to the center manifold theorem that
applies in the vicinity of a bifurcation (see Holmes, 2005, for a general and historical
perspective). These special variables express the low dimensional character of the overall
organization. In a complex system, composed of many elements, behaving in a nonlinear way
and with nonlinear interactions, it is not possible to determine and take into account the
detailed behaviour of each and every degree of freedom, nor it is possible to deduce the
patterns’ behaviour from the behaviour of isolated components. However, organizational
principles can be deciphered, by a focus on the patterns dynamics themselves (Schöner &
Kelso, 1988). The dynamics of coordination patterns are described by dynamical systems (see
Schöner et al., 1995; Strogatz 1994, for introductions), they are mapped onto attractors of
collective variables in phase space, the stability of which is considered crucial, in that it pulls
(attracts) the different elements (e.g., limbs, muscular synergies,...) of the system into the
preferred overall mode of operation given goals and other constraints. Stability is defined here
as asymptotic stability of invariant stable stationary solutions of dynamical systems. This line
of inquiry has been best unfolded in the study of relative timing between limbs that are not
mechanically coupled. Recently, a similar approach was applied in a context which includes
both mechanical and neurophysiological properties (Venkadesan, Guckenheimer & Valeras
Cuevas, 2007).
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2. Skills and Variability
A classical feature of skilled actions was discovered in the early 20th century by
Bernstein (1967), who demonstrated that the extreme accuracy resulting from hitting the same
spot on the anvil contrasts with the observation that the trajectories of the multijoint arm were
always different. Similarly, throwing a dart to the same target position can be achieved with
many different release positions and release angles.
Figure 3. Bernstein (1967) well known description of a blacksmith hitting an anvil with a hammer showing
more variance at the joints angles than in the spatial position of the hammer.
These observations indicate that a movement is never performed in the exact same way (it
always possesses some degree of variability) but a pattern of organization is common to each
sample. Variability in this sense is a hallmark property of human perceptuo-motor skill.
Variability may be exploited to obtain vital information about the “control structure”
of the system, or the essential components of the movement (Latash et al., 2003; Scholz &
Schöner, 1999). A coordination pattern constitutes a transient, “soft-” and task- specific,
assembly. To be proficient, or ‘dexterous’, it has to resist unavoidable internal and external
perturbations, and must possess stability. Stability measures tell us what is /are the
functionally relevant (stable) pattern(s). Human goal-directed skilled movement is
characterized by multistability: different stable patterns are available for a fixed set of
conditions and parameters. Different type of variability have been considered, mainly one
arising from the functional redundancy characterizing the movement itself, visible in the covariation of the components of the effector system (e.g., joints), and one arising from the
noise inherent to any biological system.
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3. Skills and redundancy
In a redundant kinematic chain, such as one’s arm or one’s leg, there is more than one
way to generate a given trajectory of the end point in Cartesian space through the motion of
the joints involved (Sporns & Edelman, 1993). Stated slightly differently, redundancy in the
task is given by the fact that different combinations of two elemental variables (joint angles)
can give identical results at the performance variables (end point). To highlight the distinction
here made between elemental and performance variables, consider two examples. The rotation
of individual joints may be used as elemental variables in kinematic studies of multijoint
reaching, and the coordinates representing the endpoint may be viewed as performance
variables. In the case of multifinger actions, neural commands issued to produce force by
individual digits may be viewed as elemental variables, while the total force or the total
moment of forces produced by the hand may be regarded as a performance variable (Latash et
al., 2003). How particular solutions are selected from the innumerable options afforded by
combinations of the many effectors (muscles, joints, and limbs) that take part in natural
movements?
Facing the so-called redundancy problem, one option is to search for minimization
principles that would provide for unique solutions. However, instead of considering
redundancy as a problem, an alternative proposition rests on the “principle of abundance”
(Latash et al., 2003): skilled adaptation doesn’t involve the elimination of degrees of freedom
but uses them all to ensure flexible and yet stable performance of motor tasks.
Learning is associated with a decrease in the variability of performance indicators.
However, this trend does not necessarily require the decrease of variability at the level of
elemental variables (Latash et al., 2003). Biological coordination builds up onto abundance by
forming spatio-temporal patterns which reduce the complexity of the effectors system.
Biological coordination takes advantage of these co-variations, synergies, coordinative
structures, or patterns, which afford for the immediate compensation of an unexpected
perturbation of one of the components (Kelso et al., 1984), a general principle often called
compensatory variability (e.g., Bardy & Laurent, 1998). In a non-redundant system,
compensation by the action of other components is not possible (Latash et al., 2003).
However, not every combination of the components leads to a change in the task variable(s),
hence the space spanned by the components’ motion does not need to be controlled in a
homogeneous way (Scholz & Schöner, 1999), and this idea shapes the framework of the
modern uncontrolled manifold theory (UCM).
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4. Recent solutions to the redundancy and variability problem
In the uncontrolled manifold theory, the variability in the high-dimensional space
spanned for instance by joint configurations can be divided into two subspaces. Whereas the
variability associated with one subspace does not correlate to task achievement (goalequivalent variables, the UCM), the variability in the other subspace affects task success (nongoal-equivalent variables).
Figure 4. Illustration of redundancy in human movement. 3 joints are used to reach in a planr movement a target
defined by 2 cartesian coordinates (a). (b) The manifold defined by the combinations of the 3 joint angles (in
radians) that produce goal equivalent effects (From Cusamano & Cesari, 2006).
The UCM is the geometrical object containing all those combinations of joint angles
that lead to the same value for task-relevant variables. This approach has also been applied to
other elemental variables, such as forces or muscle activations.
The main operational prediction of the UCM theory is that more variance of elemental
variables configurations lies within the UCM than outside of it. Unlike other variance analysis
methods like PCA for instance, the UCM approach includes a model based variance analysis.
The idea is that movement variability is partitioned depending on task goals with, one the one
hand, variability along dimensions directly related to task success and, on the other hand,
unimportant variability that will not impair goal achievement. The increase in the variability
in the UCM relative to that of the “non goal equivalent variables subspace”, implies that the
‘‘non-essential’’ variables may be selectively released from control, being “maintained” into
the UCM. Hence, little control over elemental variables is needed as long as they stay within
the UCM (thus, the term “uncontrolled”). Variations of the components orthogonal to that
sub-space are “resisted” in a way that signs a control process.
Todorov and Jordan’s (2002) stochastic optimal feedback control theory develops this
notion by postulating that the sensorimotor system keeps its options open until the last
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possible moment, and choose the adequate motor commands online, by making optimal use of
the most recent sensory data. This optimal motor control obeys a “minimum intervention”
principle, a principle that is implicit in the UCM theory. In line with the UCM theory,
variability is allowed in task-irrelevant dimensions and corrections along movement
trajectories only occur when they interfere with the goal of the task. The aim of the UCM
theory is to capture the way control is simplified by the CNS. The adaptive trajectory and the
movement regulation emerge from this control law. The observed trial to trial variability is
explicitly accounted by these two approaches. Accordingly, adapted behaviour in multidegrees of freedom movement is not characterized by a unique solution, but a set of solutions
in a redundant system. In each specific trial, one solution is selected but, during the repetition
of the action in another trial, under the very same constraints, another solution from the same
sub-set is likely to be selected, due to the stochastic (random fluctuations) contributions.
One final note of caution on the redundancy theme should be added here. The locus of
the redundancy in skilled movements may actually go beyond the kinematics of the effector
apparatus. For instance there is growing interest for the hypothesis of redundancy in the motor
cortex neural network (Rokni et al., 2007).
5. Stability of coordination patterns against noise
We have seen that motor planning and trajectory formation have been recently
modelled as the minimization of variability under the signal dependent (multiplicative) noise
assumption. When larger spatial accuracy is required by the task, the shape of trajectories
apparently follows the rule that smaller signal implies less noise (smaller nervous signal sent
to the muscles for smaller torque, hence smaller acceleration) and thus less variability of the
end point effectors’ position in physical space. Operationally, this situation is easily
implemented in the classical Fitts’ task, in which typically a pointer can be moved
rhythmically by hand toward two stationary targets, and the duration of movement is lawfully
related to the target’s width and the distance between targets (Fitts, 1954). This task offers a
paradigm of choice for the study of variability (Todorov & Jordan, 2002).
In the dynamical formulation of human coordination, the presence of variability has
been modelled in a standard way by adding “dynamical” Gaussian delta correlated noise to
the equations of motion (Schöner et al., 1986), under the hypothesis that underlying
fluctuations evolve from more microscopic level at a much faster time scale than functional
behaviour. The main idea, by taking this option, is to describe all the “structure”, the
correlations and order present in the behaviour, by the deterministic part of the model, hence
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the addition of random contributions that are in contrast totally uncorrelated. These
assumptions are generally in agreement with the measurement of variability at much faster
time scales than the adaptive movement, mainly found in various elements in the nervous
system (Calvin and Stevens, 1967; Stein et al., 2005), ranging from ions channels opening at
cortical synapses to ensemble neurons population. Note that noise is also present at other
levels involved in motor control and trajectory formation, for instance in muscles and in the
environment. This modelling led to new quantitative predictions, deduced by these
assumptions and based on Langevin and Fokker-Planck formulations, verified experimentally
in the well known phase transition phenomenon in bimanual coordination (Kelso et al., 1986),
and qualitative predictions verified in postural coordination (Bardy et al., 2002).
Dynamical systems models of coordination dynamics focus mainly on topology of
dynamics of functionally relevant behavioural variables (fixed point attractors, limit cycles
attractors, excitable behaviour, relaxation oscillations, synchronization), its changes with
bifurcations (qualitative changes in behaviour), which focuses strongly on the key issue of
stability of the adopted solutions. Dynamical systems models of coordination dynamics
emphasize the abstractness of the control variables. Consider again the classical Fitts pointing
task, the underlying periodic pattern in phase space (position against velocity) is invariant
over very different effectors implementations, including interpersonal cooperative pointing to
targets (Mottet et al., 2001). Stability can be quantified in stationary behaviour by the variance
of the fixed point, or by applying a small perturbation. For instance relative timing between
rhythmically moving limbs proved a stable variable in that after a phasic perturbation,
mechanical (Scholtz & Kelso, 1989; Scholtz Kelso & Schöner, 1987), or perceptual
perturbation (Yamanishi, Kawato & Suzuki, 1979; Bardy et al., 2002), relative timing returns
to its value before the perturbation was applied. In a pointing task, like the classical Fitts’
task, the stability confers essential functional properties: robustness against finite random
perturbations inherent to the system, and thus the interplay between stability and random
fluctuations may explain in principle the observed spatial variability in physical space. Note
that from the early developments in the mathematical theory of dynamical systems the focus
on stability was justified by the necessity to ensure persistence, robustness, and
“observability” against fluctuations unavoidable in any real physical- natural system
(Andronov et al., 1966, see page xviii of the Introduction chapter). No other source of
variability is considered in this framework, and without random fluctuations no variability is
allowed, the deterministic part of the models being perfectly regular. Some confusion can
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arise however because, in a fully deterministic system without any random contribution,
quasi-periodic regime can give rise to quite irregular behaviour (Bergé, Pommeau, & Vidal,
1984). To date, it has been shown that the variability in the movement attributed to quasiperiodic deterministic behaviours instead of stochastic contributions in human coordination
dynamics (Schmidt & Turvey, 1993) was due to a specific choice of coordinates for the
calculations (Fuchs et al., 1996). This source of variability is characterized by a time scale and
structure clearly separated from the hypothesized random fluctuations, hence no confusion
between the two is possible. A more difficult problem is posed when variability is attributed
to a chaotic behaviour. To the best of our knowledge, a fundamentally chaotic character of
these basic discrete or rhythmic movements has not been demonstrated. A chaotic nature of
coordination may contradict the separation of time scales (ie, Haken’s slaving principle)
which have been used with significant success to select dominant variables in the study of
basic human coordination phenomena (Haken et al., 1985). The distinction between chaotic
and stochastic processes is an open issue, both theoretically and in a more applied data
analysis perspective.
Hence the point of view provided by Harris and Wolpert (1998), or Todorov (2002),
can be complemented by being aware that noise must be considered not only under the signal
dependent assumption and minimization principle, but also in the interplay with stability.
Stability here is investigated by a focus on the behaviour of the so-called coordination
variables, which is rooted in both sensory and motor processes. Two simple ideas may be
further developed. Firstly, if the coordination pattern is very stable, to reach a given spatial
accuracy level, the minimization of command signals amplitude that are corrupted by
multiplicative noise will be less relevant than when less stability is achieved. Secondly, again
to reach a given spatial accuracy level, what is the most efficient solution (according to a
criteria to be defined): to increase stability of the end point trajectory versus to minimize the
command signals amplitude? Furthermore, when spatial accuracy and a high level of force/
torque is required, which is very often the case in sports, does the minimum variance
hypothesis collapses? This could be possibly sorted out in further numerical and/or
experimental studies.
6. Recent development in the study of skills
A next step toward the capture of the full complexity of perceptuo-motor skills was
proposed by recent research accomplished on juggling skills. Juggling proved a very active
paradigm in the study of skills in multi-degrees of freedom movements (Beek & Lewbel,
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1995; Beek & Van Santvoord, 1992; Beek & Turvey, 1992; Post et al., 2000). Achieving a
juggling task imposes strong constraints onto the spatio-temporal pattern of coordination
between the limbs, hence requires the acquisition with learning of stable rhythmic movement
along with strong couplings between the hands (Huys et al., 2003; Post et al., 2000). These
constraints shape the overall coordination in a pattern regular enough to be actually phrased in
a systematic way by the so-called Shannon theorem of juggling (See Beek & Lewbel, 1995,
for a presentation). To avoid collision between balls during the flight, and allow regular
sequences of catches and tosses by the two hands, the balls’ trajectories must be highly
ordered.
In particular, in the classic 3 balls cascade, the periods between the 3 balls have to be
maintained very stationary. To comply with the task, the juggler must acquire perceptuomotor skills that result in stable frequency and phase locked balls motions, decidedly a classic
feature in skilled perception-action coordination! We ran preliminary capture and analysis of
the 3D movements of a skilled juggler. This dominant feature of juggling skills is illustrated
by phase difference calculated between the trajectories of the hands along the vertical (Z) and
the medio-lateral axis (X) in Figure 5. The distributions are very narrow, which indicates a
very low variability and hence a strong coupling between the hands.
Figure 5. Phase locking between the hands of a juggling expert illustrated by the distributions of the relative
phase (Top left) for the movements along the horizontal (X) and vertical (Z) axis. The trajectories of the two
hands are displayed in the frontal plane (Top right) and individually as a function of time (Bottom) (The data
were collected by Oxford Metrics).
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Figure 6. Top: The trajectories of the left and right hand in the X and Y directions in a 3 balls cascade pattern by
a high skilled juggler. Bottom: snapshots of the movement along X and Y of the right hand (The data were
collected by Oxford Metrics).
Figure 7. A representative trial illustrating the phase locking between the hands along the Y axis (forwardbackward movement). Data are band-pass filtered to eliminate the slow drift before the estimation of the phases.
(Top) Left the distribution of the phase difference, Right a zooming view of the movement of the hands.
(Middle) Time series of the Y displacement of the hands showing a time evolution of the amplitude and the
presence of a slow component. (Bottom) The time series of the phase difference displayed important deviations
from stationarity, indicative of a loose coupling (The data were collected by Oxford Metrics).
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Differently, along the Y axis, firstly a high degree of variability in the time evolution of the
amplitude was measured (Figure 6), and secondly a loose coupling can be inferred from the
phase difference calculated between the hands for this coordinate (Figure 7).
These first results seem to indicate that the time evolution along the antero-posterior
axis (Y) differs from what is classically obtained along the X and Z coordinates, that is, strong
coupling between rather harmonic movements. The presence of a slow component in the Y
time series, along with a variation of the amplitude may indicate a postural influence onto the
hands’ movement, and/or the locus of a control from trial-to-trial at the catches that has been
ignored in the available literature to the best of our knowledge. Moreover the loose coupling
estimated for this coordinate motivates further analysis.
The overall temporal order in juggling can be traduced in the vocabulary of spatial and
temporal symmetries, and then be used to demonstrate analytically the necessary reduction of
dimensionality of the 3D motion of the 3 balls, estimated by a PCA analysis (Post et al.,
2000). It is not surprising that a long practice of juggling is accompanied by a reduction of
dimension the balls motion (Figure 3).
trials
Figure 8. Proportion of variance of the 3 balls trajectories recorded in 3D explained by the principal components,
normalized to unity (vertical axis), ranked by the order of magnitude of the variance explained from 1st to 9th
(axis labelled k), and as a function of practice trials from 9th to 31th (axis labelled trials)(From Huys et al., 2004).
One sees clearly how the two first components become more and more prominent as practice evolves, the
remaining components explaining less and less variance. The PCA analysis was applied to the 9 dimensions
vector composed by the 3 coordinates of the 3 balls. The plane actually spanned by the two first modes is the
frontal plane.
Hence, on the one hand juggling is an enormously complex object for the scientist,
but, on the other hand it possesses in essence a very well ordered organization which leaves
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hope for a successful application of the coordination dynamics theoretical and experimental
framework.
A new approach proposed to track the various time scales at which the different
subsystems involved in the execution of the task changed with learning (Huys et al., 2003;
2004). Such a tack has seldom been followed in traditional research on learning.
Traditionally, outcome measures (e.g., spatial error in dart throwing) or variables having a
very direct bearing on task achievement (e.g., end- effector kinematics) are used to infer
learning.
This new approach was applied to the acquisition of basic juggling patterns such as the
classical 3 balls cascade (Huys et al., 2004). The components of the subsystems considered
important for juggling were: gaze, balls’ pattern, postural sway, and breathing. The main idea
was to decipher the evolution of the assembly of these components into a global functional
organization. Due to its essential periodic nature, juggling skill is often captured by frequency
and phase locking variables, such as frequency ratio between balls motion and hand
movement, reflected in the proportion of hand loop time that a hand transports an object
(Beek & Turvey, 1992), and relative phase. The variance of these variables inform about the
strength of the interactions between the components involved, which reflects the degree of
coordination order within the ensemble.
Figure 9. An analysis of skill acquisition in juggling which takes into account the evolvement of coordinations
between sub-components (arrows added for illustration) between subcomponents (From Huys et al, 2003).
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In this study, the eyes-balls coordination, the between-balls coordination, and the
balls-posture coordination were mainly investigated. Tracking longitudinal changes in these
indexes of assembly among the components shed light on the multiform dynamics of the
acquisition process. In particular learning was characterized by a temporal hierarchy (Huys et
al., 2004). Put simply, this means that some components are assembled together earlier than
others. Changes in frequency locking preceded changes in phase locking, and both took place
before actual improvements in performance variables, like the number of successive cycles
achieved. Finally, the results indicated that some changes evolved gradually while others were
sudden and rapid.
This line of research opens up new grounds for the understanding of the still hidden
facets of acquisition of perceptuo-motor skills, using a very rich task, juggling, which
provides a fundamentally rhythmic ordering and a large and redundant whole body
organization.
Acknowledgements
Julien Lagarde thanks Scott Kelso for constant encouragements and inspiration in the study of
coordination dynamics. The authors thank Oxford Metrics for providing the expert juggler
data. This paper was written with the support of the IP SKILLS FP6-IST-035005 from the
EC.
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