Biologically Plausible Models of Motor Control
Introduction
To date, models of visuo-motor control in biological systems, have, to a
large extent, been confined to systems capable of performing simple
sensory-to-motor transformations. For example, in employing neural algorithms to
control the SoftArm, the research effort of the group was
devoted to developing networks that were capable of learning the
transformations between the visual coordinates of the end effector of
the robot and the motor commands necessary to position the end
effector at a given point. In
contrast, however, movement in biological systems is the result
of information processing occurring concurrently in a hierarchy of
motor centers within the nervous
system.
Furthermore, while visual information is of great importance to
movement it does not constitute the sole source of input to the
nervous system. Proprioceptive input, that is information derived
from sensors which signal the internal states of limbs themselves, is
of the utmost importance for accurate motor control. This fact is
reflected in the considerable area of the cerebral cortex devoted to
processing information of this type. We want to clarify the manner
in which
the various centers associated with motor control within the cerebral
cortex contribute to motor control. Furthermore, we wish to elucidate the manner
in which these motor centers can jointly program and coordinate movement. This work is
undertaken by Ken Wallace, a post-doctoral researcher who joined the group in 1992, having
completed graduate research at the University of Oxford.
Description
During visually guided movements, information related to the visual
field will initiate the process of programming the required
movement. However, proprioceptive input will also be required to
indicate the correct context within which the movement should be
performed. This is necessary because limbs have many more degrees of
freedom than is strictly necessary to allow movement in space. This
introduces a degree of redundancy to the problem in which different
muscles can be employed in varying fashions to achieve the same
results. Furthermore, the ability of individual muscles to contribute
to
movement is, in general, dependent upon the starting and end points
of
the movement. Accurate control of movement requires, therefore, that
the central nervous system is capable of taking account of these
factors when calculating the optimal pattern of muscle recruitment to
achieve the desired movement. In other words, a degree of ``context
sensitivity" must be introduced into the programming of particular
movements.
In extending the techniques and neural architectures that have been
developed during the period of funding provided by the Carver
Charitable Trust, our attention has now focussed upon models that are
capable of accounting for the processing occurring within several
distinct areas of the cerebral cortex. This issue draws largely from the existing body of knowledge
regarding how individual areas of the brain respond during movement.
The parietal cortex, for example, is known to be intimately involved
in the association of exteroceptive input, that is information
regarding the external environment, and proprioceptive sensory
input. As such, the parietal cortex is able to
associate visual signals regarding target and limb position with
afferent input provided by
body sensors indicating the current position of the limb. On the other hand, several structures, including the parietal cortex, sensory
cortex and
motor cortex, have been implicated in formulating the correct context
of a movement.
We have developed a model which takes account of some of the
principal
stages responsible for sensory to motor transformations found within
the cerebral cortex. This model explicitly accounts for processing
occurring within the visual and the parietal cortices. In addition, it
includes a lumped model of the motor areas of the cerebral cortex,
mid-brain and spinal segmental level of motor control as well as
certain types of proprioceptive information
regarding the internal state of the limb. The neural networks of this
simulation learn through the random exploration of the workspace of
the
SoftArm, in a similar fashion to the way a child makes random
movements during play. During this process the system learns maps of
commands which are capable of positioning the SoftArm at particular
locations within the workspace. The figure
illustrates
the development of one such motor map, used to control movement of
the
"wrist" of the SoftArm, at four points during learning. The top left
frame illustrates the state of this map prior to any learning. Here
the
colored squares represent the states of the individual motor cells
which constitute this map. The top right hand frame illustrates the
organization that has evolved in this map, following a period of
learning corresponding to 1000 time steps. As can be seen, the basic
structure of the map has already become evident. The lower left and
right frames illustrate the subsequent development of this map after
another 1000 and 2000 time steps, respectively. Only after this
learning
phase is the system capable of performing coordinated movement.
The development over time of a motor map used to control movement of the
"wrist" of the SoftArm. Colors represent the states of individual motor cells
which constitute the map. The state of each cell is initially set randomly (top
left) with the final structure of the map (bottom right) evolving during the
learningprocess.
To date, we have been successful in employing this model to control
coarse positioning of the SoftArm: at present, the error in the
absolute position attained by the movement is between 3 and 9cm. The
learning observed using this model is, however, very characteristic
of
the early stages of skilled movement acquisition observed during the
development of motor skills in primates: highly accurate movements
are
only possible once the ability to learn more approximate positioning
skills has been acquired. In addition, it is important
to
separate the distinct issues of positioning the limb and manipulation
of the hand. In primates these functions, although related, reflect
the action of distinct areas of not only the motor cortex, but also
the
basal ganglia and the cerebellum.
To pursue this work we have recently turned our attention to the
question of how we can model the next stage of the learning process,
that is the acquisition of more skilled movements. In this respect we
are currently investigating how context sensitivity may be introduced
into the present simulations. One particularly interesting aspect of
the work employs the mechanical characteristics of the SoftArm. The
compliance of the arm can be adjusted such that movements which are
programmed in a similar manner reach entirely different end points in
the workspace, depending upon the values specified for the muscles of
the SoftArm. Such a situation is very
reminiscent of the situation found in primates where it has
been postulated that joint stiffness, the reciprocal of joint
compliance, is explicitly modulated to achieve the desired end point
of a
movement.
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