Shadmehr R (1991), A computational
theory for posture and movement in a multi-joint limb. Technical Report 91-7,
Center for Neural Engineering,
Abstract
Our goal is to
describe a computational framework for control of posture and movement in a
multi-joint limb, consistent with the constraints imposed by the neural and
mechanical properties of the system.
The idea is to describe a reasonable model of the musculo-skeletal
system and then ask how to go about maintaining posture at a given place, vary
stiffness, or initiate motion. We
search for a coherent way of organizing a pre-motoneuronal,
spinal based control system which can translate relatively high level commands
from the supra-spinal centers into the native language of the muscles. We approached these questions by
initially building a muscle model.
A derivation is provided which supports the hypothesis that the static
response of a muscle and its reflex system can be viewed as a non-linear spring
with an adjustable resting length.
Citing experimental data, the class of models where a muscle is viewed
as a non-linear spring with an adjustable stiffness can be rejected. The issue of actuator redundancy and
postural stability with muscles is examined through control of an inverted
pendulum. The potential energy of a
musculo-skeletal system is derived and it is
suggested that the task of postural control can be viewed as sculpting an
energy landscape so that there is a local minimum associated with the desired
limb configuration. An algorithm
for producing this landscape is proposed: we define a postural module as a
synergy of muscles which can be activated to produce a class of torque
functions which all have a zero value at a specified equilibrium position. Postural modules form a distributed set
of stiffness controllers, and by co-activation of these modules it is possible
to encode the reachable space and control the limb’s stiffness. We describe a computational framework in
which postural modules can account for the observed limitations in voluntary
control of stiffness in man. It appears that a shift in the equilibrium
position of the limb can account for the experimental data regarding the EMG
during initiation of arm movement, while the same data in compatible with
predictions of three competing hypotheses.
The framework of postural modules also accounts for the perceptual
errors which exist when subjects are asked to guess the characteristics of
compliant objects. Certain
kinematics of the frog wiping reflex may be explained when the framework of
postural modules is applied to generation of movement in a multi-joint
limb. Finally, a learning algorithm
is applied to compensate for the dynamics of a limb during rapid movements
through production of a virtual equilibrium trajectory.