Shadmehr R (1991), A computational theory for posture and movement in a multi-joint limb. Technical Report 91-7, Center for Neural Engineering, University of Southern California, Los Angeles, CA.

 

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.