CONTROL OF EQUILIBRIUM POSITION AND STIFFNESS THROUGH POSTURAL MODULES

If muscles are viewed as spring-like torque generators, then the integ ral of torque with respect to joint angle is the potential energy of t hat muscle. An energy function for the musculoskeletal system can be d efined by summing the energy contribution of each muscle and the poten tial energy stored in the limb. Any local minimum in this energy lands cape is a possible equilibrium position for the limb. The gradient of this function with respect to joint angles is a torque field, and the task of postural control is to find a set of muscle activations to pro duce a desired field. We consider one technique by which this approxim ation may be achieved: A postural module is defined as a synergy of mu scles that produce a class of torque functions that converge at a cons tant equilibrium position, but whose stiffness at this position varies as a function of activation of the postural module. For a single-join t system, we show that through control of two such modules it is possi ble to produce any stiffness at any desired equilibrium position. To e xtend this scheme to a multijoint system, we initially derive the mech anical constraints on the shape of the restoring force field when a mu ltijoint limb is displaced from equilibrium. Next, we consider volunta ry control of the force field when the human arm is displaced from equ ilibrium: Mussa-Ivaldi, Hogan, and Bizzi (1985) have suggested that su bjects are unable to voluntarily change the shape and orientation of t he field, although they can readily scale it. This suggests existence of a limitation on the independent recruitment of arm muscles. We show , through simulation, that the inability to voluntarily control the sh ape and orientation of the restoring force field can be attributed to an organization of postural modules that act as local stiffness contro llers. We propose that through coactivation, postural modules coarsely encode the work space and serve as an intermediate control system in the motor control hierarchy.