Stability constraints for the distributed control of motor behavior

We have investigated the relation between static stability of a limb, equilibrium-point control, and the ill-posed problem of coordinating a redundant ensemble of muscles. Geometrically, equilibrium-point control is equivalent to establishing a mapping between the command signals delivered to the muscles and the equilibrium configurations of a limb. A necessary condition for the existence of such mapping is that the limb be stable across the workspace. We analyzed how this condition may be translated into precise biomechanical constraints for single-and multi-joint limbs. The satisfaction of these constraints is necessary for the equilibrium-point hypothesis to be a viable control paradigm. We show how these same constraints are sufficient to insure the successful operation of a distributed algorithm based upon minimization of potential energy that computes the muscle-control signals corresponding to a desired time sequence of equilibrium points.