Nonlinear force fields: A distributed system of control primitives for representing and learning movements

Electrophysiological studies have suggested the presence of a modular structure in the output stages of the motor system. In this structure, independent modules are connected to specific groups of muscles and generate nonlinear fields of force acting upon the controlled limbs. This paper explores the computational consequences of this structure in the framework of multivariate approximation. Movements are generated through the selection of independent modules and through the vectorial superposition of their output fields. It is shown that complex joint motions of a multi-segmental mechanism may be obtained by determining a set of time-independent parameters which scale the amplitude of each module's field. In addition, optimization results suggest that a system of such modules may evolve to improve the execution of smooth movements of the mechanism's endpoint across the whole workspace. The observed improvements generalize beyond the set of movements used to guide the optimisation. These findings indicate that a rich repertoire of behaviors may be learned by adapting a system of force fields obtained from the combination of multiple viscoelastic actuators.