Harmonic functions as a basis for motor control and planning

Abstract

Harmonic functions are presented as a mechanism for robot control and planning. These functions produce smooth trajectories which are amenable to fast control. Obstacle avoidance based on harmonic functions is complete: If a path to the goal exists, the technique described here will find that path. Otherwise, it will detect that no such path exists. Harmonic functions have a number of other properties which are useful for robotics applications: they can be used to construct admittance controllers, they can be implemented using resistive networks, and they can be used for planning the trajectories of nonholonomic systems. Finally, recent results in neuroscience regarding the basal ganglia allow the formulation of a theory of basal ganglia function based in part on harmonic functions computed over various state spaces.