Feedback stabilization of a spherical mobile robot

In this paper we discuss the problem of reconfiguring a sphere, rolling without slipping on a flat surface, from an arbitrary initial configuration to a desired final configuration. We propose a control algorithm that utilizes two control actions that are applied alternately. The individual control actions cause trajectories that are circular arcs and straight line segments. Through judicious choice of the sequence of individual control actions based on state feedback, we construct a control strategy that stabilizes the sphere to its desired configuration. Simulation results are presented to demonstrate the efficacy of the strategy.