Dynamic model and motion planning for a pendulum-actuated spherical rolling robot

This paper deals with the dynamics and motion planning for a spherical rolling robot with a pendulum actuated by two motors. First a dynamic model for the rolling robot is established. In general, not all feasible kinematic trajectories of the rolling carrier are dynamically realizable. A notable exception is when the contact trajectories on the sphere and on the plane are geodesic lines. Based on this consideration, a motion planning strategy for complete reconfiguration of the rolling robot is proposed. The strategy consists of two trivial movements and a non-trivial maneuver that is based on tracing multiple spherical triangles. To compute the sizes and the number of triangles, a reachability diagram is constructed. To define the control torques realizing the rest-to-rest motion along the geodesic lines, two possible approaches are suggested. A computational algorithm, implementing the motion planning strategy, is developed and verified under simulation.