Motion Planning for a Pendulum-Driven Rolling Robot Tracing Spherical Contact Curves

This paper deals with motion planning problems for spherical rolling robots driven by a two degree of freedom pendulum. A full dynamic model for this system is first introduced. Then, assuming that the contact path is specified and the sphere moves in pure rolling mode, the full dynamic model is reduced by imposing virtual constraints. A timing control law, based on the Beta function, for tracing the contact curves in rest-to-rest motion is constructed. The constructed control law is verified under simulation for tracing Viviani's curve and the Loxodrome on the sphere.