Trajectory Tracking Control of a Rolling Disk on a Smooth Manifold

This paper studies the trajectory tracking control problem for a vertical rolling disk on an arbitrary smooth surface in ℝ
³
. The disk is assumed to roll without slipping about its axis and turn about the surface normal. A nonlinear controller is designed for the trajectory tracking of the disk based on a kinematic model that is globally defined on the manifold without singularities or ambiguities. The theoretical results are specialized for two different surfaces; a flat surface and a paraboloidal surface. Simulation results are included to illustrate the effectiveness of the tracking control law on the smooth surfaces.