A geometric motion planning for a spin-rolling sphere on a plane

Abstract

The paper deals with motion planning for a spin-rolling sphere when the sphere follows an optimal straight path on a plane. Since the straight line constrains the sphere’s motion, controlling the sphere’s spin motion is essential to converge to a desired full configuration of the sphere. In this paper, we show a new geometric-based planning approach that is based on a full-state description of this nonlinear system. First, the problem statement of the motion planning is posed. Next, we develop a geometric controller implemented as a virtual surface by using the Darboux frame kinematics. This virtual surface generates arc-length-based inputs for controlling the trajectories of the sphere. Then, an iterative algorithm is designed to tune these inputs for the desired configurations. Finally, the feasibility of the proposed approach is verified by simulations.