Motion Planning of a Spin-Rolling Sphere on a Plane

TL;DR

This paper introduces a geometric motion planning approach for a spin-rolling sphere constrained to a straight path, utilizing a full-state description and virtual surface control to achieve desired configurations.

Contribution

It presents a novel geometric-based planning method using Darboux frame kinematics and an iterative algorithm for spin-rolling sphere control on a plane.

Findings

The approach effectively plans sphere trajectories under constraints.

Simulation results verify the feasibility of the proposed method.

Abstract

The paper deals with motion planning for a spin-rolling sphere when the sphere follows a straight path on a plane. Since the motion of the sphere is constrained by the straight line, the control of the sphere's spin motion is essential to converge to a desired 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. The feasibility of the proposed approach is verified by simulations.