Motion Planning of a Spin-Rolling Sphere on a Plane
This addresses motion control for robotic or mechanical systems involving rolling spheres, but appears incremental as it builds on existing geometric methods for a specific constrained scenario.
The paper tackled motion planning for a spin-rolling sphere moving along a straight path on a plane by developing a geometric-based controller using Darboux frame kinematics, and verified its feasibility through simulations.
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.