Control of a Sphere Rolling on a Plane with Constrained Rolling Motion

In this paper, we discuss control of contact coordinates for a contact point between a sphere and a plane with pure rolling contact by using iterative closed paths on the sphere with contstrained rolling motion. We first analyze the boundary of the reachable area by the closed path with constrained rolling motion. Utilizing the result, we second propose a method which converge all the contact coordinates to a target point by the iteration of a finite number of the closed paths. A numerical example where the rolling motion is restricted to the area on the semisphere shows the effectiveness of the proposed method.