A local-local planning algorithm for rolling objects

In this paper, we consider planning motions of objects of regular shape rolling on a plane among obstacles. Theoretical foundations and applications of this type of operations in robotic manipulation and locomotion have been discussed elsewhere. In this paper, we propose a novel algorithm that improves upon existing techniques in that: i) it is finitely computable and predictable (an upper bound on the computations necessary to reach a given goal within a tolerance can be given), and ii) it possesses a topological (local-local) property which enables obstacles and workspace limitations to be dealt with in an effective way.