Rolling Polyhedra on a Plane; Analysis of the Reachable Set

The problem of dexterous manipulation of objects, i.e. of arbitrary relocation and reorientation of rigid bodies by action of some mechanism, is considered. We build upon previous results on the possibility of implementing dexterous “robot hands” with few actuators, which can be afforded through the exploitation of nonholonomic rolling of regular surfaces. In this paper we focus on the manipulation of polyhedral objects, and prove a necessary and sufficient controllability–like result, which discloses some of the interesting aspects and perspectives of this problem.