Planning Motions of Polyhedral Parts by Rolling

The nonholonomic nature of rolling between rigid bodies can be exploited to achieve dextrous manipulation of industrial parts with minimally complex robotic effectors. While for parts with smooth surfaces a relatively well-developed theory exists, planning for parts with only piecewise smooth surfaces is largely an open problem. The problem of arbitrarily displacing and reorienting a polyhedron by means of rotations about edges belonging to a fixed plane is considered. Relevant theoretical results are reviewed, and a polynomial time algorithm is proposed that allows planning such motions. The effects of finite accuracy in representing problem data, as well as the operational and computational complexity of the method are considered in detail