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 r obotic effecters. While for parts with smooth surfaces a relatively well-de veloped theory exists, planning for parts with only piecewise smooth surfac es 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. Relevan t theoretical results are reviewed, and a polynomial time algorithm is prop osed that allows planning such motions. The effects of finite accuracy in r epresenting problem data, as well as the operational and computational comp lexity of the method are considered in detail.