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.