Mechanical parts orienting: The case of a polyhedron on a table

The problem of orienting a part resting on a table by tilting the table is considered. The initial orientation of the part is assumed to be completely unknown. The objective is to tilt the table in a manner that reduces the uncertainty in the part's orientation. This work focuses on three-dimensional polyhedral parts, with finite friction between the parts and the table, and for which all transitions between different face-table contacts may be regarded as rotations across edges. A planner that determines a sequence of tilting operations designed to minimize the uncertainty in the part's orientation is proposed. The planner runs in time O(n4), where n is the number of faces of the polyhedron. The planner produces a sequence of O(n) distinct tilts