A motion planning algorithm for convex polyhedra in contact under translation and rotation

Motion of objects in contact plays an important role in the mechanical assembly by manipulators. This paper presents a motion planning algorithm for the case that a convex polyhedron translates and rotates in contact with another one. The rotation of the moving one is parameterized by a special unitary 2×2 matrix to have the algebraic representation of the contact conditions between the polyhedra. We present an algorithm to determine a sequence of the topological contact states whose asymptotic time complexity is optimal. We also present an algorithm to obtain a `roadmap´ by solving the algebraic equations. The principle idea is `astute geometric formulations make the algebraic problem easier to solve´. The algorithms are implemented and examples are shown