A Simple and E cient Procedure for Polyhedral Assembly Partitioning under In nitesimal Motions

We study the following problem: given a collection of polyhedral parts in 3D, determine whether there is a subset of the parts that can be moved as a rigid body by an in nitesimal translation and rotation, without colliding with the rest of the parts. A negative result implies that the object whose constituent parts are the given collection cannot be taken apart with two hands. A positive result, together with the list of movable parts and their direction of motion, can be used in an assembly sequence planner. This problem has attracted considerable attention within and outside of the robotics community. We devise an e cient algorithm to solve this problem. Our solution is based on the ability to focus only on selected portions of the tangent space of rigid motions and to e ciently access these portions. The algorithm is complete (in the sense that it is guaranteed to nd a solution if one exists), simple, and improves signi cantly over the best previously known solutions to this problem. We report preliminary experimental results of an implementation of our algorithm.