A Simple and Effeicient Procedure for Polyhedral Assembly Partitioning under Infinitesimal Motions

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