A simple and efficient procedure for polyhedral assembly partitioning under infinitesimal motions

Abstract

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 infinitesimal translation and rotation, without colliding with the rest of the parts, AS. 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 efficient 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 efficiently access these portions. The algorithm is complete (in the sense that it is guaranteed to find a solution if one exists), simple, and improves significantly over the best previously known solutions. We report experimental results with an implementation of our algorithm.