Orienting a Part with Shape Variation

Industrial parts are manufactured to tolerances as no production process is capable of delivering perfectly identical parts. It is unacceptable that a plan for a manipulation task that was determined on the basis of a CAD model of a part fails on some manufactured instance of that part, and therefore it is crucial that the admitted shape variations are systematically taken into account during the planning of the task. We study the problem of orienting a part with given admitted shape variations by means of pushing with a single frictionless jaw. We use a very general model for admitted shape variations that only requires that any valid instance must contain a given convex polygon PI while it must be contained in another convex polygon PE. The problem that we solve is to determine, for a given h, the sequence of h push actions that puts all valid instances of a part with given shape variation into the smallest possible interval of final orientations. The resulting algorithm runs in O(hn) time, where n = |PI | + |PE|