Independent contact regions for local force closure grasps

A grasp g is said to achieve local force closure with respect to a given external wrench wext if g can resist wext as well as any wrench in some neighborhood of wext, with grasp quality no less than some threshold Q. Such grasps are particularly useful for tasks that do not require an object to be completely restrained: such as holding an object so that it does not fall, or picking up objects and dropping them into a container. If we allow the use of disc-fingers in contact with convex vertices of a polygonal object P, then any given wext acting on P can be resisted by a 2-finger grasp. We show how to compute the set of all 2-finger grasp configurations with contacts on given boundary features of P that are capable of resisting a given wext with quality at least Q. We also show that any grasp in the interior of such a grasp set achieves local force closure with respect to wext. By finding the largest square contained in such a grasp set we can obtain maximal independent contact regions for local force closure grasps of P with contacts on a given pair of features.