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.

We introduce the concept of Local Force Closure. We define a local force closure grasp as a grasp which is capable of resisting some given external wrench as well as (through local variation in contact wrenches) any wrench in some neighborhood of the given wrench, with grasp quality exceeding some given threshold. Local force closure is useful in applications where a grasp only needs to resist some given external wrench, rather than fully constraining object, but where there is some uncertainty regarding the exact external wrench that needs to be resisted, or where there is a possibility of having to cope with some (relatively small) unknown disturbance forces. We show that by allowing disc-shaped fingers in contact with convex vertices of a polygonal object, any given wrench can be resisted by just two frictionless fingers. For a given polygonal object with n vertices and an external wrench wext, we show how to find all pairs of features of P, that admit grasps capable of resisting wextwith grasp quality greater or equal to some threshold Q, in O(n3/2+ε+ K) time, where K is the number of pairs in the output and ε is some arbitrarily small, positive constant. We then show how to adapt our algorithm to guarantee that the features reported, admit local force closure grasps.

We extend the notion of grasp metrics to partial force-closure grasps. We describe two metrics which measure the maximum and sum, respectively, of the forces that need to be applied at the contacts involved in a grasp, in order to exert some given unit wrench on the grasped object. For a given object P of complexity O(n) and a pure force T, we describe efficient algorithms which compute all combinations of m features (edges of polygons or facets of polyhedra) that admit grasps capable of exerting T such that the value of our metric is greater than some threshold. In particular, we show that if P is a polygon, all pairs of edges that admit frictionless two-finger grasps capable of exerting T can be computed in O(n log2n+K) time, where K is the number of pairs of edges in the output. Also, all two-finger grasps with friction of a polyhedral object can be computed in O(n3/2+ε+ K') time and all frictionless three-finger grasps of a polyhedron can be computed in O(n5/2+ε+ K') time, where K0is the number of pairs or triples of facets that satisfy some slightly weaker condition and ε is some arbitrarily small, positive constant.

We propose a technique which significantly simplifies the computation of frictionless force-closure grasps of a curved planar part$P$. We use a colored projection scheme from the three-dimensional wrench space to two-dimensional screens, which allows us to reduce the problem of identifying combinations of arcs and concave vertices of$P$that admit frictionless force-closure grasps, to colored intersection searching problems in the screens. We show how to combine this technique with existing intersection searching algorithms to obtain efficient, output-sensitive algorithms to compute all force-closure grasps of$P$, where at most four hard, frictionless point contacts exert exactly four wrenches on$P$. If the boundary of$P$consists of$n$algebraic arcs of constant complexity and$m$concave vertices, we show how to compute all force-closure grasps with:four contacts along four arcs in$O(n^{8/3}\log ^{1/3}n+K)$time;