An Enhanced Ray-Shooting Approach to Force-Closure Problems

Abstract

Force-closure is a fundamental topic in grasping research. Relevant problems include force-closure test, quality evaluation, and grasp planning. Implementing the well-known force-closure condition that the origin of the wrench space lies in the interior of the convex hull of primitive wrenches, Liu presented a ray-shooting approach to force-closure test. Because of its high efficiency in 3D work space and no limitation on the contact number of a grasp, this approach is advanced. Achieving some new results of convex analysis, this paper enhances the above approach in three aspects. (a) The exactness is completed. In order to avoid trouble or mistakes, the dimension of the convex hull of primitive wrenches is taken into account, which is always ignored until now. (b) The efficiency is increased. A shortcut which skips some steps of the original force-closure test is found. (c) The scope is extended. Our simplified ray-shooting approach yields a grasp stability index suitable for grasp planning. Numerical examples in fixturing and grasping show the enhancement superiority.