Friction uncertainty and contact position uncertainty may have a disastrous effect on the closure properties of grasps. This paper reflects our approach to handling these uncertainties in force-closure analysis. The former uncertainty is measured by the possible reduction rate κ of friction coefficients, while the radius ρ of contact regions is used to quantify the latter uncertainty. The actual contact point may deviate from the desired position but not farther than ρ • ρ S , the supremum of ρ without loss of force-closure, indicates the grasp tolerance to contact position uncertainty. For investigating the above uncertainties systematically, we propose three new problems in force-closure: whether a grasp with given κ and ρ achieves forceclosure, what value ρ S equals if κ is given, and how ρ S varies versus κ. To facilitate their solutions, we extend the scope of the infinitesimal motion approach from form-closure analysis to force-closure. A necessary and sufficient condition for force-closure is deduced by means of the duality between some convex cones, which play the key role in solving the problems. Finally, efficient algorithms are developed and applied to two illustrative examples.

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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.

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