Coping with the Grasping Uncertainties in Force-closure Analysis

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 force-closure, 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.