A Numerical Test for the Closure Properties of 3-D Grasps

This paper presents a numerical test for the closure properties (force closure and form closure) of multifingered grasps. For three-dimensional (3-D) grasps with frictional point contacts or soft contacts, the numerical test is formulated as a convex constrained optimization problem without linearization of the friction cone. For 3-D frictionless grasps, it can be calculated by solving a single linear program. The proposed numerical test (along with the rank of the grasp matrix) provides an efficient tool for the analysis of the force-closure property and the relative force-closure property.