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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.
Zhu et al. (Tue,) studied this question.