Grasp synthesis and fixture layout design in discrete domain

This paper presents an efficient algorithm for grasp synthesis and fixture layout design in discrete domain. Given N candidate contact points on the surface of a 3D object, the algorithm determines a minimal subset from the candidate points so that they construct a grasp or a fixture with form-closure property. The proposed algorithm is implemented by solving a single linear program. It has been shown that, a minimal subset of the contact points that achieves form-closure can be directly identified from the optimal basic solution vector of the linear program, provided that the solution vector is non-degenerate. The proposed algorithm has a straightforward geometric interpretation, which has also been described in the paper. The primary advantage of the proposed algorithm is its computational simplicity, of which the overall complexity is O(N). Numerical examples have been presented to verify the effectiveness and efficiency of the algorithm, which show that the computational time cost of the algorithm is much less than the existing techniques described in the literature.