Abstract: A nonlinear programming algorithm suitable for both qualitative and quantitative analyses of force-closure in multi-fingered robotic grasping is proposed. Based on the force equilibrium equations, the relationship between the external wrench space and the manipulation force space at any contact is investigated. Constrained force set, strictly constrained force set and normal force set are proposes and their relationships are detailed. In the basis of the convexity of frictional constraints, the necessary and sufficient conditions for force-closure and partially force-closure are derived. Accordingly, an algorithm for testing the closure properties is presented. A quantitative index, which is applicable to evaluating the grasp contact stability, is also put forward. Some examples are given to illustrate the efficiency of the proposed algorithm.

Key words: Force-closure, Form-closure, Nonlinear, programming