A qualitative test for N-finger force-closure grasps on planar objects with applications to manipulation and finger gaits

This paper presents a force-closure test function for an n-finger grasp on a planar object with friction. All n-finger grasps can be represented by an n-dimensional contact space. The critical conditions of the test function are used to define force-closure curves which are the boundaries of force-closure sets in the contact configuration space. We show that the force closure sets can be decomposed into subsets in which m (m < n) fingers satisfy force closure. We also prove that m = 6 is an upper bound on the order of the force closure subsets. These subsets are required for planning finger gait maneuvers which are force-closure in all phases of the gait. The characteristics of these subsets are discussed, and an algorithm to enumerate them is given. The application of the test function and the contact configuration space formulation to multifinger object manipulation and finger gait planning is demonstrated by an example.