Computing n-finger force-closure grasps on polygonal objects

This paper presents an efficient algorithm for computing all n-finger force-closure grasps on a polygonal object. This algorithm is based on a new qualitative test algorithm for force-closure grasps which recursively transforms the problem in the three dimensional wrench space to a problem in an one dimensional space. We demonstrate that non-force-closure grasps are two convex polytopes in the space of n parameters that represent grasp points on sides of the polygon. Therefore, the force-closure grasp region is calculated by subtracting the convex polytopes from the parameter space. The qualitative test algorithm takes O(n(3)) time and the grasp computation algorithm takes O(n(3) log n) time for n less than or equal to 3 and O(n(3n/2)) time for n > 3, where n is the number of the fingers. The efficiency of the algorithms is confirmed with simulations.