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 nonforce-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(n³) time and the grasp computation algorithm takes O(n³ log n) time for n⩽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