Positive Span of Force and Torque Components of Four-Fingered Three-Dimensional Force-Closure Grasps

We consider a 3D grasping problem. We propose a test of Ropf³-positive span of force cones and a test of Ropf³-positive span of their torque set. Our methods consider directly the quadratic force cone without pyramidal linearization of a cone. The conditions can be computed in a constant time and they are used as a heuristic for 3D force closure test. We also show that our proposed heuristic greatly improve the performance of existing grasp testing algorithms.