An efficient algorithm for computing a 3D form-closure grasp

This paper presents a simple and efficient algorithm to calculate the fingertip positions which ensure a form-closure grasp. The algorithm first arbitrarily chooses a grasp on the given faces of the object. If the selected grasp is not form-closure, the origin O of the wrench space lies outside of the convex hull of the primitive contact wrenches. In this case, the algorithm properly moves the fingertip positions at a fixed step on the faces so that the primitive contact wrenches move towards the origin O until the origin is eventually contained by the convex hull after iterations of the operation. The form-closure property is checked by our ray-shooting based qualitative test algorithm. The motion of the fingertip positions at every step is determined by a quadratic programming problem. Finally we have implemented the proposed algorithm and verified its efficiency with three numerical examples