Computation of fingertip positions for a form-closure grasp

This paper proposes a simple and efficient algorithm for computing a form-closure grasp on a 3D polyhedral object. This algorithm searches for a form-closure grasp from a "good" initial grasp in a promising search direction that pulls the convex hull of the primitive contact wrenches towards the origin of the wrench space. The "good" initial grasp is a set of contact points that minimizes the distance between the origin and the centroid of the primitive contact wrenches, and can be calculated by the quadratic programming. The local promising search direction at every step is readily determined by the ray-shooting based qualitative test algorithm developed in our early work. By using the "good" initial grasp, the iteration times of search can be significantly reduced so that a form-closure grasp can be found more efficiently. Since the algorithm adopts a local search strategy, its computational cost is less dependent on the complexity of the object surfacer. Finally, the algorithm was implemented and its efficiency ascertained by three examples.