Constructing 3D frictional form-closure grasps of polyhedral objects

Assuming that grasp points of n-1 fingers on a polyhedral object are given and the n-1 fingers do not achieve a form-closure grasp, this paper proposes an efficient algorithm for computing all grasp points on the object for the n-th finger to achieve a form-closure grasp with other n-1 fingers. A sufficient and necessary condition is developed for forming the form-closure grasp. Based on the sufficient and necessary condition, we transform the grasp computation to a problem of: 1) computing the convex cone of the primitive contact wrenches of the n-1 fingers; and 2) checking the intersection between a circular region and a convex polygon in a 2D space. We have implemented the algorithm and confirmed its usefulness by an example