Real-time contact force distribution using a polytope hierarchy in the grasp wrench set

Abstract

Abstract This paper presents an efficient approach to contact force distribution, which is aimed at computing optimal contact forces to generate the required wrench for grasping an object. It has been derived in the previous work that this problem can be reduced to computing the intersection of the ray originating from the origin along the required wrench with the boundary of the grasp wrench set. Noticing that the grasp wrench set is fixed once contact positions are determined, we propose an algorithm to pre-compute a hierarchy of polytopes in the grasp wrench set and a list of facets from the interior of the grasp wrench set to its boundary. Then, the ray’s intersection can be quickly found by searching the list of facets and optimal contact forces can be computed in real time. Numerical examples show that the online computation of the proposed approach is one order of magnitude faster than the latest algorithm to compute the ray’s intersection and two orders of magnitude faster than general-purpose optimization algorithms. This approach to contact force distribution is an iterative solution that can run until reaching a desired accuracy.