Computing the best grasp in a discrete point set

Abstract

This paper solves the problem of computing the best grasp in a discrete point set based on a popular grasp quality measure, namely the largest origin-centered ball contained in the grasp wrench set. So far, the solution to this problem is very limited. Noticing that the quality measure for a grasp is equal to the minimum value of the support function of its grasp wrench set over all directions and its computation together with force closure test can be fulfilled by evaluating the support function in a sequence of directions, we can quickly determine that a new grasp is worse whenever its support function in the sequence of directions or any other specific direction is less than the quality value of the current best grasp and avoid further computation. Furthermore, we enumerate candidate grasps in the point set in an adaptive way such that grasps that are more likely to outperform the current best grasp will be checked first, which helps find the best grasp earlier and significantly reduce the number of candidate grasps to be fully examined. With the aid of the adaptive enumeration and the quick comparison of grasps, the proposed algorithm takes tens of seconds to several hours on a normal PC to compute the best grasp in tens to hundreds of points on 3-D objects and it is two to several orders of magnitude faster than the brute-force search.