Computing the best grasp in a discrete point set with wrench-oriented grasp quality measures

Abstract

This paper presents a novel solution to the problem of computing the best grasp in a discrete point set where the performance quality of a grasp is measured by its capability to apply wrenches to the grasped object. First, it is revealed that various wrench-oriented grasp quality measures, considering different physical properties of a grasp, can be written in a unified form as the maximum scale factor of a gauge set in a grasp wrench set. Also, it has been deduced that the maximum scale factor is equal to the minimum value of the support function of the grasp wrench set over all directions and can be computed by evaluating the support function in a sequence of directions. On this basis, we can quickly determine that a new grasp is worse than the current best grasp if the support function of its grasp wrench set in any direction in the sequence or any particular direction is less than the quality value of the current best grasp. In this way, there is no need to calculate the exact quality value of the new grasp. 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 quick grasp comparison and the adaptive grasp enumeration, 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. Moreover, the wrench-oriented grasp quality measures and the proposed algorithm are extended to the real scenario involving robot hands to predict and compute the best grasps on objects in reachable contact point sets of fingertips by given hand poses.