On the grasping stability and optimality under external perturbations

Abstract

There are two types of grasping analysis in robotics research: find the grasping force distributions among the grasping fingers when given the contact points and find a good set of the contact points when given the shape of the object. Each kind of problem is associated with optimality and stability analysis. In this article, we investigate the grasping stability and optimality issues under the influence of external perturbations. A rotation-displacement geometry model is used in computing the changes of grasping forces under external perturbations. Using these results, we present the concept of perturbation closure, which plays the central role in our analysis. A method for finding the local minimal perturbation resisting forces required for non-slip contacts is developed based on this concept. A grasp so determined is guaranteed to be stable if the external perturbations do not exceed the threshold. Based on this property, we develop a quantitative measurement that can be used to evaluate the performance of different grasping configurations. One can use this measurement to determine the best grasping configuration from a set of perturbation resisting grasps. This actually gives a method which enables the optimal grasping configuration to be found. Both two-dimensional and three-dimensional cases are discussed in detail for determining the perturbation closure, the local minimal perturbation resisting force, and the perturbation resisting grasp. Examples are given at the end of the article to illustrate our idea. ©1999 John Wiley & Sons, Inc.