On the grasping stability and optimality under external perturbations

In this paper, we investigate the grasping stability and optimality issues under the influence of external perturbations. We develop a quantitative measurement that could be used to evaluate the performance of different grasping configurations on a given object. This actually gives a solution to the grasping analysis problem for find the points of contact when given the shape of the object. A rotation-displacement geometry model is used in computing the change of equilibrium grasping forces under perturbation. Using this result, we present the concept of force mapping closure that plays the central role in our analysis. A method for finding the minimum finger grasping 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