The Immobilizing Three - Fingergrasps of Planar

This paper addresses the problem of computing frictionless three-nger immobilizing grasps of two-dimensional objects whose boundaries are described by polynomial splines. Using the mobility theory of Rimon and Burdick, we rst develop a set of equations that describe the immobilization constraints. We then present a grasp planning algorithm which uses exact cell decomposition and ho-motopy continuation techniques to construct an explicit description of the immo-bilization regions (including sample points) in the contact connguration space. The problem of nding optimal immobilizing grasps reduces to hill climbing in each of these regions. We have implemented the proposed approach and present some preliminary results.