Computing the immobilizing three-finger grasps of planar objects

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