ON THE STABILITY AND INSTANTANEOUS VELOCITY OF GRASPED FRICTIONLESS OBJECTS

Grasp and manipulation planning of slippery objects often relies on the "form closure" grasp, which is stable regardless of the external force applied to the object. Despite its importance, an efficient quantitative test for form closure valid for any number of contact points has not been available. The primary contribution of this paper is the introduction of such a test formulated as a linear program, the optimal objective value of which provides a measure of how far a grasp is from losing form closure. When the grasp does not have form closure, manipulation planning requires a means to predict the object's stability and instantaneous velocity, given the joint velocities of the hand. The "classical" approach to computing these quantities is to solve the systems of kinematic inequalities corresponding to all possible combinations of separating or sliding at the contacts. All combinations resulting in the interpenetration of bodies or the infeasibility of the equilibrium equations are rejected. The remaining combination (sometimes there am more than one) is consistent with all the constraints and is used to compute the velocity of the manipulated object and the contact forces, which indicate whether or not the object is stable. Our secondary contribution is the formulation of a linear program whose solution yields the same information as the classical approach. The benefit of this formulation is that explicit testing of all possible combinations of contact interactions is usually avoided by the algorithm used to solve the linear program.