Easy and fast evaluation of grasp stability by using ellipsoidal approximation of friction cone

This paper presents an easy and fast method of testing force closure when a multi-fingered hand grasps an object. Different from previous methods, we consider approximating the friction cone by using a few ellipsoids. By using this method, the total force/moment set applied to the grasped object can be obtained by a common set of multiple ellipsoids. This method is effective since we can test the force closure by simply calculating the inequalities of quadratic form. Moreover, by using the ellipsoidal approximation, we propose an easy method of evaluating the grasp stability. We show that the grasp stability can be calculated by using simple equations. The effectiveness of the proposed method is verified by several numerical examples where we show that the proposed method is fairly accurate and can evaluate the grasp stability faster than conventional methods.