On quality functions for grasp synthesis, fixture planning, and coordinated manipulation

Planning a proper set of contact points on a given object/workpiece so as to satisfy a certain optimality criterion is a common problem in grasp synthesis for multifingered robotic hands and in fixture planning for manufacturing automation. In this paper, we formulate the grasp planning problem as optimization problems with respect to three grasp quality functions. The physical significance and properties of each quality function are explained, and computation of the corresponding gradient flows is provided. One noticeable property of some of these quality functions is that the optimal solutions are also force-closure grasps if they do exist for the given object. Furthermore, when specialized to two-fingered or three-fingered grasps on a spherical object, the optimal solutions become the familiar antipodal grasp, or the symmetric grasp, respectively. Thus, by following the gradient flows with arbitrary initial conditions, the optimal grasp synthesis problem is solved for objects with smooth geometries manipulated by hands with any number of fingers. Also, note that our solutions do not involve linearization of the friction cones. We discuss two simplified versions of these problems when real-time solutions are needed, e.g., coordinated manipulation of a robotic hand with contact points servoing. We give simulation and experimental results illustrating validity of the proposed approach for optimal grasp planning.