Optimization of robot gripping forces and worst case loading

We consider the optimization of the vector of gripping forces that support a known generalized force acting on the gripped object—a rigid body or a mechanism. Working in the framework of finite dimensional normed vector spaces and their dual spaces, the cost function to be minimized is assumed to be a norm on the space of gripping forces. We present an expression for the optimum which depends on the external force and the kinematics of the gripping system. Next, assuming that optimal gripping forces are applied using force control, and assuming that there is a bound on the norm of the admissible gripping forces, we characterize the largest norm of an external force that the gripping system may support, that is, the norm of the worst case loading that may be applied and still be supported. A few simple examples are given for the sake of illustration.