Minimizing Object Strain Energy for Coordination of Multiple Robotic Mechanisms

This paper discusses the force distribution problem in coordination of multiple robotic mechanisms. To define the more physically motivated criterion in choosing internal forces, the relationship between the elastic strain energy stored in the object and the forces and moments applied by robotic mechanisms is discussed. Based on the several assumptions, it is shown that the elastic strain energy of object is represented as a quadratic form of the forces and moments. We propose to minimize the object strain energy in choosing the internal forces and moments. The minimal strain energy criterion is identical to the minimal force criterion when all the spring constants of object are uniform at all the contact points and all the directions of each contact point. The algorithms for the minimal strain energy criterion are proposed for both of the case where each robotic manipulator grasps the object rigidly and the case where robotic fingers grasp the object with frictional point contacts.