Optimal control for maximizing potential energy in a variable stiffness joint

Robot arms with intrinsically elastic joints became very popular over the last years. Considerable effort has been put into designing complex systems that are equipped with variable joint elasticity between motor and link. However, in contrast to the field of passively elastic locomotion, the control of elastic manipulators, where the elasticity is not considered to be a parasitic effect, is still a very young field. Recently, the optimal exploitation of the inherent arm dynamics has been identified as an interesting new problem in robot motion control. In particular, the use of the joint elasticity as a temporary energy storage mechanism e.g. for executing 'explosive' motions as throwing is a promising new aspect. In this paper, we investigate the basic problem of how to optimally store potential energy into a variable stiffness joint, which is strongly related to the maximization of its kinetic energy. We provide an analytic solution for the problem and give a physical interpretation of the optimal strategy in terms of the system's kinetic and potential energy.