Parametric optimization of stored energy in robots with regenerative drive systems

The paper formulates and solves the problem of finding a set of physical (design) parameters that maximize stored energy in electromechanical robots with regenerative drive systems. The robot is assumed to include semi-active and fully-active joints. Semi-active joints exchange power only with the robot, and are assumed to use (ultra)capacitors for storage. Fully-active joints are conventional in the sense that external power is used for actuation. The semi-active joints are controlled for trajectory tracking by a previously-published virtual control strategy whereby a control law is first designed and then implemented via a virtual matching law. A set of reference trajectories and a virtual controller capable of achieving asymptotic tracking are assumed as given. Equations are derived for the energy stored in the ultracapacitors of the semi-active joints in terms of manipulator parameters. The paper obtains closed-form solutions for the maximizing parameters. It is shown that a unique solution always exists and that it corresponds to a unique global maximum for the stored energy between any two times. A numerical example with a double inverted pendulum and cart system with semi-active and fully-active joints demonstrates the results.