Minimum Control Energy in Multibody Systems Using Gravity and Springs

Abstract

In this study, we examined the problem of minimizing the energy consumption of multibody systems using passive elastic elements for energy storage. In a previous paper(1), we only considered the motion in the horizontal plane. In this paper, we allowed spatial motion under gravity. Firstly, based on the linearized equations of motion, we analyzed the relationship between the consumed energy and the operating time using optimal control theory. Then, we derived a condition for the operating time to be optimal, and proposed an optimal design method for springs. Finally, we demonstrated the effectiveness of our design method by applying it to robot manipulator arms.