Periodic motion generation with a time-varying offset for fully actuated torque-driven mechanical systems using energy regulation

This paper presents a novel approach to generate desired periodic motions for torque-driven fully actuated mechanical systems. The proposed scheme is based on a recent control design method which relies on energy shaping plus damping injection. The energy regulation is formulated as a control objective and then the controller is designed. A change of coordinates and a suitable nonlinear damping injection design play a key role in generating the desired periodic motion. An interesting characteristic of the proposed scheme is that the periodic motion with a time-varying offset (trend component) can be specified by the user. This can be useful for mechanical systems that demand non-static periodic motion, for tasks such as obstacle avoidance or fluid mixing. Through the proposed methodology, the closed-loop system is expressed as a nonlinear autonomous differential equation and its stability is analyzed by using LaSalle’s Theorem and the Poincaré-Bendixson criterion. Numerical simulations on a two-degree-of-freedom manipulator arm illustrate the performance of the proposed scheme.