Spatio-temporal stiffness optimization with switching dynamics

Abstract

We address the optimal control problem of robotic systems with variable stiffness actuation (VSA) including switching dynamics and discontinuous state transitions. Our focus in this paper is to consider dynamic tasks that have multiple phases of movement, contacts and impacts with the environment with a requirement of exploiting passive dynamics of the system. By modelling such tasks as a hybrid dynamical system with time-based switching, we develop a systematic methodology to simultaneously optimize control commands, time-varying stiffness profiles and temporal aspect of the movement such as switching instances and total movement duration to exploit the benefits of VSA. Numerical evaluations on a brachiating robot driven with VSA and a hopping robot equipped with variable stiffness springs demonstrate the effectiveness of the proposed approach. Furthermore, hardware experiments on a two-link brachiating robot with VSA highlight the applicability of the proposed framework in a challenging task of brachiation.