Spatio-temporal stiffness optimization with switching dynamics

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 havemultiple phases ofmovement, contacts and impactswith 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 Electronic supplementary material The online version of this article (doi:10.1007/s10514-015-9537-x) contains supplementary material, which is available to authorized users. An earlier version of this paper was presented in part at the Robotics: Science and Systems Conference, 2012 and the IEEE/RSJ International Conference on Intelligent Robots and Systems, 2013. B Sethu Vijayakumar [email protected] Jun Nakanishi [email protected] Andreea Radulescu [email protected] David J. Braun [email protected] 1 School of Informatics, University of Edinburgh, Edinburgh, UK 2 Present Address: Institute for Cognitive Systems, Technical University of Munich, Munich, Germany 3 Present Address: Engineering Product Development, Singapore University of Technology and Design, Singapore, Singapore 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.