Adaptation in a variable parallel elastic actuator for rotary mechanisms towards energy efficiency

Abstract This paper is concerned with the presentation of a parallel compliance adaptation method for systems equipped with rotary motion mechanisms towards obtaining energy efficiency in cyclic tasks over a reasonable range of task frequency variations. In this work, we first introduce a variable parallel elastic actuator (VPEA) design for implementation on uni-directional joints that can respond in line with the torque requirements caused by frequency variations in rotary mechanisms. Then, in the next step, we propose two design approaches namely “general method” and “frequency-based method” for the VPEA along with the stiffness adjustment approaches both in offline and online manners. The optimality and convergence of the adaptation method for the proposed rotary VPEA are also analytically proved in general to be globally exponentially stable in the sense of Lyapunov. Finally, to demonstrate the applicability and efficiency of our VPEA, we deployed it in a robotic leg model as the case study. The simulation results demonstrate the stability and convergence of our adaptation rule and highlight the performance of the proposed VPEA in increasing energy efficiency over a wide range of task frequency variations.