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.

本文关注的是为配备旋转运动机制的系统提出一种并行顺应性适应方法，以在合理的任务频率变化范围内获得循环任务的能量效率。在这项工作中，我们首先介绍了一种用于在单向关节上实施的可变平行弹性执行器 (VPEA) 设计，该设计可以根据旋转机构频率变化引起的扭矩要求做出响应。然后，在下一步中，我们提出了两种设计方法，即“通用方法”和“基于频率的方法””对于 VPEA 以及离线和在线方式的刚度调整方法。所提出的旋转 VPEA 的自适应方法的最优性和收敛性也被分析证明通常在 Lyapunov 意义上是全局指数稳定的。最后，为了证明我们的 VPEA 的适用性和效率，我们将其部署在机器人腿模型中作为案例研究。仿真结果证明了我们的适应规则的稳定性和收敛性，并突出了所提出的 VPEA 在广泛的任务频率变化范围内提高能源效率的性能。