Parallel Compliance Design for Increasing Robustness and Efficiency in Legged Locomotion–Theoretical Background and Applications

Bipedal locomotion in uncertain environments is a challenging control problem. In order to reduce the effect of imprecise and noisy measurements, performance enhancement, and energy consumption reduction, many researchers employ compliant elements in the robot structure, parallel to the control system. However, there is no systematic methodology for concurrent design of compliant components and the controller. In a primary article, we introduced a method for the simultaneous design of the controller and compliant elements to increase the walking robustness against uncertainties, based on hybrid zero dynamics (HZD) analysis. The overall controller comprising the HZD controller and parallel compliance (PC) is called the HPC controller. In this article, we present two levels of extension:1) extended HPC (EHPC):an extended HPC with fewer constraining assumptions; 2) concurrent control and parallel compliance design (CPC):a generalized version of concurrent control and PC design, which is applicable for any gait control approach, and is not limited to HZD. In this article, apply the Lyapunov, boundedness, and input to state stability concepts to analyze the EHPC's walking robustness. Detailed step-by-step design of this controller for a compass gait model and the MATLAB codes are also provided. An experimental study on a hopper robot supports the generalization in the CPC method to apply to other controllers while pneumatic artificial muscles are utilized as tunable PCs.