Enhancing energy efficiency in bipedal locomotion: Energy regularization control and lower limbs design with resilience ankle

Energy efficiency is crucial for bipedal locomotion. However, conventional motion tracking algorithms face challenges in incorporating energy-related factors, as energy terms with coupled nonlinear characteristics are difficult to integrate into a quadratic programming problem subject to dynamics equality constraints. In this paper, we propose the Energy-Regularized control Lyapunov function algorithm. This algorithm combines a double inverted pendulum model predictive control with a control Lyapunov function quadratic programming. The proposed control Lyapunov function quadratic programming formulation incorporates instantaneous mechanical power into a dynamics inequality constraint, enabling energy-optimized motion tracking. Moreover, we introduce an energy-efficient bipedal lower-limb structure incorporating a resilient passive ankle structure. To evaluate our approach, 3D dynamic walking experiments are conducted. The results validate both the hardware and control algorithm. Experimental results demonstrate superiority on torso stability and the energy-efficient locomotion. This study offers practical value for energy-efficient bipedal locomotion.