Stable Locomotion of Biped Robot With Gaits of Sinusoidal Harmonics

This article introduces a method incorporating the gait and feedback controller design for a four-link biped robot. Inspired by the human gait and previous biped work, we propose a class of periodic gaits composed from the sum of sinusoidal harmonics up to the second order. This class of gaits, parameterized by design parameters, satisfies the impact model of the biped dynamics and enables us to design the step length and average walking velocity explicitly. The satisfaction of the impact model introduces constraints on design parameters, which together with the explicit parameterization significantly reduces the number of the design variables. Compared to the hybrid zero dynamics (HZD) method, the process of the gait design requires fewer parameters and shorter computation time, and thus, it can be conducted in real-time systems. The state-feedback controller is then proposed to ensure that the periodic gait is the limit cycle of the closed-loop system and its stability is theoretically guaranteed based on the Poincaré section method. Due to the explicit parameterization, the controller can be easily extended to achieve walking on different slopes with the same step length and average walking velocity. Finally, the theoretical result is verified by simulations for biped walking on different slopes with various gaits and controller parameters. The controller is found to be robust to external disturbance and model uncertainty.