Foot Placement Compensator Design for Humanoid Walking Based on Discrete Control Lyapunov Function

In this paper, an online foot position compensator (FPC) is proposed for improving the robustness of humanoid walking based on orbital energy conservation and discrete control Lyapunov function (DCLF), with which the asymptotic stability of the humanoid system can be maintained and, thus, the foot placement control is achieved. The online FPC is developed based on linear model predictive control (MPC) by replanning the trajectories of the center of mass (CoM) and properly placing the footsteps to resist external disturbances and recover the walking posture. To further improve the robustness of the humanoid robots to suppress strong external disturbance, a strategy of upper body posture control is proposed. The presented controller stabilizes the humanoid robot by utilizing hip joints to modulate the upper body posture online. Webots simulations and real experiments on a full-body NAO humanoid robot verify the effectiveness of the proposed methods.