Fixed-time disturbance observer-based centroidal model predictive control with phase switching for robust humanoid locomotion

Achieving robust locomotion for humanoid robots under strong external forces and complex terrain disturbances is a significant challenge. Existing methods generally lack the ability to estimate external disturbances, often relying on noticeable state errors caused by the disturbances to make adjustments. This leads to insufficient disturbance rejection, especially under strong disturbances. To address this issue, this paper proposes a centroidal model predictive control (CMPC) framework integrated with fixed-time disturbance observer (FTDO). The novel FTDO is designed to estimate unknown disturbance forces and torques, using Lyapunov theory to ensure that the estimation errors converge within a fixed time, regardless of initial conditions. The estimated disturbances are explicitly incorporated into the CMPC prediction model, enabling the comprehensive suppression of unknown disturbances through multi-step contact-wrench optimization. Furthermore, a slope estimation method guided by the orientation of the preceding support foot is proposed. By fusing slope estimation, swing time, touchdown events, and hip-ankle coordinated motion adjustments, a robust support-swing phase switching strategy is constructed. This strategy effectively mitigates frequent premature or delayed foot contact, particularly on long-distance uneven terrains such as slopes. Extensive simulations and experiments on the torque-controlled humanoid robot BHR-8FC demonstrate that the proposed method can adapt to various uneven terrains and exhibits strong resistance to external disturbances.