A Combined Impedance and Optimization-Based Nonlinear MPC Approach for Stable Humanoid Locomotion

Achieving dynamic stability in bipedal locomotion against sustained external disturbances remains a significant challenge in humanoid robotics. Traditional methods, such as zero moment point (ZMP) preview control, often lack the reactive compliance and predictive planning necessary for robust performance on uneven terrain or under continuous force. This paper proposes a novel control framework that synergistically integrates a resistance torso compliance controller with a nonlinear model predictive control (NMPC)-based walking pattern generator. The compliance controller actively modulates the torso’s dynamics via impedance control, creating a virtual mass–spring–damper system that absorbs impacts and generates counterforces to resist sustained pushes. Concurrently, the NMPC module reformulates gait generation as a real-time optimization problem, simultaneously determining optimal footstep positions and orientations while respecting nonlinear constraints derived from centroidal momentum dynamics. Simulation results demonstrate that this integrated approach reduces the maximum ZMP error by 34.1% and the RMS ZMP error by 37.3% compared to traditional ZMP preview control, with a 38.9% improvement in settling time after a disturbance. This work establishes that the tight coupling of reactive impedance control and predictive optimization provides a foundational framework for enhancing the robustness and adaptability of bipedal locomotion.