Gravity-Compensated Model Predictive Control and Whole-Body Optimization for Humanoid Locomotion

Abstract Achieving stable and coordinated locomotion in high-dimensional humanoid robots remains challenging, particularly considering variations in support phases, model uncertainties, and redundancy arising from multi-degrees-of-freedom joints. To address these issues, a predictive control framework that integrates gravity-compensated model predictive control (GC-MPC) with hierarchical whole-body control (WBC) was proposed, targeting force prediction issues under varying contact conditions. The introduction of distributed reference plantar forces derived from rigid-body dynamics into the MPC formulation enabled more stable and physically consistent force tracking (by a controller) across support transitions. The developed hierarchical WBC was efficiently integrated with GC-MPC, featuring flat-foot constraints for enhanced contact stability and task allocation to resolve kinematic redundancy. This enables a real-time joint-level control under physical and task constraints, effectively mitigating the gap between the predicted and the actual system behavior, improving robustness in high-dimensional humanoid systems. The proposed approach was validated on AzureLoong, a full-size humanoid robot (1.85 m, 75.5 kg) via simulation and physical experiments. The obtained results demonstrated a stable walking performance, balance control, accurate torso tracking, and smooth transitions under diverse motion commands, achieving a 25.57% reduction in the average decay rate of the plantar force prediction. This work reliably deploys predictive control on large-scale humanoid systems and establishes a solid foundation for subsequent integration with, e.g., navigation, manipulation, reinforcement learning-based whole body, or predictive control, particularly for the responsive locomotion control under diverse and concurrent task commands.