Phase-based Nonlinear Model Predictive Control for Humanoid Walking Stabilization with Single and Double Support Time Adjustments

Balance control for humanoid robots has been extensively studied to enable robots to navigate in real-world environments. However, balance controllers that explicitly optimize the durations of both the single support phase, also known as step timing, and the Double Support Phase (DSP) have not been widely explored due to the inherent nonlinearity of the associated optimization problem. Consequently, many recent approaches either ignore the DSP or adjust its duration based on heuristics or on linearization techniques that rely on sequential coordination of balance strategies. This study proposes a novel phase-based nonlinear Model Predictive Control (MPC) framework that simultaneously optimizes Zero Moment Point~(ZMP) modulation, step location, step timing, and DSP duration to maintain balance under external disturbances. In simulation, the proposed controller was compared with two state-of-the-art frameworks that rely on heuristics or sequential coordination of balance strategies under two scenarios: forward walking on terrain emulating compliant ground and external push recovery while walking in place. Overall, the findings suggest that the proposed method offers more flexible coordination of balance strategies than the sequential approach, and consistently outperforms the heuristic approach. The robustness and effectiveness of the proposed controller were also validated through experiments with a real humanoid robot.

A Model Predictive Capture Point Control Framework for Robust Humanoid Balancing via Ankle, Hip, and Stepping Strategies

The robust balancing capability of humanoid robots against disturbances has been considered as one of the crucial requirements for their practical mobility in real-world environments. In particular, many studies have been devoted to the efficient implementation of the three balance strategies, inspired by human balance strategies involving ankle, hip, and stepping strategies, to endow humanoid robots with human-level balancing capability. In this paper, a robust balance control framework for humanoid robots is proposed. Firstly, a novel Model Predictive Control (MPC) framework is proposed for Capture Point (CP) tracking control, enabling the integration of ankle, hip, and stepping strategies within a single framework. Additionally, a variable weighting method is introduced that adjusts the weighting parameters of the Centroidal Angular Momentum (CAM) damping control over the time horizon of MPC to improve the balancing performance. Secondly, a hierarchical structure of the MPC and a stepping controller was proposed, allowing for the step time optimization. The robust balancing performance of the proposed method is validated through extensive simulations and real robot experiments. Furthermore, a superior balancing performance is demonstrated, particularly in the presence of disturbances, compared to a state-of-the-art Quadratic Programming (QP)-based CP controller that employs the ankle, hip, and stepping strategies. The supplementary video is available at https://youtu.be/CrD75UbYzdc