  The robust balancing capability of humanoid robots has been considered one of
the crucial requirements for their mobility in real environments. In
particular, many studies have been devoted to the efficient implementation of
human-inspired ankle, hip, and stepping strategies, to endow humanoids with
human-level balancing capability. In this paper, a robust balance control
framework for humanoids is proposed. Firstly, a 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.
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 simulations and real
robot experiments. Furthermore, a superior balancing performance is
demonstrated 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/7Y4CykTpgrw
