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

The contact sequence of humanoid walking consists of single and double support phases (SSP and DSP), and their coordination through proper duration and dynamic transition based on the robot's state is crucial for maintaining walking stability. Numerous studies have investigated phase duration optimization as an effective means of improving walking stability. This paper presents a phase-based Nonlinear Model Predictive Control (NMPC) framework that jointly optimizes Zero Moment Point (ZMP) modulation, step location, SSP duration (step timing), and DSP duration within a single formulation. Specifically, the proposed framework reformulates the nonlinear DCM (Divergent Component of Motion) error dynamics into a phase-consistent representation and incorporates them as dynamic constraints within the NMPC. The proposed framework also guarantees ZMP input continuity during contact-phase transitions and disables footstep updates during the DSP, thereby enabling dynamically reliable balancing control regardless of whether the robot is in SSP or DSP. The effectiveness of the proposed method is validated through extensive simulation and hardware experiments, demonstrating improved balance performance under external disturbances.