Humanoid Walking Stabilization via Model Predictive Control with Step Adjustment Based on the 3D Divergent Component of Motion

In this paper, as an approach to stabilize humanoid walking where the height of CoM varies, a Novel Model Predictive Control framework based on three dimensional Divergent Component of Motion (3D-DCM) is proposed. To ensure the feasible utilization of contact forces for maintaining humanoid balance, constraints on the control inputs, Virtual Repellent Point (VRP) and footstep adjustment, and their correlation are analytically formulated into a quadratic form, resulting a Quadratically Constrained Quadratic Programming. Additionally, to enable the humanoid robot to withstand disturbances over a broader range of strides or safely navigates various terrains without encountering knee stretch, the distance between the CoM and the foot is constrained in the 3D-CoM trajectory planner. The effectiveness of the proposed method is validated through simulations and real-robot experiments in scenarios involving external disturbances and step down.