Bipedal Robust Walking on Uneven Footholds: Piecewise Slope LIPM with Discrete Model Predictive Control

This study presents an enhanced theoretical formulation for bipedal hierarchical control frameworks under uneven terrain conditions. Specifically, owing to the inherent limitations of the Linear Inverted Pendulum Model (LIPM) in handling terrain elevation variations, we develop a Piecewise Slope LIPM (PS-LIPM). This innovative model enables dynamic adjustment of the Center of Mass (CoM) height to align with topographical undulations during single-step cycles. Another contribution is proposed a generalized Angular Momentum-based LIPM (G-ALIP) for CoM velocity compensation using Centroidal Angular Momentum (CAM) regulation. Building upon these advancements, we derive the DCM step-to-step dynamics for Model Predictive Control MPC formulation, enabling simultaneous optimization of step position and step duration. A hierarchical control framework integrating MPC with a Whole-Body Controller (WBC) is implemented for bipedal locomotion across uneven stepping stones. The results validate the efficacy of the proposed hierarchical control framework and the theoretical formulation.