Impact-Aware Robust Convex Model Predictive Control for Quadruped Locomotion on Uncertain Terrain

Abstract

Deploying legged robots in complex environments requires robust traversal capabilities on unstructured terrain. However, existing locomotion controllers may exhibit degraded robustness when subjected to rapidly varying terrain-induced impact disturbances. To address this challenge, we propose an impact-aware robust convex model predictive control (IRCMPC) for quadruped locomotion by explicitly modeling terrain-induced impacts as bounded uncertainties in the single rigid body (SRB) dynamics. The proposed IRCMPC integrates robust control principles into the model predictive control to handle the impact disturbances experienced by the robot. First, we model a momentum-based bound on the maximum potential impact at each step and introduce a relaxation factor that reduces conservatism when severe impacts are unlikely to occur. We then formulate a robust min–max MPC problem and transform this problem into a standard quadratic optimization problem to ensure computational efficiency. Comparative simulation and hardware experiments on a Unitree Go2 robot demonstrate that IRCMPC improves locomotion robustness under intensified impact conditions where conventional convex model predictive control (CMPC) fails. The results further show that, in the tested scenarios, IRCMPC achieves a more favorable trade-off between traversal robustness and tracking performance than adaptive nonlinear centroidal model predictive control (ANCMPC).