Robust Model Predictive Control for Quadruped Locomotion Under Model Uncertainties and External Disturbances

Abstract

Model Predictive Control (MPC) enables agile and robust locomotion in quadruped robots but is sensitive to model uncertainties and environmental variations. This paper presents a Tube-Based Robust MPC (TR-MPC) framework for quadruped locomotion under uncertainties, modeled as parameter mismatches and additive disturbances. TR-MPC constructs an Invariant Ellipsoid to bound errors induced by uncertainties, ensuring convergent error trajectories. A Semi-Definite Programming (SDP) problem with Linear Matrix Inequality (LMI) constraints is solved offline to minimize the ellipsoid size, while a linear feedback term stabilizes error dynamics, guaranteeing stability within uncertainty bounds. Simulations and experiments demonstrate TR-MPC’s robustness: the robot achieves stable trotting under a 14 kg load (123% of its weight) and recovers from a 1.4 m/s impact while carrying 10 kg (88% of its weight). This framework significantly enhances robustness in dynamic and uncertain environments.