Liquid-Augmented MPC in Quadrupedal Robot for Disturbance Learning

This paper presents a Liquid-Augmented Model Predictive Control (LA-MPC) framework for robust and adaptive motion control of quadrupedal robots operating under dynamic disturbances. The proposed approach integrates liquid neural dynamics into the predictive control loop, endowing the controller with real-time disturbance learning and model adaptation capabilities. System dynamics are formulated by linearizing single-rigid-body motion in three-dimensional space, while the liquid module continuously refines latent representations of unmodeled perturbations through its internal memory dynamics. The resulting hybrid predictive controller captures both short-term physical consistency and long-term disturbance evolution. By embedding the learned disturbance model within the MPC cost and constraint structure, the control law is reformulated as a quadratic program that can be solved efficiently in real time. Simulation on a quadrupedal platform demonstrates that the proposed LA-MPC achieves superior disturbance rejection, gait stability, and trajectory tracking accuracy compared to several popular learning baselines. The framework was further tested on the MuJoCo simulation platform, confirming its feasibility and practicality for agile quadrupedal locomotion in uncertain environments.