LNO-Driven Deep RL-MPC: Hierarchical Adaptive Control Architecture for Dynamic Legged Locomotion

Agile quadruped robots are ideal for performing heavy-load transportation tasks in industrial settings; however, the uncertainty of external disturbances and distribution shifts pose significant challenges to system stability. We propose a complex dynamics modeling method based on the liquid neural operator (LNO), which achieves over 92% accuracy in dynamics prediction across various unknown environments. The high-fidelity dynamics model generated by LNO is controlled by a novel deep model predictive control (DMPC) method, which–to our knowledge–represents the first successful application of Koopman operator theory to real-world dynamic control of legged robots. The DMPC is equivalent to a constrained convex quadratic programming problem through state variable reconstruction. Moreover, we design a deep reinforcement learning-MPC (RL-MPC) hierarchical control architecture based on LNO, where embedding the LNO into RL policy exploration establishes a new paradigm for bridging the sim-to-real gap through operator-theoretic feature learning, enabling the robot to demonstrate high adaptability under changes in load or environment. The proposed method improves the load-to-weight ratio of the Unitree A1 robot to 1.25, and it is capable of withstanding multiple impacts with a 15 kg load. Experimental results demonstrate that the comprehensive load-bearing capacity of the A1 remarkably surpasses the State-of-the-Art achievements.