Full-Order Sampling-Based MPC for Torque-Level Locomotion Control via Diffusion-Style Annealing

Due to high dimensionality and non-convexity, real-time optimal control using full-order dynamics models for legged robots is challenging. Therefore, Nonlinear Model Predictive Control (NMPC) approaches are often limited to reduced-order models. Sampling-based MPC has shown potential in nonconvex even discontinuous problems, but often yields suboptimal solutions with high variance, which limits its applications in high-dimensional locomotion. This work introduces DIAL-MPC (Diffusion-Inspired Annealing for Legged MPC), a sampling-based MPC framework with a novel diffusion-style annealing process. Such an annealing process is supported by the theoretical landscape analysis of Model Predictive Path Integral Control (MPPI) and the connection between MPPI and single-step diffusion. Algorithmically, DIAL-MPC iteratively refines solutions online and achieves both global coverage and local convergence. In quadrupedal torque-level control tasks, DIAL-MPC reduces the tracking error of standard MPPI by $13.4$ times and outperforms reinforcement learning (RL) policies by $50\%$ in challenging climbing tasks without any training. In particular, DIAL-MPC enables precise real-world quadrupedal jumping with payload. To the best of our knowledge, DIAL-MPC is the first training-free method that optimizes over full-order quadruped dynamics in real-time.