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

Haoru Xue, Chaoyi Pan, Zeji Yi, Guannan Qu, Guanya Shi

Keywords: Model Predictive Control, Sampling-based Optimization, Optimal Control, Reinforcement Learning, Whole-Body Control, Legged Locomotion

TL;DR: DIAL-MPC is the first training-free method achieving real-time whole-body torque control using full-order dynamics.

Abstract:

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 or local approximations. 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 a 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.

Submission Number: 20