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

arXiv: https://arxiv.org/abs/2409.15610 · HTML: https://mlsanity.com/paper/2409.15610/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Sep 2024.

## Built on by (most cited first, 25 of 25)

- [SPIDER: Scalable Physics-Informed Dexterous Retargeting](https://mlsanity.com/paper/2511.09484/) (2025)
- [Learning Getting-Up Policies for Real-World Humanoid Robots](https://mlsanity.com/paper/2502.12152/) (2025)
- [The Duality of Generative AI and Reinforcement Learning in Robotics: A Review](https://mlsanity.com/paper/2410.16411/) (2024)
- [Ego-Vision World Model for Humanoid Contact Planning](https://mlsanity.com/paper/2510.11682/) (2025)
- [Equality Constrained Diffusion for Direct Trajectory Optimization](https://mlsanity.com/paper/2410.01939/) (2024)
- [Generative Predictive Control: Flow Matching Policies for Dynamic and Difficult-to-Demonstrate Tasks](https://mlsanity.com/paper/2502.13406/) (2025)
- [Chasing Stability: Humanoid Running via Control Lyapunov Function Guided Reinforcement Learning](https://mlsanity.com/paper/2509.19573/) (2025)
- [Unifying Model Predictive Path Integral Control, Reinforcement Learning, and Diffusion Models for Optimal Control and Planning](https://mlsanity.com/paper/2502.20476/) (2025)
- [Generative Models From and For Sampling-Based MPC: A Bootstrapped Approach For Adaptive Contact-Rich Manipulation](https://mlsanity.com/paper/2510.14643/) (2025)
- [Diffusion-Based Forecasting for Uncertainty-Aware Model Predictive Control](https://mlsanity.com/paper/2503.15095/) (2025)
- [Model Predictive Adversarial Imitation Learning for Planning from Observation](https://mlsanity.com/paper/2507.21533/) (2025)
- [Warm-Starting Collision-Free Model Predictive Control With Object-Centric Diffusion](https://mlsanity.com/paper/2601.02873/) (2026)
- [Offline Discovery of Interpretable Skills from Multi-Task Trajectories](https://mlsanity.com/paper/2602.01018/) (2026)
- [Model Tensor Planning](https://mlsanity.com/paper/2505.01059/) (2025)
- [PegasusFlow: Parallel Rolling-Denoising Score Sampling for Robot Diffusion Planner Flow Matching](https://mlsanity.com/paper/2509.08435/) (2025)
- [GeCCo -- a Generalist Contact-Conditioned Policy for Loco-Manipulation Skills on Legged Robots](https://mlsanity.com/paper/2509.17582/) (2025)
- [PAD-TRO: Projection-Augmented Diffusion for Direct Trajectory Optimization](https://mlsanity.com/paper/2510.04436/) (2025)
- [Adaptive Linear Path Model-Based Diffusion](https://mlsanity.com/paper/2602.02831/) (2026)
- [Global Convergence of Sampling-Based Nonconvex Optimization through Diffusion-Style Smoothing](https://mlsanity.com/paper/2605.16520/) (2026)
- [Training-Free Imitation Learning with Closed-Form Diffusion Policies](https://mlsanity.com/paper/2606.01238/) (2026)
- [Shield-Loco: Shielding Locomotion Policies with Predictive Safety Filtering](https://mlsanity.com/paper/2606.07193/) (2026)
- [GRACE: Gradient-Free Robot Action Generation via Combined Diffusion-MPPI Posterior Mean Estimation](https://mlsanity.com/paper/2607.21661/) (2026)
- [Accelerating Visual Policy Learning with Sampling-Based Model Predictive Control](https://mlsanity.com/paper/2609.20575/) (2026)
- [Training-Free Diffusion Planning with Analytical Local Scores](https://mlsanity.com/paper/2610.01959/) (2026)
- [VAMPS: Visual and Motor Policies from Sampling-Based Planning](https://mlsanity.com/paper/2610.05331/) (2026)

## Abstract (arXiv)

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.