# RuN: Residual Policy for Natural Humanoid Locomotion

arXiv: https://arxiv.org/abs/2509.20696 · HTML: https://mlsanity.com/paper/2509.20696/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in RL for robot locomotion and manipulation, one of 15 directions in Deep reinforcement learning methods.
- Builds on 22 of its 28 references that are in the map.
- First posted on arXiv 25 Sep 2025.

## Placed in

- Deep reinforcement learning methods / [RL for robot locomotion and manipulation](https://mlsanity.com/deeprl/rl-for-robot-locomotion-and-manipulation/)

## Builds on (most cited first, 22 of 22)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [AMASS: Archive of Motion Capture as Surface Shapes](https://mlsanity.com/paper/1904.03278/) (2019)
- [Human Motion Diffusion Model](https://mlsanity.com/paper/2209.14916/) (2022)
- [Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks](https://mlsanity.com/paper/1506.03099/) (2015)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [T2M-GPT: Generating Human Motion from Textual Descriptions with Discrete Representations](https://mlsanity.com/paper/2301.06052/) (2023)
- [TEMOS: Generating diverse human motions from textual descriptions](https://mlsanity.com/paper/2204.14109/) (2022)
- [Action2Motion: Conditioned Generation of 3D Human Motions](https://mlsanity.com/paper/2007.15240/) (2020)
- [EDGE: Editable Dance Generation From Music](https://mlsanity.com/paper/2211.10658/) (2022)
- [Asymmetric Actor Critic for Image-Based Robot Learning](https://mlsanity.com/paper/1710.06542/) (2017)
- [Real-World Humanoid Locomotion with Reinforcement Learning](https://mlsanity.com/paper/2303.03381/) (2023)
- [Character Controllers Using Motion VAEs](https://mlsanity.com/paper/2103.14274/) (2021)
- [HUMANISE: Language-conditioned Human Motion Generation in 3D Scenes](https://mlsanity.com/paper/2210.09729/) (2022)
- [Learning Agile Soccer Skills for a Bipedal Robot with Deep Reinforcement Learning](https://mlsanity.com/paper/2304.13653/) (2023)
- [Reinforcement Learning for Versatile, Dynamic, and Robust Bipedal Locomotion Control](https://mlsanity.com/paper/2401.16889/) (2024)
- [Humanoid Parkour Learning](https://mlsanity.com/paper/2406.10759/) (2024)
- [Blind Bipedal Stair Traversal via Sim-to-Real Reinforcement Learning](https://mlsanity.com/paper/2105.08328/) (2021)
- [HOVER: Versatile Neural Whole-Body Controller for Humanoid Robots](https://mlsanity.com/paper/2410.21229/) (2024)
- [Humanoid-Gym: Reinforcement Learning for Humanoid Robot with Zero-Shot Sim2Real Transfer](https://mlsanity.com/paper/2404.05695/) (2024)
- [Whole-body Humanoid Robot Locomotion with Human Reference](https://mlsanity.com/paper/2402.18294/) (2024)
- [Natural Humanoid Robot Locomotion with Generative Motion Prior](https://mlsanity.com/paper/2503.09015/) (2025)
- [Optimizing Bipedal Locomotion for The 100m Dash With Comparison to Human Running](https://mlsanity.com/paper/2508.03070/) (2025)

## Built on by (most cited first, 1 of 1)

- [SPRINT: Efficient Spectral Priors for Humanoid Athletic Sprints](https://mlsanity.com/paper/2605.28549/) (2026)

## Abstract (arXiv)

Enabling humanoid robots to achieve natural and dynamic locomotion across a wide range of speeds, including smooth transitions from walking to running, presents a significant challenge. Existing deep reinforcement learning methods typically require the policy to directly track a reference motion, forcing a single policy to simultaneously learn motion imitation, velocity tracking, and stability maintenance. To address this, we introduce RuN, a novel decoupled residual learning framework. RuN decomposes the control task by pairing a pre-trained Conditional Motion Generator, which provides a kinematically natural motion prior, with a reinforcement learning policy that learns a lightweight residual correction to handle dynamical interactions. Experiments in simulation and reality on the Unitree G1 humanoid robot demonstrate that RuN achieves stable, natural gaits and smooth walk-run transitions across a broad velocity range (0-2.5 m/s), outperforming state-of-the-art methods in both training efficiency and final performance.