# GaitSpan: Growing Humanoid Locomotion from Walking to Running

arXiv: https://arxiv.org/abs/2607.12114 · HTML: https://mlsanity.com/paper/2607.12114/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 39 of its 59 references that are in the map.
- First posted on arXiv 13 Jul 2026.

## Builds on (most cited first, 30 of 39)

- [Isaac Gym: High Performance GPU-Based Physics Simulation For Robot Learning](https://mlsanity.com/paper/2108.10470/) (2021)
- [Curriculum Learning for Reinforcement Learning Domains: A Framework and Survey](https://mlsanity.com/paper/2003.04960/) (2020)
- [Automatic Goal Generation for Reinforcement Learning Agents](https://mlsanity.com/paper/1705.06366/) (2017)
- [Accelerating Reinforcement Learning with Learned Skill Priors](https://mlsanity.com/paper/2010.11944/) (2020)
- [Real-World Humanoid Locomotion with Reinforcement Learning](https://mlsanity.com/paper/2303.03381/) (2023)
- [HumanPlus: Humanoid Shadowing and Imitation from Humans](https://mlsanity.com/paper/2406.10454/) (2024)
- [BeyondMimic: From Motion Tracking to Versatile Humanoid Control via Guided Diffusion](https://mlsanity.com/paper/2508.08241/) (2025)
- [Extreme Parkour with Legged Robots](https://mlsanity.com/paper/2309.14341/) (2023)
- [Expressive Whole-Body Control for Humanoid Robots](https://mlsanity.com/paper/2402.16796/) (2024)
- [ASAP: Aligning Simulation and Real-World Physics for Learning Agile Humanoid Whole-Body Skills](https://mlsanity.com/paper/2502.01143/) (2025)
- [SONIC: Supersizing Motion Tracking for Natural Humanoid Whole-Body Control](https://mlsanity.com/paper/2511.07820/) (2025)
- [Sim-to-Real Learning of All Common Bipedal Gaits via Periodic Reward Composition](https://mlsanity.com/paper/2011.01387/) (2020)
- [Humanoid Parkour Learning](https://mlsanity.com/paper/2406.10759/) (2024)
- [Minimizing Energy Consumption Leads to the Emergence of Gaits in Legged Robots](https://mlsanity.com/paper/2111.01674/) (2021)
- [Legged Robots that Keep on Learning: Fine-Tuning Locomotion Policies in the Real World](https://mlsanity.com/paper/2110.05457/) (2021)
- [Humanoid Locomotion as Next Token Prediction](https://mlsanity.com/paper/2402.19469/) (2024)
- [Humanoid Locomotion and Manipulation: Current Progress and Challenges in Control, Planning, and Learning](https://mlsanity.com/paper/2501.02116/) (2025)
- [Advancing Humanoid Locomotion: Mastering Challenging Terrains with Denoising World Model Learning](https://mlsanity.com/paper/2408.14472/) (2024)
- [Adapting Rapid Motor Adaptation for Bipedal Robots](https://mlsanity.com/paper/2205.15299/) (2022)
- [KungfuBot: Physics-Based Humanoid Whole-Body Control for Learning Highly-Dynamic Skills](https://mlsanity.com/paper/2506.12851/) (2025)
- [BFM-Zero: A Promptable Behavioral Foundation Model for Humanoid Control Using Unsupervised Reinforcement Learning](https://mlsanity.com/paper/2511.04131/) (2025)
- [HITTER: A HumanoId Table TEnnis Robot via Hierarchical Planning and Learning](https://mlsanity.com/paper/2508.21043/) (2025)
- [HumanMimic: Learning Natural Locomotion and Transitions for Humanoid Robot via Wasserstein Adversarial Imitation](https://mlsanity.com/paper/2309.14225/) (2023)
- [Learning Free Gait Transition for Quadruped Robots via Phase-Guided Controller](https://mlsanity.com/paper/2201.00206/) (2022)
- [Revisiting Reward Design and Evaluation for Robust Humanoid Standing and Walking](https://mlsanity.com/paper/2404.19173/) (2024)
- [Learning Bipedal Walking for Humanoids with Current Feedback](https://mlsanity.com/paper/2303.03724/) (2023)
- [Tailoring Solution Accuracy for Fast Whole-body Model Predictive Control of Legged Robots](https://mlsanity.com/paper/2407.10789/) (2024)
- [KungfuBot2: Learning Versatile Motion Skills for Humanoid Whole-Body Control](https://mlsanity.com/paper/2509.16638/) (2025)
- [Continual Learning from Demonstration of Robotics Skills](https://mlsanity.com/paper/2202.06843/) (2022)
- [Achieving Stable High-Speed Locomotion for Humanoid Robots with Deep Reinforcement Learning](https://mlsanity.com/paper/2409.16611/) (2024)

## Abstract (arXiv)

A humanoid that can walk should not relearn locomotion from scratch to jog or run. Yet current approaches often obtain gait diversity by prescribing gait schedules, imitating motion clips, training experts to switch between or distilling skills into one policy. These strategies can produce impressive behaviors, but offer limited flexibility across continuous speed commands, terrains, and morphologies. We study skill growth with GaitSpan, a framework that expands a pretrained, basic walking policy into faster locomotion. It treats walking as a seed skill: reusable motor structure for balance, support, body coordination, and contact transition that can be regenerated at new rhythms, extended into longer/higher strides, and corrected by residual adaptation. This expansion has three aspects: 1) rhythm generation, which modulates the frozen walking policy with multiple internal clocks and learns command-conditioned combinations of the resulting canonical actions; 2) stride shaping, which rewards dynamic locomotion patterns appropriate for higher commanded speeds using a physically grounded objective inspired by spring-loaded inverted pendulum dynamics; and 3) residual adaptation, which captures motion details not accounted for by rhythm generation or stride shaping. GaitSpan is the first to deliver a single command-conditioned humanoid policy that spans walking, jogging, and running-like regimes covering a continuous speed range, transfers across morphologies, and deploys zero-shot on unseen sim-to-sim, and real-world terrains. Compared with baselines either trained with multi-experts or imitation from humans, it learns faster and achieves stronger gait performance.