# SWAP: Symmetric Equivariant World-Model for Agile Robot Parkour

arXiv: https://arxiv.org/abs/2606.19928 · HTML: https://mlsanity.com/paper/2606.19928/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Humanoid and legged locomotion world models, one of 11 directions in World models.
- Builds on 6 of its 30 references that are in the map.
- First posted on arXiv 18 Jun 2026.

## Placed in

- World models / [Humanoid and legged locomotion world models](https://mlsanity.com/wm/humanoid-and-legged-locomotion-world-models/)

## Builds on (most cited first, 6 of 6)

- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Robot Parkour Learning](https://mlsanity.com/paper/2309.05665/) (2023)
- [On-Robot Learning With Equivariant Models](https://mlsanity.com/paper/2203.04923/) (2022)
- [Parkour in the Wild: Learning a General and Extensible Agile Locomotion Policy Using Multi-expert Distillation and RL Fine-tuning](https://mlsanity.com/paper/2505.11164/) (2025)
- [Symmetry-Guided Memory Augmentation for Efficient Locomotion Learning](https://mlsanity.com/paper/2502.01521/) (2025)

## Abstract (arXiv)

While latent world models enable the proactive predictions required for extreme parkour, their purely data-driven nature forces them to redundantly encode left-right symmetric interactions as independent patterns. This inflates the learning burden and hinders the capture of geometric regularities, restricting the latent space's efficiency for downstream policies. To address this, we propose SWAP, an end-to-end equivariant symmetric world model. This framework embeds symmetry directly into both the world model and the actor-critic networks. In real-world tests, the robot leaps across a 2.13 m gap and climbs a 1.63 m platform, breaking records for quadruped parkour. Furthermore, the framework exhibits robust geometric generalization to unseen mirrored terrains and exceptional zero-shot transferability across diverse outdoor environments. These results demonstrate that symmetry equivariance is an effective structural prior for pushing the physical boundaries of learned legged locomotion.