# Canonical Policy: Learning Canonical 3D Representation for SE(3)-Equivariant Policy

arXiv: https://arxiv.org/abs/2505.18474 · HTML: https://mlsanity.com/paper/2505.18474/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Robot manipulation imitation learning, one of 13 directions in Offline RL and imitation learning from data.
- First posted on arXiv 24 May 2025.

## Placed in

- Offline RL and imitation learning from data / [Robot manipulation imitation learning](https://mlsanity.com/offlinerl/robot-manipulation-imitation-learning/)

## Built on by (most cited first, 7 of 7)

- [TacVLA: Contact-Aware Tactile Fusion for Robust Vision-Language-Action Manipulation](https://mlsanity.com/paper/2603.12665/) (2026)
- [Lift3D-VLA: Lifting VLA Models to 3D Geometry and Dynamics-Aware Manipulation](https://mlsanity.com/paper/2607.06564/) (2026)
- [See like a Robot: Robot-Centric Pointmaps for VLA Models](https://mlsanity.com/paper/2607.11498/) (2026)
- [SAVLA: Symmetry-Aware Vision-Language-Action Models for Robotic Manipulation](https://mlsanity.com/paper/2609.16641/) (2026)
- [UNIC: Learning Unified Multimodal Extrinsic Contact Estimation](https://mlsanity.com/paper/2601.04356/) (2026)
- [RayViT: Ray-Conditioned Visual Representations for Viewpoint-Robust Imitation Learning](https://mlsanity.com/paper/2607.29622/) (2026)
- [Equivariant Visual-Tactile Diffusion Policy for Contact-Rich Manipulation](https://mlsanity.com/paper/2610.03333/) (2026)

## Abstract (arXiv)

Visual Imitation learning has achieved remarkable progress in robotic manipulation, yet generalization to unseen objects, scene layouts, and camera viewpoints remains a key challenge. Recent advances address this by using 3D point clouds, which provide geometry-aware, appearance-invariant representations, and by incorporating equivariance into policy architectures to exploit spatial symmetries. However, existing equivariant approaches often lack interpretability and rigor due to unstructured integration of equivariant components. We introduce canonical policy, a principled framework for 3D equivariant imitation learning that unifies 3D point cloud observations under a canonical representation. We first establish a theory of 3D canonical representations, enabling equivariant observation-to-action mappings by grouping both seen and novel point clouds to a canonical representation. We then propose a flexible policy learning pipeline that leverages geometric symmetries from canonical representation and the expressiveness of modern generative models. We validate canonical policy on 12 diverse simulated tasks and 4 real-world manipulation tasks across 16 configurations, involving variations in object color, shape, camera viewpoint, and robot platform. Compared to state-of-the-art imitation learning policies, canonical policy achieves an average improvement of 18.0% in simulation and 39.7% in real-world experiments, demonstrating superior generalization capability and sample efficiency. For more details, please refer to the project website: https://zhangzhiyuanzhang.github.io/cp-website/.