# E(2)-Equivariant Graph Planning for Navigation

arXiv: https://arxiv.org/abs/2309.13043 · HTML: https://mlsanity.com/paper/2309.13043/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 53 references that are in the map.
- First posted on arXiv 22 Sep 2023.

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

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [RT-1: Robotics Transformer for Real-World Control at Scale](https://mlsanity.com/paper/2212.06817/) (2022)
- [Habitat: A Platform for Embodied AI Research](https://mlsanity.com/paper/1904.01201/) (2019)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Vision-and-Language Navigation: Interpreting visually-grounded navigation instructions in real environments](https://mlsanity.com/paper/1711.07280/) (2017)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [Object Goal Navigation using Goal-Oriented Semantic Exploration](https://mlsanity.com/paper/2007.00643/) (2020)
- [DD-PPO: Learning Near-Perfect PointGoal Navigators from 2.5 Billion Frames](https://mlsanity.com/paper/1911.00357/) (2019)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Minigrid & Miniworld: Modular & Customizable Reinforcement Learning Environments for Goal-Oriented Tasks](https://mlsanity.com/paper/2306.13831/) (2023)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [A General Theory of Equivariant CNNs on Homogeneous Spaces](https://mlsanity.com/paper/1811.02017/) (2018)
- [Geometric and Physical Quantities Improve E(3) Equivariant Message Passing](https://mlsanity.com/paper/2110.02905/) (2021)
- [Cognitive Mapping and Planning for Visual Navigation](https://mlsanity.com/paper/1702.03920/) (2017)
- [Value Iteration Networks](https://mlsanity.com/paper/1602.02867/) (2016)
- [What Can Neural Networks Reason About?](https://mlsanity.com/paper/1905.13211/) (2019)
- [MDP Homomorphic Networks: Group Symmetries in Reinforcement Learning](https://mlsanity.com/paper/2006.16908/) (2020)
- [Habitat-Matterport 3D Semantics Dataset](https://mlsanity.com/paper/2210.05633/) (2022)
- [SO(2)-Equivariant Reinforcement Learning](https://mlsanity.com/paper/2203.04439/) (2022)
- [Semantic Visual Navigation by Watching YouTube Videos](https://mlsanity.com/paper/2006.10034/) (2020)
- [Graph Neural Networks are Dynamic Programmers](https://mlsanity.com/paper/2203.15544/) (2022)
- [Learning Symmetric Embeddings for Equivariant World Models](https://mlsanity.com/paper/2204.11371/) (2022)
- [Path Planning using Neural A* Search](https://mlsanity.com/paper/2009.07476/) (2020)
- [A Wigner-Eckart Theorem for Group Equivariant Convolution Kernels](https://mlsanity.com/paper/2010.10952/) (2020)
- [SSCNav: Confidence-Aware Semantic Scene Completion for Visual Semantic Navigation](https://mlsanity.com/paper/2012.04512/) (2020)
- [Gated Path Planning Networks](https://mlsanity.com/paper/1806.06408/) (2018)

## Built on by (most cited first, 6 of 6)

- [SE(3)-Equivariant Robot Learning and Control: A Tutorial Survey](https://mlsanity.com/paper/2503.09829/) (2025)
- [MATCH POLICY: A Simple Pipeline from Point Cloud Registration to Manipulation Policies](https://mlsanity.com/paper/2409.15517/) (2024)
- [Equivariant Action Sampling for Reinforcement Learning and Planning](https://mlsanity.com/paper/2412.12237/) (2024)
- [REViT: Roto-reflection Equivariant Convolutional Vision Transformer](https://mlsanity.com/paper/2606.25318/) (2026)
- [ODTFormer: Efficient Obstacle Detection and Tracking with Stereo Cameras Based on Transformer](https://mlsanity.com/paper/2403.14626/) (2024)
- [Pix2Act: Image-Space Manipulation Policies with Equivariant Augmentation](https://mlsanity.com/paper/2607.11167/) (2026)

## Abstract (arXiv)

Learning for robot navigation presents a critical and challenging task. The scarcity and costliness of real-world datasets necessitate efficient learning approaches. In this letter, we exploit Euclidean symmetry in planning for 2D navigation, which originates from Euclidean transformations between reference frames and enables parameter sharing. To address the challenges of unstructured environments, we formulate the navigation problem as planning on a geometric graph and develop an equivariant message passing network to perform value iteration. Furthermore, to handle multi-camera input, we propose a learnable equivariant layer to lift features to a desired space. We conduct comprehensive evaluations across five diverse tasks encompassing structured and unstructured environments, along with maps of known and unknown, given point goals or semantic goals. Our experiments confirm the substantial benefits on training efficiency, stability, and generalization. More details can be found at the project website: https://lhy.xyz/e2-planning/.