mlsanityData to 14 Oct 2026

E(2)-Equivariant Graph Planning for Navigation

arXiv 2309.13043 ↗First posted 22 Sep 2023cs.RO cs.AIcited by 6

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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/.

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

39 of 53 references.

References · 39

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  2. 2017Graph Attention Networkscited by 8,923
  3. 2017Neural Message Passing for Quantum Chemistrycited by 3,487
  4. 2022RT-1: Robotics Transformer for Real-World Control at Scalecited by 2,061
  5. 2019Habitat: A Platform for Embodied AI Researchcited by 1,191
  6. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,167
  7. 2016Group Equivariant Convolutional Networkscited by 1,165
  8. 2017Vision-and-Language Navigation: Interpreting visually-grounded navigation instructions in real environmentscited by 1,027
  9. 2021E(n) Equivariant Graph Neural Networkscited by 965
  10. 2019General E(2)-Equivariant Steerable CNNscited by 446
  11. 2020Object Goal Navigation using Goal-Oriented Semantic Explorationcited by 429
  12. 2019DD-PPO: Learning Near-Perfect PointGoal Navigators from 2.5 Billion Framescited by 362
27 more
  1. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 354
  2. 2023Minigrid & Miniworld: Modular & Customizable Reinforcement Learning Environments for Goal-Oriented Taskscited by 327
  3. 2016Steerable CNNscited by 305
  4. 2018A General Theory of Equivariant CNNs on Homogeneous Spacescited by 228
  5. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 228
  6. 2017Cognitive Mapping and Planning for Visual Navigationcited by 212
  7. 2016Value Iteration Networkscited by 160
  8. 2019What Can Neural Networks Reason About?cited by 159
  9. 2020MDP Homomorphic Networks: Group Symmetries in Reinforcement Learningcited by 142
  10. 2022Habitat-Matterport 3D Semantics Datasetcited by 110
  11. 2022SO(2)-Equivariant Reinforcement Learningcited by 84
  12. 2020Semantic Visual Navigation by Watching YouTube Videoscited by 60
  13. 2022Graph Neural Networks are Dynamic Programmerscited by 55
  14. 2022Learning Symmetric Embeddings for Equivariant World Modelscited by 54
  15. 2020Path Planning using Neural A* Searchcited by 52
  16. 2020A Wigner-Eckart Theorem for Group Equivariant Convolution Kernelscited by 46
  17. 2020SSCNav: Confidence-Aware Semantic Scene Completion for Visual Semantic Navigationcited by 44
  18. 2018Gated Path Planning Networkscited by 31
  19. 2019Differentiable Algorithm Networks for Composable Robot Learningcited by 24
  20. 2020Group Equivariant Deep Reinforcement Learningcited by 24
  21. 2022Toward Compositional Generalization in Object-Oriented World Modelingcited by 22
  22. 2017Generalized Value Iteration Networks: Life Beyond Latticescited by 16
  23. 2022Integrating Symmetry into Differentiable Planning with Steerable Convolutionscited by 6
  24. 2022Deep Reinforcement Learning based Robot Navigation in Dynamic Environments using Occupancy Values of Motion Primitivescited by 6
  25. 2022Scaling up and Stabilizing Differentiable Planning with Implicit Differentiationcited by 6
  26. 2023Equivariant Single View Pose Prediction Via Induced and Restricted Representationscited by 6
  27. 2021Towards real-world navigation with deep differentiable plannerscited by 4

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 3; 2025: 1; 2026: 2.

6 papers.

  1. 2025SE(3)-Equivariant Robot Learning and Control: A Tutorial Surveycited by 10
  2. 2024MATCH POLICY: A Simple Pipeline from Point Cloud Registration to Manipulation Policiescited by 6
  3. 2024Equivariant Action Sampling for Reinforcement Learning and Planningcited by 4
  4. 2026REViT: Roto-reflection Equivariant Convolutional Vision Transformercited by 1
  5. 2024ODTFormer: Efficient Obstacle Detection and Tracking with Stereo Cameras Based on Transformercited by 0
  6. 2026Pix2Act: Image-Space Manipulation Policies with Equivariant Augmentationcited by 0