mlsanityData to 14 Oct 2026

Fourier Transporter: Bi-Equivariant Robotic Manipulation in 3D

arXiv 2401.12046 ↗First posted 22 Jan 2024cs.RO cs.LGcited by 33

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Abstract (arXiv)

Many complex robotic manipulation tasks can be decomposed as a sequence of pick and place actions. Training a robotic agent to learn this sequence over many different starting conditions typically requires many iterations or demonstrations, especially in 3D environments. In this work, we propose Fourier Transporter (FourTran) which leverages the two-fold SE(d)xSE(d) symmetry in the pick-place problem to achieve much higher sample efficiency. FourTran is an open-loop behavior cloning method trained using expert demonstrations to predict pick-place actions on new environments. FourTran is constrained to incorporate symmetries of the pick and place actions independently. Our method utilizes a fiber space Fourier transformation that allows for memory-efficient construction. We test our proposed network on the RLbench benchmark and achieve state-of-the-art results across various tasks.

Key facts. Cited by 33 papers in the map (data through 14 Oct 2026). Builds on 43 of its 52 references that are in the map. First posted on arXiv 22 Jan 2024.

Builds on

43 of 52 references.

References · 43

  1. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  2. 2016Group Equivariant Convolutional Networkscited by 1,165
  3. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 746
  4. 2019RLBench: The Robot Learning Benchmark & Learning Environmentcited by 689
  5. 2021Perceiver IO: A General Architecture for Structured Inputs & Outputscited by 629
  6. 2021CLIPort: What and Where Pathways for Robotic Manipulationcited by 622
  7. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 607
  8. 2022Perceiver-Actor: A Multi-Task Transformer for Robotic Manipulationcited by 551
  9. 2019General E(2)-Equivariant Steerable CNNscited by 446
  10. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 354
  11. 2020Transporter Networks: Rearranging the Visual World for Robotic Manipulationcited by 344
  12. 2016Steerable CNNscited by 305
31 more
  1. 2021Vector Neurons: A General Framework for SO(3)-Equivariant Networkscited by 305
  2. 2018A General Theory of Equivariant CNNs on Homogeneous Spacescited by 228
  3. 2023RVT: Robotic View Transformer for 3D Object Manipulationcited by 225
  4. 2021Neural Descriptor Fields: SE(3)-Equivariant Object Representations for Manipulationcited by 209
  5. 2017Robotic Pick-and-Place of Novel Objects in Clutter with Multi-Affordance Grasping and Cross-Domain Image Matchingcited by 125
  6. 2021Coarse-to-Fine Q-attention: Efficient Learning for Visual Robotic Manipulation via Discretisationcited by 122
  7. 2018Closing the Loop for Robotic Grasping: A Real-time, Generative Grasp Synthesis Approachcited by 120
  8. 2019Self-supervised 6D Object Pose Estimation for Robot Manipulationcited by 101
  9. 2021A comprehensive survey on point cloud registrationcited by 84
  10. 2022SO(2)-Equivariant Reinforcement Learningcited by 84
  11. 2021Independent SE(3)-Equivariant Models for End-to-End Rigid Protein Dockingcited by 82
  12. 2022You Only Demonstrate Once: Category-Level Manipulation from Single Visual Demonstrationcited by 81
  13. 2020Learning to Rearrange Deformable Cables, Fabrics, and Bags with Goal-Conditioned Transporter Networkscited by 78
  14. 2016Multi-view Self-supervised Deep Learning for 6D Pose Estimation in the Amazon Picking Challengecited by 70
  15. 2021Implicit-PDF: Non-Parametric Representation of Probability Distributions on the Rotation Manifoldcited by 65
  16. 2021Equivariant Q Learning in Spatial Action Spacescited by 62
  17. 2022Equivariant Descriptor Fields: SE(3)-Equivariant Energy-Based Models for End-to-End Visual Robotic Manipulation Learningcited by 56
  18. 2022Sample Efficient Grasp Learning Using Equivariant Modelscited by 53
  19. 2022TAX-Pose: Task-Specific Cross-Pose Estimation for Robot Manipulationcited by 47
  20. 2020A Wigner-Eckart Theorem for Group Equivariant Convolution Kernelscited by 46
  21. 2022Equivariant Transporter Networkcited by 46
  22. 2019PyRep: Bringing V-REP to Deep Robot Learningcited by 44
  23. 2022On-Robot Learning With Equivariant Modelscited by 42
  24. 2022MIRA: Mental Imagery for Robotic Affordancescited by 26
  25. 2022SEIL: Simulation-augmented Equivariant Imitation Learningcited by 23
  26. 2021Steerable Partial Differential Operators for Equivariant Neural Networkscited by 22
  27. 2023Local Neural Descriptor Fields: Locally Conditioned Object Representations for Manipulationcited by 21
  28. 2023Leveraging Symmetries in Pick and Placecited by 19
  29. 2023Image to Sphere: Learning Equivariant Features for Efficient Pose Predictioncited by 18
  30. 2023Equivariant Single View Pose Prediction Via Induced and Restricted Representationscited by 6
  31. 2022NIFT: Neural Interaction Field and Template for Object Manipulationcited by 4

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 12; 2025: 15; 2026: 6.

33 papers.

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  1. 20243D Diffuser Actor: Policy Diffusion with 3D Scene Representationscited by 282
  2. 2024RVT-2: Learning Precise Manipulation from Few Demonstrationscited by 137
  3. 2024EquiBot: SIM(3)-Equivariant Diffusion Policy for Generalizable and Data Efficient Learningcited by 75
  4. 2024Equivariant Diffusion Policycited by 66
  5. 2025FP3: A 3D Foundation Policy for Robotic Manipulationcited by 32
  6. 2024ActionFlow: Equivariant, Accurate, and Efficient Policies with Spatially Symmetric Flow Matchingcited by 26
  7. 2024Imagination Policy: Using Generative Point Cloud Models for Learning Manipulation Policiescited by 18
  8. 2024RiEMann: Near Real-Time SE(3)-Equivariant Robot Manipulation without Point Cloud Segmentationcited by 12
  9. 2025Geometry-aware RL for Manipulation of Varying Shapes and Deformable Objectscited by 10
  10. 2025SE(3)-Equivariant Robot Learning and Control: A Tutorial Surveycited by 10
  11. 2025SE(3)-Equivariant Diffusion Policy in Spherical Fourier Spacecited by 8
  12. 2024MATCH POLICY: A Simple Pipeline from Point Cloud Registration to Manipulation Policiescited by 6
21 more
  1. 2025Constraint-Preserving Data Generation for Visuomotor Policy Learningcited by 6
  2. 2024Equivariant Offline Reinforcement Learningcited by 5
  3. 2025A Practical Guide for Incorporating Symmetry in Diffusion Policycited by 5
  4. 20253D Equivariant Visuomotor Policy Learning via Spherical Projectioncited by 5
  5. 2024Equivariant Action Sampling for Reinforcement Learning and Planningcited by 4
  6. 2025EfficientFlow: Efficient Equivariant Flow Policy Learning for Embodied AIcited by 4
  7. 2025On Universality of Deep Equivariant Networkscited by 3
  8. 2025Partially Equivariant Reinforcement Learning in Symmetry-Breaking Environmentscited by 3
  9. 2025Coarse-to-Fine 3D Keyframe Transportercited by 2
  10. 2025Generalizable Hierarchical Skill Learning via Object-Centric Representationcited by 2
  11. 2024BiEquiFormer: Bi-Equivariant Representations for Global Point Cloud Registrationcited by 1
  12. 2024Precise Pick-and-Place using Score-Based Diffusion Networkscited by 1
  13. 2025On Uncertainty Calibration for Equivariant Functionscited by 1
  14. 2025DidSee: Diffusion-Based Depth Completion for Material-Agnostic Robotic Perception and Manipulationcited by 0
  15. 2025Multi-Group Equivariant Augmentation for Reinforcement Learning in Robot Manipulationcited by 0
  16. 2026Group-Invariant Unsupervised Skill Discovery: Symmetry-aware Skill Representations for Generalizable Behaviorcited by 0
  17. 2026Differential Amplifier-Inspired AmpAttention for Multi-View Robotic Manipulationcited by 0
  18. 2026Action Map Policy: Learning 3D Closed-loop Manipulation via Pixel Classificationcited by 0
  19. 2026Pix2Act: Image-Space Manipulation Policies with Equivariant Augmentationcited by 0
  20. 2026EquivDP3: A SIM(3)-Invariant Point-Cloud Encoder for Data-Efficient Humanoid Loco-Manipulationcited by 0
  21. 2026Equivariant Visual-Tactile Diffusion Policy for Contact-Rich Manipulationcited by 0