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Fourier Transporter: Bi-Equivariant Robotic Manipulation in 3D
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Proposes Fourier Transporter (FourTran), a bi-equivariant behavior-cloning pick-place policy that lifts crop features over SO(3) and applies a fiber-space Fourier transform, evaluated on RLBench and Ravens.
Problem
Sample-efficient learning of pick-and-place manipulation policies in SE(3), where action orientation makes learning hard and existing methods need many demonstrations and lack SO(3) bi-equivariance.
Approach
Parameterize place action distributions over SO(3) as Wigner D-matrix Fourier coefficients inside a 3D translational convolution, with a dynamic steerable kernel generated from the pick crop via lifting over a finite rotation set and a fiber-space Fourier transform, enforcing independent SE(d) symmetries of pick and place.
Key results
- With 10 demos, FourTran reaches 80/92/100/26.6/66.6 success on stack-blocks/stack-cups/stack-wine/place-cups/put-plate, versus best baseline RVT-Single at 9.3/13.3/33.3/1.3/54.6 on those tasks (RVT-Multi 91 on stack-wine).
- With only 5 demos, FourTran reaches 76 on stack-blocks and 88 on stack-cups, outperforming baselines trained with 10 demos.
- On Ravens assembling-kits-10 at 15°, FourTran gets 86.2 vs 85.0 for Equivariant Transporter and 80.0 for Transporter Net; at 7.5° it gets 78.0 vs 76.0 and 64.0.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use FourTran instead of the strongest reported baseline | 3D RLBench pick-and-place policies · RLBench stack-blocks, stack-cups, stack-wine, place-cups, and put-plate (10 demos) | success rate (%): 52 -> 80; 26.4 -> 92; 91.0 -> 100; 4.0 -> 26.6; 54.6 -> 66.6 | Helped |
| Use FourTran instead of Equivariant Transporter | Ravens pick-and-place policies · Block-insertion-10, 7.5° | success rate (%): 98.0 -> 100 | Helped |
| Use FourTran instead of Equivariant Transporter | Ravens pick-and-place policies · Assembling-kits-10, 15° and 7.5° | success rate (%): 85.0 -> 86.2; 76.0 -> 78.0 | Helped |
| Use FourTran instead of Equivariant Transporter | Ravens pick-and-place policies · Sweeping-piles-10 | success rate (%): 100 -> 99.8 | Hurt |
| Replace equivariant ψ U-Net with a traditional U-Net (ablation) | FourTran · RLBench stack-blocks, stack-wine, phone-on-base, and put-plate (5 demos) | success rate (%): 76 -> 76; 100 -> 96; 96 -> 96; 32 -> 24 | Mixed |
| Remove lifting and Fourier transform and directly generate irreducible features (ablation) | FourTran · RLBench stack-blocks, stack-wine, phone-on-base, and put-plate (5 demos) | success rate (%): 76 -> 72; 100 -> 88; 96 -> 96; 32 -> 28 | Hurt |
Surprising findings
- Ablation removing the equivariance of the crop encoder psi or removing lifting and the Fourier transform performs nearly as well as the full model, suggesting the equivariant constraints are weak in practice.
Limitations
- Open-loop control without path planning or collision awareness.
- Limited to single-task setting; not language-conditioned multi-task.
- Equivariant 3D convolutions require relatively large GPU memory.
Experimental setup
Datasets: RLBench Ravens benchmark
Benchmarks: RLBench (stack-blocks, stack-cups, stack-wine, place-cups, put-plate) Ravens (block-insertion, assembling-kits, sweeping-piles)
Metrics: success rate (%)
Baselines: PerAct RVT C2FARM-BC Transporter Net Equivariant Transporter
Builds on: Transporter Networks Equivariant Transporter Perceiver Neural Descriptor Fields
Closest papers by meaning
- RDT-1B: a Diffusion Foundation Model for Bimanual Manipulation (ICLR 2025 · similarity 0.86)
- ET-SEED: EFFICIENT TRAJECTORY-LEVEL SE(3) EQUIVARIANT DIFFUSION POLICY (ICLR 2025 · similarity 0.86)
- SE(3)-Equivariant Diffusion Policy in Spherical Fourier Space (ICML 2025 · similarity 0.86)
- GravMAD: Grounded Spatial Value Maps Guided Action Diffusion for Generalized 3D Manipulation (ICLR 2025 · similarity 0.85)
- Spatial-Temporal Graph Diffusion Policy with Kinematic Modeling for Bimanual Robotic Manipulation (CVPR 2025 · similarity 0.85)
- Fourier Controller Networks for Real-Time Decision-Making in Embodied Learning (ICML 2024 · similarity 0.85)
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