# SE(3)-Equivariant Relational Rearrangement with Neural Descriptor Fields

arXiv: https://arxiv.org/abs/2211.09786 · HTML: https://mlsanity.com/paper/2211.09786/

## Key facts

- Cited by 51 papers in the map (data through 14 Oct 2026).
- Builds on 72 of its 83 references that are in the map.
- First posted on arXiv 17 Nov 2022.

## Builds on (most cited first, 30 of 72)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Compositional Visual Generation with Composable Diffusion Models](https://mlsanity.com/paper/2206.01714/) (2022)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [iMAP: Implicit Mapping and Positioning in Real-Time](https://mlsanity.com/paper/2103.12352/) (2021)
- [INeRF: Inverting Neural Radiance Fields for Pose Estimation](https://mlsanity.com/paper/2012.05877/) (2020)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [Transporter Networks: Rearranging the Visual World for Robotic Manipulation](https://mlsanity.com/paper/2010.14406/) (2020)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [6-DOF GraspNet: Variational Grasp Generation for Object Manipulation](https://mlsanity.com/paper/1905.10520/) (2019)
- [Contact-GraspNet: Efficient 6-DoF Grasp Generation in Cluttered Scenes](https://mlsanity.com/paper/2103.14127/) (2021)
- [Neural Descriptor Fields: SE(3)-Equivariant Object Representations for Manipulation](https://mlsanity.com/paper/2112.05124/) (2021)
- [Ditto: Building Digital Twins of Articulated Objects from Interaction](https://mlsanity.com/paper/2202.08227/) (2022)
- [Rearrangement: A Challenge for Embodied AI](https://mlsanity.com/paper/2011.01975/) (2020)
- [Vision-Only Robot Navigation in a Neural Radiance World](https://mlsanity.com/paper/2110.00168/) (2021)
- [kPAM: KeyPoint Affordances for Category-Level Robotic Manipulation](https://mlsanity.com/paper/1903.06684/) (2019)
- [Dense Object Nets: Learning Dense Visual Object Descriptors By and For Robotic Manipulation](https://mlsanity.com/paper/1806.08756/) (2018)
- [A micro Lie theory for state estimation in robotics](https://mlsanity.com/paper/1812.01537/) (2018)
- [Deformed Implicit Field: Modeling 3D Shapes with Learned Dense Correspondence](https://mlsanity.com/paper/2011.13650/) (2020)
- [Dex-NeRF: Using a Neural Radiance Field to Grasp Transparent Objects](https://mlsanity.com/paper/2110.14217/) (2021)

## Built on by (most cited first, 30 of 51)

- [ReKep: Spatio-Temporal Reasoning of Relational Keypoint Constraints for Robotic Manipulation](https://mlsanity.com/paper/2409.01652/) (2024)
- [Learning to Act from Actionless Videos through Dense Correspondences](https://mlsanity.com/paper/2310.08576/) (2023)
- [Distilled Feature Fields Enable Few-Shot Language-Guided Manipulation](https://mlsanity.com/paper/2308.07931/) (2023)
- [EquiBot: SIM(3)-Equivariant Diffusion Policy for Generalizable and Data Efficient Learning](https://mlsanity.com/paper/2407.01479/) (2024)
- [Equivariant Diffusion Policy](https://mlsanity.com/paper/2407.01812/) (2024)
- [Diffusion-EDFs: Bi-equivariant Denoising Generative Modeling on SE(3) for Visual Robotic Manipulation](https://mlsanity.com/paper/2309.02685/) (2023)
- [DINOBot: Robot Manipulation via Retrieval and Alignment with Vision Foundation Models](https://mlsanity.com/paper/2402.13181/) (2024)
- [Compositional Diffusion-Based Continuous Constraint Solvers](https://mlsanity.com/paper/2309.00966/) (2023)
- [EquivAct: SIM(3)-Equivariant Visuomotor Policies beyond Rigid Object Manipulation](https://mlsanity.com/paper/2310.16050/) (2023)
- [Deep Generative Models in Robotics: A Survey on Learning from Multimodal Demonstrations](https://mlsanity.com/paper/2408.04380/) (2024)
- [A Survey of Embodied Learning for Object-Centric Robotic Manipulation](https://mlsanity.com/paper/2408.11537/) (2024)
- [Shelving, Stacking, Hanging: Relational Pose Diffusion for Multi-modal Rearrangement](https://mlsanity.com/paper/2307.04751/) (2023)
- [Leveraging SE(3) Equivariance for Learning 3D Geometric Shape Assembly](https://mlsanity.com/paper/2309.06810/) (2023)
- [UAD: Unsupervised Affordance Distillation for Generalization in Robotic Manipulation](https://mlsanity.com/paper/2506.09284/) (2025)
- [SparseDFF: Sparse-View Feature Distillation for One-Shot Dexterous Manipulation](https://mlsanity.com/paper/2310.16838/) (2023)
- [Local Neural Descriptor Fields: Locally Conditioned Object Representations for Manipulation](https://mlsanity.com/paper/2302.03573/) (2023)
- [A General Theory of Correct, Incorrect, and Extrinsic Equivariance](https://mlsanity.com/paper/2303.04745/) (2023)
- [Lifelong Robot Learning with Human Assisted Language Planners](https://mlsanity.com/paper/2309.14321/) (2023)
- [Imagination Policy: Using Generative Point Cloud Models for Learning Manipulation Policies](https://mlsanity.com/paper/2406.11740/) (2024)
- [One-shot Imitation Learning via Interaction Warping](https://mlsanity.com/paper/2306.12392/) (2023)
- [Bi-KVIL: Keypoints-based Visual Imitation Learning of Bimanual Manipulation Tasks](https://mlsanity.com/paper/2403.03270/) (2024)
- [NeRFs in Robotics: A Survey](https://mlsanity.com/paper/2405.01333/) (2024)
- [HyP-NeRF: Learning Improved NeRF Priors using a HyperNetwork](https://mlsanity.com/paper/2306.06093/) (2023)
- [Few-Shot In-Context Imitation Learning via Implicit Graph Alignment](https://mlsanity.com/paper/2310.12238/) (2023)
- [Leveraging Locality to Boost Sample Efficiency in Robotic Manipulation](https://mlsanity.com/paper/2406.10615/) (2024)
- [RiEMann: Near Real-Time SE(3)-Equivariant Robot Manipulation without Point Cloud Segmentation](https://mlsanity.com/paper/2403.19460/) (2024)
- [AnyPlace: Learning Generalized Object Placement for Robot Manipulation](https://mlsanity.com/paper/2502.04531/) (2025)
- [NeuSE: Neural SE(3)-Equivariant Embedding for Long-Term Object-Based Simultaneous Localization and Mapping](https://mlsanity.com/paper/2303.07308/) (2023)
- [SE(3)-Equivariant Robot Learning and Control: A Tutorial Survey](https://mlsanity.com/paper/2503.09829/) (2025)
- ["Set It Up!": Functional Object Arrangement with Compositional Generative Models](https://mlsanity.com/paper/2405.11928/) (2024)

## Abstract (arXiv)

We present a method for performing tasks involving spatial relations between novel object instances initialized in arbitrary poses directly from point cloud observations. Our framework provides a scalable way for specifying new tasks using only 5-10 demonstrations. Object rearrangement is formalized as the question of finding actions that configure task-relevant parts of the object in a desired alignment. This formalism is implemented in three steps: assigning a consistent local coordinate frame to the task-relevant object parts, determining the location and orientation of this coordinate frame on unseen object instances, and executing an action that brings these frames into the desired alignment. We overcome the key technical challenge of determining task-relevant local coordinate frames from a few demonstrations by developing an optimization method based on Neural Descriptor Fields (NDFs) and a single annotated 3D keypoint. An energy-based learning scheme to model the joint configuration of the objects that satisfies a desired relational task further improves performance. The method is tested on three multi-object rearrangement tasks in simulation and on a real robot. Project website, videos, and code: https://anthonysimeonov.github.io/r-ndf/