# Leveraging Symmetries in Pick and Place

arXiv: https://arxiv.org/abs/2308.07948 · HTML: https://mlsanity.com/paper/2308.07948/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 72 references that are in the map.
- First posted on arXiv 15 Aug 2023.

## Builds on (most cited first, 30 of 46)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [End-to-End Training of Deep Visuomotor Policies](https://mlsanity.com/paper/1504.00702/) (2015)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Perceiver IO: A General Architecture for Structured Inputs & Outputs](https://mlsanity.com/paper/2107.14795/) (2021)
- [CLIPort: What and Where Pathways for Robotic Manipulation](https://mlsanity.com/paper/2109.12098/) (2021)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Perceiver-Actor: A Multi-Task Transformer for Robotic Manipulation](https://mlsanity.com/paper/2209.05451/) (2022)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [PCN: Point Completion Network](https://mlsanity.com/paper/1808.00671/) (2018)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Transporter Networks: Rearranging the Visual World for Robotic Manipulation](https://mlsanity.com/paper/2010.14406/) (2020)
- [Leveraging Demonstrations for Deep Reinforcement Learning on Robotics Problems with Sparse Rewards](https://mlsanity.com/paper/1707.08817/) (2017)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Neural Descriptor Fields: SE(3)-Equivariant Object Representations for Manipulation](https://mlsanity.com/paper/2112.05124/) (2021)
- [Deep Dynamics Models for Learning Dexterous Manipulation](https://mlsanity.com/paper/1909.11652/) (2019)
- [kPAM: KeyPoint Affordances for Category-Level Robotic Manipulation](https://mlsanity.com/paper/1903.06684/) (2019)
- [Learning Synergies between Pushing and Grasping with Self-supervised Deep Reinforcement Learning](https://mlsanity.com/paper/1803.09956/) (2018)
- [Robotic Pick-and-Place of Novel Objects in Clutter with Multi-Affordance Grasping and Cross-Domain Image Matching](https://mlsanity.com/paper/1710.01330/) (2017)
- [Closing the Loop for Robotic Grasping: A Real-time, Generative Grasp Synthesis Approach](https://mlsanity.com/paper/1804.05172/) (2018)
- [Self-supervised 6D Object Pose Estimation for Robot Manipulation](https://mlsanity.com/paper/1909.10159/) (2019)
- [Equivariant Point Network for 3D Point Cloud Analysis](https://mlsanity.com/paper/2103.14147/) (2021)
- [You Only Demonstrate Once: Category-Level Manipulation from Single Visual Demonstration](https://mlsanity.com/paper/2201.12716/) (2022)
- [Learning to Rearrange Deformable Cables, Fabrics, and Bags with Goal-Conditioned Transporter Networks](https://mlsanity.com/paper/2012.03385/) (2020)
- [Learning to Manipulate Deformable Objects without Demonstrations](https://mlsanity.com/paper/1910.13439/) (2019)
- [KeyPose: Multi-View 3D Labeling and Keypoint Estimation for Transparent Objects](https://mlsanity.com/paper/1912.02805/) (2019)
- [Equivariant Q Learning in Spatial Action Spaces](https://mlsanity.com/paper/2110.15443/) (2021)

## Built on by (most cited first, 19 of 19)

- [Equivariant Diffusion Policy](https://mlsanity.com/paper/2407.01812/) (2024)
- [Fourier Transporter: Bi-Equivariant Robotic Manipulation in 3D](https://mlsanity.com/paper/2401.12046/) (2024)
- [ActionFlow: Equivariant, Accurate, and Efficient Policies with Spatially Symmetric Flow Matching](https://mlsanity.com/paper/2409.04576/) (2024)
- [Imagination Policy: Using Generative Point Cloud Models for Learning Manipulation Policies](https://mlsanity.com/paper/2406.11740/) (2024)
- [RiEMann: Near Real-Time SE(3)-Equivariant Robot Manipulation without Point Cloud Segmentation](https://mlsanity.com/paper/2403.19460/) (2024)
- [SE(3)-Equivariant Diffusion Policy in Spherical Fourier Space](https://mlsanity.com/paper/2507.01723/) (2025)
- [MATCH POLICY: A Simple Pipeline from Point Cloud Registration to Manipulation Policies](https://mlsanity.com/paper/2409.15517/) (2024)
- [Constraint-Preserving Data Generation for Visuomotor Policy Learning](https://mlsanity.com/paper/2508.03944/) (2025)
- [Equivariant Offline Reinforcement Learning](https://mlsanity.com/paper/2406.13961/) (2024)
- [A Practical Guide for Incorporating Symmetry in Diffusion Policy](https://mlsanity.com/paper/2505.13431/) (2025)
- [3D Equivariant Visuomotor Policy Learning via Spherical Projection](https://mlsanity.com/paper/2505.16969/) (2025)
- [Eq.Bot: Enhance Robotic Manipulation Learning via Group Equivariant Canonicalization](https://mlsanity.com/paper/2511.15194/) (2025)
- [Precise Pick-and-Place using Score-Based Diffusion Networks](https://mlsanity.com/paper/2409.09725/) (2024)
- [On Uncertainty Calibration for Equivariant Functions](https://mlsanity.com/paper/2510.21691/) (2025)
- [Learning Nonholonomic Dynamics with Constraint Discovery](https://mlsanity.com/paper/2410.15201/) (2024)
- [Trajectory Entropy Reinforcement Learning for Robust Robot Motor Skill Learning](https://mlsanity.com/paper/2505.04193/) (2025)
- [Multi-Group Equivariant Augmentation for Reinforcement Learning in Robot Manipulation](https://mlsanity.com/paper/2508.11204/) (2025)
- [Multi-Task Reinforcement Learning of Drone Aerobatics by Exploiting Geometric Symmetries](https://mlsanity.com/paper/2602.10997/) (2026)
- [Pix2Act: Image-Space Manipulation Policies with Equivariant Augmentation](https://mlsanity.com/paper/2607.11167/) (2026)

## Abstract (arXiv)

Robotic pick and place tasks are symmetric under translations and rotations of both the object to be picked and the desired place pose. For example, if the pick object is rotated or translated, then the optimal pick action should also rotate or translate. The same is true for the place pose; if the desired place pose changes, then the place action should also transform accordingly. A recently proposed pick and place framework known as Transporter Net captures some of these symmetries, but not all. This paper analytically studies the symmetries present in planar robotic pick and place and proposes a method of incorporating equivariant neural models into Transporter Net in a way that captures all symmetries. The new model, which we call Equivariant Transporter Net, is equivariant to both pick and place symmetries and can immediately generalize pick and place knowledge to different pick and place poses. We evaluate the new model empirically and show that it is much more sample efficient than the non-symmetric version, resulting in a system that can imitate demonstrated pick and place behavior using very few human demonstrations on a variety of imitation learning tasks.