# MATCH POLICY: A Simple Pipeline from Point Cloud Registration to Manipulation Policies

arXiv: https://arxiv.org/abs/2409.15517 · HTML: https://mlsanity.com/paper/2409.15517/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 59 of its 80 references that are in the map.
- First posted on arXiv 23 Sep 2024.

## Builds on (most cited first, 30 of 59)

- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [RLBench: The Robot Learning Benchmark & Learning Environment](https://mlsanity.com/paper/1909.12271/) (2019)
- [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)
- [Segment Anything in High Quality](https://mlsanity.com/paper/2306.01567/) (2023)
- [Deep Closest Point: Learning Representations for Point Cloud Registration](https://mlsanity.com/paper/1905.03304/) (2019)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [PREDATOR: Registration of 3D Point Clouds with Low Overlap](https://mlsanity.com/paper/2011.13005/) (2020)
- [3D Diffuser Actor: Policy Diffusion with 3D Scene Representations](https://mlsanity.com/paper/2402.10885/) (2024)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [RVT: Robotic View Transformer for 3D Object Manipulation](https://mlsanity.com/paper/2306.14896/) (2023)
- [Neural Descriptor Fields: SE(3)-Equivariant Object Representations for Manipulation](https://mlsanity.com/paper/2112.05124/) (2021)
- [Go-ICP: A Globally Optimal Solution to 3D ICP Point-Set Registration](https://mlsanity.com/paper/1605.03344/) (2016)
- [PRNet: Self-Supervised Learning for Partial-to-Partial Registration](https://mlsanity.com/paper/1910.12240/) (2019)
- [Act3D: 3D Feature Field Transformers for Multi-Task Robotic Manipulation](https://mlsanity.com/paper/2306.17817/) (2023)
- [3D Diffusion Policy: Generalizable Visuomotor Policy Learning via Simple 3D Representations](https://mlsanity.com/paper/2403.03954/) (2024)
- [Hierarchical Diffusion Policy for Kinematics-Aware Multi-Task Robotic Manipulation](https://mlsanity.com/paper/2403.03890/) (2024)
- [A comprehensive survey on point cloud registration](https://mlsanity.com/paper/2103.02690/) (2021)
- [SO(2)-Equivariant Reinforcement Learning](https://mlsanity.com/paper/2203.04439/) (2022)
- [DexPoint: Generalizable Point Cloud Reinforcement Learning for Sim-to-Real Dexterous Manipulation](https://mlsanity.com/paper/2211.09423/) (2022)
- [EquiBot: SIM(3)-Equivariant Diffusion Policy for Generalizable and Data Efficient Learning](https://mlsanity.com/paper/2407.01479/) (2024)
- [Fast and Robust Iterative Closest Point](https://mlsanity.com/paper/2007.07627/) (2020)
- [Equivariant Diffusion Policy](https://mlsanity.com/paper/2407.01812/) (2024)
- [Equivariant Q Learning in Spatial Action Spaces](https://mlsanity.com/paper/2110.15443/) (2021)
- [Equivariant Descriptor Fields: SE(3)-Equivariant Energy-Based Models for End-to-End Visual Robotic Manipulation Learning](https://mlsanity.com/paper/2206.08321/) (2022)
- [Fast Point Cloud Generation with Straight Flows](https://mlsanity.com/paper/2212.01747/) (2022)
- [PolarNet: 3D Point Clouds for Language-Guided Robotic Manipulation](https://mlsanity.com/paper/2309.15596/) (2023)

## Built on by (most cited first, 6 of 6)

- [Two by Two: Learning Multi-Task Pairwise Objects Assembly for Generalizable Robot Manipulation](https://mlsanity.com/paper/2504.06961/) (2025)
- [AnyPlace: Learning Generalized Object Placement for Robot Manipulation](https://mlsanity.com/paper/2502.04531/) (2025)
- [A Practical Guide for Incorporating Symmetry in Diffusion Policy](https://mlsanity.com/paper/2505.13431/) (2025)
- [OMP: One-step Meanflow Policy with Directional Alignment](https://mlsanity.com/paper/2512.19347/) (2025)
- [Action Map Policy: Learning 3D Closed-loop Manipulation via Pixel Classification](https://mlsanity.com/paper/2607.10706/) (2026)
- [Pix2Act: Image-Space Manipulation Policies with Equivariant Augmentation](https://mlsanity.com/paper/2607.11167/) (2026)

## Abstract (arXiv)

Many manipulation tasks require the robot to rearrange objects relative to one another. Such tasks can be described as a sequence of relative poses between parts of a set of rigid bodies. In this work, we propose MATCH POLICY, a simple but novel pipeline for solving high-precision pick and place tasks. Instead of predicting actions directly, our method registers the pick and place targets to the stored demonstrations. This transfers action inference into a point cloud registration task and enables us to realize nontrivial manipulation policies without any training. MATCH POLICY is designed to solve high-precision tasks with a key-frame setting. By leveraging the geometric interaction and the symmetries of the task, it achieves extremely high sample efficiency and generalizability to unseen configurations. We demonstrate its state-of-the-art performance across various tasks on RLBench benchmark compared with several strong baselines and test it on a real robot with six tasks.