# CoPa: General Robotic Manipulation through Spatial Constraints of Parts with Foundation Models

arXiv: https://arxiv.org/abs/2403.08248 · HTML: https://mlsanity.com/paper/2403.08248/

## Key facts

- Cited by 99 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Mar 2024.

## Built on by (most cited first, 30 of 99)

- [ReKep: Spatio-Temporal Reasoning of Relational Keypoint Constraints for Robotic Manipulation](https://mlsanity.com/paper/2409.01652/) (2024)
- [EmbodiedBench: Comprehensive Benchmarking Multi-modal Large Language Models for Vision-Driven Embodied Agents](https://mlsanity.com/paper/2502.09560/) (2025)
- [DreamVLA: A Vision-Language-Action Model Dreamed with Comprehensive World Knowledge](https://mlsanity.com/paper/2507.04447/) (2025)
- [VLABench: A Large-Scale Benchmark for Language-Conditioned Robotics Manipulation with Long-Horizon Reasoning Tasks](https://mlsanity.com/paper/2412.18194/) (2024)
- [Magma: A Foundation Model for Multimodal AI Agents](https://mlsanity.com/paper/2502.13130/) (2025)
- [RoboSpatial: Teaching Spatial Understanding to 2D and 3D Vision-Language Models for Robotics](https://mlsanity.com/paper/2411.16537/) (2024)
- [RoboTwin: Dual-Arm Robot Benchmark with Generative Digital Twins](https://mlsanity.com/paper/2504.13059/) (2025)
- [OmniSpatial: Towards Comprehensive Spatial Reasoning Benchmark for Vision Language Models](https://mlsanity.com/paper/2506.03135/) (2025)
- [OneTwoVLA: A Unified Vision-Language-Action Model with Adaptive Reasoning](https://mlsanity.com/paper/2505.11917/) (2025)
- [DexGraspVLA: A Vision-Language-Action Framework Towards General Dexterous Grasping](https://mlsanity.com/paper/2502.20900/) (2025)
- [InternVLA-M1: A Spatially Guided Vision-Language-Action Framework for Generalist Robot Policy](https://mlsanity.com/paper/2510.13778/) (2025)
- [Manipulate-Anything: Automating Real-World Robots using Vision-Language Models](https://mlsanity.com/paper/2406.18915/) (2024)
- [RoboTwin: Dual-Arm Robot Benchmark with Generative Digital Twins (early version)](https://mlsanity.com/paper/2409.02920/) (2024)
- [Code-as-Monitor: Constraint-aware Visual Programming for Reactive and Proactive Robotic Failure Detection](https://mlsanity.com/paper/2412.04455/) (2024)
- [SpatialPIN: Enhancing Spatial Reasoning Capabilities of Vision-Language Models through Prompting and Interacting 3D Priors](https://mlsanity.com/paper/2403.13438/) (2024)
- [SoFar: Language-Grounded Orientation Bridges Spatial Reasoning and Object Manipulation](https://mlsanity.com/paper/2502.13143/) (2025)
- [ImagineNav: Prompting Vision-Language Models as Embodied Navigator through Scene Imagination](https://mlsanity.com/paper/2410.09874/) (2024)
- [3DFlowAction: Learning Cross-Embodiment Manipulation from 3D Flow World Model](https://mlsanity.com/paper/2506.06199/) (2025)
- [Learning Precise Affordances from Egocentric Videos for Robotic Manipulation](https://mlsanity.com/paper/2408.10123/) (2024)
- [RoboCerebra: A Large-scale Benchmark for Long-horizon Robotic Manipulation Evaluation](https://mlsanity.com/paper/2506.06677/) (2025)
- [Exploring the Limits of Vision-Language-Action Manipulations in Cross-task Generalization](https://mlsanity.com/paper/2505.15660/) (2025)
- [BUMBLE: Unifying Reasoning and Acting with Vision-Language Models for Building-wide Mobile Manipulation](https://mlsanity.com/paper/2410.06237/) (2024)
- [FP3: A 3D Foundation Policy for Robotic Manipulation](https://mlsanity.com/paper/2503.08950/) (2025)
- [ZeroMimic: Distilling Robotic Manipulation Skills from Web Videos](https://mlsanity.com/paper/2503.23877/) (2025)
- [CoA-VLA: Improving Vision-Language-Action Models via Visual-Textual Chain-of-Affordance](https://mlsanity.com/paper/2412.20451/) (2024)
- [UAD: Unsupervised Affordance Distillation for Generalization in Robotic Manipulation](https://mlsanity.com/paper/2506.09284/) (2025)
- [Local Policies Enable Zero-shot Long-horizon Manipulation](https://mlsanity.com/paper/2410.22332/) (2024)
- [Robotic Visual Instruction](https://mlsanity.com/paper/2505.00693/) (2025)
- [PALM: Progress-Aware Policy Learning via Affordance Reasoning for Long-Horizon Robotic Manipulation](https://mlsanity.com/paper/2601.07060/) (2026)
- [Trust the PRoC3S: Solving Long-Horizon Robotics Problems with LLMs and Constraint Satisfaction](https://mlsanity.com/paper/2406.05572/) (2024)

## Abstract (arXiv)

Foundation models pre-trained on web-scale data are shown to encapsulate extensive world knowledge beneficial for robotic manipulation in the form of task planning. However, the actual physical implementation of these plans often relies on task-specific learning methods, which require significant data collection and struggle with generalizability. In this work, we introduce Robotic Manipulation through Spatial Constraints of Parts (CoPa), a novel framework that leverages the common sense knowledge embedded within foundation models to generate a sequence of 6-DoF end-effector poses for open-world robotic manipulation. Specifically, we decompose the manipulation process into two phases: task-oriented grasping and task-aware motion planning. In the task-oriented grasping phase, we employ foundation vision-language models (VLMs) to select the object's grasping part through a novel coarse-to-fine grounding mechanism. During the task-aware motion planning phase, VLMs are utilized again to identify the spatial geometry constraints of task-relevant object parts, which are then used to derive post-grasp poses. We also demonstrate how CoPa can be seamlessly integrated with existing robotic planning algorithms to accomplish complex, long-horizon tasks. Our comprehensive real-world experiments show that CoPa possesses a fine-grained physical understanding of scenes, capable of handling open-set instructions and objects with minimal prompt engineering and without additional training. Project page: https://copa-2024.github.io/