# ReKep: Spatio-Temporal Reasoning of Relational Keypoint Constraints for Robotic Manipulation

arXiv: https://arxiv.org/abs/2409.01652 · HTML: https://mlsanity.com/paper/2409.01652/

## Key facts

- Cited by 315 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 112 of its 164 references that are in the map.
- First posted on arXiv 3 Sep 2024.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)

## Builds on (most cited first, 30 of 112)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [BLIP-2: Bootstrapping Language-Image Pre-training with Frozen Image Encoders and Large Language Models](https://mlsanity.com/paper/2301.12597/) (2023)
- [BLIP: Bootstrapping Language-Image Pre-training for Unified Vision-Language Understanding and Generation](https://mlsanity.com/paper/2201.12086/) (2022)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control](https://mlsanity.com/paper/2307.15818/) (2023)
- [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020)
- [Vision Transformers Need Registers](https://mlsanity.com/paper/2309.16588/) (2023)
- [VoxPoser: Composable 3D Value Maps for Robotic Manipulation with Language Models](https://mlsanity.com/paper/2307.05973/) (2023)
- [Dynamic 3D Gaussians: Tracking by Persistent Dynamic View Synthesis](https://mlsanity.com/paper/2308.09713/) (2023)
- [Eyes Wide Shut? Exploring the Visual Shortcomings of Multimodal LLMs](https://mlsanity.com/paper/2401.06209/) (2024)
- [SpatialVLM: Endowing Vision-Language Models with Spatial Reasoning Capabilities](https://mlsanity.com/paper/2401.12168/) (2024)
- [When and why vision-language models behave like bags-of-words, and what to do about it?](https://mlsanity.com/paper/2210.01936/) (2022)
- [Winoground: Probing Vision and Language Models for Visio-Linguistic Compositionality](https://mlsanity.com/paper/2204.03162/) (2022)
- [CoTracker: It is Better to Track Together](https://mlsanity.com/paper/2307.07635/) (2023)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [FoundationPose: Unified 6D Pose Estimation and Tracking of Novel Objects](https://mlsanity.com/paper/2312.08344/) (2023)
- [MONet: Unsupervised Scene Decomposition and Representation](https://mlsanity.com/paper/1901.11390/) (2019)
- [The Neuro-Symbolic Concept Learner: Interpreting Scenes, Words, and Sentences From Natural Supervision](https://mlsanity.com/paper/1904.12584/) (2019)
- [Deep ViT Features as Dense Visual Descriptors](https://mlsanity.com/paper/2112.05814/) (2021)
- [Simple Open-Vocabulary Object Detection with Vision Transformers](https://mlsanity.com/paper/2205.06230/) (2022)
- [Integrated Task and Motion Planning](https://mlsanity.com/paper/2010.01083/) (2020)
- [TAPIR: Tracking Any Point with per-frame Initialization and temporal Refinement](https://mlsanity.com/paper/2306.08637/) (2023)
- [PointOdyssey: A Large-Scale Synthetic Dataset for Long-Term Point Tracking](https://mlsanity.com/paper/2307.15055/) (2023)
- [RoboPoint: A Vision-Language Model for Spatial Affordance Prediction for Robotics](https://mlsanity.com/paper/2406.10721/) (2024)

## Built on by (most cited first, 30 of 315)

- [FAST: Efficient Action Tokenization for Vision-Language-Action Models](https://mlsanity.com/paper/2501.09747/) (2025)
- [CoT-VLA: Visual Chain-of-Thought Reasoning for Vision-Language-Action Models](https://mlsanity.com/paper/2503.22020/) (2025)
- [TraceVLA: Visual Trace Prompting Enhances Spatial-Temporal Awareness for Generalist Robotic Policies](https://mlsanity.com/paper/2412.10345/) (2024)
- [EmbodiedBench: Comprehensive Benchmarking Multi-modal Large Language Models for Vision-Driven Embodied Agents](https://mlsanity.com/paper/2502.09560/) (2025)
- [MolmoAct: Action Reasoning Models that can Reason in Space](https://mlsanity.com/paper/2508.07917/) (2025)
- [HybridVLA: Collaborative Diffusion and Autoregression in a Unified Vision-Language-Action Model](https://mlsanity.com/paper/2503.10631/) (2025)
- [VLABench: A Large-Scale Benchmark for Language-Conditioned Robotics Manipulation with Long-Horizon Reasoning Tasks](https://mlsanity.com/paper/2412.18194/) (2024)
- [Embodied Agent Interface: Benchmarking LLMs for Embodied Decision Making](https://mlsanity.com/paper/2410.07166/) (2024)
- [3DSRBench: A Comprehensive 3D Spatial Reasoning Benchmark](https://mlsanity.com/paper/2412.07825/) (2024)
- [RoboSpatial: Teaching Spatial Understanding to 2D and 3D Vision-Language Models for Robotics](https://mlsanity.com/paper/2411.16537/) (2024)
- [AHA: A Vision-Language-Model for Detecting and Reasoning Over Failures in Robotic Manipulation](https://mlsanity.com/paper/2410.00371/) (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)
- [GRAPE: Generalizing Robot Policy via Preference Alignment](https://mlsanity.com/paper/2411.19309/) (2024)
- [DexGraspVLA: A Vision-Language-Action Framework Towards General Dexterous Grasping](https://mlsanity.com/paper/2502.20900/) (2025)
- [VLA-Cache: Efficient Vision-Language-Action Manipulation via Adaptive Token Caching](https://mlsanity.com/paper/2502.02175/) (2025)
- [InternVLA-M1: A Spatially Guided Vision-Language-Action Framework for Generalist Robot Policy](https://mlsanity.com/paper/2510.13778/) (2025)
- [PointWorld: Scaling 3D World Models for In-The-Wild Robotic Manipulation](https://mlsanity.com/paper/2601.03782/) (2026)
- [RoboTwin: Dual-Arm Robot Benchmark with Generative Digital Twins (early version)](https://mlsanity.com/paper/2409.02920/) (2024)
- [Large VLM-based Vision-Language-Action Models for Robotic Manipulation: A Survey](https://mlsanity.com/paper/2508.13073/) (2025)
- [SpatialReasoner: Towards Explicit and Generalizable 3D Spatial Reasoning](https://mlsanity.com/paper/2504.20024/) (2025)
- [Code-as-Monitor: Constraint-aware Visual Programming for Reactive and Proactive Robotic Failure Detection](https://mlsanity.com/paper/2412.04455/) (2024)
- [4D-VLA: Spatiotemporal Vision-Language-Action Pretraining with Cross-Scene Calibration](https://mlsanity.com/paper/2506.22242/) (2025)
- [GenSim2: Scaling Robot Data Generation with Multi-modal and Reasoning LLMs](https://mlsanity.com/paper/2410.03645/) (2024)
- [TGRPO :Fine-tuning Vision-Language-Action Model via Trajectory-wise Group Relative Policy Optimization](https://mlsanity.com/paper/2506.08440/) (2025)
- [Pure Vision Language Action (VLA) Models: A Comprehensive Survey](https://mlsanity.com/paper/2509.19012/) (2025)
- [VidMan: Exploiting Implicit Dynamics from Video Diffusion Model for Effective Robot Manipulation](https://mlsanity.com/paper/2411.09153/) (2024)
- [SoFar: Language-Grounded Orientation Bridges Spatial Reasoning and Object Manipulation](https://mlsanity.com/paper/2502.13143/) (2025)
- [RT-Affordance: Affordances are Versatile Intermediate Representations for Robot Manipulation](https://mlsanity.com/paper/2411.02704/) (2024)
- [NovaFlow: Zero-Shot Manipulation via Actionable Flow from Generated Videos](https://mlsanity.com/paper/2510.08568/) (2025)

## Abstract (arXiv)

Representing robotic manipulation tasks as constraints that associate the robot and the environment is a promising way to encode desired robot behaviors. However, it remains unclear how to formulate the constraints such that they are 1) versatile to diverse tasks, 2) free of manual labeling, and 3) optimizable by off-the-shelf solvers to produce robot actions in real-time. In this work, we introduce Relational Keypoint Constraints (ReKep), a visually-grounded representation for constraints in robotic manipulation. Specifically, ReKep is expressed as Python functions mapping a set of 3D keypoints in the environment to a numerical cost. We demonstrate that by representing a manipulation task as a sequence of Relational Keypoint Constraints, we can employ a hierarchical optimization procedure to solve for robot actions (represented by a sequence of end-effector poses in SE(3)) with a perception-action loop at a real-time frequency. Furthermore, in order to circumvent the need for manual specification of ReKep for each new task, we devise an automated procedure that leverages large vision models and vision-language models to produce ReKep from free-form language instructions and RGB-D observations. We present system implementations on a wheeled single-arm platform and a stationary dual-arm platform that can perform a large variety of manipulation tasks, featuring multi-stage, in-the-wild, bimanual, and reactive behaviors, all without task-specific data or environment models. Website at https://rekep-robot.github.io/.