# Acting in Meters: Learning Metric Interactions for Precise Robotic Manipulation

arXiv: https://arxiv.org/abs/2609.18243 · HTML: https://mlsanity.com/paper/2609.18243/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Embodied and robot world models, one of 11 directions in World models.
- Builds on 32 of its 48 references that are in the map.
- First posted on arXiv 16 Sep 2026.

## Placed in

- World models / [Embodied and robot world models](https://mlsanity.com/wm/embodied-and-robot-world-models/)
- Vision-language-action models / [Human-video and latent-action pretraining](https://mlsanity.com/vla/human-video-and-latent-action-pretraining/)

## Builds on (most cited first, 30 of 32)

- [π0.5: a Vision-Language-Action Model with Open-World Generalization](https://mlsanity.com/paper/2504.16054/) (2025)
- [GR00T N1: An Open Foundation Model for Generalist Humanoid Robots](https://mlsanity.com/paper/2503.14734/) (2025)
- [SmolVLA: A Vision-Language-Action Model for Affordable and Efficient Robotics](https://mlsanity.com/paper/2506.01844/) (2025)
- [SpatialVLA: Exploring Spatial Representations for Visual-Language-Action Model](https://mlsanity.com/paper/2501.15830/) (2025)
- [RoboTwin 2.0: A Scalable Data Generator and Benchmark with Strong Domain Randomization for Robust Bimanual Robotic Manipulation](https://mlsanity.com/paper/2506.18088/) (2025)
- [World Action Models are Zero-shot Policies](https://mlsanity.com/paper/2602.15922/) (2026)
- [Fast-WAM: Do World Action Models Need Test-time Future Imagination?](https://mlsanity.com/paper/2603.16666/) (2026)
- [Causal World Modeling for Robot Control](https://mlsanity.com/paper/2601.21998/) (2026)
- [Cosmos Policy: Fine-Tuning Video Models for Visuomotor Control and Planning](https://mlsanity.com/paper/2601.16163/) (2026)
- [GR-2: A Generative Video-Language-Action Model with Web-Scale Knowledge for Robot Manipulation](https://mlsanity.com/paper/2410.06158/) (2024)
- [Unified World Models: Coupling Video and Action Diffusion for Pretraining on Large Robotic Datasets](https://mlsanity.com/paper/2504.02792/) (2025)
- [GigaWorld-Policy: An Efficient Action-Centered World--Action Model](https://mlsanity.com/paper/2603.17240/) (2026)
- [π0.7: a Steerable Generalist Robotic Foundation Model with Emergent Capabilities](https://mlsanity.com/paper/2604.15483/) (2026)
- [StarVLA: A Lego-like Codebase for Vision-Language-Action Model Developing](https://mlsanity.com/paper/2604.05014/) (2026)
- [TesserAct: Learning 4D Embodied World Models](https://mlsanity.com/paper/2504.20995/) (2025)
- [Unified 4D World Action Modeling from Video Priors with Asynchronous Denoising](https://mlsanity.com/paper/2604.26694/) (2026)
- [MiMo-Embodied: X-Embodied Foundation Model Technical Report](https://mlsanity.com/paper/2511.16518/) (2025)
- [Native Video-Action Pretraining for Generalizable Robot Control](https://mlsanity.com/paper/2607.08639/) (2026)
- [From Foundation to Application: Improving VLA Models in Practice](https://mlsanity.com/paper/2607.06403/) (2026)
- [HumanEgo: Zero-Shot Robot Learning from Minutes of Human Egocentric Videos](https://mlsanity.com/paper/2605.24934/) (2026)
- [WAM4D: Fast 4D World Action Model via Spatial Register Tokens](https://mlsanity.com/paper/2606.14048/) (2026)
- [Learning 4D Geometric Priors for Inference-Efficient World Action Models](https://mlsanity.com/paper/2607.05468/) (2026)
- [LaMP: Learning Vision-Language-Action Policy with 3D Scene Flow as Latent Motion Prior](https://mlsanity.com/paper/2603.25399/) (2026)
- [GeoSem-WAM: Geometry- and Semantic-Aware World Action Models](https://mlsanity.com/paper/2606.03188/) (2026)
- [Geometric Action Model for Robot Policy Learning](https://mlsanity.com/paper/2606.17046/) (2026)
- [GigaWorld-Policy-0.5: A Faster and Stronger WAM Empowered by AutoResearch](https://mlsanity.com/paper/2607.13960/) (2026)
- [GEM-4D: Geometry-Enhanced Video World Models for Robot Manipulation](https://mlsanity.com/paper/2605.22882/) (2026)
- [Planning Takes More Than Token Prediction: Causal Plan for Benchmarking and Building Physically Grounded Embodied Reasoners](https://mlsanity.com/paper/2606.01810/) (2026)
- [μ0: A Scalable 3D Interaction-Trace World Model](https://mlsanity.com/paper/2606.13769/) (2026)
- [PointAction: 3D Points as Universal Action Representations for Robot Control](https://mlsanity.com/paper/2606.03943/) (2026)

## Abstract (arXiv)

Vision-Language-Action models and World-Action Models have advanced language-conditioned robotic manipulation, yet often leave metric relations among actions, objects, and scene geometry implicit. Human manipulation combines semantic understanding of task-relevant objects with spatial feedback that guides hand motion relative to objects and their surroundings. Inspired by this, we introduce a metric interaction framework that models object-level and scene-level interactions in physical Cartesian space at a shared metric scale. At the object level, Interaction-Centric Tokens (ICTs) explicitly represent end-effector pose trajectories relative to manipulated objects and are jointly denoised with actions, providing physically grounded interaction supervision. At the scene level, the Metric Action Interaction Field (MAIF) uses action and ICT queries to attend to metric scene point-cloud features and learns geometry-conditioned action corrections. Through two-stage adaptation, our framework improves diverse VLA and WAM baselines with a small number of additional parameters and training steps. Experiments demonstrate average success-rate gains of 0.80 and 3.59 percentage points on LIBERO and RoboTwin 2.0, respectively, alongside gains of 6.80 percentage points on real-world tasks and 7.45 percentage points on their out-of-distribution variants.