# Geometric Fabrics: Generalizing Classical Mechanics to Capture the Physics of Behavior

arXiv: https://arxiv.org/abs/2109.10443 · HTML: https://mlsanity.com/paper/2109.10443/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Sep 2021.

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

- [Motion Policy Networks](https://mlsanity.com/paper/2210.12209/) (2022)
- [DexPBT: Scaling up Dexterous Manipulation for Hand-Arm Systems with Population Based Training](https://mlsanity.com/paper/2305.12127/) (2023)
- [DexTransfer: Real World Multi-fingered Dexterous Grasping with Minimal Human Demonstrations](https://mlsanity.com/paper/2209.14284/) (2022)
- [CabiNet: Scaling Neural Collision Detection for Object Rearrangement with Procedural Scene Generation](https://mlsanity.com/paper/2304.09302/) (2023)
- [Learning Riemannian Stable Dynamical Systems via Diffeomorphisms](https://mlsanity.com/paper/2211.03169/) (2022)
- [SplaTraj: Camera Trajectory Generation with Semantic Gaussian Splatting](https://mlsanity.com/paper/2410.06014/) (2024)
- [Deep Reactive Policy: Learning Reactive Manipulator Motion Planning for Dynamic Environments](https://mlsanity.com/paper/2509.06953/) (2025)
- [Hierarchical Policy Blending as Inference for Reactive Robot Control](https://mlsanity.com/paper/2210.07890/) (2022)
- [Cascaded Diffusion Models for Neural Motion Planning](https://mlsanity.com/paper/2505.15157/) (2025)
- [PUMA: Deep Metric Imitation Learning for Stable Motion Primitives](https://mlsanity.com/paper/2310.12831/) (2023)
- [From Single Images to Motion Policies via Video-Generation Environment Representations](https://mlsanity.com/paper/2505.19306/) (2025)
- [Learning Orbitally Stable Systems for Diagrammatically Teaching](https://mlsanity.com/paper/2309.10298/) (2023)
- [Toward Generalist Neural Motion Planners for Robotic Manipulators: Challenges and Opportunities](https://mlsanity.com/paper/2603.24318/) (2026)
- [Flow Motion Policy: Manipulator Motion Planning with Flow Matching Models](https://mlsanity.com/paper/2604.07084/) (2026)
- [A Probabilistic Relaxation of the Two-Stage Object Pose Estimation Paradigm](https://mlsanity.com/paper/2306.00892/) (2023)
- [World-Task Factorization for Robot Learning](https://mlsanity.com/paper/2606.02027/) (2026)
- [ELMP: Efficient Learning for Motion Planning via Analytical Policy Gradients](https://mlsanity.com/paper/2607.00215/) (2026)
- [NeurRAFT: Robot Motion Planning via Anchor-Level Flow Matching with Clearance-Aware Preference Tuning](https://mlsanity.com/paper/2608.24026/) (2026)
- [WeaveRL: Weaving Reconstruction into Scene-Aware Fabrics for Perceptive Reinforcement Learning](https://mlsanity.com/paper/2609.18685/) (2026)

## Abstract (arXiv)

Classical mechanical systems are central to controller design in energy shaping methods of geometric control. However, their expressivity is limited by position-only metrics and the intimate link between metric and geometry. Recent work on Riemannian Motion Policies (RMPs) has shown that shedding these restrictions results in powerful design tools, but at the expense of theoretical stability guarantees. In this work, we generalize classical mechanics to what we call geometric fabrics, whose expressivity and theory enable the design of systems that outperform RMPs in practice. Geometric fabrics strictly generalize classical mechanics forming a new physics of behavior by first generalizing them to Finsler geometries and then explicitly bending them to shape their behavior while maintaining stability. We develop the theory of fabrics and present both a collection of controlled experiments examining their theoretical properties and a set of robot system experiments showing improved performance over a well-engineered and hardened implementation of RMPs, our current state-of-the-art in controller design.