# Geometric Fabrics for the Acceleration-based Design of Robotic Motion

arXiv: https://arxiv.org/abs/2010.14750 · HTML: https://mlsanity.com/paper/2010.14750/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Oct 2020.

## Built on by (most cited first, 7 of 7)

- [EDMP: Ensemble-of-costs-guided Diffusion for Motion Planning](https://mlsanity.com/paper/2309.11414/) (2023)
- [Potential Based Diffusion Motion Planning](https://mlsanity.com/paper/2407.06169/) (2024)
- [Composable Energy Policies for Reactive Motion Generation and Reinforcement Learning](https://mlsanity.com/paper/2105.04962/) (2021)
- [Hierarchical Policy Blending as Inference for Reactive Robot Control](https://mlsanity.com/paper/2210.07890/) (2022)
- [Hierarchical Policy Blending As Optimal Transport](https://mlsanity.com/paper/2212.01938/) (2022)
- [TamedPUMA: safe and stable imitation learning with geometric fabrics](https://mlsanity.com/paper/2503.17432/) (2025)
- [Sum of Costs Diffusion with Dynamic Guidance for Motion Planning](https://mlsanity.com/paper/2605.24690/) (2026)

## Abstract (arXiv)

This paper describes the pragmatic design and construction of geometric fabrics for shaping a robot's task-independent nominal behavior, capturing behavioral components such as obstacle avoidance, joint limit avoidance, redundancy resolution, global navigation heuristics, etc. Geometric fabrics constitute the most concrete incarnation of a new mathematical formulation for reactive behavior called optimization fabrics. Fabrics generalize recent work on Riemannian Motion Policies (RMPs); they add provable stability guarantees and improve design consistency while promoting the intuitive acceleration-based principles of modular design that make RMPs successful. We describe a suite of mathematical modeling tools that practitioners can employ in practice and demonstrate both how to mitigate system complexity by constructing behaviors layer-wise and how to employ these tools to design robust, strongly-generalizing, policies that solve practical problems one would expect to find in industry applications. Our system exhibits intelligent global navigation behaviors expressed entirely as provably stable fabrics with zero planning or state machine governance.