# Dynamic Optimization Fabrics for Motion Generation

arXiv: https://arxiv.org/abs/2205.08454 · HTML: https://mlsanity.com/paper/2205.08454/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 May 2022.

## Built on by (most cited first, 2 of 2)

- [TamedPUMA: safe and stable imitation learning with geometric fabrics](https://mlsanity.com/paper/2503.17432/) (2025)
- [The Field Knows: Cross-Dimensional Geometry from Navigation to Black Holes](https://mlsanity.com/paper/2608.07566/) (2026)

## Abstract (arXiv)

Optimization fabrics are a geometric approach to real-time local motion generation, where motions are designed by the composition of several differential equations that exhibit a desired motion behavior. We generalize this framework to dynamic scenarios and non-holonomic robots and prove that fundamental properties can be conserved. We show that convergence to desired trajectories and avoidance of moving obstacles can be guaranteed using simple construction rules of the components. Additionally, we present the first quantitative comparisons between optimization fabrics and model predictive control and show that optimization fabrics can generate similar trajectories with better scalability, and thus, much higher replanning frequency (up to 500 Hz with a 7 degrees of freedom robotic arm). Finally, we present empirical results on several robots, including a non-holonomic mobile manipulator with 10 degrees of freedom and avoidance of a moving human, supporting the theoretical findings.