# Non-singular Cooperative Guiding Vector Field Under a Homotopy Equivalence Transformation

arXiv: https://arxiv.org/abs/2308.06934 · HTML: https://mlsanity.com/paper/2308.06934/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Aug 2023.

## Built on by (most cited first, 1 of 1)

- [Guiding Vector Field Generation via Score-based Diffusion Model](https://mlsanity.com/paper/2604.24487/) (2026)

## Abstract (arXiv)

The present article advances the concept of a non-singular cooperative guiding vector field under a homotopy equivalence transformation. Firstly, the derivation of a guiding vector field, based on a non-singular vector field, is elaborated to navigate a transformed path from another frame. The existence of such vector fields is also deliberated herein. Subsequently, a coordination vector field derived from the guiding vector field is presented, incorporating an in-depth analysis concerning the impact of the vector field parameters. Lastly, the practical implementation of this novel vector field is demonstrated by its applications to 2-D and 3-D cooperative moving path following issues, establishing its efficacy.