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

TL;DR

This paper introduces a new non-singular cooperative guiding vector field that uses homotopy equivalence to improve path following in multi-agent systems, with practical 2D and 3D applications.

Contribution

It develops a novel vector field based on homotopy transformation, ensuring non-singularity and cooperative guidance for path following tasks.

Findings

Effective in 2D and 3D cooperative path following

Ensures non-singular, stable guidance vector fields

Demonstrates practical applicability in multi-agent navigation

Abstract

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.