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.Comment: 12 pages, 12 figures, submitting to TAC at presen