Non-singular cooperative guiding vector field under a homotopy equivalence transformation

The present article introduces the concept of a non-singular cooperative guiding vector field under a homotopy equivalence transformation. Initially, an innovative non-singular guiding vector field is derived, which is capable of guiding the controlled robot to follow a path in a moving frame. Furthermore, the properties of homotopy equivalence transformation are explored to establish the existence of the aforementioned vector field. Subsequently, a cooperative vector field, based on an extensive parameter consensus protocol, is introduced, including an in-depth analysis of the impact of vector field parameters. Then, the practical implementation of this innovative vector field is demonstrated through its application to cooperative path following in both 2-D and 3-D scenarios, showcasing its effectiveness. Finally, for a non-holonomic robot at constant speed, a moving path following control law based on the guiding vector field is presented, along with a discussion on speed constraint.