Spontaneous-Ordering Platoon Control for Multirobot Path Navigation Using Guiding Vector Fields

In this article, we propose a distributed guiding vector-field (DGVF) algorithm for a team of robots to form a spontaneous-ordering platoon moving along a predefined desired path in the n-dimensional Euclidean space. Particularly, by adding a path parameter as an additional virtual coordinate to each robot, the DGVF algorithm can eliminate the singular points where the vector fields vanish, and govern robots to approach a closed and even self-intersecting desired path. Then, the interactions among neighboring robots and a virtual target robot through their virtual coordinates enable the realization of the desired platoon; in particular, relative parametric displacements can be achieved with arbitrary ordering sequences. Rigorous analysis is provided to guarantee the global convergence of the spontaneous-ordering platoon on the common desired path from any initial positions. Two-dimensional experiments using three HUSTER-0.3 unmanned surface vessels (USVs) are conducted to validate the practical effectiveness of the proposed DGVF algorithm, and 3-D numerical simulations are presented to demonstrate its effectiveness and robustness when tackling higher dimensional multirobot path-navigation missions and some robots breakdown.