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 <italic>spontaneous-ordering</italic> platoon moving along a predefined desired path in the <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula>-dimensional Euclidean space. Particularly, by adding a path parameter as an additional virtual coordinate to each robot, the DGVF algorithm can eliminate the <italic>singular points</italic> where the vector fields vanish, and govern robots to approach a <italic>closed</italic> and even <italic>self-intersecting</italic> 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 <italic>spontaneous-ordering</italic> 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.