In this paper, 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 to the spontaneous-ordering platoon on the common desired path from any initial positions. 2D experiments using three HUSTER-0.3 unmanned surface vessels (USVs) are conducted to validate the practical effectiveness of the proposed DGVF algorithm, and 3D numerical simulations are presented to demonstrate its effectiveness and robustness when tackling higher-dimensional multi-robot path-navigation missions and some robots breakdown.

翻译：本文提出一种分布式引导向量场（DGVF）算法，用于实现机器人团队在n维欧氏空间中沿预定义期望路径自发排序移动的编队控制。具体而言，通过为每个机器人添加路径参数作为额外虚拟坐标，DGVF算法能够消除向量场消失的奇异点，并引导机器人逼近封闭甚至自交的期望路径。随后，相邻机器人之间以及虚拟目标机器人通过虚拟坐标的相互作用，可实现期望的编队模式；特别地，能够以任意排序序列实现相对参数位移。本文提供了严格的理论分析，保证从任意初始位置出发都能全局收敛至共享期望路径上的自发排序编队。通过三艘HUSTER-0.3无人水面艇（USV）的二维实验验证了所提DGVF算法的实际有效性，同时通过三维数值仿真展示了该算法在处理高维多机器人路径导航任务及部分机器人故障时的有效性与鲁棒性。