It is essential in many applications to impose a scalable coordinated motion control on a large group of mobile robots, which is efficient in tasks requiring repetitive execution, such as environmental monitoring. In this paper, we design a guiding vector field to guide multiple robots to follow possibly different desired paths while coordinating their motions. The vector field uses a path parameter as a virtual coordinate that is communicated among neighboring robots. Then, the virtual coordinate is utilized to control the relative parametric displacement between robots along the paths. This enables us to design a saturated control algorithm for a Dubins-car-like model. The algorithm is distributed, scalable, and applicable for any smooth paths in an $n$-dimensional configuration space, and global convergence is guaranteed. Simulations with up to fifty robots and outdoor experiments with fixed-wing aircraft validate the theoretical results.

翻译：在许多应用中,有必要对一大批移动机器人实施可扩缩的协调动作控制,这对于执行需要重复执行的任务(如环境监测)是有效的。在本文中,我们设计了一个指导矢量场,指导多个机器人在协调其动作的同时遵循不同的预期路径。矢量场使用一个路径参数作为虚拟坐标,在相邻的机器人之间传递。然后,虚拟坐标被用来控制沿路径的机器人之间的相对参数迁移。这使我们能够为类似杜宾斯汽车的模型设计饱和控制算法。算法分布、可扩缩和适用于美元维配置空间中的任何光滑路径,并且保证全球汇合。模拟多达50个机器人,与固定翼飞机进行室外实验,验证理论结果。