We design a distributed coordinated guiding vector field (CGVF) for a group of robots to achieve ordering-flexible motion coordination while maneuvering on a desired two-dimensional (2D) surface. The CGVF is characterized by three terms, i.e., a convergence term to drive the robots to converge to the desired surface, a propagation term to provide a traversing direction for maneuvering on the desired surface, and a coordinated term to achieve the surface motion coordination with an arbitrary ordering of the robotic group. By setting the surface parameters as additional virtual coordinates, the proposed approach eliminates the potential singularity of the CGVF and enables both the global convergence to the desired surface and the maneuvering on the surface from all possible initial conditions. The ordering-flexible surface motion coordination is realized by each robot to share with its neighbors only two virtual coordinates, i.e. that of a given target and that of its own, which reduces the communication and computation cost in multi-robot surface navigation. Finally, the effectiveness of the CGVF is substantiated by extensive numerical simulations.

翻译：我们设计了一种分布式协调制导向量场(CGVF)，用于实现一组机器人在期望的二维曲面上机动时的排序灵活运动协调。该CGVF由三项构成，即：驱动机器人收敛至期望曲面的收敛项、提供在期望曲面上机动穿越方向的传播项，以及实现任意机器人编队排序下的曲面运动协调的协调项。通过将曲面参数设置为附加虚拟坐标，所提方法消除了CGVF的潜在奇异性，并使得从所有可能初始条件出发，既能全局收敛至期望曲面，又能在曲面上实现机动。排序灵活的曲面运动协调通过每个机器人仅与其邻居共享两个虚拟坐标（即给定目标坐标及其自身坐标）来实现，这降低了多机器人曲面导航中的通信与计算成本。最后，通过大量数值仿真验证了CGVF的有效性。