This work proposes a novel 2-D formation control scheme for acyclic triangulated directed graphs (a class of minimally acyclic persistent graphs) based on bipolar coordinates with (almost) global convergence to the desired shape. Prescribed performance control is employed to devise a decentralized control law that avoids singularities and introduces robustness against external disturbances while ensuring predefined transient and steady-state performance for the closed-loop system. Furthermore, it is shown that the proposed formation control scheme can handle formation maneuvering, scaling, and orientation specifications simultaneously. Additionally, the proposed control law is implementable in agents' arbitrarily oriented local coordinate frames using only low-cost onboard vision sensors, which are favorable for practical applications. Finally, a formation maneuvering simulation study verifies the proposed approach.

翻译：本文提出了一种基于双极坐标的新型二维编队控制方案，适用于无环三角有向图（一类最小无环持久图），并实现了（几乎）全局收敛至期望形状。采用预设性能控制方法设计了一种分散控制律，该控制律能够避免奇异性问题，并引入对外部干扰的鲁棒性，同时确保闭环系统的瞬态与稳态性能满足预定要求。进一步证明，所提出的编队控制方案可同时处理编队机动、缩放及方向规范。此外，该控制律可在任意定向的局部坐标系中实现，且仅需使用低成本机载视觉传感器，这有利于实际应用。最后，通过编队机动仿真研究验证了所提方法的有效性。