This paper addresses the problem of formation control for a quadrotor swarm (QS) system with directed graph topology under external environmental disturbances and unreliable internal state acquisition. The proposed distributed robust control framework, based on a gemetric controller, incorporates $\mathcal{L}_1$ adaptive controllers and differentiator systems. First, the geometric formation controller is designed to implement the formation control of the nominal system. Then, $\mathcal{L}_1$ adaptive controllers are designed separately for each quadrotor’s position loop and attitude loop subsystems to address the effects of uncertainties such as external time-varying disturbances (matched and unmatched disturbances) and different mass variations of quadrotors. Furthermore, the differentiator system is devised to accurately estimate the higher-order derivatives of the non-directly-measurable velocity information and the virtual translation control signal, which enhances system accuracy while reducing computational complexity. The Lyapunov stability theory is employed to analyze the stability of the closed-loop system. Finally, the effectiveness and exceptional performance of this approach in QS formation control were validated through numerical simulation and experimental results. Note to Practitioners—The inspiration for this article comes from the issue of formation control in a cluster of quadrotor drones, which is also applicable to formation control in other types of drones. In this paper, a formation control algorithm based on $\mathcal{L}_1$ adaptive control strategy and arbitrary-order differentiation is designed. This algorithm can address not only the issue of time-varying wind disturbances frequently encountered during quadrotor drone flights but also the effects of unpredictable velocities and inconsistent masses of quadrotor drones. The disturbance rejection capability of this scheme enables quadrotor drones to be applied more safely and reliably in complex environments for search and rescue missions and surveillance tasks. Eliminating the need for linear velocity measurements reduces sensor costs and enhances system reliability and stability. The proposed formation control scheme allows the QS system to have different masses for each UAV, which can be applied to tasks such as collaboration logistics transportation, material delivery and crop spraying. Preliminary physical experiments have validated the feasibility of the proposed scheme, although it has not been applied in practical scenarios yet. In future research, we intend to equip each drone in the QS system with objects of different masses to achieve collaboration material transportation and delivery in complex environments.

中文翻译：

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$\mathcal{L}_{1}$未知干扰下无线速度反馈的多四旋翼飞行器自适应控制编队跟踪


本文解决了外部环境干扰和不可靠的内部状态采集下具有有向图拓扑的四旋翼集群（QS）系统的编队控制问题。所提出的分布式鲁棒控制框架基于几何控制器，包含 $\mathcal{L}_1$ 自适应控制器和微分器系统。首先，设计几何编队控制器来实现标称系统的编队控制。然后，为每个四旋翼飞行器的位置环和姿态环子系统分别设计$\mathcal{L}_1$自适应控制器，以解决外部时变干扰（匹配和不匹配干扰）和四旋翼不同质量变化等不确定性的影响。此外，微分器系统被设计为精确估计不可直接测量的速度信息和虚拟平移控制信号的高阶导数，这提高了系统精度，同时降低了计算复杂度。采用李雅普诺夫稳定性理论来分析闭环系统的稳定性。最后，通过数值模拟和实验结果验证了该方法在QS编队控制中的有效性和优异性能。从业者注意——本文的灵感来自于四旋翼无人机集群中的编队控制问题，这也适用于其他类型无人机的编队控制。本文设计了一种基于$\mathcal{L}_1$自适应控制策略和任意阶微分的编队控制算法。 该算法不仅可以解决四旋翼无人机飞行过程中经常遇到的时变风扰问题，还可以解决四旋翼无人机速度不可预测和质量不一致的影响。该方案的抗扰能力使得四旋翼无人机能够更加安全可靠地应用于复杂环境下的搜救任务和监视任务。消除线速度测量的需要降低了传感器成本并增强了系统的可靠性和稳定性。所提出的编队控制方案允许QS系统为每架无人机提供不同的质量，可应用于协作物流运输、物资输送和农作物喷洒等任务。初步的物理实验验证了该方案的可行性，但尚未应用于实际场景。在未来的研究中，我们打算为QS系统中的每架无人机配备不同质量的物体，以实现复杂环境下的协作物资运输和投递。