This work investigates the self-organization of multi-agent systems into closed trajectories, a common requirement in unmanned aerial vehicle (UAV) surveillance tasks. In such scenarios, smooth, unbiased control signals save energy and mitigate mechanical strain. We propose a decentralized control system architecture that produces a globally stable emergent structure from local observations only; there is no requirement for agents to share a global plan or follow prescribed trajectories. Central to our approach is the formulation of an injective virtual embedding induced by rotations from the actual agent positions. This embedding serves as a structure-preserving map around which all agent stabilize their relative positions and permits the use of well-established linear control techniques. We construct the embedding such that it is topologically equivalent to the desired trajectory (i.e., a homeomorphism), thereby preserving the stability characteristics. We demonstrate the versatility of this approach through implementation on a swarm of Quanser QDrone quadcopters. Results demonstrate the quadcopters self-organize into the desired trajectory while maintaining even separation.

翻译：本研究探讨了多智能体系统在闭轨迹上的自组织行为，这是无人机监视任务中的常见需求。在此类场景中，平滑、无偏的控制信号能够节约能源并减轻机械应力。我们提出了一种分散式控制系统架构，该架构仅通过局部观测即可产生全局稳定的涌现结构；智能体无需共享全局规划或遵循预设轨迹。我们方法的核心在于构建一个由实际智能体位置旋转诱导的单射虚拟嵌入。该嵌入作为一个保持结构的映射，所有智能体依此稳定其相对位置，并允许使用成熟的线性控制技术。我们构建的嵌入在拓扑结构上与期望轨迹等价（即存在同胚映射），从而保持了稳定性特征。通过在Quanser QDrone四旋翼无人机集群上的实现，我们展示了该方法的通用性。实验结果表明，四旋翼无人机能够自组织形成期望轨迹，同时保持均匀间距。