Drone light shows (DLShows) represent a rapidly growing application of swarm robotics, creating captivating aerial displays through the synchronized flight of hundreds or thousands of unmanned aerial vehicles (UAVs) as environmentally friendly and reusable alternatives to traditional pyrotechnics. This domain presents unique challenges in optimally assigning drones to visual waypoints and generating smooth, collision-free trajectories at a very large scale. This article introduces the Unified Assignment and Trajectory Generation (UATG) framework. The proposed approach concurrently solves two core problems: the optimal assignment of drones to designated goal locations and the generation of dynamically feasible, collision-free, time-parameterized trajectories. The UATG framework is specifically designed for DLShows, ensuring minimal transition times between formations and guaranteeing inter-drone collision avoidance. A key innovation is its exceptional computational efficiency, enabling the coordination of large-scale in real-time; for instance, it computes the optimal assignment and trajectories for 1008 drones in approximately one second on a standard laptop. Extensive simulations in realistic environments validate the framework's performance, demonstrating its capability to orchestrate complex formations, from alphanumeric characters to intricate 3D shapes, with precision and visual smoothness. This work provides a critical advancement for the DLShow industry, offering a practical and scalable solution for generating complex aerial choreography and establishing a valuable benchmark for ground control station software designed for the efficient coordination of multiple UAVs. A supplemental animated simulation of this work is available at https://youtu.be/-Fjrhw03594.

翻译：无人机灯光秀是群体机器人技术中快速发展的应用领域，通过数百或数千架无人机的同步飞行创造出引人入胜的空中展示，作为传统烟火表演的环保可重复利用替代方案。该领域在超大规模场景下面临两项独特挑战：将无人机最优分配至视觉航点，以及生成平滑无碰撞的飞行轨迹。本文提出统一分配与轨迹生成（UATG）框架，该方案同时解决两个核心问题：将无人机最优分配至指定目标位置，以及生成动态可行、无碰撞且含时间参数的轨迹。UATG框架专为无人机灯光秀设计，能够确保编队转换时间最小化并保证无人机间避碰。其关键创新在于卓越的计算效率——可在标准笔记本电脑上约1秒内完成1008架无人机的最优分配与轨迹计算。通过在逼真环境中的大量仿真验证，该框架展示了从字母数字字符到复杂三维形状的编队编排能力，兼顾精度与视觉平滑性。本研究为无人机灯光秀行业提供了关键进展，为生成复杂空中编排提供了实用可扩展解决方案，并为设计多无人机高效协调的地面控制站软件建立了重要基准。本研究的补充动画演示见https://youtu.be/-Fjrhw03594。