On the Problems of Drone Formation and Light Shows

This paper addresses the challenges associated with drone formation and light shows, presenting an algorithm with a complexity of O(MNLO) tailored for drone light show applications. The problem has traditionally been addressed using vector methods in previous research; however, their application becomes challenging when dealing with the intricacies of UAV swarms. Therefore, the proposed UAV formation algorithm embraces the voxel data structure and maze-running methodology to effectively address the complexities inherent in UAV swarm scenarios. The algorithm comprises three integral components: task assignment, obstacle-avoidance path-planning, and fault tolerance. In the initial phase, task assignment elucidates the methodology for assigning starting points and unassigned end-points of UAV flights, with a time complexity of O(L3logL), where L represents the number of drones. The subsequent phase introduces two distinct methods, namely detour and stay-and-forward, to address the issue of obstacle-avoidance path-planning. Both methods exhibit time complexities of O(NL), with N denoting the number of voxels. The final phase proposes a fault-tolerant mechanism to ensure smooth performance of drone light shows in the event of a drone failure during formation. To ensure uninterrupted performance, the backup drones execute collision avoidance for each frame at the onset, with a complexity of O(NLO), where O signifies the number of backup drones. The aggregate time complexity of the main algorithm, encompassing the aforementioned three components, is O(MNLO), where M denotes the number of main frames. The proposed method may reduce time consumption by seamlessly integrating collision computation into Blender, thus obviating the need for manual adjustments and offering advancements in both algorithmic efficiency and fault-tolerant performance for drone light shows.