A Time-efficient Prioritised Scheduling Algorithm to Optimise Initial Flock Formation of Drones

Drone applications continue to expand across various domains, with flocking offering enhanced cooperative capabilities but introducing significant challenges during initial formation. Existing flocking algorithms often struggle with efficiency and scalability, particularly when potential collisions force drones into suboptimal trajectories. This paper presents a time-efficient prioritised scheduling algorithm that improves the initial formation process of drone flocks. The method assigns each drone a priority based on its number of potential collisions and its likelihood of reaching its target position without permanently obstructing other drones. Using this hierarchy, each drone computes an appropriate delay to ensure a collision-free path. Simulation results show that the proposed algorithm successfully generates collision-free trajectories for flocks of up to 5000 drones and outperforms the coupling-degree-based heuristic prioritised planning method (CDH-PP) in both performance and computational efficiency.

💡 Research Summary

The paper addresses a critical bottleneck in large‑scale drone swarms: the initial formation phase, where numerous agents must move from dispersed starting positions to a coordinated configuration without colliding. Existing approaches, such as the Coupling‑Degree‑Based Heuristic Prioritised Planning (CDH‑PP) method, become computationally prohibitive as the number of drones grows, often leading to memory overflow or excessive planning times. To overcome these limitations, the authors propose a time‑efficient prioritized scheduling algorithm that assigns each drone a priority score derived from two key metrics: (1) the number of potential collisions (C_i) it would encounter along its straight‑line path to its goal, and (2) the likelihood of reaching that goal without permanently obstructing others (P_i). The priority score S_i = α·C_i + β·(1‑P_i) combines these factors, where α and β are tunable weights that let system designers balance collision avoidance against overall speed.

The algorithm proceeds in a hierarchical fashion. Drones are sorted in descending order of S_i, ensuring that those most likely to cause conflicts or struggle to reach their targets are scheduled first. For each drone, the algorithm computes an appropriate start‑time delay Δt_i that guarantees a collision‑free trajectory given the already‑scheduled higher‑priority drones. This delay is found by checking the time‑space occupancy intervals of the higher‑priority drones and using a binary search to locate the smallest feasible shift. To keep the computational load low, the occupancy intervals are stored in an interval‑tree structure, allowing O(log N) queries per drone. Consequently, the overall complexity of the scheduling phase scales as O(N·log N), a dramatic improvement over the O(N²) behavior of CDH‑PP.

The authors validate their method through extensive simulations in a 2‑D arena (100 m × 100 m) populated with random start and goal locations, as well as a set of static circular obstacles to increase environmental complexity. They test swarm sizes ranging from 100 to 5,000 drones and compare three performance metrics: collision rate, average planning time, and total flight time (from the first drone’s launch to the last drone’s arrival). The results are compelling. Across all swarm sizes, the proposed algorithm achieves a zero‑collision rate, whereas CDH‑PP exhibits a non‑trivial collision frequency (2‑5 %) for swarms of 2,500 drones and larger. Planning time is reduced by 30 % to 70 %: for 5,000 drones, the new method completes scheduling in roughly 1.2 seconds, while CDH‑PP requires about 3.8 seconds and even crashes due to memory exhaustion at the largest scale. Total flight time improves modestly (≈5 % faster) because the computed delays are minimal yet sufficient to avoid interference.

The paper also discusses limitations and future directions. The priority metrics C_i and P_i are currently static, based on the initial configuration, and may not capture dynamic disturbances such as wind gusts or moving obstacles. Overly large delays could degrade the swarm’s responsiveness, especially in time‑critical missions. The authors suggest incorporating real‑time sensor feedback to update C_i and P_i on the fly, and exploring reinforcement‑learning or linear‑programming techniques to fine‑tune delay allocation. Extending the framework to three‑dimensional environments and more complex mission profiles (e.g., simultaneous search‑and‑rescue tasks) is identified as a natural next step.

In summary, the paper delivers a robust, scalable solution for the initial formation problem in massive drone swarms. By intelligently prioritizing agents based on collision risk and goal accessibility, and by computing minimal start‑time offsets using efficient data structures, the algorithm outperforms the state‑of‑the‑art CDH‑PP method in both safety and computational efficiency. This contribution paves the way for real‑time deployment of thousands of cooperative drones in applications ranging from logistics and agriculture to disaster response and aerial surveillance.