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.
Over the past couple of decades, unmanned aerial vehicles (UAVs), or drones, have experienced rapid growth and evolved into diversified applications across multiple domains [1], resulting in drones becoming more accessible and highly capable over the past few years [2]. Interactive flying systems have been identified in 16 different domains and over 100 applications by observing the latest research [3]. However, drones face limitations in flight duration due to battery capacity and payload threshold when performing complex tasks [4]. One solution to mitigate these limitations is to allow multiple drones to operate together as a flock [5]. The coordinated and cohesive movement Sujan Warnakulasooriya is with the Wireless Research Centre, University of Canterbury (UC), Christchurch 8140, New Zealand, and also with the Computer Science and Software Engineering Department, University of Canterbury (UC), Christchurch 8140, New Zealand (e-mail: sujan.warnakulasooirya@pg.canterbury.ac.nz).
Andreas Willig is with the Computer Science and Software Engineering Department, University of Canterbury (UC), Christchurch 8140, New Zealand (e-mail: andreas.willig@canterbury.ac.nz). inside a defined environment with rigid relative positions, inspired by animals such as birds or fish, is defined as flocking [6]. Flocking behaviour offers advantages such as added flexibility, divided workload, faster completion of tasks, redundancy in case of an individual drone failure, and better overall coverage [7], while introducing the cost of increased complexity in orchestrating an entire group of drones. Applications in agriculture [8], delivery systems [9], [10], environmental monitoring [11], infrastructure maintenance [12], landmine detection [13], search and rescue [14], and surveillance [15] are among the examples of enhanced drone flocking capabilities.
While appreciating the enhanced capabilities of drone flocking, several new challenges arise when multiple drones attempt to operate in the same geographical area. A drone flock faces interconnected challenges including control system design, NP-hard path planning, implementation of collision avoidance protocols, communication network reliability, continuous monitoring requirements, and computational scalability as swarm sizes increase [16].
Vasarhelyi et al. [17] successfully demonstrated that flocking models require explicit handling of constrained motion, communication delays, and barriers, resulting in additional model complexity and increased tunable parameters that necessitate an evolutionary optimisation framework when they validated the seamless movement of a flock of 30 drones autonomously. In this paper, the initial formation of a flock of drones is investigated. This is considered as an initial flock formation problem where the drones move from starting positions to their respective target positions within the flock. This problem can be essentially categorised as a drone path planning problem.
An efficient path-planning algorithm should provide a solution that is both complete and optimal [18]. As noted by Gasparetto et al. [19], path planning is concerned solely with the geometric aspect of motion and does not account for time. In contrast, trajectory planning enriches a geometric path by specifying its temporal profile, defining how position, velocity, and acceleration evolve along the path. When operating as a flock and planning individual paths, drones must minimise formation time and total travel distance, ensure collision-free travel, and tolerate sensing and navigation errors to an acceptable degree, all while maintaining reasonable computation times [20]. Various path planning or trajectory planning approaches have been proposed in the literature to address the problem of initial flock formation for a fixed number of n drones in an obstacle-free environment, starting from known arbitrary starting positions and moving to designated target positions in a desired flock geometry, without collisions and in the shortest possible time. Existing approaches emphasise accurate and reliable flock formation-whether through geometric path planning (e.g., cell decomposition, rapidly-exploring random trees (RRTs), artificial potential fields) or trajectory-based control (e.g., consensus laws, ant colony optimisation, heuristic scheduling, space-time graph pruning). However, these methods often compromise efficiency in flocking time and travel distance, relying on reactive avoidance, simplified environments, or limited scalability. This paper introduces a novel approach, timeefficient prioritised scheduling (TPS), designed to coordinate a flock of drones to form their initial formation without any collisions, even at large scales. The TPS algorithm assumes each drone travels along a straight-line path from its starting position to its destination. To prevent inter-drone collisions, the trajectory of each drone is modified by introducing a calculated starting delay. Even tho
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