A method for determining the topology of swarm elements relative to the leader and an algorithm for constructing a spatial matrix of unmanned aerial vehicles placement

Pavlo Marchenko

Abstract


The use of unmanned aerial vehicles (UAVs) as part of swarms of unmanned systems enables the enhancement of task performance efficiency, but their control systems require ongoing development. The subject of study in this article is a method for determining the topology of swarm elements relative to the leader and an algorithm for constructing a spatial placement matrix. The object of study is the process of controlling swarm systems. The purpose of the article is to develop a mathematical method for determining the topology of a swarm relative to the leader and an algorithm for constructing a space matrix for the placement of unmanned aerial vehicles in a swarm to keep its elements relative to the leader on the main route. In writing the article, a systematic analysis of the processes controlling unmanned systems and the synthesis of methods and algorithms for their functioning were employed. The following results were obtained in the course of the study. A mathematical method for determining the topology of swarm elements has been developed, and a periodic attraction/repulsion function has been proposed that determines the position of the driven UAV in the swarm relative to the leader. The sequence of UAV swarm formation is proposed: assigning a swarm leader and determining its location, determining the coordinates of the driven UAVs relative to the leader to build a spatial matrix of the location of elements in the swarm, determining the positions and speeds of the driven UAVs at each stage of the flight and obtaining the resulting route trajectory. An algorithm for constructing a spatial matrix for placing UAVs in a swarm and keeping its elements relative to the leader on the route trajectory, which implements the proposed attraction/repulsion function, has been developed. The functioning of the algorithm was tested by modeling the process of building a UAV swarm moving in space along a route for typical geometric shapes (line, square, wedge) in the Python software environment. Conclusions: the determination of the position of the driven UAVs in the swarm relative to the leader is mathematically formalized by the developed periodic three-dimensional attraction/repulsion function, considering the rotation of the swarm element in space. The algorithm for constructing a spatial matrix allows UAVs to be placed in accordance with the established geometric shape and to maintain the specified speed of the elements and ensure that the maximum distance between the UAVs and the leader is not exceeded during movement.

Keywords


swarm; unmanned aerial vehicle; leader; slave; topology of swarm elements; spatial matrix; algorithm; attraction/repulsion function

References


Golembo, V. A., & Melnikov, R. G. Orhanizatsiya roboty hrupy bezpilotnykh litalʹnykh aparativ [Organization of work of a group of unmanned aerial vehicles]. Visnyk Natsionalʹnoho universytetu “Lʹvivsʹka politekhnika”. Seriya: Komp’yuterni systemy ta merezhi. L’viv, NU “L’vivs’ka politekhnika”, 2018, no. 905, pp. 56-63. Available at: https://ena.lpnu.ua/handle/ntb/47212. (accessed 7.3.2025). (In Ukrainian).

Chandran, I., & Vipin, K. Multi-UAV Networks for Disaster Monitoring: Challenges and Opportunities from a Network Perspective. Drone Systems and Applications, 2024, vol. 12, pp. 1-28. DOI: 12. 10.1139/dsa-2023-0079.

Ariante, G., Ponte, S., Papa, U., Greco, A., & Del Core, G. Ground Control System for UAS Safe Landing Area Determination (SLAD) in Urban Air Mobility Operations. Sensors, 2022, vol. 22, no. 9:3226. DOI: 10.3390/s22093226.

Chepizhenko, V., Pavlova, S., Pisarchuk, A., Zakharin, F., & Ponomarenko S. Navigatsiya i upravleniye slozhnymi dinamicheskimi sistemami [Navigation and control of complex dynamic systems]. LAP LAMBERT Academic Publishing, 2018. 176 p. (In Russian).

Poghosyan, S., Poghosyan, V., Abrahamyan, S., Lazyan, A., Astsatryan, H., Alaverdyan, Y., & Eguiazarian, K. Cloud-based mathematical models for self-organizing swarms of UAVs: design and analysis. Drone Systems and Applications, 2024. vol. 12, pp. 1-12. DOI: 10.1139/dsa-2023-0039.

Tang, J., Liang, Y., & Li, K. Dynamic Scene Path Planning of UAVs Based on Deep Reinforcement Learning. Drones, 2024, vol. 8 Iss.2, 60. pp. 1-21. DOI:10.3390/drones8020060.

Gazi, V., Passino, K. M. Stability analysis of swarms. IEEE Transactions on Automatic Control, 2003, vol. 48, no 4, pp. 692-697.

Gazi, V., Passino K. M. Stability analysis of social foraging swarms. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 2004, vol. 34, no 1, pp. 539-557.

Shi, H., Xie, G. Collective Dynamics of Swarms with a New Attraction/Repulsion Function. Mathematical Problems in Engineering, 2011, vol. 2011, Article no. 735248. 13 p. DOI: 10.1155/2011/735248.

Ann, S., Kim, Y., & Ahn, J. Area Allocation Algorithm for Multiple UAVs Area Coverage Based on Clustering and Graph Method. IFAC-PapersOnLine, 2015, vol. 48, no. 9, pp. 204-209. DOI: 10.1016/j.ifacol.2015.08.084.

Marchenko, P. A., & Ponomarenko, S. O. Improved algorithm for constructing a collision-free route for multi-agent swarm robotic systems. Visnyk NTUU “KPI”. Seriya Radiotekhnika, Radioaparatobuduvannya, 2024, no. 98, pp. 5-15. DOI: 10.20535/RADAP.2024.98.5-12.

Ezhov, S. M., Makarets, M. V., & Romanenko, O. V. Classichna mechanica [Classical mechanics]. Kyiv, VPTS “Kyyivs’kyy universytet”. 2008. 480 p.




DOI: https://doi.org/10.32620/aktt.2025.3.10