Deterministic Area Coverage by UAV Swarms via Multi-Eulerian Rotor-Router Walks
DOI:
https://doi.org/10.51408/1963-0142Keywords:
UAV swarm, Rotor-router model, Eulerian walk, Area surveillance, Self-organizing systemAbstract
The deterministic area coverage problems for UAV swarms based on multi-Eulerian rotor-router walks are investigated. The rotor-router model provides a quasi-random analogue of random walks with strong structural properties. The loop reversibility theorem is used; that is, under mild connectivity assumptions on the underlying discretized environment, a swarm of UAVs executing coordinated multi-Eulerian rotorrouter walks achieves complete area coverage, in the sense that each directed edge is traversed exactly once by a single UAV. The results establish provable coverage guarantees that are robust to asynchronous execution. Furthermore, the loop reversibility theorem is generalized to the case of repeated coverage, where the area should be covered a prescribed number M of times, without requiring global synchronization among UAVs at the end of each traversal cycle. A multi-user and multi-agent platform has been developed to support mission planning and coordinated supervision of self-organizing UAV swarms.
References
E. Bonabeau, M. Dorigo, and G. Theraulaz, “Swarm intelligence: From natural to artificial systems”, Oxford University Press, New York, 1999.
S. Javaid, M.J. Khan, A. Rehman, and A. Al-Fuqaha, “Communication and control in collaborative UAVs: Recent advances and future trends”, IEEE Transactions on Intelligent Transportation Systems, vol. 24, pp. 5719–5739, 2023.
J. Guo, Y. Liu, Z. Wang, and H. Zhang, “Collision-free formation tracking control for multiple quadrotors under switching directed topologies: Theory and experiment”, Aerospace Science and Technology, vol. 131, Article 108007, 2022.
Y. Chen, Y. Zhang, and Z. Wang, “Trajectory optimization of multiple quad-rotor UAVs in collaborative assembling task”, Chinese Journal of Aeronautics, vol. 29, pp. 184–201, 2016.
S. Ghambari, A.H. Gandomi, and A. Dehghan, “UAV path planning techniques: A survey”, RAIRO–Operations Research, vol. 58, pp. 2951–2989, 2024.
J. Tang, H. Duan, and S. Lao, “Swarm intelligence algorithms for multiple unmanned aerial vehicles collaboration: A comprehensive review”, Artificial Intelligence Review, vol. 56, no. 4, pp. 4295–4327, 2023.
V.B. Priezzhev, D. Dhar, A. Dhar, and S. Krishnamurthy, “Eulerian walkers as a model of self-organized criticality”, Physical Review Letters, vol. 77, pp. 5079–5082, 1996.
A.E. Holroyd, L. Levine, K. M´esz´aros, Y. Peres, J. Propp, and D. Wilson, “Chip-firing and rotor-routing on directed graphs”, in In and Out of Equilibrium 2, Progress in Probability, vol. 60, Birkh¨auser, Basel, pp. 331–364, 2008.
V.S. Poghosyan and V.B. Priezzhev, “Euler tours and unicycles in the rotor-router model”, Journal of Statistical Mechanics: Theory and Experiment, P06003, 2014.
V.V. Papoyan, V.S. Poghosyan, and V.B. Priezzhev, “Loop reversibility and subdiffusion of the rotor-router walk”, Journal of Physics A: Mathematical and Theoretical, vol. 48, no. 28, 285203, 2015.
V.V. Papoyan, V.S. Poghosyan, and V.B. Priezzhev, “Spiral structures in the rotorrouter walk”, Journal of Statistical Mechanics: Theory and Experiment, 043207, 2016.
S. Poghosyan, V. Poghosyan, S. Abrahamyan, A. Lazyan, H. Astsatryan, and Y. Alaverdyan, “Cloud-based mathematical models for self-organizing swarms of UAVs: Design and analysis”, Drone Systems & Applications, vol. 12, pp. 1–12, 2024.
V. Poghosyan, S. Poghosyan, A. Lazyan, A. Atashyan, D. Hayrapetyan, and H. Astsatryan, “Self-organizing multi-user UAV swarm simulation platform”, Programming and Computer Software, vol. 49, no. 1, pp. S7–S15, 2023.
A. Atashyan, A. Lazyan, D. Hayrapetyan, H. Astsatryan, V. Poghosyan, and S. Poghosyan, “Mission preparation for self-organizing UAV swarms on a multi-user platform”, Programming and Computer Software, vol. 50, no. 1, pp. S39–S46, 2024.
S. Poghosyan, V. Poghosyan, H. Astsatryan, and Ye. Alaverdyan, “Decentralized privacy provision in dynamically reconfigurable and self-organizing aero-physical cyber systems”, Physics of Particles and Nuclei, vol. 56, no. 6, pp. 1309–1317, 2025.
“Self-Organized UAV Swarm Demo”, Online resource, December 2025. Available: https://www.youtube.com/watch?v=HvQkU4Wotjg
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