Far Eastern Mathematical Journal

To content of the issue

Protection of the network structure by autonomous vehicles

Guzev M.A., Tsitsiashvili G.Sh., Osipova M.A.

2018, issue 2, P. 177-182

Abstract

Two strategies of protection of network group of bodies from penetration of foreign object are analysed. The first strategy is based on the individual protection of each body, the second involves the use of autonomous vehicles for integrated network protection. It is shown that in the second case the ratio of the minimum number of vehicles required for detection with probability one foreign object to the number of vehicles used in the first strategy is inversely proportional to the square root of the number of elements of the network structure.

Keywords: mobile object, autonomous vehicle, the probability of detection

Download the article (PDF-file)

References

[1] A.C. Corte, A. Battista, F. dellIsola, “Referential description of the evolution of swarm of robots interacting with the closer neighbours: Perspectives of continuum modelling via higher gradient continua”, International Journal of Non-Linear Mechanics, 80, (2016), 209–220. [2] M. Brambilla, E. Ferrante, M. Birattari, M. Dorigo, “Swarm robotics:a review from the swarm engineering perspective”, Swarm Intell., 7:1, (2013), 1–41. [3] A. Adamatzky, J. Jones, “Towards Physarum robots: computing and manipulating on water surface”, J. Bionic Eng., 5:4, (2008), 348–357. [4] N. Bellomo, F. Brezzi, “Mathematics, complexity and multi scale features of large systems of self-propelled particles”, Math. Models Methods Appl. Sci., 25, (2016), 207–214. [5] M.A. Herrero, J. Soler, “Cooperation, competition, organization: The dynamics of interacting living populations”, Math. Models Methods Appl. Sci., 25, (2015), 2407–2415. [6] M. Kardar, Statistical Physics of Particles, Cambridge University Press, 2007. [7] G.M. Zaslavsky, The Physics of Chaos in Hamiltonian Systems. Second edition, Imperial College Press, 2007. [8] V.P. Maslov, “Nonlinear Averages in Economics”, Mathematical Notes, 78:3-4, (2005), 347–363. [9] B. Alspach, “Searching and sweeping graphs: a brief survey”, Le Matematiche, 59:1, 2, (2006), 5–37. [10] P. Kafka, J. Faigl, P. Vana, “Random Inspection Tree Algorithm in visual inspection with a realistic sensing model and differential constraints”, IEEE International Conference on Robotics and Automation (ICRA), 2016, 2782–2787. [11] C.M. Monasterio, G. Oshanin, G. Schehr, “First passages for a search by a swarm of independent random searchers”, Journal of Statistical Mechanics: Theory and Experiment, 2011:6, (2011), 6–22. [12] E. Galceran, M. Carreras, “A survey on coverage path planning for robotics?”, Robotics and Autonomous Systems, 61:12, (2013), 1258–1276. [13] T.H. Chung, G. A. Hollinger, V. Isler, “Search and pursuit-evasion in mobile robotics”, Autonomous Robots, 31:4, (2011), 299–316. [14] M.A. Guzev, G.SH. TSitsiashvili, M.A. Osipova, “Veroyatnost’ obnaruzheniya postoronnego mobil’nogo ob”yekta neobitayemymi podvodnymi apparatami”, Materialy sed’moy vserossiyskoy nauchno-tekhnicheskoy konferentsii "Tekhnicheskiye problemy osvoyeniya mirovogo okeana", 2017, 426–433. [15] M.A. Guzev, G.SH. TSitsiashvili, M.A. Osipova, M.S. Sporyshev, “Veroyatnost’ obnaruzheniya postoronnego mobil’nogo ob”yekta neobitayemymi podvodnymi apparatami kak resheniye zadachi Byuffona”, Dal’nevostochnyy matematicheskiy zhurnal, 2, (2017), 191–200. [16] M.A. Guzev, G.Sh. Tsitsiashvili, M.A. Osipova, M.S. Sporyshev, “Probability of detection of an extraneous mobile object by autonomous unmanned underwater vehicles as a solution of the Buffon problem”, ArXiv: 1801.10318 [cs.RO], 2018. [17] V. Vavilov, A. Ustinov, “Okruzhnosti na reshetkakh”, Kvant, 6, (2006). [18] G.H. Hardy, “On the Expression of a Number as the Sum of Two Squares”, Quart. J. Math., 46, (1915), 263–283. [19] G.H. Hardy, Ramanujan, Twelve Lectures on Subjects Suggested by His Life and Work, Chelsea, New York, 1999. [20] M.N. Huxley, “Integer points, exponential sums and the Riemann zeta function”, Number theory for the millennium, II, (2002), 275–290.

To content of the issue