ISSN 2071-8594

Russian academy of sciences


Gennady Osipov

M.V. Khachumov Problems of group pursuit of a target in a perturbed environment


We consider game-theoretic problems of group pursuit of a target under perturbations. The objects are the unmanned flight vehicles (FVs), which mathematical models are determined by transfer functions that describe the double-loop control system with autopilot and settings, providing necessary stability of the flight. In accordance with the separation principle, without loss of generality, solutions are considered in the pitch plane. In the case of antagonistic game the speed of the target is higher than the speed of the pursuers. The problem is solved when meeting of one of the pursuers with the target is occurred, or in the case when the target runs away from its pursuers. The task of following the target consists in rapprochement of the FVs group having some random arrangement with the target and flight along it during the set observation time. The target having lower speed seeks to evade as far as possible from its pursuers. Finally, in the task of following the given route, each aircraft should fly along its trajectory, given by the motion of the corresponding reference target. In the process of tasks solving each FV implements a set of heuristic behavioral strategies in the perturbed environment, using the rules of pitch angle and speed selection. In the experimental part of the paper situations typical for the solution of these problems are modelled.


Unmanned flight vehicles, intelligent control, control rules, group interaction, target pursuit, differential games, modeling

PP. 46-54.


1. Friesz T.L. Dynamic optimization and differential Games.– International Series in Operations Research & Management Science, Springer Science + Business Media, LLC, 2010, 502 p.
2. Wei Lin. Differential games for multi-agent systems under distributed information. – A dissertation submitted for the degree of Doctor of Philosophy, University of Central Florida, 2013, 117 p.
3. Krasovskiy N.N., Kotelnikova A.N. Stokhasticheskoe upravlenie v determinirovannoy differentsialnoy igre sblizheniya–ukloneniya//Avtomatika i telemekhanika, 2011, № 2, s. 93–110.
4. Ukhobotov V.I., Zaytseva O.V. Igrovaya zadacha impulsnoy vstrechi so smeshannym ogranicheniem na upravlenie vtorogo igroka// Vestnik YuUrGU. Seriya Matematika, fizika, khimiya, 2007, Vyp. 9, № 19, s. 55-60.
5. Vagin D.A. Presledovanie zhestko skoordinirovannykh ubegayushchikh. Dis. kand. fiz.-mat. nauk: 01.01.02: Izhevsk, 2003. – 102 c.
6. Dongxu Li. Multi-player pursuit-evasion differential games. – A dissertation submitted for the degree of Doctor of Philosophy, The Ohio State University, 2006, 151 p.7. Wei M., Chen G., Cruz J. B., Haynes L., Pham K., Blasch E. Multi-pursuer multi-evader pursuit-evasion games with jamming confrontation. – Journal of Aerospace Computing, Information, and Communication, 2007, vol. 4, no. 3, pp. 693–706.
8. Sidney N., Givigi Jr., Schwartz H. M. Decentralized strategy selection with learning automata for multiple pursuer evader games. – Adaptive Behavior, 2014, vol. 22, pp. 221-234.
9. Petrov N.N. Ob odnoy zadache presledovaniya so mnogimi ubegayushchimi. – Vestnik Udmur. un-ta, 2000, № 1, s. 131-136.
10. Petrov N.N. Prostoe presledovanie zhestkosoedinennykh ubegayushchikh//Avtomatika i telemekhanika, 1997, № 12, s. 89-95.
11. Petrosyan L.A., Rikhsiev B.B. Presledovanie na ploskosti. M.: Nauka, 1991. – 95 s.
12. Abramov N.S., Makarov D.A., Khachumov M.V. Controlling Flight Vehicle Spatial Motion Along a Given Route. – Automation and Remote Control, June 2015, Vol.76, No.6, pp.1070-1080.
13. Abramov N.S., Khachumov M.V. Modelirovanie provodki po marshrutu bespilotnogo letatelnogo apparata kak zadachi presledovaniya tseli//Aviakosmicheskoe priborostroenie, № 9, 2013, s.9-22.