employee
Ulan-Ude, Ulan-Ude, Russian Federation
The article describes the model of group pursuit of a single target by the chase method. All objects participating in the pursuit model move with a constant modulo speed. One of the participants in the process moves along a certain trajectory and releases objects at specified intervals, the task of which is to achieve the goal by the chase method. All objects have restrictions on the curvature of the motion path. A single target, in turn, is tasked with achieving the target that releases objects using the parallel approach method. For each pursuing object, a detection area is formed in the form of two beams. The object's velocity vector is directed along the bisector of the angle formed by such rays. If the target enters the detection area, then the object starts pursuit and the velocity vector is directed to the target. If the target leaves the detection area, then the object makes a uniform and rectilinear movement. The task is to implement a dynamic model of multiple group pursuit, where each object has its own tasks, implemented by the chase method. As an example, where the model developed in the article could be in demand, the following example can be given. Consider the movement of a low-maneuverable object that is overtaking a faster target. As a means of protection, instead of releasing passive heat traps, it is proposed to drop a variety of autonomously controlled weapons. An analysis of existing studies has shown that such means of protecting aircraft do not exist. The results of the research can be in demand in the design of unmanned aerial vehicles with elements of autonomous control and artificial intelligence.
pursuit; chase method; target; pursuer; trajectory; correction
1. Abramyanc T.G. Uklonenie gruppovoy celi v trehmernom prostranstve [Tekst] / T.G. Abramyanc, E.P. Maslov, V.P. Yahno // Avtomatika i telemehanika. – 2008. – № 5. – S. 3–14.
2. Ayzeks R. Differencial'nye igry [Tekst] / R. Ayzeks. – M.: Mir, 1967. – 480 s.
3. Bannikov A.C. Nekotorye nestacionarnye zadachi gruppovogo presledovaniya [Tekst] / A.C. Bannikov // Izvestiya Instituta matematiki i informatiki UdGU. – 2013. – Vyp. 1 (41). – C. 3–46.
4. Bogdanov A.V. Metody samonavedeniya istrebiteley i raket klassa «vozduh-vozduh» na gruppovuyu vozdushnuyu cel': monogr. [Tekst]/ A.V. Bogdanov, A.A. Filonov, A.A. Kovalev [i dr.] pod red. Kuchina A.A. – Krasnoyarsk: Izd-vo Sibirskogo feder. un-ta. – 2014. – 168 s.
5. Video, rezul'taty modelirovaniya zadachi presledovaniya. URL: https://www.youtube.com/watch?v=t9cxOgk6bdk (data obrascheniya: 12.02.2022).
6. Video, rezul'taty modelirovaniya zadachi presledovaniya. URL: https://youtu.be/keZ5fzd2o3Q (data obrascheniya: 12.02.2022).
7. Video, rezul'taty modelirovaniya zadachi presledovaniya. URL: https://youtu.be/ODS75MCwjGg (data obrascheniya: 20.02.2022).
8. Video, rezul'taty modelirovaniya zadachi presledovaniya. URL: https://youtu.be/oHowdT2n5-U (data obrascheniya: 20.02.2022).
9. Video, rezul'taty modelirovaniya zadachi presledovaniya. URL: https://youtu.be/5_-0TurWvwQ (data obrascheniya: 05.03.2022).
10. Video, rezul'taty modelirovaniya zadachi presledovaniya. URL: https://www.youtube.com/watch?v=JcBrYjfaXTg (data obrascheniya: 05.03.2022).
11. Gusyatnikov P.B. Differencial'naya igra ubeganiya m lic [Tekst] / P.B. Gusyatnikov // Izvestiya AN SSSR. Tehnicheskaya kibernetika. – 1978. – № 6. – S. 22–32.
12. Gusyatnikov P.B. Differencial'naya igra ubeganiya [Tekst] / P.B. Gusyatnikov // Kibernetika. – 1978. – № 4. – S. 72–77.
13. Gusyatnikov P.B. Ubeganie odnogo nelineynogo ob'ekta ot neskol'kih bolee inertnyh presledovateley [Tekst] / P.B. Gusyatnikov // Differencial'nye uravneniya. – 1976. – T. 12. – № 2. – S. 1316–1324.
14. Dubanov A.A. Modelirovanie traektoriy ot presledovatelya do celi s ogranicheniyami na kriviznu i s zadannymi kraevymi usloviyami:programma dlya EVM. № 2020614336; zayavl. 20.03.20; opubl. 31.03.20. Byul. № 4.
15. Ignat'ev S.A. Funkcional'nye vozmozhnosti sredy wolfram mathematica dlya vizualizacii krivyh liniy i poverhnostey [Tekst] / S.A. Ignat'ev, A.I. Folomkin, E.H. Muratbakeev // Geometriya i grafika. – 2021. – T. 9. – № 1. – S. 39-45. – DOI: 10.12737/2308-4898-2021-9-1-29-38.
16. Korotkiy V.A. Konstruirovanie G2-gladkoy sostavnoy krivoy na osnove kubicheskih segmentov Bez'e [Tekst] / V.A. Korotkiy // Geometriya i grafika – 2021. – T. 9. – № 2. – S. 12-28. – DOI: 10.12737/2308-4898-2021-9-1-3-19.
17. Korotkiy V.A. Kubicheskie krivye v inzhenernoy geometrii [Tekst] / V.A. Korotkiy // Geometriya i grafika. – 2020. – T. 8. – № 3. – S. 3-24. DOI: 10.12737/2308-4898-2020-3-24.
18. Krasovskiy N.N. Pozicionnye differencial'nye igry [Tekst] / N.N. Krasovskiy, A.I. Subbotin: monogr. – M.: Fizmatlit, 1974. – 456 s.
19. Kuz'mina L.I. Raschet dliny traektorii dlya zadachi presledovaniya [Tekst] / L.I. Kuz'mina, Yu.V. Osipov // Vestnik MGSU. – 2013. – № 12. – S. 20–26. – DOI: 10.22227/1997-0935.2013.12.20-26.
20. Nikitchenko S.N. Imitacionnaya model' zadachi vzaimnogo presledovaniya [Tekst] / S.N. Nikitchenko, A.A. Bassauer // Regional'naya informatika i informacionnaya bezopasnost':cb. tr. mezhdunar. konf. Sankt-Peterburg. – 2018. – Vyp. 5. – S. 479–483.
21. Panchuk K.L. Ciklograficheskaya interpretaciya i komp'yuternoe reshenie odnoy sistemy algebraicheskih uravneniy [Tekst] / Panchuk K.L., Lyubchinov E.V. // Geometriya i grafika. – 2019. – T. 7. – № 3. – S. 3-14. – DOI: 10.12737/article_5dce5e528e4301/77886978.
22. Petrosyan L.A. Differencial'nye igry presledovaniya [Tekst] / L.A. Petrosyan. - Leningrad: Izd-vo LGU. – 1977. – 222 c.
23. Sycheva A.A. Funkcional'no-voksel'noe modelirovanie krivyh Bez'e [Tekst] / A.A. Sycheva // Geometriya i grafika. – 2022. – T. 9. – № 4. – S. 63-72. – DOI: 10.12737/2308-4898-2022-9-4-63-72.
24. Hachumov M.V. Zadachi gruppovogo presledovaniya celi v usloviyah vozmuscheniy [Tekst] / M.V. Hachumov // Iskusstvennyy intellekt i prinyatie resheniy. – 2016. – № 2. – S. 46–54.
25. Hachumov M.V. Reshenie zadachi sledovaniya za cel'yu avtonomnym letatel'nym apparatom [Tekst] / M.V. Hachumov // Iskusstvennyy intellekt i prinyatie resheniy. – 2015. – № 2. – S. 45–52.
