employee
Ulan-Ude, Ulan-Ude, Russian Federation
UDK 00 Наука в целом (информационные технологии - 004)
UDK 004.896 Искусственный интеллект в промышленных системах. Интеллектуальные САПР и АСУ. Интеллектуальные роботы
Currently, computer simulation in virtual reality systems has a special status. In order for a computer model to meet the requirements of the tasks it models, it is necessary that the mathematical apparatus correctly describe the simulated phenomena. In this monograph, the simulation of pursuit problems is carried out. An adaptive modeling of the behavior of both pursuers and targets is carried out. An iterative calculation of the trajectories of the participants in the pursuit problem is carried out. The main attention is paid to the methods of pursuit and parallel rendezvous. These methods are taken as the basis of the study and are modified in the future. The scientific novelty of the study is the iterative calculation of the trajectories of the participants in the pursuit task when moving at a constant speed, while following the predicted trajectories. The predicted trajectories form a one-parameter network of continuous lines of the first order of smoothness. The predicted trajectories are calculated taking into account the restrictions on the curvature of the participant in the pursuit problem. The fact of restrictions on curvature can be interpreted as restrictions on the angular frequency of rotation of the object of the pursuit problem. Also, the novelty is the calculation of the iterative process of group pursuit of multiple targets, when targets are hit simultaneously or at specified intervals. The calculation of the parameters of the network of predicted trajectories is carried out with a curvature variation in order to achieve the desired temporal effect. The work also simulates the adaptive behavior of the pursuer and the target. The principle of behavior can be expressed on the example of a pursuer with a simple phrase: "You go to the left - I go to the left." This happens at each iteration step in terms of choosing the direction of rotation. For the purpose, the principle of adaptive behavior is expressed by the phrase: "You go to the left - I go to the right." The studies, algorithms and models presented in the monograph can be in demand in the design of autonomously controlled unmanned aerial vehicles with elements of artificial intelligence. The task models in the monograph are supplemented with many animated images, where you can see the research process. Also, the tasks have an implementation in a computer mathematics system and can be transferred to virtual reality systems if necessary.
Pursuer, target, trajectory, modeling, pursuit, parallel approach, surface, projecting plane.
1. Krasovskiy, N.N. Pozicionnye differencial'nye igry/ N.N. Krasovskiy, A.I. Subbotin. – M.: Fizmatlit, 1974. – 456 s.
2. Petrosyan, L.A. Differencial'nye igry presledovaniya/ L.A. Petrosyan. – L.: Izd-vo LGU, 1977. – 222 s.
3. Packo, V.S. Igra «shofer-ubiyca» i ee modifikacii/ V.S. Packo, V.L. Turova // Vestnik Udmurtskogo universiteta, Matematika. – 2008. - Vyp. 2. – S. 105-110.
4. Ayzeks, R. Differencial'nye igry / R. Ayzeks. – M.: Mir, 1967. – 480 s.
5. Merz, A.W. The game of two identical cars/ A.W. Merz // Journal of optimization and application. – 1972. – 9 (5) – P. 324-343.
6. Breakwell, J. V. Toward a complete solution of the homicidal chaueur game/ J. V. Breakwell, A.W. Merz// Proc. of the 1st Int. Conf. on the Theory and Application of Dierential Games. Amherst, Massachusetts – 1969. - P. III-1 – III-5.
7. Merz, A. W. The homicidal chauffer - a differential game / A. W. Merz // PhD thesis. Stanford University – 1971.
8. Lewin, J. Decoy in pursuit-evasion games/ J. Lewin// PhD Thesis. Stanford University – 1973.
9. Lewin, J. The surveillance-evasion game of degree/ J. Lewin, J. V. Breakwell// J. Opt. Theory Appl. – 1975. – 16 (34) – P. 339-353.
10. Lewin, J. Conic surveillance evasion/ J. Lewin, G. J. Olsder// J. Opt. Theory Appl. – 1979. – 27 (1) – P. 107-125.
11. Cardaliaguet P. Numerical methods for optimal control and dierential games/ P. Cardaliaguet, M. Quincampoix, P. Saint-Pierre// Ceremade CNRS URA 749 – 1995.
12. Cardaliaguet P. Set-valued numerical analysis for optimal control and dierential games / P. Cardaliaguet, M. Quincampoix, P. Saint-Pierre// Theory and Numerical Methods – Springer: Berlin – 1999. – P. 177-247.
13. Dubins, L. E. On curves of minimal length with a constraint on average curvature and with prescribed initial and terminal positions and tangents/ L. E. Dubins// Amer. J. Math. – 1957. – 79 – P. 497-516.
14. Reeds, J. A. Optimal paths for a car that goes both forwards and backwards/ J. A. Reeds, L. A. Shepp// Pacic J. Math. – 1990. – 145 (2) – P. 367-393.
15. Berdyshev, Yu.I. Ob optimal'nom po bystrodeystviyu upravlenii obobschennoy mashinoy Dubinsa/ Yu.I. Berdyshev// Tr. IMM UrO RAN – 2016. – 22 (1) – S. 26-35.
16. Pontryagin, L.S. Princip maksimuma v optimal'nom upravlenii/ M.: Nauka, 1989. – 64 s.
17. Bellman, R. Prikladnye zadachi dinamicheskogo programmirovaniya/ R. Bellman, S. Dreyfus. - M.: Nauka, 1965. – 460 s.
18. Kan, V. L. Teoriya proporcional'noy navigacii/ V.L. Kan, A.S. Kel'zon. – Leningrad: Sudostroenie, 1965. – 423 s.
19. Sozinov, P.A. Kinematicheskiy analiz metodov proporcional'noy navigacii primenitel'no k navedeniyu zenitnoy upravlyaemoy rakety na ballisticheskuyu cel'/ P.A. Sozinov, B. N. Gorevich // Vestnik koncerna VKO «Almaz - Antey» - 2022. – 2 – S. 74-92.
20. Krineckiy, E.I. Sistemy samonavedeniya/ E.I. Krineckiy. – M.: Mashinostroenie, 1970. – 236 s.
21. Mizrohi, V. Ya. Proektirovanie upravleniya zenitnyh raket/ V.Ya. Mizrohi. – M.: «Ekslibris - Press», 2010. – 252 s.
22. Zarchan, P. Tactical and Strategic Missile Guidance/ P. Zarchan. – American Institute of Aeronautic and Astronautic, 2012. – 1095 p.
23. Golubev, I.S., Svetlov, V.G. Proektirovanie zenitnyh upravlyaemyh raket/ I.I. Arhangel'skiy, P.P. Afanas'ev, E.G. Bolotov, I.S. Golubev, A.M. Matveenko, V.Ya. Mizrohi, V.N. Novikov, S.N. Ostapenko, V.G. Svetlov. – M.: Izd-vo MAI, 2001. – 732 s.
24. Nenartovich, N.E. BDMS – sistema protivoraketnoy oborony SShA. Analiz i modelirovanie/ N.E. Nenartovich, B.N. Gorevich. – M.: PAO «NPO «Almaz», 2020. – 351 s.
25. Pan'kov, S.Ya. Teoriya i metodika upravleniya aviaciey: ucheb. Posobie. V 2 ch./ S.Ya. Pan'kov, Yu.E. Zaburaev, A.M. Matveev. – Ul'yanovsk: UVAU GA, 2006. – 371 s.
26. Lenov, N.. Zenitnye raketnye kompleksy VVS stran NATO/ N. Lenov, V. Viktorov// Zarubezhnoe voennoe obozrenie. — M.: «Krasnaya Zvezda», 1975. —2. — S. 61—66.
27. Demidov V. Sovershenstvovanie sistem ZURO v kapitalisticheskih stranah/ V. Demidov, N. Kutyev// Zarubezhnoe voennoe obozrenie. — M.: «Krasnaya Zvezda», 1975. — № 5. — S. 52—57.
28. Dubinkin, E. Razrabotka i proizvodstvo zenitnogo vooruzheniya Armii SShA/ E. Dubinkin, S. Pryadilov// Zarubezhnoe voennoe obozrenie. — M.: «Krasnaya Zvezda», 1983. — № 3. — S. 30—34.
29. Abramyanc, T.G. Uklonenie podvizhnyh ob'ektov ot obnaruzheniya na ploskosti i v prostranstve/ T.G. Abramyanc, E.P. Maslov, V.P. Yahno// Problemy upravleniya. – 2008. - № 3. – S. 2-13.
30. Galyaev, A.A. Uklonenie podvizhnogo ob'ekta ot odinochnogo obnaruzhitelya na zadannoy skorosti/ A.A. Galyaev, P.V. Lysenko, V.P. Yahno// Problemy upravleniya. – 2020. - № 1. – S. 83-91.
31. Galyaev A.A. Zadacha ukloneniya ot podvizhnogo odinochnogo nablyudatelya na ploskosti v konfliktnoy srede/ A.A. Galyaev// Avtomatika i telemehanika. — 2014. — № 6. — S. 28—37. [Galyaev, A.A. Evasion on Plane from a Single Mobile Observer in the Conflict Environment // Automation and Remote Control. — 2014. — Vol. 75, no. 6. — P. 1017—1024.]
32. Andreev K.V., Rubinovich E.Ya. Traektornoe upravlenie nablyudatelem/ K.V. Andreev, E.Ya. Rubinovich // Avtomatika i telemehanika. — 2016. — № 1. — S. 134—162. [Andreev, K.V., Rubinovich, E.Ya. // Moving observer trajectory control by angular measurements in tracking problem // Automation and Remote Control. — 2016. — Vol. 77, no. 1. — P. 106—129.]
33. Shevchenko, I.I. Successive Pursuit with a Bounded Detection / I.I. Shevchenko// Journal of Opt. Theory and Appl. — 1997. — Vol. 95. — N 1. — P. 25—48.
34. Video, rezul'taty modelirovaniya zadachi presledovaniya. URL: https://www.youtube.com/watch?v=C7imOTjEgQQ (data obrascheniya: 9.07.2022)
35. Video, rezul'taty modelirovaniya zadachi presledovaniya. URL: https://www.youtube.com/watch?v=0-qA8Q2fcwE (data obrascheniya: 9.07.2022)
36. Video, rezul'taty modelirovaniya zadachi presledovaniya. URL: https://youtu.be/arCQYrLZGxk (data obrascheniya: 9.07.2022)
37. Video, rezul'taty modelirovaniya zadachi presledovaniya. URL: https://youtu.be/dBGalSwRclg (data obrascheniya: 9.07.2022)
38. Video, rezul'taty modelirovaniya zadachi presledovaniya. URL: https://www.youtube.com/watch?v=lvHvKzEjU4U
39. Hachumov, M.V. Upravlenie gruppoy bespilotnyh letatel'nyh apparatov, osnovannoe na produkcionnyh pravilah/ M.V. Hachumov// 4-aya Nauchno-Prakticheskaya Internet-konferenciya, Mezhdisciplinarnye issledovaniya v oblasti matematicheskogo modelirovaniya i informatiki. - 2014 - S. 249-254.
40. Hachumov, M.V. Zadachi gruppovogo presledovaniya celi v usloviyah vozmuscheniy/ M.V. Hachumov// Iskusstvennyy intellekt i prinyatie resheniy. – 2015 – № 2 – S. 45-52.
41. Petrov, N.N. K zadache gruppovogo presledovaniya/ N.N. Petrov// Izvestiya Instituta Matematiki i Informatiki. Izhevsk. – 2002 – T. 2 (25) – S. 73-74.
42. Pshenichnyy, B.N. Prostoe presledovanie neskol'kimi ob'ektami/ B.N. Pshenichnyy// Kibernetika. - 1976 - №3 - S. 145–146.
43. Pshenichnyy, B.N. Zadacha ob uklonenii ot vstrechi v differencial'nyh igrah/ B.N. Pshenichnyy, A.A. Chikriy// Zhurnal vychislitel'noy matematiki i matematicheskoy fiziki. – 1974 - T. 14. №6 - S. 416–427.
44. Samatov, B.T., Zadacha presledovaniya–ubeganiya pri integral'no-geometricheskih ogranicheniyah na upravleniya presledovatelya/ B.T. Samatov// Avtomatika i telemehanika. - 2013 - № 7 – S.17–28.
45. Mamatov, M.Sh. Igrovaya zadacha presledovaniya i ubeganiya s upravleniem, zadannym raznostnymi uravneniyami vtorogo poryadka/ M.Sh. Mamatov// Izvestiya Instituta matematiki i informatiki Udmurtskogo gosudarstvennogo universiteta. - 2006 – T. 3(36) - S. 95-96.
46. Bannikov, A.C., Nekotorye nestacionarnye zadachi gruppovogo presledovaniya / A.C. Bannikov// Izvestiya Instituta matematiki i informatiki UdGU. - 2013 - Vyp. 1 (41) - S.3-46.
47. Bannikov, A.S. Nestacionarnaya zadacha gruppovogo presledovaniya/ A.C. Bannikov//Trudy Matematicheskogo centra imeni N.I. Lobachevskogo. Kazan': Izd-vo Kazanskogo matematicheskogo obschestva. - 2006 - T. 34 - S. 26–28.
48. Bannikov, A.S. Nestacionarnaya zadacha gruppovogo presledovaniya/ A.S. Bannikov// Problemy teoreticheskoy i prikladnoy matematiki, tr. 39-y Vseros. molodezh. konf., 28 yanv.–1 fev., 2008 , g. Ekaterinburg: UrO RAN - 2008 - S. 221–223.
49. Izmest'ev, I.V. Zadacha presledovaniya malomanevrennyh ob'ektov s terminal'nym mnozhestvom v forme kol'ca/ I.V. Izmest'ev, V. I. Uhobotov // VINITI RAN, Moskva. - 2018. S.25–31
50. Blagodatskih, A.I. Konfliktnoe vzaimodeystvie grupp upravlyaemyh ob'ektov/ A.I. Blagodatskih, N.N. Petrov // Izhevsk: Izd-vo Udmurt. un-ta. - 2009. - 266 s.
51. Pontryagin, L.S. Lineynaya differencial'naya igra ubeganiya / L.S. Pontryagin //Tr. MIAN SSSR. — 1971. — T. 112. — S. 30—63.
52. Pontryagii, L. S. K teorii differencial'nyh igr/ L. S. Pontryagii// Uspehi matematicheskih nauk. – 1966 - t. XXI, vyp. 4 – S. 219-274.
53. Pontryagin, L. S. Matematicheskaya teoriya optimal'nyh processov / L. S. Pontryagin, V. G. Boltyanskiy, R. V. Gamkrelidze, E. F. Mischenko//M.: Nauka - 1983 – S.392.
54. Pontryagin, L.S. Zadacha ob ubeganii odnogo upravlyaemogo ob'ekta ot drugogo / L.S. Pontryagin, E.F. Mischenko//DAN SSSR – 1969 - T. 189. №4 - S. 721–723.
55. Pontryagin, L.S. Zadacha ob uklonenii ot vstrechi v lineynyh differencial'nyh igrah/ L.S. Pontryagin, E.F. Mischenko// Differencial'nye uravneniya . - 1971 - T. 7. №3 - S. 436–445.
56. Malofeev, O.A. Igra prostogo presledovaniya na ploskosti s prepyatstviem / O.A. Malofeev, L.A. Petrosyan// Sb. trudov in-ta matematiki Sib. otd. AN SSSR – 1971 - Vyp. 9 - S. 31–42.
57. Fleming, W.H. The convergence problem for differential games / W.H. Fleming // J. Math. Ann. and Appl - 1961 – № 3 - P.102-116.
58. Fleming, W.H. A note on differential games of prescribed durations, Contribution to the theory of games / W.H. Fleming// Ann. Of Math. Studies – 1957 - № 3 – P.407-412.
59. Ashkenazi, V.O. Primenenie teorii igr v voennom dele / V.O. Ashkenazi // Sbornik perevodov s angliyskogo pod redakciey Ashkenazi V.O. - Izdatel'stvo «Sovetskoe Radio», M. , 1961. – S. 362.
60. Parthasarathi, T. Nekotorye voprosy teorii igr dvuh lic/ T. Parthasarathi, T. Raghavan. - M.: Mir. - 1974.- S.296
61. Azamov, A. Struktura diskretnyh igr presledovaniya i ubeganiya/ A. Azamov // Izvestiya AN RUz, seriya fiz.- mat. Nauk. – 1984 - №2 - S. 3–8
62. Burdakov, S.V. Algoritmy upravleniem dvizheniya mobil'nym robotom v zadache presledovaniya/ S.V. Burdakov, P.A. Sizov// Nauchno-tehnicheskie vedomosti Sankt-Peterburgskogo gosudarstvennogo politehnicheskogo universiteta. Informatika. Telekommunikacii. Upravlenie. – 2014 - № 6 (210) - S. 49-58.
63. Canudas de Wit, C. Theory of Robot Control/ C. Canudas de Wit, B. Siciliano, G. Bastin // London: Springer – Verlag - 199 – P.392.
64. Marcos, A. M. Vieira. Scalable and Practical Pursuit-Evasion with Networked Robots A. M. Marcos, Govindan Ramesh, S. Gaurav Sukhatme// Journal of Intelligent Service Robotics. Special Issue on Networked Robots. – 2009. – N 2. – P. 247–263.
65. Chikriy, A.A. Konfliktno upravlyaemye processy/ A.A. Chikriy – Kiev: Nauk. Dumka - 1992 – S.384
66. Rihsiev B.B. Differencial'nye igry s prostymi dvizheniyami/ B.B. Rihsiev – Tashkent: FAN – 1989 – 232 s.
67. Petrosjan, Leon A. Differential Games of Pursuit/ Leon A. Petrosjan - World Scientific Publishing Company - 1993 - P. 340 ( ISBN 978-9810209797)
68. Petrosyan, L. A. Subgame-consistent Economic Optimization/ L. A. Petrosyan, D. W. K. Yeung – Springer - 2012 — P. 396
69. Petrosjan, Leon A. Game Theory/ Leon A. Petrosjan, N. A. Zenkevich - World Scientific Publisher – 1996 — P.350
70. Video, rezul'taty modelirovaniya zadachi presledovaniya. URL: https://www.youtube.com/watch?v=rsMGA1ICo7M (data obrascheniya: 9.07.2022)
71. Video, rezul'taty modelirovaniya zadachi presledovaniya. URL: https://www.youtube.com/watch?v=hGieKXNiuz8 (data obrascheniya: 9.07.2022)
72. Video, rezul'taty modelirovaniya zadachi presledovaniya. URL: https://www.youtube.com/watch?v=qNXdykK21Z8 (data obrascheniya: 9.07.2022)
73. Video, rezul'taty modelirovaniya zadachi presledovaniya. URL: https://www.youtube.com/watch?v=06qgINE4j8U (data obrascheniya: 9.07.2022)
74. Video, rezul'taty modelirovaniya zadachi presledovaniya. URL: https://www.youtube.com/watch?v=xszwIyTHUec (data obrascheniya: 9.07.2022)
75. Video, rezul'taty modelirovaniya zadachi presledovaniya. URL: https://youtu.be/JlUmh6DTrA4 (data obrascheniya: 9.07.2022)
76. Video, rezul'taty modelirovaniya zadachi presledovaniya. URL: https://www.youtube.com/watch?v=UQ5bVKjVqZ4 (data obrascheniya: 9.07.2022)
77. Video, rezul'taty modelirovaniya zadachi presledovaniya. URL: https://youtu.be/aC4PuXTgVS0 (data obrascheniya: 9.07.2022)
78. Video, rezul'taty modelirovaniya zadachi presledovaniya. URL: https://youtu.be/sLy7Jvppf4A (data obrascheniya: 9.07.2022)
79. Video, rezul'taty modelirovaniya zadachi presledovaniya. URL: https://youtu.be/WqsFkD2XwIw (data obrascheniya: 9.07.2022)
80. Video, rezul'taty modelirovaniya zadachi presledovaniya. URL: https://youtu.be/NNJDJOJT34I (data obrascheniya: 9.07.2022)
81. Video, rezul'taty modelirovaniya zadachi presledovaniya. URL: https://www.youtube.com/watch?v=tdbgoNoby3A (data obrascheniya: 9.07.2022)
82. Video, rezul'taty modelirovaniya zadachi presledovaniya. URL: https://youtu.be/8nDUSi3ENB4 (data obrascheniya: 9.07.2022)
83. Video, rezul'taty modelirovaniya zadachi presledovaniya. URL: https://www.youtube.com/watch?v=7VNHNwCbWrg (data obrascheniya: 9.07.2022)
84. Video, rezul'taty modelirovaniya zadachi presledovaniya. URL: https://youtu.be/F6MTsWZL2BY (data obrascheniya: 9.07.2022)
85. Volkov, V. Ya. Graficheskie optimizacionnye modeli mnogofaktornyh processov/ V. Ya. Volkov, M.A. Chizhik - Monografiya, g. Omsk, Izdatel'sko-poligraficheskiy centr OGIS, 644099, Omsk, ul. Krasnogvardeyskaya, 9 – 2009 – S. 101
86. Bolotov, V. P. Mnogomernaya geometriya: monogr. / V. P. Bolotov. – Vladivostok, MGU im. adm. G. I. Nevel'skogo – 2004 – S.256
87. Filippov, P. V. Nachertatel'naya geometriya mnogomernogo prostranstva i ee prilozheniya / P. V. Filippov – L.: Izd-vo LGU - 1979 – 280 s.
88. Radischev, V. P. O primenenii geometrii chetyreh izmereniy k postroeniyu raznovesnyh fiziko-himicheskih diagramm / V. P. Radischev - Izv. SFHA. – M. – 1947 – T. 15 – S. 129–134