{"id":8176,"date":"2026-03-22T14:43:28","date_gmt":"2026-03-22T14:43:28","guid":{"rendered":"https:\/\/izvestiyakbncran.ru\/?page_id=8176"},"modified":"2026-04-10T13:30:02","modified_gmt":"2026-04-10T12:30:02","slug":"25-4-4-en","status":"publish","type":"page","link":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-4-4-en\/","title":{"rendered":"25.4.4 En"},"content":{"rendered":"\n

Numerical method for solving the optimization problem of trajectory control and formation maintenance by a group of autonomous UAVs with predictive models<\/strong><\/h1>\n\n\n\n

K.Yu. Ganshin, D.L. Vinokursky, O.S. Mezentseva, Ph.V. Samoilov<\/strong><\/p>\n\n\n\n

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Upload the full text<\/strong><\/strong><\/p>\n\n\n\n

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Abstract<\/strong>:<\/strong> <\/em>The article is devoted to the development of a numerical method for solving the optimization problem of trajectory control of a single UAV based on the penalty functions method with computational acceleration. The article described a numerical method for finding a solution to the trajectory control problem, presented as a quadratic programming problem, using the penalty function method with Aitken’s
computational acceleration.<\/p>\n\n\n\n

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Keywords<\/strong>:<\/em><\/strong> trajectory generation algorithms, UAV mathematical model, numerical method, Aitken\u2019s acceleration, penalty function, Lagrange<\/p>\n\n\n\n

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For citation<\/strong>.<\/strong> Ganshin K.Yu., Vinokursky D.L., Mezentseva O.S., Samoilov F.V. Numerical method for solving the optimization problem of trajectory control and formation maintenance by a group of autonomous UAVs with predictive models. News of the Kabardino-Balkarian Scientific Center of RAS<\/em>. 2023. No. 4(114). Pp. 55\u201360. DOI: 10.35330\/1991-6639-2023-4-114-55-60<\/p>\n\n\n\n

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R<\/strong>eferences<\/summary>\n
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  1. Jezierski A. A comparison of LQR and MPC control algorithms of an inverted pendulum \/ A. Jezierski, J. Mozaryn, D. Suski. Advances in Intelligent Systems and Computing. Cham: Springer International Publishing. 2017. Pp. 65\u201376.<\/li>\n\n\n\n
  2. \u0141awry\u0144czuk M. Introduction to model predictive control \/\/ in book \u00abNonlinear Predictive Control Using Wiener Models\u00bb. Cham: Springer International Publishing. 2022. Pp. 3\u201340.<\/li>\n\n\n\n
  3. Richalet J., Rault A., Testud J. et al. Model predictive heuristic control. Automatica (Oxf.). No. 14 (5). Pp. 413\u2013428.<\/li>\n\n\n\n
  4. Vinogradov A.M., Krasil\u2019shchik I.S. What is the Hamiltonian formalism? Russian mathematical surveys. 1975. Vol. 30. No. 1. Pp. 177\u2013202.<\/li>\n\n\n\n
  5. Garcia G.A., Kim A.R., Jackson E. et al. Modeling and flight control of a commercial nano quadrotor \/\/ International Conference on Unmanned Aircraft Systems (ICUAS). IEEE. 2017. DOI: 10.1109\/icuas.2017.7991439-2017.<\/li>\n\n\n\n
  6. Chinedu Amata Amadi W.S. Design and implementation of Model Predictive Control on Pixhawk Flight Controller. Stellenbosch University. 2018.<\/li>\n\n\n\n
  7. Giernacki W., Skwierczynski M., Witwicki W. et al. Crazyflie 2.0 quadrotor as a platform for research and education in robotics and control engineering. 22nd International Conference on Methods and Models in Automation and Robotics (MMAR). IEEE. 2017. DOI: 10.1109\/mmar.2017.8046794-2017.<\/li>\n\n\n\n
  8. Arnold V.I., Kozlov V.V., Nejshtadt A.I. Mathematical aspects of classical and celestial mechanics. Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Fundamental\u2019nye Napravleniya<\/em>. 1985. No. 3. Pp. 5\u2013290. (in Russian)<\/li>\n\n\n\n
  9. Wills A.G., Heath W.P. Barrier function based model predictive control. Automatica: the journal of IFAC, the International Federation of Automatic Control. 2004. No. 8(40). Pp. 1415\u20131422.<\/li>\n\n\n\n
  10. Gopal V., Biegler L.T. Large scale inequality constrained optimization and control. IEEE Control Systems Magazine. 1998. No. 18(6). Pp. 59\u201368.<\/li>\n\n\n\n
  11. Faddeev D.K., Faddeeva V.N. Vychislitel’nyye metody lineynoy algebry<\/em> [Computational methods of linear algebra]. Leningrad: Nauka, 1975 (in Russian)<\/li>\n\n\n\n
  12. Aitken A.C. XXV. \u2013 On Bernoulli\u2019s numerical solution of algebraic equations. Proceedings of the Royal Society of Edinburgh. 1927. (46). Pp. 289\u2013305.<\/li>\n<\/ol>\n<\/details>\n\n\n\n
    Information about the authors<\/strong><\/summary>\n
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    Ganshin Konstantin Yuryevich<\/strong>, graduate student, Institute of Information Technologies and Telecommunications, North-Caucasus Federal University;
    355017, Russia, Stavropol, 1, Pushkin street;
    ORCID: https:\/\/orcid.org\/0000-0001-7495-0736
    Vinokursky Dmitry Leonidovich<\/strong>, Ph.D. (Phys. & Math.), Associate Professor, Institute of Information Technologies and Telecommunications, North-Caucasus Federal University;
    355017, Russia, Stavropol, 1, Pushkin street;
    dlvinokursky@gmail.com, ORCID: https:\/\/orcid.org\/0000-0002-5225-8076
    Mezentseva Oksana Stanislavovna<\/strong>, Ph.D. (Phys. & Math.) Associate Professor, Institute of Information Technologies and Telecommunications, North-Caucasus Federal University;
    355017, Russia, Stavropol, 1, Pushkin street;
    ORCID: https:\/\/orcid.org\/0000-0001-5503-1056
    Samoilov Philipp Vladimirovich<\/strong>, Ph.D. (Phys. & Math.), Associate Professor, Institute of Information Technologies and Telecommunications, North-Caucasus Federal University;
    355017, Russia, Stavropol, 1, Pushkin street;
    ORCID: https:\/\/orcid.org\/0000-0003-3555-4479<\/p>\n\n\n\n

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    <\/p>\n","protected":false},"excerpt":{"rendered":"

    Numerical method for solving the optimization problem of trajectory control and formation maintenance by a group of autonomous UAVs with predictive models K.Yu. Ganshin, D.L. Vinokursky, O.S. Mezentseva, Ph.V. Samoilov Upload the full text Abstract: The article is devoted to the development of a numerical method for solving the optimization problem of trajectory control of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"wp-custom-template-home","meta":{"footnotes":""},"class_list":["post-8176","page","type-page","status-publish","hentry"],"yoast_head":"\n25.4.4 En - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-4-4-en\/\" \/>\n<meta property=\"og:locale\" content=\"ru_RU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"25.4.4 En - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb\" \/>\n<meta property=\"og:description\" content=\"Numerical method for solving the optimization problem of trajectory control and formation maintenance by a group of autonomous UAVs with predictive models K.Yu. 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