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<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" article-type="research-article" dtd-version="1.2" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">RUDN Journal of Engineering Research</journal-id><journal-title-group><journal-title xml:lang="en">RUDN Journal of Engineering Research</journal-title><trans-title-group xml:lang="ru"><trans-title>Вестник Российского университета дружбы народов. Серия: Инженерные исследования</trans-title></trans-title-group></journal-title-group><issn publication-format="print">2312-8143</issn><issn publication-format="electronic">2312-8151</issn><publisher><publisher-name xml:lang="en">Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University)</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">44847</article-id><article-id pub-id-type="doi">10.22363/2312-8143-2025-26-1-7-16</article-id><article-id pub-id-type="edn">JNLPXG</article-id><article-categories><subj-group subj-group-type="toc-heading" xml:lang="en"><subject>Articles</subject></subj-group><subj-group subj-group-type="toc-heading" xml:lang="ru"><subject>Статьи</subject></subj-group><subj-group subj-group-type="article-type"><subject>Research Article</subject></subj-group></article-categories><title-group><article-title xml:lang="en">Application of Machine Learning for Adaptive Trajectory Control of UAVs Under Uncertainty</article-title><trans-title-group xml:lang="ru"><trans-title>Применение машинного обучения для адаптивного управления траекториями БПЛА в условиях неопределенности</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0007-4549-172X</contrib-id><contrib-id contrib-id-type="spin">8696-5057</contrib-id><name-alternatives><name xml:lang="en"><surname>Ermilov</surname><given-names>Alexander S.</given-names></name><name xml:lang="ru"><surname>Ермилов</surname><given-names>Александр Сергеевич</given-names></name></name-alternatives><bio xml:lang="en"><p>Postgraduate student of the Department of Mechanics and Control Processes, Academy of Engineering</p></bio><bio xml:lang="ru"><p>аспирант кафедры механики и процессов управления, инженерная академия</p></bio><email>eemilov-sasha@yandex.ru</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-3880-6662</contrib-id><contrib-id contrib-id-type="spin">3969-6707</contrib-id><name-alternatives><name xml:lang="en"><surname>Saltykova</surname><given-names>Olga A.</given-names></name><name xml:lang="ru"><surname>Салтыкова</surname><given-names>Ольга Александровна</given-names></name></name-alternatives><bio xml:lang="en"><p>PhD in Physical and Mathematical Sciences, Associate Professor of the Department of Mechanics and Control Processes, Academy of Engineering</p></bio><bio xml:lang="ru"><p>кандидат физико-математических наук, доцент кафедры механики и процессов управления, инженерная академия</p></bio><email>saltykova-oa@rudn.ru</email><xref ref-type="aff" rid="aff1"/></contrib></contrib-group><aff-alternatives id="aff1"><aff><institution xml:lang="en">RUDN University</institution></aff><aff><institution xml:lang="ru">Российский университет дружбы народов</institution></aff></aff-alternatives><pub-date date-type="pub" iso-8601-date="2025-06-02" publication-format="electronic"><day>02</day><month>06</month><year>2025</year></pub-date><volume>26</volume><issue>1</issue><issue-title xml:lang="en"/><issue-title xml:lang="ru"/><fpage>7</fpage><lpage>16</lpage><history><date date-type="received" iso-8601-date="2025-07-04"><day>04</day><month>07</month><year>2025</year></date></history><permissions><copyright-statement xml:lang="en">Copyright ©; 2025, Ermilov A.S., Saltykova O.A.</copyright-statement><copyright-statement xml:lang="ru">Copyright ©; 2025, Ермилов А.С., Салтыкова О.А.</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="en">Ermilov A.S., Saltykova O.A.</copyright-holder><copyright-holder xml:lang="ru">Ермилов А.С., Салтыкова О.А.</copyright-holder><ali:free_to_read xmlns:ali="http://www.niso.org/schemas/ali/1.0/"/><license><ali:license_ref xmlns:ali="http://www.niso.org/schemas/ali/1.0/">https://creativecommons.org/licenses/by-nc/4.0</ali:license_ref></license></permissions><self-uri xlink:href="https://journals.rudn.ru/engineering-researches/article/view/44847">https://journals.rudn.ru/engineering-researches/article/view/44847</self-uri><abstract xml:lang="en"><p>The article explores the potential of applying machine learning (ML) for adaptive trajectory control of unmanned aerial vehicles (UAVs) under uncertainty. The concepts of ML algorithms and the classification of UAVs by purpose, size, and weight are examined. To analyze control methods, theoretical approaches such as ensemble learning, neural networks, and probabilistic models are applied, enabling real-time adaptation of flight trajectories. Additionally, mathematical models are presented and illustrated with formulas describing the dynamics of interaction between the control system, external disturbances, and control inputs. Parameters such as system adaptability, trajectory correction accuracy, and stability under challenging conditions are studied to assess the accuracy and efficiency of the proposed algorithms. The study also investigates the impact of computational power limitations on the real-time performance of algorithms. The integration of data from various sensors is considered crucial for improving the accuracy and reliability of the control system. Special attention is given to the practical application of ML for environmental change prediction and flight trajectory optimization. Examples of real-world ML algorithm implementations include successful developments by Russian and foreign companies, demonstrating high levels of autonomy and adaptive control. The results show that ML significantly enhances UAV autonomy and safety, ensuring reliable trajectory corrections even under uncertain conditions. Further research could focus on developing collective control for UAV groups and improving real-time ML integration. This would expand UAV functionality, improve efficiency, and reduce resource consumption.</p></abstract><trans-abstract xml:lang="ru"><p>Исследованы возможности применения машинного обучения (МО) для адаптивного управления траекториями беспилотных летательных аппаратов (БПЛА) в условиях неопределенности. Изучены концепции алгоритмов МО и классификация БПЛА по назначению, размеру и весу. Для анализа методов управления применялись теоретические подходы, такие как ансамблевое обучение, нейронные сети и вероятностные модели, позволяющие адаптировать траектории полета в реальном времени. В дополнение к этому представлены математические модели, которые проиллюстрированы формулами, описывающими динамику взаимодействия системы управления с внешними возмущениями и управляющими воздействиями. Для оценки точности и эффективности предложенных алгоритмов изучены параметры, включающие адаптивность системы, точность корректировки маршрутов и устойчивость в сложных условиях. Также исследовано влияние ограничений вычислительных мощностей на работу алгоритмов в реальном времени. Рассмотрена роль интеграции данных с различных датчиков для повышения точности и надежности системы управления. Особое внимание уделено практическому применению МО для прогнозирования изменений окружающей среды и оптимизации полетных траекторий. Примеры использования алгоритмов МО в реальных проектах включают успешные разработки российских и зарубежных компаний, демонстрирующие высокую автономность и адаптивность управления. Результаты исследования демонстрируют, что использование МО позволяет существенно повысить автономность и безопасность БПЛА, обеспечивая надежную корректировку маршрутов даже в условиях неопределенности. Дальнейшие исследования могут быть направлены на разработку коллективного управления группами БПЛА и улучшение интеграции МО в реальном времени. Это позволит расширить функциональность БПЛА, повысить их эффективность, а также снизить ресурсозатраты.</p></trans-abstract><kwd-group xml:lang="en"><kwd>machine learning</kwd><kwd>adaptive control</kwd><kwd>unmanned aerial vehicles</kwd><kwd>drones</kwd><kwd>flight trajectories</kwd><kwd>algorithms</kwd><kwd>autonomy</kwd></kwd-group><kwd-group xml:lang="ru"><kwd>беспилотные летательные аппараты</kwd><kwd>дроны</kwd><kwd>траектории полета</kwd><kwd>алгоритмы машинного обучения</kwd></kwd-group><funding-group/></article-meta></front><body></body><back><ref-list><ref id="B1"><label>1.</label><citation-alternatives><mixed-citation xml:lang="en">Obukhov AD, Nazarova AO. A control method based on computer vision and machine learning technologies for adaptive systems. Мechatronics, Automation, Control. 2023;24(1):14-23. (In Russ.) https://doi.org/10.17587/mau.24.14-23 EDN: YZTOPE</mixed-citation><mixed-citation xml:lang="ru">Обухов А.Д., Назарова А.О. 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