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<article article-type="research-article" dtd-version="1.3" 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" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">novtexmech</journal-id><journal-title-group><journal-title xml:lang="ru">Мехатроника, автоматизация, управление</journal-title><trans-title-group xml:lang="en"><trans-title>Mekhatronika, Avtomatizatsiya, Upravlenie</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1684-6427</issn><issn pub-type="epub">2619-1253</issn><publisher><publisher-name>Commercial Publisher «New Technologies»</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17587/mau.25.43-52</article-id><article-id custom-type="elpub" pub-id-type="custom">novtexmech-1488</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ДИНАМИКА, БАЛЛИСТИКА И УПРАВЛЕНИЕ ДВИЖЕНИЕМ ЛЕТАТЕЛЬНЫХ АППАРАТОВ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>DYNAMICS, BALLISTICS AND CONTROL OF AIRCRAFT</subject></subj-group></article-categories><title-group><article-title>Методика синтеза регулятора мультикоптера, функционирующего в качестве агента роевой системы по методу квазитеплового движения</article-title><trans-title-group xml:lang="en"><trans-title>Methodology for the Synthesis of a Multicopter Controller Acting as a Swarm Agent using the Thermal Motion Equivalent Method</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Гейс</surname><given-names>Э. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Heiss</surname><given-names>E. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Э. А. Гейс, мл. науч. сотр., </p><p>Тула.</p></bio><bio xml:lang="en"><p>E. A. Heiss,  Postgraduate student,</p><p>Tula.</p></bio><email xlink:type="simple">edheiss73@outlook.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Морозов</surname><given-names>О. О.</given-names></name><name name-style="western" xml:lang="en"><surname>Morozov</surname><given-names>O. O.</given-names></name></name-alternatives><bio xml:lang="ru"><p>О. О. Морозов, канд. тех. наук, доц., </p><p>Тула.</p></bio><bio xml:lang="en"><p>O. O. Morozov,</p><p>Tula.</p></bio><email xlink:type="simple">omo@sau.tsu.tula.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Козырь</surname><given-names>А. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Kozyr</surname><given-names>A. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>А. В. Козырь, канд. тех. наук, ст. науч. сотр., </p><p>Тула.</p></bio><bio xml:lang="en"><p>A. V. Kozyr,</p><p>Tula.</p></bio><email xlink:type="simple">Kozyr_A_V@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Ефромеев</surname><given-names>А. Г.</given-names></name><name name-style="western" xml:lang="en"><surname>Efromeev</surname><given-names>A. G.</given-names></name></name-alternatives><bio xml:lang="ru"><p>А. Г. Ефромеев, канд. тех. наук, доц., </p><p>Тула.</p></bio><bio xml:lang="en"><p>A. G. Efromeev,</p><p>Tula.</p></bio><email xlink:type="simple">age.sau@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>ФГБОУ ВО "Тульский государственный университет"</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Tula State University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2024</year></pub-date><pub-date pub-type="epub"><day>10</day><month>01</month><year>2024</year></pub-date><volume>25</volume><issue>1</issue><fpage>43</fpage><lpage>52</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Commercial Publisher «New Technologies», 2024</copyright-statement><copyright-year>2024</copyright-year><copyright-holder xml:lang="ru">Commercial Publisher «New Technologies»</copyright-holder><copyright-holder xml:lang="en">Commercial Publisher «New Technologies»</copyright-holder><license xlink:href="https://mech.novtex.ru/jour/about/submissions#copyrightNotice" xlink:type="simple"><license-p>https://mech.novtex.ru/jour/about/submissions#copyrightNotice</license-p></license></permissions><self-uri xlink:href="https://mech.novtex.ru/jour/article/view/1488">https://mech.novtex.ru/jour/article/view/1488</self-uri><abstract><p>Статья посвящена разработке метода синтеза системы управления беспилотным летательным аппаратом мультикоптерного типа, функционирующим в составе роевой системы. Движение агентов в роевой системе организуется методом квазитеплового движения. Идея метода заключается в поведенческом повторении агентами ро я теплового движения атомов. При практической реализации метода квазитеплового движения важно обеспечить постоянство скорости и изотропность динамики агентов. Нарушение этих свойств приведет к невыполнению поставленных перед роевой системой задач, например, задачи разведки территории, вследствие уменьшения среднеквадратичной скорости агентов до нуля. Предлагается вариант решения обозначенных проблем, заключающийся в синтезе модального регулятора для тестовой системы "агент—границы допустимой области" для наименее быстродействующего канала управления, который обеспечивает постоянство среднеквадратичной скорости агента. Синтезированный регулятор как фильтр используется в быстродействующих каналах — втором горизонтальном и вертикальном. В быстродействующих каналах предлагается дополнительно использовать фильтр, приводящий их динамику к наименее быстродействующему каналу, тем самым обеспечивая изотропность. Изотропность летательного аппарата мультикоптерного типа обеспечивается, в том числе, ограничением максимальной длины эквивалентного вектора поля. Синтез выполнялся по упрощенной математической модели динамики мультикоптера, получаемой при малых отклонениях летательного аппарата от вертикали и не учитывающей силы Кориолиса. На основе полученных результатов разработана методика синтеза системы управления мультикоптером для функционирования в составе роевой системы. Приводятся результаты численного моделирования как одиночного аппарата в замкнутом пространстве, так и роевой системы с учетом нелинейной динамики квадрокоптера. Преимуществом предлагаемой методики является простота синтеза по линейной модели. Результаты численного моделирования подтверждают работоспособность разработанного метода.</p></abstract><trans-abstract xml:lang="en"><p>The paper is dedicated to the development of a method for the synthesis of the control system of a swarm multicopter. The motion of the agents in the swarm is organised by the thermal motion equivalent method. The idea of the method is the behavioral similarity of the thermal motion of the atoms by the agents. In the practical implementation of the thermal motion equivalent method, it is important to ensure constancy of velocity and isotropy of agent dynamics. Violating these properties will cause the swarm to fail a mission, such as an area exploration, by reducing the RMS speed of the agents to zero. The proposed solution to these problems is to synthesize a modal controller for the agent-boundaries test system for the slowest control channel, thereby ensuring RMS velocity constancy of the agent. The synthesized controller is used as a filter in the fast-acting channels, the second horizontal channel and the vertical channel. In the fast-acting channels, an additional filter is proposed to bring their dynamics to the slowest channel, thereby ensuring isotropy. The inclusion of a limit on the maximum length of the equivalent field vector ensures isotropy. The synthesis was carried out using a simplified multicopter dynamics mathematical model, obtained with small UAV deviations from the vertical and without considering the Coriolis force. The methodology for the synthesis of a multicopter control system for functioning as part of a swarm is developed using the obtained results. Numerical simulation results of both a single vehicle in closed space and a swarm using a more complete nonlinear dynamic quadcopter model are presented. The proposed method has the advantage of simple synthesis using a linear model. Numerical simulation results confirm the operability of the developed methodology.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>групповое управление</kwd><kwd>рой БПЛА</kwd><kwd>модальный регулятор</kwd><kwd>метод квазитеплового движения</kwd></kwd-group><kwd-group xml:lang="en"><kwd>group control</kwd><kwd>swarm control</kwd><kwd>UAV swarm</kwd><kwd>modal controller</kwd><kwd>thermal motion equivalent method</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Статья подготовлена при финансовой поддержке Министерства науки и высшего образования РФ в рамках государственного задания по теме "Развитие теории прикладных интеллектуальных систем вооружения и военной техники" (FEWG-2022-0003).</funding-statement><funding-statement xml:lang="en">The article was prepared with the financial support of the Ministry of Science and Higher Education of the Russian Federation within the framework of a state assignment on the topic "Development of the theory of applied intelligent weapons systems and military equipment" (FEWG-2022-0003).</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Shao R., Tao R., Liu Y., Yang Y., Li D., Chen J. UAV cooperative search in dynamic environment based on hybridlayered APF // EURASIP Journal on Advances in Signal Processing. 2021. Vol. 2021, N. 1. P. 101.</mixed-citation><mixed-citation xml:lang="en">Shao R., Tao R., Liu Y., Yang Y., Li D., Chen J. UAV cooperative search in dynamic environment based on hybrid-layered APF, EURASIP Journal on Advances in Signal Processing, 2021, vol. 2021, no. 1, p. 101.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Kalyaev I., Kapustyan S., Ivanov D., Korovin I., Usachev L., Schaefer G. A novel method for distribution of goals among UAVs for oil field monitoring // 2017 6th International Conference on Informatics, Electronics and Vision &amp; 2017 7th International Symposium in Computational Medical and Health Technology (ICIEV-ISCMHT), Himeji, Hyogo, Japan. 2017. P. 1—4.</mixed-citation><mixed-citation xml:lang="en">Kalyaev I., Kapustyan S., Ivanov D., Korovin I., Usachev L., Schaefer G. A novel method for distribution of goals among UAVs for oil field monitoring, 6th International Conference on Informatics, Electronics and Vision &amp; 2017 7th International Symposium in Computational Medical and Health Technology (ICIEV-ISCMHT), 2017, pp. 1—4.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Sutantyo D., Kernbach S., Nepomnyashchikh V., Levi P. Multi-Robot Searching Algorithm Using Levy Flight and Artificial Potential Field // 2010 8th IEEE International Workshop on Safety, Security, and Rescue Robotics, Bremen, Germany. 2011. P. 1—6.</mixed-citation><mixed-citation xml:lang="en">Sutantyo D., Kernbach S., Nepomnyashchikh V., Levi P. Multi-Robot Searching Algorithm Using Levy Flight and Artificial Potential Field, 8th IEEE International Workshop on Safety, Security, and Rescue Robotics, SSRR-2010, 2011, no. 1, pp. 1—6.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Batinovic A., Ivanovic A., Petrovic T., Bogdan S. A Shadowcasting-Based Next-Best-View Planner for Autonomous 3D Exploration // IEEE Robotics and Automation Letters. 2022. Vol. 7, N. 2. P. 2969—2976.</mixed-citation><mixed-citation xml:lang="en">Batinovic A., Ivanovic A., Petrovic T., Bogdan S. A Shadowcasting-Based Next-Best-View Planner for Autonomous 3D Exploration, IEEE Robotics and Automation Letters, 2022, vol.7, no. 2, pp. 2969—2976.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Seraj E., Silva A., Gombolay M. Multi-UAV planning for cooperative wildfire coverage and tracking with quality-of-service guarantees // Autonomous Agents and Multi-Agent Systems. 2022. Vol. 36, N. 2. https://doi.org/10.1007/s10458-022-09566-6.</mixed-citation><mixed-citation xml:lang="en">Seraj E., Silva A., Gombolay M. Multi-UAV planning for cooperative wildfire coverage and tracking with quality-of-service guarantees, Autonomous Agents and Multi-Agent Systems, 2022, vol. 36, no. 2, pp. 39.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Feng L., Katupitiya J. Vector field based control of quadrotor uavs for wildfire boundary monitoring // Journal of Intelligent &amp; Robotic Systems. 2022. Vol. 106, N. 1. https://doi.org/10.1007/s10846-022-01731-z.</mixed-citation><mixed-citation xml:lang="en">Feng L., Katupitiya J. Vector field based control of quadrotor uavs for wildfire boundary monitoring, Journal of Intelligent &amp; Robotic Systems, 2022, vol. 106, no. 1, pp. 27.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Kolling A., Walker P., Chakraborty N., Sycara K., Lewis M. Human interaction with robot swarms: a survey // IEEE Transactions on Human-Machine Systems. 2016. Vol. 46, N. 1. P. 9—26.</mixed-citation><mixed-citation xml:lang="en">Kolling A., Walker P., Chakraborty N., Sycara K., Lewis M. Human interaction with robot swarms: a survey, IEEE Transactions on Human-Machine Systems, 2016, vol. 46, no. 1, pp. 9—26.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Xu J., Hu C. Recent progress on multiple-unmanned aerial vehicle collision avoidance algorithms // 2020 Chinese Automation Congress (CAC), Shanghai, China. 2020. P. 7349—7354.</mixed-citation><mixed-citation xml:lang="en">Xu J., Hu C. Recent progress on multiple-unmanned aerial vehicle collision avoidance algorithms, Proceedings of 2020 Chinese Automation Congress (CAC), China, 2020, pp. 7349—7354.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Ильичев К. В., Манцеров С. А. Разработка масштабируемой мобильной робототехнической системы роевого взаимодействия // Вестник Пермского национального исследовательского политехнического университета. Электротехника, информационные технологии, системы управления. 2017. № 21. С. 91—108.</mixed-citation><mixed-citation xml:lang="en">Ilichev K. V., Mancerov S. A. Development of a scalable mobile robotic swarming system, Vestnik Permskogo nacional’nogo issledovatel’skogo politekhnicheskogo universiteta. Elektrotekhnika, informacionnye tekhnologii, sistemy upravleniya, 2017, no. 21, pp. 91—108 (in Russian).</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Karpov V., Karpova I. Formation of control structures in static swarms // Procedia Engineering. 2015. N. 100. P. 1459—1468.</mixed-citation><mixed-citation xml:lang="en">Karpov V., Karpova I. Formation of control structures in static swarms, Procedia Engineering, 2015, no. 100, pp. 1459—1468.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Zhang D., Duan H. Switching topology approach for UAV formation based on binary-tree network // J. Frankl. Inst. 2017. Vol. 356. P. 835—859.</mixed-citation><mixed-citation xml:lang="en">Zhang D., Duan H. Switching topology approach for UAV formation based on binary-tree network, J. Frankl. Inst., 2017, vol. 356, pp. 835—859.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Bayındır L. A review of swarm robotics tasks // Neurocomputing. 2016. Vol. 172. P. 292—321.</mixed-citation><mixed-citation xml:lang="en">Bayındır L. A review of swarm robotics tasks, Neurocomputing, 2016, vol. 172, pp. 292—321.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Wang X., Li S., Yu X., Yang J. Distributed active antidisturbance consensus for leader-follower higher-order multi-agent systems with mismatched disturbances // IEEE Transactions on Automatic Control. 2017. Vol. 62, N. 11. P. 5795—5801.</mixed-citation><mixed-citation xml:lang="en">Wang X., Li S., Yu X., Yang J. Distributed active antidisturbance consensus for leader-follower higher-order multi-agent systems with mismatched disturbances, IEEE Transactions on Automatic Control, 2017, vol. 62, no. 11, pp. 5795—5801.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Wang T., Zhao S., Xia Y., Pan Z., Tian H. Consensus control of large-scale uav swarm based on multi-layer graph // Drones. 2022. Vol. 6, N. 12. https://doi.org/10.3390/drones6120402.</mixed-citation><mixed-citation xml:lang="en">Wang T., Zhao S., Xia Y., Pan Z., Tian H. Consensus control of large-scale uav swarm based on multi-layer graph, Drones, 2022, vol. 6, no. 12.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Ерофеева В. А., Иванский Ю. В., Кияев В. И. Управление роем динамических объектов на базе мультиагентного подхода // Компьютерные инструменты в образовании. 2015. № 6. С. 34—42.</mixed-citation><mixed-citation xml:lang="en">Erofeeva V. A., Ivansky Y. V., Kiyaev V. I. Dynamic object swarm management based on a multi-agent approach, Komp’yuternye instrumenty v obrazovanii, 2015, no. 6, pp. 34—42 (in Russian).</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Wilhelm J., Clem G. Vector field uav guidance for path following and obstacle avoidance with minimal deviation // Journal of Guidance, Control, and Dynamics. 2019. Vol. 42. P. 1—9.</mixed-citation><mixed-citation xml:lang="en">Wilhelm J., Clem G. Vector field uav guidance for path following and obstacle avoidance with minimal deviation, Journal of Guidance, Control, and Dynamics, 2019, vol. 42, pp. 1—9.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Муслимов Т. З. Алгоритмы управления строем автономных беспилотных летательных аппаратов самолетного типа с помощью метода векторного поля // Системы управления, связи и безопасности. 2019. Т. 4. С. 187—213.</mixed-citation><mixed-citation xml:lang="en">Muslimov T. Z. Algorithms for controlling the formation of autonomous unmanned aircraft using the vector field method, Sistemy upravleniya, svyazi i bezopasnosti, 2019, vol. 4, pp. 187—213 (in Russian).</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Платонов А. К., Карпов И. И., Кирильченко А. А. Метод потенциалов в задаче прокладки трассы // Препринт. Институт прикладной математики АН СССР. 1974. № 124. С. 27.</mixed-citation><mixed-citation xml:lang="en">Platonov A. K., Karpov I. I., Kirilchenko A. A. Method of potentials in the routing problem, Institut prikladnoj matematiki AN SSSR, 1974, no. 124, pp. 27 (in Russian).</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Khatib O. Real-time obstacle avoidance for manipulators and mobile robots // 1985 IEEE International Conference on Robotics and Automation, St. Louis, MO, USA. 1985. P. 500—505.</mixed-citation><mixed-citation xml:lang="en">Khatib O. Real-time obstacle avoidance for manipulators and mobile robots, Proceedings. 1985 IEEE International Conference on Robotics and Automation, 1985, pp. 500—505.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Heiss E., Morozov O., Efromeev A. Assessing the similarity of atoms’ thermal motion behavior by swarm agents // 2022 4th International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency (SUMMA), Lipetsk, Russia. 2022. P. 92—96.</mixed-citation><mixed-citation xml:lang="en">Heiss E., Morozov O., Efromeev A. Assessing the similarity of atoms’ thermal motion behavior by swarm agents, Procee dings of 2022 4th International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency (SUMMA), Lipetsk, IEEE, 2022, pp. 92—96.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Zhou X., Wen X., Wang Z., Gao Y., Li H., Wang Q., Yang T., Lu H., Cao Y., Xu C., Gao F. Swarm of micro flying robots in the wild // Science Robotics. 2022. Vol. 7, N. 66. P. 1—17.</mixed-citation><mixed-citation xml:lang="en">Zhou X., Wen X., Wang Z., Gao Y., Li H., Wang Q., Yang T., Lu H., Cao Y., Xu C., Gao F. Swarm of micro flying robots in the wild, Science Robotics, 2022, vol. 7, no. 66, pp. 1—17.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Миронова Г. А., Брандт Н. Н., Салецкий А. М. Молекулярная физика и термодинамика в вопросах и задачах / Учеб. пособ. СПб.: Лань, 2012. 480 с.</mixed-citation><mixed-citation xml:lang="en">Mironova G. A., Brandt N. N., Saletsky A. M. Molecular physics and thermodynamics in questions and problems: Textbook, SPb, Lan’, 2012, 480 p. (in Russian).</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Borisov O. I., Gromov V. S., Pyrkin A. A., Bobtsov A. A., Nikolaev N. A. Output Robust Control with Anti-Windup Compensation for Quadcopters // IFAC-PapersOnLine. 2016. Vol. 49, N. 13. P. 287—292.</mixed-citation><mixed-citation xml:lang="en">Borisov O. I., Gromov V. S., Pyrkin A. A., Bobtsov A. A., Nikolaev N. A. Output Robust Control with Anti-Windup Compensation for Quadcopters, IFAC-PapersOnLine, 2016, vol. 49, no. 13, pp. 287—292.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Никитин Д. А. Адаптивная система управления квадрокоптером на основе кватернионной модели вращений // Управление большими системами: сборник трудов. 2017. № 69. С. 76—101.</mixed-citation><mixed-citation xml:lang="en">Nikitin D. A. Adaptive quadcopter control system based on a quaternion rotation model, Upravlenie bol’shimi sistemami: sbornik trudov, 2017, no. 69, pp. 76—101 (in Russian).</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
