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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">izvestswsu</journal-id><journal-title-group><journal-title xml:lang="ru">Известия Юго-Западного государственного университета</journal-title><trans-title-group xml:lang="en"><trans-title>Proceedings of the Southwest State University</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2223-1560</issn><issn pub-type="epub">2686-6757</issn><publisher><publisher-name>ЮЗГУ</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.21869/2223-1560-2024-28-2-20-36</article-id><article-id custom-type="elpub" pub-id-type="custom">izvestswsu-1261</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>Машиностроение и машиноведение</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>Mechanical engineering and machine science</subject></subj-group></article-categories><title-group><article-title>Математическое моделирование траекторного управления движением трёхколесного мобильного робота</article-title><trans-title-group xml:lang="en"><trans-title>Mathematical modeling of trajectory motion control of a three-wheeled mobile robot</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-0597-8505</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Политов</surname><given-names>Е. Н.</given-names></name><name name-style="western" xml:lang="en"><surname>Politov</surname><given-names>E. N.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Политов Евгений Николаевич, кандидат технических наук, старший научный сотрудник кафедры механики, мехатроники и робототехники</p><p>ул. 50 лет Октября, д. 94, г. Курск 305040</p></bio><bio xml:lang="en"><p>Evgeniy N. Politov, Cand. of Sci. (Engineering), Senior Researcher of Mechanics, Mechatronics and Robotics Departmen</p><p>50 Let Oktyabrya str. 94, Kursk 305040</p></bio><email xlink:type="simple">politovyevgeny@rambler.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-2902-1721</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Мальчиков</surname><given-names>А. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Mal’chikov</surname><given-names>A. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Мальчиков Андрей Васильевич, кандидат технических наук, старший научный сотрудник кафедры механики, мехатроники и робототехники</p><p>ул. 50 лет Октября, д. 94, г. Курск 305040</p><p> </p><p>ResearcherID N-8856-2016</p></bio><bio xml:lang="en"><p>Andrey V. Mal’chikov, Cand. of Sci. (Engineering), Senior Researcher of Mechanics, Mechatronics and Robotics Department</p><p>50 Let Oktyabrya str. 94, Kursk 305040</p><p>ResearcherID N-8856-2016</p></bio><email xlink:type="simple">zveroknnp@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0002-7306-098X</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Звонарев</surname><given-names>И. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Zvonarev</surname><given-names>I. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Звонарев Илья Александрович, кафедра механики, мехатроники и робототехники</p><p>ул. 50 лет Октября, д. 94, г. Курск 305040</p></bio><bio xml:lang="en"><p>Ilya A. Zvonarev, Mechanics, Mechatronics and Robotics Department</p><p>50 Let Oktyabrya str. 94, Kursk 305040</p></bio><email xlink:type="simple">zveroknnp@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Юго-Западный государственный университет</institution></aff><aff xml:lang="en"><institution>Southwest State University</institution></aff></aff-alternatives><pub-date pub-type="collection"><year>2024</year></pub-date><pub-date pub-type="epub"><day>28</day><month>06</month><year>2024</year></pub-date><volume>28</volume><issue>2</issue><fpage>20</fpage><lpage>36</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Политов Е.Н., Мальчиков А.В., Звонарев И.А., 2024</copyright-statement><copyright-year>2024</copyright-year><copyright-holder xml:lang="ru">Политов Е.Н., Мальчиков А.В., Звонарев И.А.</copyright-holder><copyright-holder xml:lang="en">Politov E.N., Mal’chikov A.V., Zvonarev I.A.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://izvestswsu.elpub.ru/jour/article/view/1261">https://izvestswsu.elpub.ru/jour/article/view/1261</self-uri><abstract><sec><title>Цель</title><p>Цель. Повышение эффективности траекторного движения трехколесных роботов за счет разработки алгоритмов системы управления и подбора параметров на основании математического моделирования движения робота вдоль путевых точек, характеризующих требуемую траекторию движения. Разработка методов планирования траекторий трехколесного мобильного робота на основе алгоритма Pure Pursuit. Разработка математической модели устройства, позволяющей получить численное решение для управляемого движения робота по путевым точкам. Анализ результатов моделирования, с целью установления применимости предлагаемых решений для задач управления двухсекционным колесным роботом для ландшафтных работ.</p></sec><sec><title>Методы</title><p>Методы. В качестве основы при разработке системы управления траекторным движением робота используется алгоритм Pure Pursuit, позволяющий формировать траектории движения робота по путевым точкам с заданными параметрами движения. При разработке математической модели использовались методы теоретической механики, механики роботов, численного интегрирования, теории управления, электротехники и электромеханики. При создании программных продуктов использованы математические пакеты Matlab/Simulink.</p></sec><sec><title>Результаты</title><p>Результаты. В результате проведенного исследования были обнаружены и подтверждены основные закономерности влияния параметра Lookahead Distance алгоритма траекторного движения Pure Pursuit на характер движения управляемого робота. Показано, что выбор величины данного параметра должен обосновываться задачами управления и условиями работы робота. Разработанная математическая модель позволила получить временные диаграммы для параметров движения робота, установить точность предлагаемых алгоритмов.</p></sec><sec><title>Заключение</title><p>Заключение. В работе установлено, что предложенный в работе алгоритм Pure Pursuit может быть использован для осуществления траекторного управления колесных мобильных роботов. Метод не требует высокой производительности вычислительной системы и обеспечивает удовлетворительные качественные и количественные характеристики управления движением.</p></sec></abstract><trans-abstract xml:lang="en"><sec><title>Purpose of reseach</title><p>Purpose of reseach. Improving the efficiency of the trajectory movement of three-wheeled robots by developing control system algorithms and selecting parameters based on mathematical modeling of robot movement along waypoints that characterize the required trajectory. Development of methods for planning the trajectories of a threewheeled mobile robot based on the Pure Pursuit algorithm. Development of a mathematical model of the device that allows to obtain a numerical solution for the controlled movement of the robot along the waypoints. Analysis of the simulation results in order to establish the applicability of the proposed solutions for the tasks of controlling a twosection wheeled robot for landscape work.</p></sec><sec><title>Methods</title><p>Methods. he Pure Pursuit algorithm is used as a basis for the development of a control system for the trajectory movement of the robot, which allows forming the trajectories of the robot along waypoints with specified motion parameters. Methods of theoretical mechanics, robot mechanics, numerical integration, control theory, electrical engineering and electromechanics were used in the development of the mathematical model. When creating software products, Matlab/Simulink mathematical packages were used.</p></sec><sec><title>Results</title><p>Results. As a result of the conducted research, the main regularities of the influence of the Lookahead Distance parameter of the Pure Pursuit trajectory algorithm on the nature of the controlled robot movement were discovered and confirmed. It is shown that the choice of the value of this parameter should be justified by the control tasks and working conditions of the robot. The developed mathematical model made it possible to obtain time diagrams for the parameters of the robot's movement, to establish the accuracy of the proposed algorithms.</p></sec><sec><title>Conclusion</title><p>Conclusion. It is established in the work that the Pure Pursuit algorithm proposed in the work can be used to implement trajectory control of wheeled mobile robots. The method does not require high performance of the computing system and provides satisfactory qualitative and quantitative characteristics of motion control.</p></sec></trans-abstract><kwd-group xml:lang="ru"><kwd>траекторное управление</kwd><kwd>алгоритм Pure Pursuit</kwd><kwd>трехколесный робот</kwd><kwd>кинематические характеристики движения</kwd><kwd>математическая модель</kwd></kwd-group><kwd-group xml:lang="en"><kwd>trajectory control</kwd><kwd>Pure Pursuit algorithm</kwd><kwd>three-wheeled robot</kwd><kwd>kinematic characteristics of movement</kwd><kwd>mathematical model</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Работа выполнена в рамках реализации программы развития ФГБОУ ВО «ЮгоЗападный государственный университет» проекта «Приоритет-2030»</funding-statement><funding-statement xml:lang="en">The work was carried out within the framework of the implementation of the development program of the Southwest State University of the project "Priority-2030"</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">Ворочаева Л.Ю., Мальчиков А.В., Савин С.И Определение диапазонов допустимых значений геометрических параметров колесного прыгающего робота // Известия Юго-Западного государственного университета. 2018. 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