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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.26.3-11</article-id><article-id custom-type="elpub" pub-id-type="custom">novtexmech-1678</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>РОБОТЫ, МЕХАТРОНИКА И РОБОТОТЕХНИЧЕСКИЕ СИСТЕМЫ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>ROBOT, MECHATRONICS AND ROBOTIC SYSTEMS</subject></subj-group></article-categories><title-group><article-title>Интерполятор, обеспечивающий высокую точность поддержания скорости рабочего органа промышленного робота. Часть II</article-title><trans-title-group xml:lang="en"><trans-title>An Interpolator, Providing High Accuracy of Industrial Robot’s End-Effector Speed. Part II</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>Ларичев</surname><given-names>Д. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Larichev</surname><given-names>D. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>студент</p></bio><email xlink:type="simple">dlaritchev@hotmail.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>Романов</surname><given-names>М. П.</given-names></name><name name-style="western" xml:lang="en"><surname>Romanov</surname><given-names>M. P.</given-names></name></name-alternatives><bio xml:lang="ru"><p>д-р техн. наук, зав. кафедрой</p></bio><email xlink:type="simple">m_romanov@mirea.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>Романов</surname><given-names>А. М.</given-names></name><name name-style="western" xml:lang="en"><surname>Romanov</surname><given-names>A. M.</given-names></name></name-alternatives><bio xml:lang="ru"><p>д-р техн. наук, проф.</p></bio><email xlink:type="simple">romanov@mirea.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>МИРЭА — Российский технологический университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>MIREA — Russian Technological University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2025</year></pub-date><pub-date pub-type="epub"><day>21</day><month>01</month><year>2025</year></pub-date><volume>26</volume><issue>1</issue><fpage>3</fpage><lpage>11</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Commercial Publisher «New Technologies», 2025</copyright-statement><copyright-year>2025</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/1678">https://mech.novtex.ru/jour/article/view/1678</self-uri><abstract><p>Интерполятор является одним из ключевых элементов систем контурного управления промышленными роботами, существенно влияющих на их точностные характеристики. В таких технологических задачах, как сварка, лазерная резка, нанесение покрытий и наплавка, помимо пространственной точности движения рабочего органа робота важную роль играет точность поддержания им скорости в процессе движения по сложным траекториям. В данной работе предлагается новое алгоритмическое обеспечение для решения задачи интерполяции при реализации контурного управления многоосевого промышленного робота, основанное на применении B-сплайнов. Предложенные алгоритмы легко адаптируются для роботов с любой кинематикой, формируя на выходе как общую траекторию движения рабочего органа робота, так и уставки по току, скорости и положению для контуров управления каждого из его приводов. В рамках исследования на основе разработанных алгоритмических решений была создана программная реализация offline-интерполятора, предназначенная для исполнения на базе контроллеров и приводов, произведенных B&amp;R Industrial Automation GmbH. В ходе натурных экспериментальных исследований, проведенных на манипуляционном роботе с кинематической схемой SCARA, было продемонстрировано, что разработанные алгоритмические решения превосходят штатный интерполятор промышленных систем управления роботами от компании B&amp;R, улучшая результаты примерно в два раза с точки зрения пространственной точности и в четыре раза с точки зрения среднеквадратического отклонения скорости. Максимальное отклонение скорости инструмента от заданных значений при использовании разработанных алгоритмов за все время проведения экспериментов не превышало 2,4 мм/c, что сравнимо с результатами наиболее современных планарных решений на базе NURBS-кривых. При этом решения, предложенные в данной работе, в отличие от планарных аналогов подходят для многомерной интерполяции. Вторая часть работы посвящена модельным и натурным экспериментальным исследованиям алгоритмов, описанных в Части I данной статьи, а также обобщению результатов работы</p></abstract><trans-abstract xml:lang="en"><p>The interpolator is one of the critical components of industrial robots control, significantly affecting their accuracy. In such technological tasks as welding, laser cutting, coating, and surfacing, in addition to the spatial accuracy of the robot’s endeffector, the accuracy of its velocity during motion along complex trajectories plays an important role. In this paper, we propose a new approach for solving the interpolation problem of a multi-axis industrial robot based on the B-splines. The proposed algorithms can be easily adapted for robots with any kinematics, generating the current, velocity, and position setpoints for the control loops of each of its actuators. A software implementation of the offline interpolator based on the proposed algorithms was developed and executed on B&amp;R industrial controllers. During the experimental studies performed on a SCARA robot, it was demonstrated that the developed algorithmic solutions outperform the standard interpolator of B&amp;R control systems, exceeding it up to 2 times in terms of spatial accuracy and up to 4 times in terms of root mean square velocity deviation. The maximum deviation of the tool’s velocity using the developed algorithms did not exceed 2.4 mm/s, comparable to the results of the most modern planar solutions based on NURBS curves. At the same time, unlike their planar analogs, the solutions proposed in this paper are suitable for multidimensional interpolation. This part is devoted to simulation and field experimental studies of the algorithms described in Part I of this paper, as well as a summary of the the research results</p></trans-abstract><kwd-group xml:lang="ru"><kwd>планирование траектории</kwd><kwd>манипулятор</kwd><kwd>промышленный робот</kwd><kwd>интеполяция</kwd><kwd>B-сплайн</kwd><kwd>кинематика</kwd><kwd>электропривод</kwd></kwd-group><kwd-group xml:lang="en"><kwd>path planning</kwd><kwd>robotic arm</kwd><kwd>industrial robot</kwd><kwd>interpolation</kwd><kwd>B-spline</kwd><kwd>kinematics</kwd><kwd>servodriv</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Tamizi M. G., Yaghoubi M., Najjaran H. A review of recent trend in motion planning of industrial robots // International Journal of Intelligent Robotics and Applications. 2023. Vol. 7, N. 2. P. 253—274.</mixed-citation><mixed-citation xml:lang="en">Tamizi M. 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