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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">gyroscopy</journal-id><journal-title-group><journal-title xml:lang="ru">Гироскопия и навигация</journal-title><trans-title-group xml:lang="en"><trans-title>Giroskopiya i Navigatsiya</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">0869-7035</issn><issn pub-type="epub">2075-0927</issn><publisher><publisher-name>AO «Концерн «ЦНИИ «Электроприбор»</publisher-name></publisher></journal-meta><article-meta><article-id custom-type="edn" pub-id-type="custom">KADJYM</article-id><article-id custom-type="elpub" pub-id-type="custom">gyroscopy-645</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>Статьи</subject></subj-group></article-categories><title-group><article-title>Трехуровневая система навигации TriLayer-Nav для роботов с дифференциальным приводом</article-title><trans-title-group xml:lang="en"><trans-title>TriLayer-Nav: A Tri-Layer Navigation Framework Integrating A*, Dynamic Window Approach, and Model Predictive Control for Differential-Drive Robots</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>Мугал</surname><given-names>У.А.Б.</given-names></name><name name-style="western" xml:lang="en"><surname>Mughal</surname><given-names>U.A.B.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Мугал Умер Ахмед Баиг. Магистрант, факультет систем управления и робототехники</p><p>С.-Петербург</p></bio><bio xml:lang="en"><p>Saint Petersburg</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Али</surname><given-names>А.</given-names></name><name name-style="western" xml:lang="en"><surname>Ali</surname><given-names>A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Али Аян. Магистрант, факультет систем управления и робототехники</p><p>С.-Петербург</p></bio><bio xml:lang="en"><p>Saint Petersburg</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Урва</surname><given-names>У.</given-names></name><name name-style="western" xml:lang="en"><surname>Urwa</surname><given-names>U.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Урва. Магистрант, факультет систем управления и робототехники</p><p>С.-Петербург</p></bio><bio xml:lang="en"><p>Saint Petersburg</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Абрамчук</surname><given-names>М. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Abramchuk</surname><given-names>M. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Абрамчук Михаил Владимирович. Кандидат технических наук, доцент, факультет систем управления и робототехники</p><p>С.-Петербург</p></bio><bio xml:lang="en"><p>Saint Petersburg</p></bio><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Университет ИТМО</institution><country>Россия</country></aff><aff xml:lang="en"><institution>ITMO University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2026</year></pub-date><pub-date pub-type="epub"><day>27</day><month>04</month><year>2026</year></pub-date><volume>34</volume><issue>1</issue><fpage>41</fpage><lpage>57</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Мугал У., Али А., Урва У., Абрамчук М.В., 2026</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="ru">Мугал У., Али А., Урва У., Абрамчук М.В.</copyright-holder><copyright-holder xml:lang="en">Mughal U., Ali A., Urwa U., Abramchuk M.V.</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://www.gyroscopy.ru/jour/article/view/645">https://www.gyroscopy.ru/jour/article/view/645</self-uri><abstract><p>В статье представлена модульная трехуровневая гибридная навигационная система, объединяющая генеральное и так называемое реактивное локальное планирование (reactive local planning) траектории и ее оптимизацию путем управления по прогнозирующим моделям. Система обеспечивает плавную, энергоэффективную и надежную навигацию наземных роботов с дифференциальным приводом. В основу ее структуры положены алгоритм А* для расчета генеральных траекторий с обходом препятствий, метод динамических окон для реактивного обхода препятствий и метод управления по прогнозирующим моделям для уточнения команд, сформированных в рамках метода динамических окон с учетом неголономности и ограничений исполнительного механизма. Различные уровни системы функционируют по каскадному принципу (А* – запускается периодически, метод динамических окон – в режиме реального времени, управление по прогнозирующим моделям – в непрерывном режиме корректировки команд). При этом осуществляется конечный контроль положения колес с помощью PID-регулятора. Проведены моделирование и проверка работоспособности системы TriLayer-Nav в условиях внешних воздействий с использованием платформы MuJoCo, которая позволяет детально воспроизвести динамику твердого тела с учетом силы трения и обратной связи привода. В протоколе моделирования основной акцент сделан на иерархической структуре команд для всей системы в целом при сохранении требуемого объема вычислений в режиме реального времени. Результаты показывают, что система TriLayer-Nav генерирует плавные траектории, уменьшает разрывы непрерывности кривых и повышает устойчивость управления. Кроме того, она гарантирует более точное определение курса и потребляет меньше энергии по сравнению с известными решениями, а ее КПД составляет 96,6%. При этом TriLayer-Nav позволяет строить траектории с большей точностью, чем системы на базе только алгоритма A* или метода динамических окон. Взаимодействие уровней обеспечивает ускоренную реакцию системы на изменения окружающих условий и инструментальный шум. Помимо прочего, благодаря нелинейному алгоритму управления по прогнозирующим моделям платформа производит вычисления в режиме реального времени, а модульная иерархическая структура дает возможность ее полномасштабной реализации в структурированных и полуструктурированных средах. Таким образом, полученные результаты убедительно доказывают, что сочетание генерального и реактивного локального планирования, а также оптимизация траектории с помощью прогнозирующих моделей значительно повышает надежность, устойчивость и энергоэффективность автономной навигации. Система TriLayer-Nav представляет собой универсальное и действенное в вычислительном отношении навигационное решение, которое может быть применено к широкому спектру наземных роботизированных систем, работающих в динамично меняющихся и неопределенных условиях.</p></abstract><trans-abstract xml:lang="en"><p>This paper introduces TriLayer-Nav, a modular tri-layer hybrid navigational system that integrates global planning, reactive local planning, and predictive control optimization to achieve smooth, energy-efficient, and robust navigation of differential-drive ground robots. The architecture employs the A* algorithm for the computation of a collisionfree global path, the Dynamic Window Approach for reactive obstacle avoidance, and Model Predictive Control for refining the Dynamic Window Approach commands while at the same time satisfying non-holonomic and actuator constraints. The different layers function in cascade (A* at a low frequency, Dynamic Window Approach in real-time, and Model Predictive Control continuously refining commands), with final wheel-level tracking being performed by a PID controller. TriLayer-Nav has undergone intensive simulation and validation in a physics-based environment exploiting the MuJoCo platform, allowing detailed modelling of rigid-body dynamics, frictional interactions, and actuator feedback. In the simulation protocol, a complete hierarchical allocation of commands was highlighted throughout the system and at the same time maintained realtime computation throughput. The findings show that TriLayer-Nav produces smoother paths with less curvature discontinuities, reduced control oscillations, better heading accuracy, and lower energy use, and with a success rate of 96.6%, while path efficiency is better than that of implementations that solely rely on A* or Dynamic Window Approach. Layer interaction provides better reaction to environmental changes and sensor noise. It is also computationally viable to run the framework in real-time by using a nonlinear Model Predictive Control solver and its modular hierarchy allows it to be implemented in structured and semi-structured environments on a large scale. To sum up, the findings deliver strong evidence that combining global planning, local reactive planner and predictive optimization is a significant improvement in enhancing the reliability, stability and energy efficiency of autonomous navigation. TriLayer-Nav is a generalizable and computationally efficient navigation solution that can be applicable to a wide range of ground robotic systems used in dynamic and uncertain environments.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>гибридная навигация</kwd><kwd>метод динамических окон</kwd><kwd>управление по прогнозирующим моделям</kwd><kwd>оптимизация траектории</kwd><kwd>робот с дифференцированным приводом</kwd><kwd>автономная навигация</kwd></kwd-group><kwd-group xml:lang="en"><kwd>hybrid navigation</kwd><kwd>Dynamic Window Approach</kwd><kwd>Model Predictive Control</kwd><kwd>trajectory optimization</kwd><kwd>differential-drive robot</kwd><kwd>autonomous navigation</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">Rodríguez-Molina, A., Herroz-Herrera, A., Aldape-Pérez, M., et al., Dynamic path planning for the differential drive mobile robot based on online metaheuristic optimization, Mathematics, 2022, vol. 10, no. 21, p. 3990, doi: 10.3390/math10213990.</mixed-citation><mixed-citation xml:lang="en">Rodríguez-Molina, A., Herroz-Herrera, A., Aldape-Pérez, M., et al., Dynamic path planning for the differential drive mobile robot based on online metaheuristic optimization, Mathematics, 2022, vol. 10, no. 21, p. 3990, doi: 10.3390/math10213990.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Chen, J. and Cheng, J., Study of robot path planning with improved A* and DWA algorithm fusion, Academic Journal of Science and Technology, 2024, vol. 9, no. 2, pp. 77–82, doi: 10.54097/vkb7a649</mixed-citation><mixed-citation xml:lang="en">Chen, J. and Cheng, J., Study of robot path planning with improved A* and DWA algorithm fusion, Academic Journal of Science and Technology, 2024, vol. 9, no. 2, pp. 77–82, doi: 10.54097/vkb7a649</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Chen, X., Yang, C., Hu, H., Gao, Y., Zhu, Q., and Shao, G., A hybrid DWA-MPC framework for coordinated path planning and collision avoidance in articulated steering vehicles, Machines, 2024, vol. 12, no. 12, p. 939. https://doi.org/10.3390/machines12120939.</mixed-citation><mixed-citation xml:lang="en">Chen, X., Yang, C., Hu, H., Gao, Y., Zhu, Q., and Shao, G., A hybrid DWA-MPC framework for coordinated path planning and collision avoidance in articulated steering vehicles, Machines, 2024, vol. 12, no. 12, p. 939. https://doi.org/10.3390/machines12120939.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Li, K., Zhang, D., Li, X., and Su, Y., A study of mobile robot path planning by fusing improved A* and DWA algorithms, Proc. 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