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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.25.559-567</article-id><article-id custom-type="elpub" pub-id-type="custom">novtexmech-1645</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>СИСТЕМНЫЙ АНАЛИЗ, УПРАВЛЕНИЕ И ОБРАБОТКА ИНФОРМАЦИИ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>SYSTEM ANALYSIS, CONTROL AND INFORMATION PROCESSING</subject></subj-group></article-categories><title-group><article-title>Метод планирования траектории движения на базе глубокой нейронной сети с векторным входом</article-title><trans-title-group xml:lang="en"><trans-title>Method of Motion Path Planning Based on a Deep Neural Network with Vector Input</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>Хамдан</surname><given-names>Н.</given-names></name><name name-style="western" xml:lang="en"><surname>Hamdan</surname><given-names>N.</given-names></name></name-alternatives><bio xml:lang="ru"><p>аспирант</p><p>г. Ростов-на-Дону</p></bio><bio xml:lang="en"><p>Postgraduate Student</p><p>Rostov-on-Don, 344006</p></bio><email xlink:type="simple">dr.nizar.abou.hamdane@gmail.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>Медведев</surname><given-names>М.</given-names></name><name name-style="western" xml:lang="en"><surname>Medvedev</surname><given-names>M.</given-names></name></name-alternatives><bio xml:lang="ru"><p>д-р техн. наук, проф.</p><p>г. Ростов-на-Дону</p></bio><bio xml:lang="en"><p>Medvedev Mikhail, Dr. Sc., Professor</p><p>Rostov-on-Don, 344006</p></bio><email xlink:type="simple">medvmihal@sfedu.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>Пшихопов</surname><given-names>В.</given-names></name><name name-style="western" xml:lang="en"><surname>Pshikhopov</surname><given-names>V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>д-р техн. наук, проф.</p><p>г. Ростов-на-Дону</p></bio><bio xml:lang="en"><p>Dr. Sc., Professor</p><p>Rostov-on-Don, 344006</p></bio><email xlink:type="simple">pshichop@rumbler.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Южный федеральный университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Southern Federal 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>07</day><month>11</month><year>2024</year></pub-date><volume>25</volume><issue>11</issue><fpage>559</fpage><lpage>567</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/1645">https://mech.novtex.ru/jour/article/view/1645</self-uri><abstract><p>Рассматривается проблема планирования движения в двумерной среде на базе нейронных сетей глубокого обучения. Как известно, глубокие нейронные сети требуют больших объемов данных и предъявляют высокие вычислительные требования к средствам обучения. Отсутствие достаточного объема данных приводит к снижению точности нейронной сети, а высокие вычислительные требования на стадии обучения ограничивают применение данной технологии в инженерной практике. В данной работе исследуются формы представления карты среды для подачи на вход нейронной сети. Векторная форма позволяет сократить объем информации, подаваемой на вход нейронной сети, однако она приводит к необходимости использовать более сложные нейронные сети. В данной статье предложена комбинированная форма представления, включающая векторную глобальную и локальную растровую карты. Векторная часть карты включает в себя положение робота, положение целевой точки и описание препятствий, аппроксимированных прямоугольной формой. Локальная растровая карта описывает ближайшую к роботу область в текущий момент времени. С помощью численного исследования показана эффективность такой формы представления данных для сверточной нейронной сети по сравнению с растровым представлением карты. Для повышения точности работы нейронной сети и устранения зацикливаний также используется уменьшение числа возможных направлений движения. Исследованы две структуры нейронных сетей, в одной из которых используется восемь возможных направлений движения, а в другой — три возможных направления движения. Показано, что при использовании трех возможных направлений устраняются зацикливания траекторий, планируемых нейронной сетью, что приводит к повышению точности. Применение векторно-растрового описания среды позволяет повысить вероятность успешного достижения целевой точки на 5...10 % по сравнению с растровым описанием среды. Также исследовано влияние числа сверточных слоев и гиперпараметров на точность обучения.</p></abstract><trans-abstract xml:lang="en"><p>The article deals with the problem of path planning in a two-dimensional environment based on deep learning neural networks. Deep neural networks require large amounts of data and place high computational requirements on computing tools. The lack of sufficient data leads to a decrease in the accuracy of the neural network, and high computational requirements at the learning stage limit the use of this technology in engineering practice. In this paper, the forms of representation of the environment for the input of a neural network are studied. Vector form allows to reduce the amount of information supplied to the input of a neural network, but it leads to the need to use more complex neural networks. In this article, a combined form of representation is proposed, including a vector global and local map layout. The vector part of the map includes the position of the robot, the position of the target point and a description of obstacles. The local raster map describes the area closest to the robot. Using numerical research, the effectiveness of this form of data representation for a precise neural network is shown, compared with the raster representation of the map. In this article, two structures of neural networks are studied, one of which uses 8 possible directions of movement, and the other uses 3 possible directions of movement. It is shown that when using 3 possible directions, the cycling of trajectories planned by the neural network is eliminated, which leads to an increase in accuracy.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>планирование траектории</kwd><kwd>нейронная сеть</kwd><kwd>глубокое обучение</kwd><kwd>векторная карта</kwd><kwd>2D-среда</kwd></kwd-group><kwd-group xml:lang="en"><kwd>path planning</kwd><kwd>neural network</kwd><kwd>deep learning</kwd><kwd>vector map</kwd><kwd>2-D environmemt</kwd></kwd-group><funding-group><funding-statement xml:lang="en">The research was carried out with support of a grant from the Russian Science Foundation No. 24-19-00063, "Theoretical foundations and methods of group control of unmanned underwater vehicles", https://rscf.ru/project/24-19-00063 / on the basis of the Federal State Educational Institution of Higher Education "Southern Federal University".</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">LeCun Y., Bengio Y., Hinton G. Deep learning, Nature, 2015, vol. 521, pp. 436—444, doi:10.1038/nature14539.</mixed-citation><mixed-citation xml:lang="en">LeCun Y., Bengio Y., Hinton G. Deep learning, Nature, 2015, vol. 521, pp. 436—444, doi:10.1038/nature14539.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Thomas A., Hedley J. FumeBot: A Deep Convolutional Neural Network Controlled Robot, Robotics, 2019, vol. 8, no. 3.</mixed-citation><mixed-citation xml:lang="en">Thomas A., Hedley J. FumeBot: A Deep Convolutional Neural Network Controlled Robot, Robotics, 2019, vol. 8, no. 3.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Mashoshin A. I. Artificial Intelligence Technologies in the Autonomous Underwater Vehicle Control Systems. Mekhatronika, Avtomatizatsiya, Upravlenie. 2022, vol. 23, no. 11, pp. 596—606 (in Russian), https://doi.org/10.17587/mau.23.596-606.</mixed-citation><mixed-citation xml:lang="en">Mashoshin A. I. Artificial Intelligence Technologies in the Autonomous Underwater Vehicle Control Systems. Mekhatronika, Avtomatizatsiya, Upravlenie. 2022, vol. 23, no. 11, pp. 596—606 (in Russian), https://doi.org/10.17587/mau.23.596-606.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Pomerleau D. A. ALVINN: An Autonomous Land Vehicle in a Neural Network, NeurIPS Proceedings, 1988, pp. 305—313.</mixed-citation><mixed-citation xml:lang="en">Pomerleau D. A. ALVINN: An Autonomous Land Vehicle in a Neural Network, NeurIPS Proceedings, 1988, pp. 305—313.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Hawke J., Shen R., Gurau C. et. al. Urban driving with conditional imitation learning, 2020 IEEE International Conference on Robotics and Automation (ICRA), 2020, pp. 251—257.</mixed-citation><mixed-citation xml:lang="en">Hawke J., Shen R., Gurau C. et. al. Urban driving with conditional imitation learning, 2020 IEEE International Conference on Robotics and Automation (ICRA), 2020, pp. 251—257.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Dotsenko A. V. Collision Avoidance System Synthesis for a Group of Robots in Unsupervised Learning Paradigm. Mekhatronika, Avtomatizatsiya, Upravlenie. 2020, vol. 21, no. 7, pp. 420—427 (in Russian), https://doi.org/10.17587/mau.21.420-427.</mixed-citation><mixed-citation xml:lang="en">Dotsenko A. V. Collision Avoidance System Synthesis for a Group of Robots in Unsupervised Learning Paradigm. Mekhatronika, Avtomatizatsiya, Upravlenie. 2020, vol. 21, no. 7, pp. 420—427 (in Russian), https://doi.org/10.17587/mau.21.420-427.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Kickia P., Gawrona T., Ćwiana K., Ozay M., Skrzypczyńskia P. Learning from experience for rapid generation of local car maneuvers. Engineering Applications of Artificial Intelligence. 2021, vol. 105.</mixed-citation><mixed-citation xml:lang="en">Kickia P., Gawrona T., Ćwiana K., Ozay M., Skrzypczyńskia P. Learning from experience for rapid generation of local car maneuvers. Engineering Applications of Artificial Intelligence. 2021, vol. 105.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Vitelli M., Chang Y., Ye Y. et. al. Safetynet: Safe planning for real-world self-driving vehicles using machine-learned policies. 2022 International Conference on Robotics and Automation (ICRA), IEEE, 2022, pp. 897—904.</mixed-citation><mixed-citation xml:lang="en">Vitelli M., Chang Y., Ye Y. et. al. Safetynet: Safe planning for real-world self-driving vehicles using machine-learned policies. 2022 International Conference on Robotics and Automation (ICRA), IEEE, 2022, pp. 897—904.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Qureshi A. H., Simeonov A., Bency M. J., Yip M. C. Motion planning networks. 2019 International Conference on Robotics and Automation (ICRA), 2019, pp. 2118—2124.</mixed-citation><mixed-citation xml:lang="en">Qureshi A. H., Simeonov A., Bency M. J., Yip M. C. Motion planning networks. 2019 International Conference on Robotics and Automation (ICRA), 2019, pp. 2118—2124.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Chiang H.-T. L., Hsu J., Fiser M., Tapia L., Faust A. RL-RRT: Kinodynamic motion planning via learning reachability estimators from RL policies, IEEE Robotics and Automation Letters, 2019, vol. 4, no. 4, pp. 4298—4305.</mixed-citation><mixed-citation xml:lang="en">Chiang H.-T. L., Hsu J., Fiser M., Tapia L., Faust A. RL-RRT: Kinodynamic motion planning via learning reachability estimators from RL policies, IEEE Robotics and Automation Letters, 2019, vol. 4, no. 4, pp. 4298—4305.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Chakravorty S., Kumar S. Generalized Sampling-Based Motion Planners. IEEE Transactions on Systems, Man, and Cybernetics — Part B: Cybernetics, 2011, vol. 41, no. 3.</mixed-citation><mixed-citation xml:lang="en">Chakravorty S., Kumar S. Generalized Sampling-Based Motion Planners. IEEE Transactions on Systems, Man, and Cybernetics — Part B: Cybernetics, 2011, vol. 41, no. 3.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Qureshi A., Ayaz Y. Potential functions based sampling heuristic for optimal path planning. Autonomous Robot, 2016, vol. 40, pp. 1079—1093.</mixed-citation><mixed-citation xml:lang="en">Qureshi A., Ayaz Y. Potential functions based sampling heuristic for optimal path planning. Autonomous Robot, 2016, vol. 40, pp. 1079—1093.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Pshikhopov V., Medvedev M., Kostjukov V., Houssein F., Kadhim A. Trajectory Planning Algorithms in Two-Dimensional Environment with Obstacles, Informatics and Automation, 2022, vol. 21, no. 3, pp. 459—492, https://doi.org/10.15622/ia.21.3.1</mixed-citation><mixed-citation xml:lang="en">Pshikhopov V., Medvedev M., Kostjukov V., Houssein F., Kadhim A. Trajectory Planning Algorithms in Two-Dimensional Environment with Obstacles, Informatics and Automation, 2022, vol. 21, no. 3, pp. 459—492, https://doi.org/10.15622/ia.21.3.1</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Kostyukov V., Medvedev M., Pshikhopov V. Global path planning algorithm in a two-dimensional environment with polygonal obstacles on the class of piecewise polygonal trajectories, Unmanned Systems, 2024.</mixed-citation><mixed-citation xml:lang="en">Kostyukov V., Medvedev M., Pshikhopov V. Global path planning algorithm in a two-dimensional environment with polygonal obstacles on the class of piecewise polygonal trajectories, Unmanned Systems, 2024.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Filimonov A. B., Filimonov N. B., Nguyen Т. К., Pham Q. P. Planning of UAV Flight Routes in the Problems of Group Patrolling of the Extended Territories. Mekhatronika, Avtomatizatsiya, Upravlenie. 2023, vol. 24, no. 7, pp. 374—381 (In Russian), https:// doi.org/10.17587/mau.24.374-381.</mixed-citation><mixed-citation xml:lang="en">Filimonov A. B., Filimonov N. B., Nguyen Т. К., Pham Q. P. Planning of UAV Flight Routes in the Problems of Group Patrolling of the Extended Territories. Mekhatronika, Avtomatizatsiya, Upravlenie. 2023, vol. 24, no. 7, pp. 374—381 (In Russian), https:// doi.org/10.17587/mau.24.374-381.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Whitley D., Starkweather T., Bogart C. Genetic Algorithms and Neural Networks: Optimization Connections and Connectivity, Parallel Computing, 1990, vol. 14.</mixed-citation><mixed-citation xml:lang="en">Whitley D., Starkweather T., Bogart C. Genetic Algorithms and Neural Networks: Optimization Connections and Connectivity, Parallel Computing, 1990, vol. 14.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Wang J., Perez L. The effectiveness of data augmentation in image classification using deep learning, ArXiv, 2017.</mixed-citation><mixed-citation xml:lang="en">Wang J., Perez L. The effectiveness of data augmentation in image classification using deep learning, ArXiv, 2017.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Gaiduk A. R., Martjanov O. V., Medvedev M. Yu., Pshikhopov V. Kh., Hamdan N., Farhood A. Neural Network Based Control System for Robots Group Operating in 2-d Uncertain Environment, Mekhatronika, Avtomatizatsiya, Upravlenie. 2020, vol. 21, no. 8, pp. 470—479, https://doi.org/10.17587/mau.21.470-479.</mixed-citation><mixed-citation xml:lang="en">Gaiduk A. R., Martjanov O. V., Medvedev M. Yu., Pshikhopov V. Kh., Hamdan N., Farhood A. Neural Network Based Control System for Robots Group Operating in 2-d Uncertain Environment, Mekhatronika, Avtomatizatsiya, Upravlenie. 2020, vol. 21, no. 8, pp. 470—479, https://doi.org/10.17587/mau.21.470-479.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Berner C., Brockman G., Chan B. et. al. Dota 2 with Large Scale Deep Reinforcement Learning, ArXiv, 2019.</mixed-citation><mixed-citation xml:lang="en">Berner C., Brockman G., Chan B. et. al. Dota 2 with Large Scale Deep Reinforcement Learning, ArXiv, 2019.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Medvedev M., Pshikhopov V., Gurenko B., Hamdan N. Path planning method for mobile robot with maneuver restrictions, Proc. of the International Conference on Electrical, Computer, Communications and Mechatronics Engineering (ICECCME), 7—8 October 2021, Mauritius, 10.1109/ICECCME52200.2021.9591090.</mixed-citation><mixed-citation xml:lang="en">Medvedev M., Pshikhopov V., Gurenko B., Hamdan N. Path planning method for mobile robot with maneuver restrictions, Proc. of the International Conference on Electrical, Computer, Communications and Mechatronics Engineering (ICECCME), 7—8 October 2021, Mauritius, 10.1109/ICECCME52200.2021.9591090.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Net-Scale Technologies, Inc. Autonomous off-road vehicle control using end-to-end learning, July 2004, Final technical report, URL: http://net-scale.com/doc/net-scale-dave-report.pdf.</mixed-citation><mixed-citation xml:lang="en">Net-Scale Technologies, Inc. Autonomous off-road vehicle control using end-to-end learning, July 2004, Final technical report, URL: http://net-scale.com/doc/net-scale-dave-report.pdf.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Bojarski M., Testa D. D., Dworakowski D. et. al. End to end learning for self-driving cars, ArXiv, 2016.</mixed-citation><mixed-citation xml:lang="en">Bojarski M., Testa D. D., Dworakowski D. et. al. End to end learning for self-driving cars, ArXiv, 2016.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Chen C., Seff A., Kornhauser A. L., Xiao J. DeepDriving: Learning Affordance for Direct Perception in Autonomous Driving, 2015 IEEE International Conference on Computer Vision (ICCV), 2015, pp. 2722—2730.</mixed-citation><mixed-citation xml:lang="en">Chen C., Seff A., Kornhauser A. L., Xiao J. DeepDriving: Learning Affordance for Direct Perception in Autonomous Driving, 2015 IEEE International Conference on Computer Vision (ICCV), 2015, pp. 2722—2730.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Geiger A., Lenz P., Stiller C., Urtasun R. Vision meets robotics: The KITTY dataset, The International Journal of Robotics Research, 2013, pp. 1231—1237.</mixed-citation><mixed-citation xml:lang="en">Geiger A., Lenz P., Stiller C., Urtasun R. Vision meets robotics: The KITTY dataset, The International Journal of Robotics Research, 2013, pp. 1231—1237.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Codevilla F., Mueller M., López A., Koltun V., Dosovitskiy A. End-to-end driving via conditional imitation learning, In 2018 IEEE International Conference on Robotics and Automation (ICRA), 2018, pp. 4693—4700.</mixed-citation><mixed-citation xml:lang="en">Codevilla F., Mueller M., López A., Koltun V., Dosovitskiy A. End-to-end driving via conditional imitation learning, In 2018 IEEE International Conference on Robotics and Automation (ICRA), 2018, pp. 4693—4700.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">LeCun Y., Muller U., Ben J., Cosatto E., Flepp B. Off-road obstacle avoidance through end-to-end learning, In NIPS, 2005.</mixed-citation><mixed-citation xml:lang="en">LeCun Y., Muller U., Ben J., Cosatto E., Flepp B. Off-road obstacle avoidance through end-to-end learning, In NIPS, 2005.</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Lei X., Zhang Z., Dong P. Dynamic Path Planning of Unknown Environment Based on Deep Reinforcement Learning, Journal of Robotics, vol. 2018, Article ID 5781591, 10 p., https:// doi.org/10.1155/2018/5781591.</mixed-citation><mixed-citation xml:lang="en">Lei X., Zhang Z., Dong P. Dynamic Path Planning of Unknown Environment Based on Deep Reinforcement Learning, Journal of Robotics, vol. 2018, Article ID 5781591, 10 p., https:// doi.org/10.1155/2018/5781591.</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Van Hasselt H., Guez A. Silver D. Deep Reinforcement Learning with Double Q-Learning[C], Proceedings of the AAAI Conference on Artificial Intelligence, 2016, vol. 30, no. 1.</mixed-citation><mixed-citation xml:lang="en">Van Hasselt H., Guez A. Silver D. Deep Reinforcement Learning with Double Q-Learning[C], Proceedings of the AAAI Conference on Artificial Intelligence, 2016, vol. 30, no. 1.</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Sung I., Choi B., Nielsen P. On the training of a neural network for online path planning with offline path planning algorithms, International Journal of Information Management, 2020, pp. 102142—102150, doi: 10.1016/j.ijinfomgt.2020.102142.</mixed-citation><mixed-citation xml:lang="en">Sung I., Choi B., Nielsen P. On the training of a neural network for online path planning with offline path planning algorithms, International Journal of Information Management, 2020, pp. 102142—102150, doi: 10.1016/j.ijinfomgt.2020.102142.</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">Wang B., Liu Z., Li Q., Prorok A. Mobile Robot Path Planning in Dynamic Environments Through Globally Guided Reinforcement Learning, IEEE Robotics and Automation Letters, 2020, vol. 5, no. 4, pp. 6932—6939, doi: 10.1109/LRA.2020.3026638.</mixed-citation><mixed-citation xml:lang="en">Wang B., Liu Z., Li Q., Prorok A. Mobile Robot Path Planning in Dynamic Environments Through Globally Guided Reinforcement Learning, IEEE Robotics and Automation Letters, 2020, vol. 5, no. 4, pp. 6932—6939, doi: 10.1109/LRA.2020.3026638.</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">Lv L. H., Zhang S. J., Ding D. R., Wang Y. X. Path Planning via an Improved DQN-Based Learning Policy? IEEE Access, 2019, vol. 7, pp. 67319—67330.</mixed-citation><mixed-citation xml:lang="en">Lv L. H., Zhang S. J., Ding D. R., Wang Y. X. Path Planning via an Improved DQN-Based Learning Policy? IEEE Access, 2019, vol. 7, pp. 67319—67330.</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">Srikonda S., Norris W. R., Nottage D., Soylemezoglu A. Deep Reinforcement Learning for Autonomous Dynamic Skid Steer Vehicle Trajectory Tracking, Robotics, 2022, vol. 11, no. 95, https://doi.org/10.3390/robotics11050095.</mixed-citation><mixed-citation xml:lang="en">Srikonda S., Norris W. R., Nottage D., Soylemezoglu A. Deep Reinforcement Learning for Autonomous Dynamic Skid Steer Vehicle Trajectory Tracking, Robotics, 2022, vol. 11, no. 95, https://doi.org/10.3390/robotics11050095.</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">Lillicrap T. P., Hunt J. J., Pritzel A. et. al. Continuous control with deep reinforcement learning, 2015, arXiv:1509.02971</mixed-citation><mixed-citation xml:lang="en">Lillicrap T. P., Hunt J. J., Pritzel A. et. al. Continuous control with deep reinforcement learning, 2015, arXiv:1509.02971</mixed-citation></citation-alternatives></ref><ref id="cit34"><label>34</label><citation-alternatives><mixed-citation xml:lang="ru">Fujimoto S., Hoof H. V., Meger D. Addressing Function Approximation Error in Actor-Critic Methods, ArXiv, 2018, abs/1802.09477.</mixed-citation><mixed-citation xml:lang="en">Fujimoto S., Hoof H. V., Meger D. Addressing Function Approximation Error in Actor-Critic Methods, ArXiv, 2018, abs/1802.09477.</mixed-citation></citation-alternatives></ref><ref id="cit35"><label>35</label><citation-alternatives><mixed-citation xml:lang="ru">Gu S., Chen G., Zhang L. et. al. Constrained Reinforcement Learning for Vehicle Motion Planning with Topological Reachability Analysis, Robotics, 2022, vol. 11, no. 81, https://doi.org/10.3390/robotics11040081</mixed-citation><mixed-citation xml:lang="en">Gu S., Chen G., Zhang L. et. al. Constrained Reinforcement Learning for Vehicle Motion Planning with Topological Reachability Analysis, Robotics, 2022, vol. 11, no. 81, https://doi.org/10.3390/robotics11040081</mixed-citation></citation-alternatives></ref><ref id="cit36"><label>36</label><citation-alternatives><mixed-citation xml:lang="ru">Stentz A. Optimal and efficient path planning for partially known environments, In Intelligent Unmanned Ground Vehicles, Springer, Boston, MA, USA, 1997, pp. 203—220.</mixed-citation><mixed-citation xml:lang="en">Stentz A. Optimal and efficient path planning for partially known environments, In Intelligent Unmanned Ground Vehicles, Springer, Boston, MA, USA, 1997, pp. 203—220.</mixed-citation></citation-alternatives></ref><ref id="cit37"><label>37</label><citation-alternatives><mixed-citation xml:lang="ru">Medvedev M., Kadhim A., Brosalin D. Development of the Neural-Based Navigation System for a Ground-Based Mobile Robot, 2021 7th International Conference on Mechatronics and Robotics Engineering, 2021, pp. 35—40.</mixed-citation><mixed-citation xml:lang="en">Medvedev M., Kadhim A., Brosalin D. Development of the Neural-Based Navigation System for a Ground-Based Mobile Robot, 2021 7th International Conference on Mechatronics and Robotics Engineering, 2021, pp. 35—40.</mixed-citation></citation-alternatives></ref><ref id="cit38"><label>38</label><citation-alternatives><mixed-citation xml:lang="ru">Medvedev M., Pshikhopov V. Path Planning of Mobile Robot Group Based on Neural Networks, Lecture Notes in Artificial Intelligence, 2020, pp. 51—62.</mixed-citation><mixed-citation xml:lang="en">Medvedev M., Pshikhopov V. Path Planning of Mobile Robot Group Based on Neural Networks, Lecture Notes in Artificial Intelligence, 2020, pp. 51—62.</mixed-citation></citation-alternatives></ref><ref id="cit39"><label>39</label><citation-alternatives><mixed-citation xml:lang="ru">Bain L. J., Engelhardt M. Introduction to Probability and Mathematical Statistics, Belmont, Duxbury Press, 1992.</mixed-citation><mixed-citation xml:lang="en">Bain L. J., Engelhardt M. Introduction to Probability and Mathematical Statistics, Belmont, Duxbury Press, 1992.</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>
