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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">gumrf</journal-id><journal-title-group><journal-title xml:lang="ru">Вестник Государственного университета морского и речного флота имени адмирала С. О. Макарова</journal-title><trans-title-group xml:lang="en"><trans-title>Vestnik Gosudarstvennogo universiteta morskogo i rechnogo flota imeni admirala S. O. Makarova</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2309-5180</issn><issn pub-type="epub">2500-0551</issn><publisher><publisher-name>ФГБОУ ВО «Государственный университет морского и речного флота имени адмирала С.О. Макарова»</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.21821/2309-5180-2024-16-2-259-270</article-id><article-id custom-type="elpub" pub-id-type="custom">gumrf-444</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>Эксплуатация водного транспорта, водные пути сообщения и гидрография</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>OPERATION OF WATER TRANSPORT, WATERWAYS AND HYDROGRAPHY</subject></subj-group></article-categories><title-group><article-title>Обзор актуальных алгоритмов по оптимизации маршрутов автономных судов</article-title><trans-title-group xml:lang="en"><trans-title>Overview of current algorithms for autonomous vessels route optimization</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>Чабак</surname><given-names>А. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Chabak</surname><given-names>A. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Чабак Артём Андреевич — аспирант,</p><p>198035, Санкт-Петербург, ул. Двинская, 5/7. </p></bio><bio xml:lang="en"><p>Chabak, Artem A. — Postgraduate Student,</p><p>5/7 Dvinskaya Str., St. Petersburg, 198035.</p></bio><email xlink:type="simple">beshan74@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>ФГБОУ ВО «ГУМРФ имени адмирала С. О. Макарова»</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Admiral Makarov State University of Maritime and Inland Shipping</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2024</year></pub-date><pub-date pub-type="epub"><day>22</day><month>05</month><year>2024</year></pub-date><volume>16</volume><issue>2</issue><fpage>259</fpage><lpage>270</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Чабак А.А., 2024</copyright-statement><copyright-year>2024</copyright-year><copyright-holder xml:lang="ru">Чабак А.А.</copyright-holder><copyright-holder xml:lang="en">Chabak A.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://journal.gumrf.ru/jour/article/view/444">https://journal.gumrf.ru/jour/article/view/444</self-uri><abstract><p>В статье выполнен обзор различных алгоритмов по оптимизации маршрутов морских автономных надводных судов. Отмечается, что актуальным и действенным методом оптимизации маршрутов является внедрение алгоритмов и программной базы по предотвращению столкновения, основанных на теории графов. Основными способами являются алгоритм Дейкстры, А*, искусственные потенциальные поля, метод «динамического окна», метод скоростного препятствия. Также отдельно рассматривается предотвращение столкновения с использованием радара морского автономного навигационного судна, геометрических факторов судов, генетического алгоритма, обучения нейронной сети. При этом большинство алгоритмов рассматривается только как теоретическое решение поставленных задач. Вместе с тем в некоторых работах описаны результаты, полученные при проведении экспериментальных натурных испытаний, а именно: нейронные сети, использующие глубокое обучение, марковский процесс принятия решений, Q-обучение; созданная с нуля система автономного предотвращения столкновения с использованием концепции поиска заменяемого пространства действий; эвристический поиск оптимального маршрута судна по Северному морскому пути с использованием алгоритма А2015. Общий анализ исследований показал, что многие авторы значительно продвинулись в своих исследованиях — в них видна положительная динамика исследования, однако необходимо совершенствовать существующие алгоритмы для решения поставленных задач, поскольку в одних работах не рассматривается расхождение с несколькими судами, в других не используется маневр, связанный с изменением скорости, в отдельных работах существует сложность настройки параметров для эффективной работы алгоритма. Не в полной мере разработан также критерий оптимальности при совместном маневрировании, учитывающий не только обеспечение минимального значения кратчайшей дистанции до судна в системе, но и другие факторы, такие как распределение обязанностей по выполнению маневров судов.</p></abstract><trans-abstract xml:lang="en"><p>An overview of multiple current algorithms for optimizing the routes of autonomous surface vessels is provided in the paper. One of the effective methods for route optimization is the implementation of algorithms and software based on graph theory to prevent collisions. Key algorithms include Dijkstra’s algorithm, A*, artificial potential fields, the “dynamic window” method, and the velocity obstacle method. Collision prevention using radar of the maritime autonomous navigation vessel, geometric vessel factors, genetic algorithms, neural network training is also separately discussed. While most algorithms are only considered theoretically, some works describe practical observations: neural networks using deep learning, Markov decision processes, Q-learning; developed autonomous collision avoidance system; heuristic search for optimal ship routes using the A2015 algorithm. Overall research analysis shows that many authors have made significant progress in their work, but the topic is not fully explored. Some works do not consider divergence with multiple vessels, while others do not utilize maneuvers involving speed changes. Certain works face challenges in parameter tuning for algorithm efficiency. The optimality criterion for multiple maneuvering, considering factors beyond minimizing the closest point of approach to another vessel, such as responsibility distribution for maneuver execution, is not fully developed. It is noted that all necessary conditions for creating a universal algorithm in the future already exist due to modern technologies and the research topic relevance.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>автономная навигация</kwd><kwd>безэкипажные суда</kwd><kwd>оптимизация маршрутов</kwd><kwd>предотвращение столкновений</kwd><kwd>планирование маршрута</kwd><kwd>актуальные алгоритмы</kwd></kwd-group><kwd-group xml:lang="en"><kwd>autonomous navigation</kwd><kwd>unmanned surface vessels</kwd><kwd>route optimization</kwd><kwd>collision avoidance</kwd><kwd>path planning</kwd><kwd>current algorithms</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">Autonomous shipping. IMO [Электронный ресурс]. — Режим доступа: https://www.imo.org/en/MediaCentre/HotTopics/Pages/Autonomous-shipping.aspx (дата обращения 10.02.2024).</mixed-citation><mixed-citation xml:lang="en">Autonomous shipping. Web. 10 Feb. 2024 &lt;https://www.imo.org/en/MediaCentre/HotTopics/Pages/Autonomous-shipping.aspx&gt;.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Триполец О. Ю. Обзор существующих методов расхождения безэкипажных судов / О. Ю. Триполец // Вестник Государственного университета морского и речного флота имени адмирала С. О. Макарова. — 2021. — Т. 13. — № 4. — С. 480–495. DOI: 10.21821/2309-5180-2021-13-4-480-495.</mixed-citation><mixed-citation xml:lang="en">Tripolets, Oleg Y. “Overview of existing methods of autonomous vessels collision avoidance.” Vestnik Gosudarstvennogo universiteta morskogo i rechnogo flota imeni admirala S. O. Makarova 13.4 (2021): 480–495. DOI: 10.21821/2309-5180-2021-13-4-480-495.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Bondy J. A. Graph Theory / J. A. Bondy, U.S.R. Murty. — 1st. ed. — Springer Publishing Company, Incorporated, 2008. — 675 p.</mixed-citation><mixed-citation xml:lang="en">Bondy, J. A., and U. S. R. Murty. Graph Theory. 1st. ed. Springer Publishing Company, Incorporated, 2008.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Татт У. Теория графов: Пер. с англ. / У. Татт. — М.: Мир, 1988. — 424 с.</mixed-citation><mixed-citation xml:lang="en">Tutte, W. T. Graph Theory. Cambridge University Press, 2001.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Уилсон Р. Введение в теорию графов / Р. Уилсон; перевод с англ. И. Г. Никитиной; под ред. Г. П. Гаврилова. — М.: Мир, 1977. — 208 с.</mixed-citation><mixed-citation xml:lang="en">Wilson, Robin J. Introduction to Graph Theory. 5th Edition. Pearson, 2010.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">bin Mohamad Rafi M. S. A. Radar-Based Collision Avoidance on Unmanned Surface Vehicles (USV) / M. S. A. bin Mohamad Rafi, W. Sediono, Z. bin Zainal Abidin // 2022 IEEE 9th International Conference on Underwater System Technology: Theory and Applications (USYS). — IEEE, 2022. — Pp. 1–7. DOI: 10.1109/USYS56283.2022.10073415.</mixed-citation><mixed-citation xml:lang="en">bin Mohamad Rafi, Muhammad Shahrul Afiq, Wahju Sediono, and Zulkifli bin Zainal Abidin. “Radar-Based Collision Avoidance on Unmanned Surface Vehicles (USV).” 2022 IEEE 9th International Conference on Underwater System Technology: Theory and Applications (USYS). IEEE, 2022. DOI: 10.1109/USYS56283.2022.10073415.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Mu D. Geometric Collision Avoidance Algorithm for Unmanned Surface Vehicle Based on Multi-objective / D. Mu, T. Li, X. Han, Y. Fan, X. Sun, Y. Liu // 2022 5th International Conference on Intelligent Autonomous Systems (ICoIAS). — IEEE, 2022. — Pp. 159–165. DOI: 10.1109/ICoIAS56028.2022.9931210.</mixed-citation><mixed-citation xml:lang="en">Mu, Dongdong, Tanghui Li, Xinjie Han, Yunsheng Fan, Xiaojie Sun, and Yanli Liu. “Geometric Collision Avoidance Algorithm for Unmanned Surface Vehicle Based on Multi-objective.” 2022 5th International Conference on Intelligent Autonomous Systems (ICoIAS). IEEE, 2022. DOI: 10.1109/ICoIAS56028.2022.9931210.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Fu Z. Method for collision avoidance by USV based on improved genetic algorithm / Z. Fu, H. Wang, Y. Gu, C. Li, H. Tong, H. Wang // Global Oceans 2020: Singapore–US Gulf Coast. — IEEE, 2020. — Pp. 01–06. DOI: 10.1109/IEEECONF38699.2020.9389254.</mixed-citation><mixed-citation xml:lang="en">Fu, Zhongjian, Hongjian Wang, Yingmin Gu, Chengfeng Li, Haiyan Tong, and Haibin Wang. “Method for collision avoidance by USV based on improved genetic algorithm.” Global Oceans 2020: Singapore–US Gulf Coast. IEEE, 2020. DOI: 10.1109/IEEECONF38699.2020.9389254.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Триполец О. Ю. Обучение нейронной сети вычислению дистанции кратчайшего сближения между судами / О. Ю. Триполец // Вестник Государственного университета морского и речного флота имени адмирала С. О. Макарова. — 2022. — Т. 14. — № 5. — С. 713–721. DOI: 10.21821/2309-5180-2022-14-5-713-721.</mixed-citation><mixed-citation xml:lang="en">Tripolets, Oleg Y. “Training a neural network to calculate the closest point of approach.” Vestnik Gosudarstvennogo universiteta morskogo i rechnogo flota imeni admirala S. O. Makarova 14.5 (2022): 713–721. DOI: 10.21821/2309-5180-2022-14-5-713-721.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Yan H. An Obstacle Avoidance Algorithm for Unmanned Surface Vehicle Based on A Star and Velocity-Obstacle Algorithms / H. Yan, Q. Zhu, Y. Zhang, Z. Li, X. Du // 2022 IEEE 6th Information Technology and Mechatronics Engineering Conference (ITOEC). — IEEE, 2022. — Vol. 6. — Pp. 77–82. DOI:10.1109/ITOEC53115.2022.9734642.</mixed-citation><mixed-citation xml:lang="en">Yan, Hongzhou, Qige Zhu, Yifan Zhang, Zhe Li, and Xiaojia Du. “An Obstacle Avoidance Algorithm for Unmanned Surface Vehicle Based on A Star and Velocity-Obstacle Algorithms.” 2022 IEEE 6th Information Technology and Mechatronics Engineering Conference (ITOEC). Vol. 6. IEEE, 2022. DOI: 10.1109/ITOEC53115.2022.9734642.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Sun X. Real-time collision avoidance control for unmanned surface vehicle based on velocity resolution method / X. Sun, G. Wang, Y. Fan, D. Mu, B. Qiu, J. Liu // 2019 Chinese Control Conference (CCC). — IEEE, 2019. — Pp. 6668–6673. DOI: 10.23919/ChiCC.2019.8866486.</mixed-citation><mixed-citation xml:lang="en">Sun, Xiaojie, Guofeng Wang, Yunsheng Fan, Dongdong Mu, Bingbing Qiu, and Jian Liu. “Real-time collision avoidance control for unmanned surface vehicle based on velocity resolution method.” 2019 Chinese Control Conference (CCC). IEEE, 2019. DOI: 10.23919/ChiCC.2019.8866486.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Zhuang J. Multiple Moving Obstacles Avoidance for USV using Velocity Obstacle Method / J. Zhuang, Y. Zhang, P. Xu, Y. Zhao, J. Luo, S. Song // 2021 IEEE International Conference on Unmanned Systems (ICUS). — IEEE, 2021. — Pp. 140–145. DOI: 10.1109/ICUS52573.2021.9641331.</mixed-citation><mixed-citation xml:lang="en">Zhuang, Jiayuan, Yuhang Zhang, Peihong Xu, Yi Zhao, Jing Luo, and Shengqing Song. “Multiple Moving Obstacles Avoidance for USV using Velocity Obstacle Method.” 2021 IEEE International Conference on Unmanned Systems (ICUS). IEEE, 2021. DOI: 10.1109/ICUS52573.2021.9641331.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Li Y. Real-time collision avoidance planning for unmanned surface vessels based on field theory / Y. Li, J. Zheng // ISA transactions. — 2020. — Vol. 106. — Pp. 233–242. DOI: 10.1016/j.isatra.2020.07.018.</mixed-citation><mixed-citation xml:lang="en">Li, Yun, and Jian Zheng. “Real-time collision avoidance planning for unmanned surface vessels based on field theory.” ISA transactions 106 (2020): 233–242. DOI: 10.1016/j.satra.2020.07.018.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Cho Y. Experimental validation of a velocity obstacle based collision avoidance algorithm for unmanned surface vehicles / Y. Cho, J. Han, J. Kim, P. Lee, S. B. Park // IFAC-PapersOnLine. — 2019. — Vol. 52. — Is. 21. — Pp. 329–334. DOI: 10.1016/j.ifacol.2019.12.328.</mixed-citation><mixed-citation xml:lang="en">Cho, Yonghoon, Jungwook Han, Jinwhan Kim, Philyeob Lee, and Shin-Bae Park. “Experimental validation of a velocity obstacle based collision avoidance algorithm for unmanned surface vehicles.” IFAC-PapersOnLine 52.21 (2019): 329–334. DOI: 10.1016/j.ifacol.2019.12.328.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Johansen T. A. Ship collision avoidance and COLREGS compliance using simulation-based control behavior selection with predictive hazard assessment / T. A. Johansen, T. Perez, A. Cristofaro // IEEE transactions on intelligent transportation systems. — 2016. — Vol. 17. — Is. 12. — Pp. 3407–3422. DOI: 10.1109/TITS.2016.2551780.</mixed-citation><mixed-citation xml:lang="en">Johansen, Tor Arne, Tristan Perez, and Andrea Cristofaro. “Ship collision avoidance and COLREGS compliance using simulation-based control behavior selection with predictive hazard assessment.” IEEE transactions on intelligent transportation systems 17.12 (2016): 3407–3422. DOI: 10.1109/TITS.2016.2551780.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Zhuang J. Collision avoidance for unmanned surface vehicles based on COLREGS / J. Zhuang, J. Luo, Y. Liu, R. Bucknall, H. Sun, C. Huang // 2019 5th International Conference on Transportation Information and Safety (ICTIS). — IEEE, 2019. — Pp. 1418–1425. DOI: 10.1109/ICTIS.2019.8883829.</mixed-citation><mixed-citation xml:lang="en">Zhuang, Jiayuan, Jing Luo, Yuanchang Liu, Richard Bucknall, Hanbing Sun, and Cheng Huang. “Collision avoidance for unmanned surface vehicles based on COLREGS.” 2019 5th International Conference on Transportation Information and Safety (ICTIS). IEEE, 2019. 1418–1425. DOI: 10.1109/ICTIS.2019.8883829.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Guan W. Autonomous Collision Avoidance of Unmanned Surface Vehicles Based on Improved A-Star and Dynamic Window Approach Algorithms / W. Guan, K. Wang // IEEE Intelligent Transportation Systems Magazine. — 2023. — Vol. 15. — Is. 3. — Pp. 36–50. DOI:10.1109/MITS.2022.3229109.</mixed-citation><mixed-citation xml:lang="en">Guan, Wei, and Kuo Wang. “Autonomous collision avoidance of unmanned surface vehicles based on improved A-star and dynamic window approach algorithms.” IEEE Intelligent Transportation Systems Magazine 15.3 (2023): 36–50. DOI: 10.1109/MITS.2022.3229109.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Wang P. Research on Local Path Planning for Autonomous Collision Avoidance of USV / P. Wang, X. Yao, Q. Fei, J. Meng // 2022 China Automation Congress (CAC) — IEEE, 2022. — Pp. 5368–5373. DOI: 10.1109/CAC57257.2022.10055154.</mixed-citation><mixed-citation xml:lang="en">Wang, Peiqi, Xiaolan Yao, Qing Fei, and Jiekun Meng. “Research on Local Path Planning for Autonomous Collision Avoidance of USV.” 2022 China Automation Congress (CAC). IEEE, 2022. 5368–5373. DOI: 10.1109/CAC57257.2022.10055154.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Chao W. A situation awareness approach for USV based on Artificial Potential Fields / W. Chao, M. Feng, W. Qing, W. Shuwu // 2017 4th International conference on Transportation Information and Safety (ICTIS) — IEEE, 2017. — Pp. 232–235. DOI: 10.1109/ICTIS.2017.8047770.</mixed-citation><mixed-citation xml:lang="en">Chao, Wu, Ma Feng, Wu Qing, and Wang Shuwu. “A situation awareness approach for usv based on artificial potential fields.” 2017 4th International Conference on Transportation Information and Safety (ICTIS). IEEE, 2017. 232–235. DOI: 10.1109/ICTIS.2017.8047770.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Chen Q. D. Vector Field-Based Guidance Method for Collision Avoidance of Unmanned Surface Vehicles / Q. D. Chen, S. W. Huang, M. H. Ho, F. Y. Chung, C. H. Chu, C. M. Liao, J. Guo // 2023 IEEE Underwater Technology (UT). — IEEE, 2023. — Pp. 1–7. DOI: 10.1109/UT49729.2023.10103386.</mixed-citation><mixed-citation xml:lang="en">Chen, Qing-Da, Sheng-Wei Huang, Ming-Hsin Ho, Feng-Yeang Chung, Chun-Han Chu, Chi-Min Liao, and Jenhwa Guo. “Vector Field-Based Guidance Method for Collision Avoidance of Unmanned Surface Vehicles.” 2023 IEEE Underwater Technology (UT). IEEE, 2023. DOI: 10.1109/UT49729.2023.10103386.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Naeem W. Collision avoidance of maritime vessels / W. Naeem, S. Campbell, M. Abu-Tair // Navigation and Control of Autonomous Marine Vehicles. — 2019. — Pp. 61–84. DOI: 10.1049/PBTR011E_ch3.</mixed-citation><mixed-citation xml:lang="en">Naeem, Wasif, Sable Campbell, and Mamun Abu-Tair. “Collision avoidance of maritime vessels.” Navigation and Control of Autonomous Marine Vehicles. 2019. 61–84. DOI: 10.1049/PBTR011E_ch3.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Lazarowska A. Ship’s Trajectory Planning for Collision Avoidance at Sea Based on Ant Colony Optimisation / A. Lazarowska // The Journal of Navigation. — 2015. — Vol. 68. — Is. 2. — Pp. 291–307. DOI: 10.1017/S0373463314000708.</mixed-citation><mixed-citation xml:lang="en">Lazarowska, Agnieszka. “Ship’s trajectory planning for collision avoidance at sea based on ant colony optimisation.” The Journal of Navigation 68.2 (2015): 291–307. DOI: 10.1017/S0373463314000708.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Yuan-hui W. Research on Optimal Planning Method of USV for Complex Obstacles / W. Yuan-hui, C. Cen // 2016 IEEE International Conference on Mechatronics and Automation. — IEEE, 2016. — Pp. 2507–2511. DOI:10.1109/ICMA.2016.7558960.</mixed-citation><mixed-citation xml:lang="en">Yuan-hui, Wang, and Chi Cen. “Research on optimal planning method of USV for complex obstacles.” 2016 IEEE International Conference on Mechatronics and Automation. IEEE, 2016. 2507–2511. DOI: 10.1109/ICMA.2016.7558960.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Gamayanti N. Global Path Planning for USV Waypoint Guidance System Using Dynamic Programming / N. Gamayanti, R. E. A. Kadir, A. Alkaff // 2020 International Seminar on Intelligent Technology and Its Applications (ISITIA). — IEEE, 2020. — Pp. 248–253. DOI: 10.1109/ISITIA49792.2020.9163712.</mixed-citation><mixed-citation xml:lang="en">Gamayanti, Nurlita, Rusdhianto Effendi Abdul Kadir, and Abdullah Alkaff. “Global Path Planning for USV Waypoint Guidance System Using Dynamic Programming.” 2020 International Seminar on Intelligent Technology and Its Applications (ISITIA). IEEE, 2020. 248–253. DOI: 10.1109/ISITIA49792.2020.9163712.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Ding F. Energy-efficient Path Planning and Control Approach of USV Based on Particle Swarm Optimization / F. Ding, Z. Zhang, M, Fu, Y. Wang, C. Wang // OCEANS 2018 MTS/IEEE Charleston. — IEEE, 2018. — Pp. 1–6. DOI: 10.1109/OCEANS.2018.8604920.</mixed-citation><mixed-citation xml:lang="en">Ding, Fuguang, Zhaoqing Zhang, Mingyu Fu, Yuanhui Wang, and Chenglong Wang. “Energy-efficient path planning and control approach of USV based on particle swarm optimization.” OCEANS 2018 MTS/IEEE Charleston. IEEE, 2018. DOI: 10.1109/OCEANS.2018.8604920.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Казакова Е. М. Применение метода роя частиц в задачах оптимизации / Е. М. Казакова // Известия Кабардино-Балкарского научного центра РАН. — 2022. — № 5 (109). — С. 48–57. DOI: 10.35330/1991-6639-2022-5-109-48-57.</mixed-citation><mixed-citation xml:lang="en">Kazakova, E.M. “Application of particle swarm method in the optimization problems.” News of the Kabardino-Balkarian Scientific Center of RAS 5(109) (2022): 48–57. DOI: 10.35330/1991-6639-2022-5-109-48-57.</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Wang C. Research on intelligent collision avoidance decision-making of unmanned ship in unknown environments / C. Wang, X. Zhang, L. Cong, J. Li, J. Zhang // Evolving Systems. — 2019. — Vol. 10. — Is. 4. — Pp. 649–658. DOI: 10.1007/s12530-018-9253-9.</mixed-citation><mixed-citation xml:lang="en">Wang, Chengbo, Xinyu Zhang, Longze Cong, Junjie Li, and Jiawei Zhang. “Research on intelligent collision avoidance decision-making of unmanned ship in unknown environments.” Evolving Systems 10.4 (2019): 649–658. DOI: 10.1007/s12530-018-9253-9.</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Акмайкин Д. А. Эвристический поиск оптимального маршрута судна по Северному морскому пути / Д. А. Акмайкин, С. Ф. Клюева, П. А. Салюк // Вестник Государственного университета морского и речного флота имени адмирала С. О. Макарова. — 2015. — № 5 (33). — С. 55–62. DOI: 10.21821/2309-5180-2015-7-5-55-62.</mixed-citation><mixed-citation xml:lang="en">Akmaykin, D.A., S. F. Klyueva, and P. A. Salyuk. “Heuristic search for the optimal route ship northern sea route.” Vestnik Gosudarstvennogo universiteta morskogo i rechnogo flota imeni admirala S. O. Makarova 5(33) (2015): 55–62. DOI: 10.21821/2309-5180-2015-7-5-55-62.</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Son N. S. On the sea trial test for the validation of an autonomous collision avoidance system of unmanned surface vehicle, ARAGON / N. S. Son, S. Y. Kim // OCEANS 2018 MTS/IEEE Charleston. — IEEE, 2018. — Pp. 1–5. DOI: 10.1109/OCEANS.2018.8604803.</mixed-citation><mixed-citation xml:lang="en">Son, Nam-Sun, and Sun-Young Kim. “On the sea trial test for the validation of an autonomous collision avoidance system of unmanned surface vehicle, ARAGON.” OCEANS 2018 MTS/IEEE Charleston. IEEE, 2018. DOI: 10.1109/OCEANS.2018.8604803.</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">Son N. S. On an Autonomous Navigation System for Collision Avoidance of Unmanned Surface Vehicle / N. S. Son // Proceedings of the ION 2013 Pacific PNT Meeting. — 2013. — Pp. 470–476.</mixed-citation><mixed-citation xml:lang="en">Son, N.S. “On an Autonomous Navigation System for Collision Avoidance of Unmanned Surface Vehicle.” Proceedings of the ION 2013 Pacific PNT Meeting. 2013. 470–476.</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>
