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<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Archiving and Interchange DTD with OASIS Tables with MathML3 v1.4 20241031//EN" "https://jats.nlm.nih.gov/archiving/1.4/JATS-archive-oasis-article1-4-mathml3.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" dtd-version="1.4" article-type="research-article" xml:lang="en"><front><journal-meta><journal-title-group><journal-title xml:lang="ru">Математическая физика и компьютерное моделирование</journal-title></journal-title-group><issn publication-format="print">2587-6325</issn><issn publication-format="electronic">2587-6902</issn></journal-meta><article-meta><article-id pub-id-type="doi">10.15688/mpcm.jvolsu.2024.1.5</article-id><article-categories><subj-group><subject>Other</subject></subj-group></article-categories><title-group><article-title xml:lang="ru">Математическое моделирование походки человека на основе пятизвенной модели антропоморфного механизма с использованием методов оптимизаци</article-title><trans-title-group xml:lang="en"><trans-title>Mathematical modeling of human gait based on a five-link anthropomorphic mechanism using optimization methods</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><name-alternatives><name xml:lang="ru"><surname>Сиволобов</surname><given-names>Сергей Владимирович</given-names></name><name xml:lang="en"><surname>Sivolobov</surname><given-names>Sergey V.</given-names></name></name-alternatives><xref ref-type="aff" rid="aff1"/><contrib-id contrib-id-type="orcid">0000-0003-1614-0393</contrib-id></contrib><aff-alternatives id="aff1"><aff xml:lang="en"><institution>Volgograd State University (Volgograd, Russian Federation)</institution></aff><aff xml:lang="ru"><institution>Волгоградский государственный университет (Волгоград, Российская Федерация)</institution></aff></aff-alternatives></contrib-group><pub-date pub-type="epub" iso-8601-date="2024-04-25"><day>25</day><month>04</month><year>2024</year></pub-date><volume>27</volume><issue>1</issue><fpage>62</fpage><lpage>85</lpage><history><date date-type="received" iso-8601-date="2023-01-10"><day>10</day><month>01</month><year>2023</year></date><date date-type="accepted" iso-8601-date="2024-02-01"><day>01</day><month>02</month><year>2024</year></date></history><permissions><license xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:title="CC BY 4.0"><ali:license_ref>https://creativecommons.org/licenses/by/4.0/</ali:license_ref><license-p xml:lang="ru">CC BY 4.0</license-p></license></permissions><abstract xml:lang="ru"><p>Рассматривается задача моделирования походки человека. Для описания движений шагающего человека используется плоская антропоморфная модель, с пятью весомыми звеньями, описывающими ноги и корпус человека. Влияние движения рук не учитывается. Управление носит импульсный характер и на интервале между началом и концом шага механизм движется по баллистической траектории. Модель описывает одноопорное движение, при котором конец опорной ноги связан с поверхностью. Состояние модели характеризуется пятью обобщенными координатами, определяющими углы отклонения от вертикали в суставах. Для моделирования реальной походки, при определении вектора начальных угловых скоростей предлагается минимизировать невязку, гарантирующую прохождение механизма через все точки заданной траектории. Антропоморфный механизм характеризуется также массово-инерционными характеристиками, точные значения которых для моделирования человека неизвестны. Для повышения точности моделирования предлагается вычислять значения этих величин путем минимизации. Для подбора оптимальных значений использовались методы безусловной оптимизации и минимизации с ограничениями. При минимизации с ограничениями удалось получить движения, наиболее приближенные к реальным. Среднее отклонение от реальных углов составило 7, 25∘ . При использовании безусловной оптимизации моделируемые движения получаются ближе к реальным (средняя ошибка составляет 3, 3 ∘ ).</p></abstract><abstract xml:lang="en" abstract-type="summary"><p>The problem of human gait modeling is considered. A flat anthropomorphic mechanism with five weighty links describing person’s legs and body is used to describe of human locomotion. The hands movements are not considered. The control is impulse and the mechanism moves along a ballistic trajectory from the interval beginning to the end. A single-support motion with ground linked support leg is described by the model. The five generalized coordinates that describe the angles deviation in a joints from the vertical is characterized the mechanism position. To simulate a real gait, when calculating the initial angular velocities vector, to minimize the residual that guarantees the mechanism passage through all points of a given trajectory is proposed. Also, mass-inertial characteristics is determine the anthropomorphic mechanism, but the modeled person’s exact values are unknown. The characteristics values varieng by the unconstrained and constrained minimization to increase the modeling accuracy is proposed. With constrained minimization the average deviation from real angles is 7.25° . With unconstrained minimization the average error is 3.3 º , but the mass-inertial characteristics may take incorrect values.</p></abstract><kwd-group xml:lang="ru"><kwd>моделирование походки</kwd><kwd>моделирование движений человека</kwd><kwd>антропоморфный механизм</kwd><kwd>модель одноопорного движения</kwd><kwd>оптимизация</kwd></kwd-group><kwd-group xml:lang="en"><kwd>gait modelling</kwd><kwd>human motion modelling</kwd><kwd>anthropomorphic mechanism</kwd><kwd>single-limb support model</kwd><kwd>optimizatio</kwd></kwd-group></article-meta></front><back><ref-list><ref id="ref1"><mixed-citation publication-type="other" xml:lang="ru">Адашевский, В. М. Теоретические основы механики биосистем / В. М. Адашевский. - Харьков: НТУ "ХПИ", 2001. - 258 c.</mixed-citation></ref><ref id="ref2"><mixed-citation publication-type="other" xml:lang="ru">Актуальные задачи управления в динамике связанных систем тел / А. С. Горобцов, П. С. Тарасов, А. В. Скориков, А. Е. Марков, С. Е. Терехов // XII Всероссийский съезд по фундаментальным проблемам теоретической и прикладной механики. - Уфа: РИЦ БашГУ, 2019. - C. 451-452. EDN: XTDVFU</mixed-citation></ref><ref id="ref3"><mixed-citation publication-type="other" xml:lang="ru">Аустен, Я. Виртуальный четырехногий робот: конструкция, управление, моделирование, эксперименты / Я. Аустен, А. М. Формальский, К. Шевалльро // Фундаментальная и прикладная математика. - 2005. - Т. 11, № 8. - C. 1-28. EDN: HSMCHD</mixed-citation></ref><ref id="ref4"><mixed-citation publication-type="other" xml:lang="ru">Борина, А. П. Система управления статически неустойчивым шагающим аппаратом / А. П. Борина // Вестник ИжГТУ им. М.Т. Калашникова. - 2023. - Т. 26, № 4. - C. 4-12. -. DOI: 10.22213/2413-1172-2023-4-4-12 EDN: YZVZJN</mixed-citation></ref><ref id="ref5"><mixed-citation publication-type="other" xml:lang="ru">Булгаков, В. Г. Специфика получения образцов для сравнительного исследования динамических признаков человека по материалам видеозаписи / В. Г. Булгаков // Вестник Владимирского юридического института. - 2010. - № 4 (17). - C. 64-67. EDN: NBLPQN</mixed-citation></ref><ref id="ref6"><mixed-citation publication-type="other" xml:lang="ru">Булгаков, В. Г. Экспертный программный модуль для исследования динамических признаков ходьбы человека / В. Г. Булгаков, В. В. Бумагин // Судебная экспертиза. - 2011. - № 3 (27). - C. 36-46. EDN: QCMGQH</mixed-citation></ref><ref id="ref7"><mixed-citation publication-type="other" xml:lang="ru">Войцицкая, К. Л. О модели тазобедренной стратегии при удержании человеком равновесия на качелях "сисо" / К. Л. Войцицкая, П. А. Кручинин, А. М. Формальский // Биомеханика-2020. - Пермь: Перм. нац. исслед. политехн. ун-т, 2020. - C. 79-83. EDN: RROOIV</mixed-citation></ref><ref id="ref8"><mixed-citation publication-type="other" xml:lang="ru">Горобцов, А. С. Глава 13. Новые механизмы двуногих и многоногих шагающих роботов / А. С. Горобцов // Новые механизмы в современной робототехнике. - М.: РИЦ Техносфера, 2018. - C. 295-315. EDN: ZVUVJJ</mixed-citation></ref><ref id="ref9"><mixed-citation publication-type="other" xml:lang="ru">Горобцов, А. С. Локомоция робота-андроида в квазистатических режимах / А. С. Горобцов // Вибрационные технологии, мехатроника и управляемые машины. - Курск: Юго-Запад. гос. ун-т, 2016. - C. 135-137. EDN: WZOXOB</mixed-citation></ref><ref id="ref10"><mixed-citation publication-type="other" xml:lang="ru">Горобцов, А. С. Теоретическая и экспериментальная отработка методов управления шаганием робота-андроида АР-600 / А. С. Горобцов, А. А. Мохов, А. А. Островский // XI Всероссийский съезд по фундаментальным проблемам теоретической и прикладной механики. - Казань: Казан. (Приволж.) федер. ун-т, 2015. - C. 1021-1023. EDN: UXFLBJ</mixed-citation></ref><ref id="ref11"><mixed-citation publication-type="other" xml:lang="ru">Горобцов, А. С. Обобщенная задача динамического уравновешивания и перспективные направления ее применения / А. С. Горобцов // Известия высших учебных заведений. Машиностроение. - 2023. - № 3 (756). - C. 14-24. -. DOI: 10.18698/0536-1044-2023-3-14-24 EDN: NGWNIB</mixed-citation></ref><ref id="ref12"><mixed-citation publication-type="other" xml:lang="ru">Гугаев, К. В. О моделировании удержания человеком равновесия на подвижной опоре в виде пресс-папье / К. В. Гугаев, П. А. Кручинин, А. М. Формальский // XI Всероссийский съезд по фундаментальным проблемам теоретической и прикладной механики. - Казань: Казан. (Приволж.) федер. ун-т, 2015. - C. 1095-1097. EDN: UXFMPT</mixed-citation></ref><ref id="ref13"><mixed-citation publication-type="other" xml:lang="ru">Иванов, А. В. Моделирование ходьбы человека с костылями / А. В. Иванов, А. М. Формальский // XI Всероссийский съезд по фундаментальным проблемам теоретической и прикладной механики. - Казань: Казан. (Приволж.) федер. ун-т, 2015. - C. 1545-1547. EDN: UXFTQV</mixed-citation></ref><ref id="ref14"><mixed-citation publication-type="other" xml:lang="ru">Исследование управляемого движения шагающих роботов методами компьютерного моделирования динамики связанных систем тел / А. С. Горобцов, Н. В. Чигиринская, М. И. Андреева, Е. А. Смирнов, А. М. Бочкин // Современные наукоемкие технологии. - 2019. - № 12-2. - C. 282-286. -. DOI: 10.17513/snt.37872 EDN: ENKVTL</mixed-citation></ref><ref id="ref15"><mixed-citation publication-type="other" xml:lang="ru">Квазиоптимальное управление движением роботов как "greedy" управление в машинном обучении / А. С. Горобцов, П. С. Тарасов, А. Е. Марков, А. В. Дианский // Робототехника и искусственный интеллект. - Красноярск: ЛИТЕРА-принт, 2022. - C. 5-8. EDN: IDVMHJ</mixed-citation></ref><ref id="ref16"><mixed-citation publication-type="other" xml:lang="ru">Климина, Л. А. Управление раскачиванием качелей / Л. А. Климина, А. М. Формальский // Устойчивость и колебания нелинейных систем управления (конференция Пятницкого). - М.: Ин-т проблем управления им. В.А. Трапезникова РАН, 2022. - C. 238-241. EDN: LMUOBW</mixed-citation></ref><ref id="ref17"><mixed-citation publication-type="other" xml:lang="ru">Колесникова, Г. П. Об одном способе моделирования походки человека / Г. П. Колесникова, А. М. Формальский // Инженерный журнал: наука и инновации. - 2014. - № 1 (25). - Article ID: 11.</mixed-citation></ref><ref id="ref18"><mixed-citation publication-type="other" xml:lang="ru">Меркурьев, И. В. Разработка математической модели робототехнического комплекса для неразрушающего контроля стальных тросов / И. В. Меркурьев, Г. Р. Сайпулаев // Математическая физика и компьютерное моделирование. - 2023. - Т. 26, № 1. - C. 49-58. -. DOI: 10.15688/mpcm.jvolsu.2023.1.4 EDN: HLTMCY</mixed-citation></ref><ref id="ref19"><mixed-citation publication-type="other" xml:lang="ru">Метод синтеза программного движения роботов с учетом заданных ограничений реакций в связях / А. С. Горобцов, А. В. Скориков, П. С. Тарасов, А. Е. Марков, А. В. Дианский // Робототехника и искусственный интеллект. - Красноярск: ЛИТЕРА-принт, 2021. - C. 199-202. EDN: MYQHLZ</mixed-citation></ref><ref id="ref20"><mixed-citation publication-type="other" xml:lang="ru">Овчинников, И. А. Моделирование походки человека в среде MatLab/Simulink / И. А. Овчинников, П. П. Коваленко, Т. М. Ву // Известия высших учебных заведений. Приборостроение. - 2016. - Т. 59, № 8. - C. 690-694. EDN: WIRXNV</mixed-citation></ref><ref id="ref21"><mixed-citation publication-type="other" xml:lang="ru">Особенности решения уравнений метода обратной задачи для синтеза устойчивого управляемого движения шагающих роботов / А. С. Горобцов, А. Е. Андреев, А. Е. Марков, А. В. Скориков, П. С. Тарасов // Тр. СПИИРАН. - 2019. - Т. 18, № 1. - C. 85-122. -. DOI: 10.15622/sp.18.1.85-122 EDN: IKCQNV</mixed-citation></ref><ref id="ref22"><mixed-citation publication-type="other" xml:lang="ru">Попов, Г. И. Биомеханика двигательной деятельности / Г. И. Попов, А. В. Самсонова. - М.: Академия, 2011. - 320 c. EDN: TRYRCZ</mixed-citation></ref><ref id="ref23"><mixed-citation publication-type="other" xml:lang="ru">Программно-аппаратный комплекс для создания и исследования систем управления локомоцией и автономным движением мобильных роботов / А. С. Горобцов, А. Е. Марков, П. С. Тарасов, А. В. Скориков, А. В. Дианский, Д. А. Степаненко // Известия Волгоградского государственного технического университета. - 2021. - № 9 (256). - C. 21-25. -. DOI: 10.35211/1990-5297-2021-9-256-21-25 EDN: HJRYZJ</mixed-citation></ref><ref id="ref24"><mixed-citation publication-type="other" xml:lang="ru">Робот с комбинированным колесно-шагающим движителем / А. С. Горобцов, А. В. Скориков, П. С. Тарасов, О. К. Чесноков // Известия Волгоградского государственного технического университета. - 2020. - № 9 (244). - C. 26-30. -. DOI: 10.35211/1990-5297-2020-9-244-26-30 EDN: ADJMKO</mixed-citation></ref><ref id="ref25"><mixed-citation publication-type="other" xml:lang="ru">Синтез локомоции шагания антропоморфного робота / А. С. Горобцов, А. Е. Андреев, А. С. Мохов, П. С. Тарасов // Робототехника и искусственный интеллект. - Красноярск: Сиб. федер. ун-т, 2016. - C. 8-12. EDN: VNQBJT</mixed-citation></ref><ref id="ref26"><mixed-citation publication-type="other" xml:lang="ru">Синтез управления роботом-андроидом в статически неустойчивых режимах / А. С. Горобцов, А. Д. Мохов, О. Г. Мохова, А. А. Островский // Теория управления и математическое моделирование. - Ижевск: Удмурт. гос. ун-т, 2015. - C. 156-157. EDN: TYVGGN</mixed-citation></ref><ref id="ref27"><mixed-citation publication-type="other" xml:lang="ru">Синтез устойчивых квазистатических режимов шагания антропоморфного робота / А. С. Горобцов, А. Е. Андреев, П. С. Тарасов, А. В. Скориков, С. К. Карцов // Известия Волгоградского государственного технического университета. - 2016. - № 6 (185). - C. 75-76. EDN: VYXADX</mixed-citation></ref><ref id="ref28"><mixed-citation publication-type="other" xml:lang="ru">Соколова, А. И. Методы идентификации человека по походке в видео / А. И. Соколова, А. С. Конушин // Труды института системного программирования РАН. - 2019. - Т. 31, № 1. - C. 69-82. -. DOI: 10.15514/ISPRAS-2019-31(1)-5 EDN: PGFXZW</mixed-citation></ref><ref id="ref29"><mixed-citation publication-type="other" xml:lang="ru">Управление локомоцией антропоморфного робота в квазистатическом режиме / А. С. Горобцов, А. Е. Андреев, А. В. Скориков, П. С. Тарасов // Робототехника и искусственный интеллект. - Красноярск: Сиб. федер. ун-т, 2016. - C. 24-28. EDN: YLVDAZ</mixed-citation></ref><ref id="ref30"><mixed-citation publication-type="other" xml:lang="ru">Формальский, А. М. Математическое моделирование поведения человека на качелях / А. М. Формальский, Л. А. Климина // XII Всероссийский съезд по фундаментальным проблемам теоретической и прикладной механики. - Уфа: РИЦ БашГУ, 2019. - C. 407-409. EDN: KNAYGO</mixed-citation></ref><ref id="ref31"><mixed-citation publication-type="other" xml:lang="ru">Формальский, А. М. Перемещение антропоморфных механизмов / А. М. Формальский. - М.: Наука, 1982. - 368 c. EDN: VUARZV</mixed-citation></ref><ref id="ref32"><mixed-citation publication-type="other" xml:lang="ru">Формальский, А. М. Управление движением неустойчивых объектов / А. М. Формальский. - М.: Физматлит, 2012. - 232 c. EDN: VXGBNZ</mixed-citation></ref><ref id="ref33"><mixed-citation publication-type="other" xml:lang="ru">Чигарев, А. В. Моделирование управляемого движения двуногого антропоморфного механизма / А. В. Чигарев, А. В. Борисов // Российский журнал биомеханики. - 2010. - Т. 15, № 1 (51). - C. 74-88.</mixed-citation></ref><ref id="ref34"><mixed-citation publication-type="other" xml:lang="ru">Экзоскелет: конструкция, управление / Г. Е. Аведиков, С. И. Жмакин, В. С. Ибрагимов, А. В. Иванов, А. И. Кобрин, П. А. Комаров, А. А. Костенко, А. С. Кузнецов, Ю. Г. Мартыненко, А. В. Кузмичев, Э. К. Лавровский, И. Е. Митрофанов, Е. В. Письменная, А. М. Формальский // XII Всероссийское совещание по проблемам управления ВСПУ-2014. - М.: Ин-т проблем управления им. В.А. Трапезникова РАН, 2014. - C. 84-90. EDN: SSHWXB</mixed-citation></ref><ref id="ref35"><mixed-citation publication-type="other" xml:lang="ru">A Reliable Gait Phase Detection System / I. P. Pappas, M. R. Popovic, T. Keller, V. Dietz, M. Morari // IEEE Transactions on Neural Systems and Rehabilitation Engineering: a Publication of the IEEE Engineering in Medicine and Biology Society. - 2001. - Vol. 9, № 2. - P. 113-125. -. DOI: 10.1109/7333.928571</mixed-citation></ref><ref id="ref36"><mixed-citation publication-type="other" xml:lang="ru">Alem, T. T. A Deep Learning Approach for Biped Robot Locomotion Interface Using a Single Inertial Sensor / T. T. Alem, J. H. Lee, Sh. Okamoto // Sensors. - 2023. - Vol. 23. - Article ID: 9841. -. DOI: 10.3390/s23249841</mixed-citation></ref><ref id="ref37"><mixed-citation publication-type="other" xml:lang="ru">Alterations in Surgical Decision Making in Patients with Cerebral Palsy Based on Three-Dimensional Gait Analysis / P. А. DeLuca, R. B. Davis, S. Ounpuu, S. Rose, R. Sirkin // Journal of Pediatric Orthopaedics. - 1997. - Vol. 17, iss. 5. - P. 608-614. -. DOI: 10.1097/00004694-199709000-00007</mixed-citation></ref><ref id="ref38"><mixed-citation publication-type="other" xml:lang="ru">Aoustin, Y. 3D Walking Biped: Optimal Swing of the Arms / Y. Aoustin, A. M. Formalskii // Multibody System Dynamics. - 2014. - Vol. 32, № 1. - P. 55-66. -. DOI: 10.1007/s11044-013-9378-3 EDN: SPPADN</mixed-citation></ref><ref id="ref39"><mixed-citation publication-type="other" xml:lang="ru">Aoustin, Y. Modeling, Control and Simulation of Upward Jump of a Biped / Y. Aoustin, A. M. Formalskii // Multibody System Dynamics. - 2013. - Vol. 29, № 4. - P. 425-445. -. DOI: 10.1007/s11044-012-9319-6 EDN: UEWDOB</mixed-citation></ref><ref id="ref40"><mixed-citation publication-type="other" xml:lang="ru">Aoustin, Y. On Optimal Swinging of the Biped Arms / Y. Aoustin, A. M. Formalskii // 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). - Nice: IEEE, 2008. - P. 2922-2927. -. DOI: 10.1109/IROS.2008.4650725</mixed-citation></ref><ref id="ref41"><mixed-citation publication-type="other" xml:lang="ru">Aoustin, Y. Strategy to Lock the Knee of Exoskeleton Stance Leg: Study in the Framework of Ballistic Walking Model / Y. Aoustin, A. M. Formalskii // Mechanisms and Machine Science. - 2016. - Vol. 39. - P. 179-195. -. DOI: 10.1007/978-3-319-30674-2_14 EDN: WWENDZ</mixed-citation></ref><ref id="ref42"><mixed-citation publication-type="other" xml:lang="ru">Aoustin, Y. Upward Jump of a Biped / Y. Aoustin, A. M. Formalskii // International Journal of Humanoid Robotics. - 2013. - Vol. 10, № 4. - Article ID: 1350032. -. DOI: 10.1142/S0219843613500321 EDN: SLNGER</mixed-citation></ref><ref id="ref43"><mixed-citation publication-type="other" xml:lang="ru">Aoustin, Y. Walking of Biped with Passive Exoskeleton: Evaluation of Energy Consumption / Y. Aoustin, A. M. Formalskii // Multibody System Dynamics. - 2018. - Vol. 43, № 1. - P. 71-96. -. DOI: 10.1007/s11044-017-9602-7 EDN: RVGNRL</mixed-citation></ref><ref id="ref44"><mixed-citation publication-type="other" xml:lang="ru">Bae, H. Biped Robot State Estimation Using Compliant Inverted Pendulum Model / H. Bae, J.-H. Oh // Robotics and Autonomous Systems. - 2018. - Vol. 108. - P. 38-50. -. DOI: 10.1016/j.robot.2018.06.004</mixed-citation></ref><ref id="ref45"><mixed-citation publication-type="other" xml:lang="ru">Bashir, K. Gait Recognition Using Gait Entropy Image / K. Bashir, T. Xiang, S. Gong // Proceedings of 3rd International Conference on Imaging for Crime Detection and Prevention (ICDP 2009). - London: IET, 2010. - P. 1-6. -. DOI: 10.1049/ic.2009.0230</mixed-citation></ref><ref id="ref46"><mixed-citation publication-type="other" xml:lang="ru">Chambers, H. G. A Practical Guide to Gait Analysis / H. G. Chambers, D. H. Sutherland // The Journal of the American Academy of Orthopaedic Surgeons. - 2002. - Vol. 10, № 3. - P. 222-231. -. DOI: 10.5435/00124635-200205000-00009</mixed-citation></ref><ref id="ref47"><mixed-citation publication-type="other" xml:lang="ru">Cho, J. Model Predictive Control of Running Biped Robot / J. Cho, J. H. Park // Applied Sciences. - 2022. - Vol. 12. - Article ID: 11183. -. DOI: 10.3390/app122111183 EDN: YIRBZN</mixed-citation></ref><ref id="ref48"><mixed-citation publication-type="other" xml:lang="ru">Compliant Gait Control Method Based on CVSLIP-FF Model for Biped Robot Walking Over Uneven Terrain / Sicheng Xie, Xinyu Li, Shengyu Lu, Jingyuan Li, Chenghao Hu, Liang Gao // ISA Transactions. - January 2024. -. DOI: 10.1016/j.isatra.2023.12.042 EDN: IGFERR</mixed-citation></ref><ref id="ref49"><mixed-citation publication-type="other" xml:lang="ru">Formalskii, A. M. Ballistic Walking Design Via Impulsive Control / A. M. Formalskii // Journal of Aerospace Engineering. - 2010. - Vol. 23, № 2. - P. 129-138. -. DOI: 10.1061/(ASCE)AS.1943-5525.0000017 EDN: MXCRHD</mixed-citation></ref><ref id="ref50"><mixed-citation publication-type="other" xml:lang="ru">Formalskii, A. M. Stabilisation and Motion Control of Unstable Objects / A. M. Formalskii. - Berlin: Walter de Gruyter GmbH, 2015. - 250 p. EDN: VTERDF</mixed-citation></ref><ref id="ref51"><mixed-citation publication-type="other" xml:lang="ru">Formalskii, A. M. Stabilization of a Double Inverted Pendulum Installed on a Seesaw / A. M. Formalskii, P. A. Kruchinin, K. L. Voitsitskaya // Mechanics of Solids. - 2021. - Vol. 56, № 8. - P. 1599-1610. -. DOI: 10.3103/S0025654421080070 EDN: OANHGW</mixed-citation></ref><ref id="ref52"><mixed-citation publication-type="other" xml:lang="ru">Formalskii, A. M. Stabilization of Unstable Mechanical Systems / A. M. Formalskii // Journal of Optimization Theory and Applications. - 2010. - Vol. 144, № 2. - P. 227-253. -. DOI: 10.1007/s10957-009-9600-x EDN: MXIRWH</mixed-citation></ref><ref id="ref53"><mixed-citation publication-type="other" xml:lang="ru">Formalskii, A. M. Unstable Mechanical Objects: Motion Control, Stabilization / A. M. Formalskii // Universal Journal of Mechanical Engineering. - 2017. - Vol. 5, № 5. - P. 150-169. -. DOI: 10.13189/ujme.2017.050503 EDN: XXYDZZ</mixed-citation></ref><ref id="ref54"><mixed-citation publication-type="other" xml:lang="ru">Gismelseed, S. A Biped Model to Predict a Wide Range of Gait and Posture Results / S. Gismelseed, A. Al Yahmedi, R. Zaier // Franklin Open. - May 2023. - Vol. 3. - Article ID: 100020. -. DOI: 10.1016/j.fraope.2023.100020</mixed-citation></ref><ref id="ref55"><mixed-citation publication-type="other" xml:lang="ru">Gugayev, K. V. A Model of Maintaining Balance by a Person on the Seesaw / K. V. Gugayev, P. A. Kruchinin, A. M. Formalskii // Journal of Applied Mathematics and Mechanics. - 2016. - Vol. 80, № 4. - P. 316-323. -. DOI: 10.1016/j.jappmathmech.2016.09.006 EDN: YUYYVL</mixed-citation></ref><ref id="ref56"><mixed-citation publication-type="other" xml:lang="ru">Han, J. Individual Recognition Using Gait Energy Image / J. Han, B. Bhanu // IEEE Transactions on Pattern Analysis and Machine Intelligence. - 2006. - Vol. 28, № 2. - P. 316-322. - DOI: http://dx.doi.org/0.1109/TPAMI.2006.38.</mixed-citation></ref><ref id="ref57"><mixed-citation publication-type="other" xml:lang="ru">Hicks, J. L. Modeling and Simulation of Normal and Pathological Gait / J. L. Hicks, M. H. Schwartz, S. L. Delp // The Identification and Treatment of Gait Problems in Cerebral Palsy. - London, UK: Mac Keith Press, 2009. - P. 285-307. -. DOI: 10.1007/s11832-010-0244-z</mixed-citation></ref><ref id="ref58"><mixed-citation publication-type="other" xml:lang="ru">Huan, T. T. Advanced Biped Gait Generator Using NARX-MLP Neural Model Optimized by Enhanced Evolutionary Algorithm / T. T. Huan, H. P. H. Anh // Vietnam Journal of Mechanics. - 2022. - Vol. 44, № 3. - P. 249-265. -. DOI: 10.15625/0866-7136/17230 EDN: YFKOAN</mixed-citation></ref><ref id="ref59"><mixed-citation publication-type="other" xml:lang="ru">Ivanov, A. V. Mathematical Modeling of Crutch Walking / A. V. Ivanov, A. M. Formalskii // Journal of Computer and Systems Sciences International. - 2015. - Vol. 54, № 2. - P. 315-329. -. DOI: 10.1134/S1064230715020082 EDN: UFSUCT</mixed-citation></ref><ref id="ref60"><mixed-citation publication-type="other" xml:lang="ru">Klimina, L. A. On the Optimal Swinging of a Swing by a Person Standing on It / L. A. Klimina, A. M. Formalskii // Journal of Computer and Systems Sciences International. - 2022. - Vol. 61, № 6. - P. 944-953. -. DOI: 10.3103/S0025654421080070 EDN: LNVGLT</mixed-citation></ref><ref id="ref61"><mixed-citation publication-type="other" xml:lang="ru">Klimina, L. A. Three-Link Mechanism as a Model of a Person on a Swing / L. A. Klimina, A. M. Formalskii // Journal of Computer and Systems Sciences International. - 2020. - Vol. 59, № 5. - P. 728-744. -. DOI: 10.1134/S1064230720050081 EDN: RXRYMZ</mixed-citation></ref><ref id="ref62"><mixed-citation publication-type="other" xml:lang="ru">Lee, L. Gait Analysis for Recognition and Classification / L. Lee, W. E. L. Grimson // Proceedings of Fifth IEEE International Conference on Automatic Face Gesture Recognition. - Washington, DC, USA: IEEE, 2002. - P. 155-162. -. DOI: 10.1109/AFGR.2002.1004148</mixed-citation></ref><ref id="ref63"><mixed-citation publication-type="other" xml:lang="ru">Leg Configuration Analysis and Prototype Design of Biped Robot Based on Spring Mass Model / J. Che, Y. Pan, W. Yan, J. Yu // Actuators. - 2022. - Vol. 11. - Article ID: 75. -. DOI: 10.3390/act11030075 EDN: CQAPTK</mixed-citation></ref><ref id="ref64"><mixed-citation publication-type="other" xml:lang="ru">Martinez, F. Simulation of Normal and Pathological Gaits Using a Fusion Knowledge Strategy / F. Martinez, C. Cifuentes, E. Romero // Journal of NeuroEngineering and Rehabilitation. - 2013. - Vol. 10. - Article ID: 73. -. DOI: 10.1186/1743-0003-10-73</mixed-citation></ref><ref id="ref65"><mixed-citation publication-type="other" xml:lang="ru">Martynenko, Y. G. Controlled Pendulum on a Movable Base / Y. G. Martynenko, A. M. Formalskii // Mechanics of Solids. - 2013. - Vol. 48, № 1. - P. 6-18. -. DOI: 10.3103/S0025654413010020 EDN: RFIIMJ</mixed-citation></ref><ref id="ref66"><mixed-citation publication-type="other" xml:lang="ru">Martynenko, Y. G. Pendulum on a Movable Base / Y. G. Martynenko, A. M. Formalskii // Doklady Mathematics. - 2011. - Vol. 84, № 1. - P. 594-599. -. DOI: 10.1134/S1064562411050115 EDN: PEEKLZ</mixed-citation></ref><ref id="ref67"><mixed-citation publication-type="other" xml:lang="ru">Methods of Increasing Service Minibots Functional Capabilities / A. Gorobtsov, A. Skorikov, P. Tarasov, A. Markov, A. Andreev // Communications in Computer and Information Science. - 2019. - Vol. 1084. - P. 191-202. -. DOI: 10.1007/978-3-030-29750-3_15 EDN: RFOCXV</mixed-citation></ref><ref id="ref68"><mixed-citation publication-type="other" xml:lang="ru">Neural Networks Trained via Reinforcement Learning Stabilize Walking of a Three-Dimensional Biped Model with Exoskeleton Applications / Ch. Liu, M. L. Audu, R. J. Triolo, R. D. Quinn // Frontiers in Robotics and AI. - 2021. - Vol. 8. - Article ID: 710999. -. DOI: 10.3389/frobt.2021.710999 EDN: QUJWKF</mixed-citation></ref><ref id="ref69"><mixed-citation publication-type="other" xml:lang="ru">Optimal Greedy Control in Reinforcement Learning / A. S. Gorobtsov, O. A. Sychev, Yu. A. Orlova, E. A. Smirnov, O. E. Grigoryeva, A. M. Bochkin, M. I. Andreeva // Sensors. - 2022. - Vol. 22, № 22. - Article ID: 8920. -. DOI: 10.3390/s22228920 EDN: GNZKOF</mixed-citation></ref><ref id="ref70"><mixed-citation publication-type="other" xml:lang="ru">Parallel Computing Technologies in the Stability Problem of Humanoid Robot Dynamic Modes / A. S. Gorobtsov, A. V. Skorikov, P. S. Tarasov, A. E. Andreev // Parallel Computational Technologies (PCT'2021). - Chelyabinsk: South Ural State University Publ., 2021. - P. 50-54. EDN: NJTUKV</mixed-citation></ref><ref id="ref71"><mixed-citation publication-type="other" xml:lang="ru">Parametric Optimization of Machine Designs Based on Mathematical Models of the Inverse Problem / A. S. Gorobtsov, A. V. Skorikov, P. S. Tarasov, A. E. Andreev // Parallel Computational Technologies (PCT'2021). - Chelyabinsk: South Ural State University Publ., 2021. - P. 55-66. EDN: PQSZQI</mixed-citation></ref><ref id="ref72"><mixed-citation publication-type="other" xml:lang="ru">Real-Time Footprint Planning and Model Predictive Control Based Method for Stable Biped Walking / S. Wang, S. Piao, X. Leng, Zh. He, X. Bai, L. Huazhong // Computational Intelligence and Neuroscience. - 2022. - Vol. 2022 (6). - Article ID: 4781747. -. DOI: 10.1155/2022/4781747</mixed-citation></ref><ref id="ref73"><mixed-citation publication-type="other" xml:lang="ru">Ren, L. Computational Models to Synthesize Human Walking / L. Ren, D. Howard, L. Kenney // Journal of Bionic Engineering. - 2006. - Vol. 3, № 3. - P. 127-138. -. DOI: 10.1016/S1672-6529(06)60016-4 EDN: DMQWPX</mixed-citation></ref><ref id="ref74"><mixed-citation publication-type="other" xml:lang="ru">Ren, L. Predictive Modelling of Human Walking Over a Complete Gait Cycle / L. Ren, R. K. Jones, D. Howard // Journal of Biomechanics. - 2007. - Vol. 40, № 7. - P. 1567-1574. -. DOI: 10.1016/j.jbiomech.2006.07.017</mixed-citation></ref><ref id="ref75"><mixed-citation publication-type="other" xml:lang="ru">Silhouette Analysis-Based Gait Recognition for Human Identification / L. Wang, T. Tan, H. Ning, W. Hu // IEEE Transactions on Pattern Analysis and Machine Intelligence. - 2003. - Vol. 25, № 12. - P. 1505-1518. -. DOI: 10.1109/TPAMI.2003.1251144</mixed-citation></ref><ref id="ref76"><mixed-citation publication-type="other" xml:lang="ru">Sivolobov, S. V. Deep Neural Network Gait Recognition in Habitoscopy Learning Process / S. V. Sivolobov // 2022 2nd International Conference on Technology Enhanced Learning in Higher Education (TELE), IEEE Xplore. - 2022. - P. 58-61. -. DOI: 10.1109/TELE55498.2022.9801064</mixed-citation></ref><ref id="ref77"><mixed-citation publication-type="other" xml:lang="ru">Sivolobov, S. V. Human Gait Feature Extraction Method / S. V. Sivolobov // Procedia Computer Science. - 2021. - Vol. 193. - P. 220-227. -. DOI: 10.1016/j.procs.2021.10.022 EDN: WUHUAK</mixed-citation></ref><ref id="ref78"><mixed-citation publication-type="other" xml:lang="ru">Sivolobov, S. V. Human Gait Model Optimization for Person Identification / S. V. Sivolobov // 2022 4th International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency (SUMMA), IEEE Xplore. - 2022. - P. 381-384. -. DOI: 10.1109/SUMMA57301.2022.9973857</mixed-citation></ref><ref id="ref79"><mixed-citation publication-type="other" xml:lang="ru">Sivolobov, S. V. Human Gait Modeling Method / S. V. Sivolobov, A. V. Khoperskov, V. V. Bumagin // IOP Conference Series: Materials Science and Engineering. - 2020. - Vol. 823. - Article ID: 012024. -. DOI: 10.1088/1757-899X/828/1/012024 EDN: ZYZCKO</mixed-citation></ref><ref id="ref80"><mixed-citation publication-type="other" xml:lang="ru">Surer, E. Methods and Technologies for Gait Analysis / E. Surer, A. Kose // Computer Analysis of Human Behavior. - London: Springer, 2011. - P. 105-123. -. DOI: 10.1007/978-0-85729-994-9_5</mixed-citation></ref><ref id="ref81"><mixed-citation publication-type="other" xml:lang="ru">The Control System Structure for the Stable Biped Robot Motion / A. S. Gorobtsov, E. N. Ryzhov, A. E. Andreev, N. I. Kohtashvili, A. S. Polyanina // Communications in Computer and Information Ssience. - 2017. - Vol. 754. - P. 231-241. -. DOI: 10.1007/978-3-319-65551-2_17 EDN: XNMKQJ</mixed-citation></ref><ref id="ref82"><mixed-citation publication-type="other" xml:lang="ru">Walking Stability of Biped Robot Based on Machine Learning Algorithm / J. Zhang, Y. Sun, Q. Jing, Y. Lu, N. Mi, X. Lian, Sh. Dong, J. Bian // Recent Advances in Materials and Manufacturing Technology. - Singapore: Springer, 2023. - P. 635-644. -. DOI: 10.1007/978-981-99-2921-4_58</mixed-citation></ref><ref id="ref83"><mixed-citation publication-type="other" xml:lang="ru">Yadav, K. Model Analysis and Control of Biped Dynamic Walker with Fault Steps in a Gait Cycle / K. Yadav. - Proceedings of the Institution of Mechanical Engineers Part C Mechanical Engineering Science. - Electronic text data. - Mode of access: https://journals.sagepub.com/doi/. - Title from screen. -. DOI: 10.1177/09544062231214701</mixed-citation></ref><ref id="ref84"><mixed-citation publication-type="other" xml:lang="en">Adashevskiy V.M. Teoreticheskie osnovy mekhaniki biosistem [Theoretical Basis of the Biosystems Mechanics]. Kharkov, NTU “KhPI” Publ., 2001. 258 p.</mixed-citation></ref><ref id="ref85"><mixed-citation publication-type="other" xml:lang="en">Gorobtsov A.S., Tarasov P.S., Skorikov A.V., Markov A.E., Terekhov S.E. Aktualnye zadachi upravleniya v dinamike svyazannykh sistem tel [Actual Control Problems in the Dynamics of Bodies Coupled Systems]. XII Vserossiyskiy syezd po fundamentalnym problemam teoreticheskoy i prikladnoy mekhaniki [The 12th All-Russian Congress on Fundamental Problems of Theoretical and Applied Mechanics]. Ufa, Bashkir State University Publ., 2019, pp. 451-452.</mixed-citation></ref><ref id="ref86"><mixed-citation publication-type="other" xml:lang="en">Austen Ya., Formalskiy A.M., Shevallro K. Virtualnyy chetyryokhnogiy robot: konstruktsiya, upravlenie, modelirovanie, eksperimenty [Virtual Quadruped: Mechanical Design, Control, Simulation, and Experimentation]. Fundamentalnaya i prikladnaya matematika [Fundamental and Applied Mathematics], 2005, vol. 11, no. 8, pp. 1-28.</mixed-citation></ref><ref id="ref87"><mixed-citation publication-type="other" xml:lang="en">Borina A.P. Sistema upravleniya staticheski neustoychivym shagayushchim apparatom [Control of Dynamic Biped Walking Robot]. Vestnik IzhGTU im. M.T. Kalashnikova, 2023, vol. 26, no. 4, pp. 4-12. DOI:http://dx.doi.org/10.22213/2413-1172-2023-4-4-12</mixed-citation></ref><ref id="ref88"><mixed-citation publication-type="other" xml:lang="en">Bulgakov V.G. Spetsifika polucheniya obraztsov dlya sravnitelnogo issledovaniya dinamicheskikh priznakov cheloveka po materialam videozapisi [Specificity of Obtaining Samples for Comparative Examination of Dynamic Features of a Man on Video Materials]. Vestnik Vladimirskogo yuridicheskogo instituta, 2010, no. 4 (17), pp. 64-67.</mixed-citation></ref><ref id="ref89"><mixed-citation publication-type="other" xml:lang="en">Bulgakov V.G., Bumagin V.V. Ekspertnyy programmnyy modul dlya issledovaniya dinamicheskikh priznakov khodby cheloveka [Expert Software for the Research of Dynamic Features of Human Walking]. Sudebnaya ekspertiza [Forensic Examination], 2011, no. 3 (27), pp. 36-46.</mixed-citation></ref><ref id="ref90"><mixed-citation publication-type="other" xml:lang="en">Voytsitskaya K.L., Kruchinin P.A., Formalskiy A.M. O modeli tazobedrennoy strategii pri uderzhanii chelovekom ravnovesiya na kachelyakh «siso» [About the Hip Strategy Model When a Person Maintains Balance on a Seesaw]. Biomekhanika-2020. Perm, Perm. nats. issled. politekhn. un-t Publ., 2020, pp. 79-83.</mixed-citation></ref><ref id="ref91"><mixed-citation publication-type="other" xml:lang="en">Gorobtsov A.S. Glava 13. Novye mekhanizmy dvunogikh i mnogonogikh shagayushchikh robotov [Chapter 13. New Mechanisms of Bipedal and Multi-Legged Walking Robots]. Novye mekhanizmy v sovremennoy robototekhnike [New Mechanisms in Modern Robotics]. Moscow, Technosphera Publ., 2018, pp. 295-315.</mixed-citation></ref><ref id="ref92"><mixed-citation publication-type="other" xml:lang="en">Gorobtsov A.S. Lokomotsiya robota-androida v kvazistaticheskikh rezhimakh [Lokomotion of the Robot Android in the Quasistatic Modes]. Vibratsionnye tekhnologii, mekhatronika i upravlyaemye mashiny [Vibration Technologies, Mechatronics and Cars]. Kursk, Yugo-Zapad. gos. un-t Publ., 2016, pp. 135-137.</mixed-citation></ref><ref id="ref93"><mixed-citation publication-type="other" xml:lang="en">Gorobtsov A.S., Mokhov A.A., Ostrovskiy A.A. Teoreticheskaya i eksperimentalnaya otrabotka metodov upravleniya shaganiem robota-androida AR-600 [Theoretical and Experimental Development of Methods for Locomotion Controlling of the AR-600 Android Robot]. XI Vserossiyskiy syezd po fundamentalnym problemam teoreticheskoy i prikladnoy mekhaniki [The 12th All-Russian Congress on Fundamental Problems of Theoretical and Applied Mechanics]. Kazan, Kazan. (Privolzh.) feder. un-t Publ., 2015, pp. 1021-1023.</mixed-citation></ref><ref id="ref94"><mixed-citation publication-type="other" xml:lang="en">Gorobtsov A.S. Obobshchennaya zadacha dinamicheskogo uravnoveshivaniya i perspektivnye napravleniya ee primeneniya [Dynamic Balance Generalized Problem and the Promising Areas of Its Application]. Izvestiya vysshikh uchebnykh zavedeniy. Mashinostroenie [BMSTU Journal of Mechanical Engineering], 2023, no. 3 (756), pp. 14-24. DOI:http://dx.doi.org/10.18698/0536-1044-2023-3-14-24</mixed-citation></ref><ref id="ref95"><mixed-citation publication-type="other" xml:lang="en">Gugaev K.V., Kruchinin P.A., Formalskiy A.M. O modelirovanii uderzhaniya chelovekom ravnovesiya na podvizhnoy opore v vide press-pape [About the Modelling of Maintaining Balance by a Person on the Seesaw]. XI Vserossiyskiy syezd po fundamentalnym problemam teoreticheskoy i prikladnoy mekhaniki [The 12th All-Russian Congress on Fundamental Problems of Theoretical and Applied Mechanics]. Kazan, Kazan. (Privolzh.) feder. un-t Publ., 2015, pp. 1095-1097.</mixed-citation></ref><ref id="ref96"><mixed-citation publication-type="other" xml:lang="en">Ivanov A.V., Formalskiy A.M. Modelirovanie khodby cheloveka s kostylyami [Modeling of Crutch Walking]. XI Vserossiyskiy syezd po fundamentalnym problemam teoreticheskoy i prikladnoy mekhaniki [XI All-Russian Congress on Fundamental Problems of Theoretical and Applied Mechanics]. Kazan, Kazan. (Privolzh.) feder. un-t Publ., 2015, pp. 1545-1547.</mixed-citation></ref><ref id="ref97"><mixed-citation publication-type="other" xml:lang="en">Gorobtsov A.S., Chigirinskaya N.V., Andreeva M.I., Smirnov E.A., Bochkin A.M. Issledovanie upravlyaemogo dvizheniya shagayushchikh robotov metodami kompyuternogo modelirovaniya dinamiki svyazannykh sistem tel [Studying of Controlled Movement of Stepping Robots by Methods of Computer Simulation of the Dynamics of Related Body Systems]. Sovremennye naukoemkie tekhnologii [Modern High Technologies], 2019, no. 12-2, pp. 282-286. DOI:http://dx.doi.org/10.17513/snt.37872</mixed-citation></ref><ref id="ref98"><mixed-citation publication-type="other" xml:lang="en">Gorobtsov A.S., Tarasov P.S., Markov A.E., Dianskiy A.V. Kvazioptimalnoe upravlenie dvizheniem robotov kak «greedy» upravlenie v mashinnom obuchenii [Quasi-Optimal Robot Motion Control as ‘‘Greedy” Control in Machine Learning]. Robototekhnika i iskusstvennyy intellekt [Robotics and Artificial Intelligence]. Krasnoyarsk, LITERA-print Publ., 2022, pp. 5-8.</mixed-citation></ref><ref id="ref99"><mixed-citation publication-type="other" xml:lang="en">Klimina L.A., Formalskiy A.M. Upravlenie raskachivaniem kacheley [Control to Pump a Swing]. Ustoychivost i kolebaniya nelineynykh sistem upravleniya (konferentsiya Pyatnitskogo) [Stability and Oscillations of Nonlinear Control Systems (Pyatnitsky conference)]. Moscow, In-t problem upravleniya im. V.A. Trapeznikova RAN Publ., 2022, pp. 238-241.</mixed-citation></ref><ref id="ref100"><mixed-citation publication-type="other" xml:lang="en">Kolesnikova G.P., Formalskiy A.M. Ob odnom sposobe modelirovaniya pokhodki cheloveka [A Way of Human Gait Modeling]. Inzhenernyy zhurnal: nauka i innovatsii [Engineering Journal: Sciense and Innovation], 2014, no. 1 (25), article ID: 11.</mixed-citation></ref><ref id="ref101"><mixed-citation publication-type="other" xml:lang="en">Merkuryev I.V., Saypulaev G.R. Razrabotka matematicheskoy modeli robototekhnicheskogo kompleksa dlya nerazrushayushchego kontrolya stalnykh trosov [Development of a Mathematical Model of a Robotic Complex for Non-Destructive Testing of Steel Cables]. Matematicheskaya fizika i kompyuternoe modelirovanie [Mathematical Physics and Computer Simulation], 2023, vol. 26, no. 1, pp. 49-58. DOI:https://doi.org/10.15688/mpcm.jvolsu.2023.1.4</mixed-citation></ref><ref id="ref102"><mixed-citation publication-type="other" xml:lang="en">Gorobtsov A.S., Skorikov A.V., Tarasov P.S., Markov A.E., Dianskiy A.V. Metod sinteza programmnogo dvizheniya robotov s uchetom zadannykh ogranicheniy reaktsiy v svyazyakh [Method of Syntesis of Robots Programmed Motion Taking Into Account Constrained Reactions in Links]. Robototekhnika i iskusstvennyy intellekt [Robotics and Artificial Intelligence]. Krasnoyarsk, LITERA-print Publ., 2021, pp. 199-202.</mixed-citation></ref><ref id="ref103"><mixed-citation publication-type="other" xml:lang="en">Ovchinnikov I.A., Kovalenko P.P., Vu T.M. Modelirovanie pokhodki cheloveka v srede MatLab/Simulink [Human Gait Modeling in MatLab/Simulink]. Izvestiya vysshikh uchebnykh zavedeniy. Priborostroenie [Journal of Instrument Engineering], 2016, vol. 59, no. 8, pp. 690-694.</mixed-citation></ref><ref id="ref104"><mixed-citation publication-type="other" xml:lang="en">Gorobtsov A.S., Andreev A.E., Markov A.E., Skorikov A.V., Tarasov P.S. Osobennosti resheniya uravneniy metoda obratnoy zadachi dlya sinteza ustoychivogo upravlyaemogo dvizheniya shagayushchikh robotov [Features of Solving the Inverse Dynamic Method Equations for the Synthesis of Stable Walking Robots Controlled Motion]. Tr. SPIIRAN [SPIIRAS Proceedings], 2019, vol. 18, no. 1, pp. 85-122. DOI:http://dx.doi.org/10.15622/sp.18.1.85-122</mixed-citation></ref><ref id="ref105"><mixed-citation publication-type="other" xml:lang="en">Popov G.I., Samsonova A.V. Biomekhanika dvigatelnoy deyatelnosti [Biomechanics of Motion Activity]. Moscow, Academia Publ., 2011. 320 p.</mixed-citation></ref><ref id="ref106"><mixed-citation publication-type="other" xml:lang="en">Gorobtsov A.S., Markov A.E., Tarasov P.S., Skorikov A.V., Dianskiy A.V., Stepanenko D.A. Programmno-apparatnyy kompleks dlya sozdaniya i issledovaniya sistem upravleniya lokomotsiey i avtonomnym dvizheniem mobilnykh robotov [Hardware and Software Complex for Creation and Research of Locomotion and Autonomous Motion Control Systems for Mobile Robots]. Izvestiya Volgogradskogo gosudarstvennogo tekhnicheskogo universiteta [Izvestia VSTU], 2021, no. 9 (256), pp. 21-25. DOI:http://dx.doi.org/10.35211/1990-5297-2021-9-256-21-25</mixed-citation></ref><ref id="ref107"><mixed-citation publication-type="other" xml:lang="en">Gorobtsov A.S., Skorikov A.V., Tarasov P.S., Chesnokov O.K. Robot s kombinirovannym kolesno-shagayushchim dvizhitelem [Robot with Combined Wheel-Stepping Mover]. Izvestiya Volgogradskogo gosudarstvennogo tekhnicheskogo universiteta [Izvestia VSTU], 2020, no. 9 (244), pp. 26-30. DOI:http://dx.doi.org/10.35211/1990-5297-2020-9-244-26-30</mixed-citation></ref><ref id="ref108"><mixed-citation publication-type="other" xml:lang="en">Gorobtsov A.S., Andreev A.E., Mokhov A.S., Tarasov P.S. Sintez lokomotsii shaganiya antropomorfnogo robota [Synthesis of Locomotion Stepping an Anthropomorphic Robotic Systems]. Robototekhnika i iskusstvennyy intellekt [Robotics and Artificial Intelligence]. Krasnoyarsk, Sib. feder. un-t Publ., 2016, pp. 8-12.</mixed-citation></ref><ref id="ref109"><mixed-citation publication-type="other" xml:lang="en">Gorobtsov A.S., Mokhov A.D., Mokhova O.G., Ostrovskiy A.A. Sintez upravleniya robotom-androidom v staticheski neustoychivykh rezhimakh [Synthesis of Control Movement of Robot-Android in Statically Unstable Modes]. Teoriya upravleniya i matematicheskoe modelirovanie [Control Theory and Mathematical Modelling]. Izhevsk, Udmurt. gos. un-t Publ., 2015, pp. 156-157.</mixed-citation></ref><ref id="ref110"><mixed-citation publication-type="other" xml:lang="en">Gorobtsov A.S., Andreev A.E., Tarasov P.S., Skorikov A.V., Kartsov S.K. Sintez ustoychivykh kvazistaticheskikh rezhimov shaganiya antropomorfnogo robota [Synthesis of Stable Quasistatic Stepping Modes of Anthropomorphic Robot]. Izvestiya Volgogradskogo gosudarstvennogo tekhnicheskogo universiteta [Izvestia VSTU], 2016, no. 6 (185), pp. 75-76.</mixed-citation></ref><ref id="ref111"><mixed-citation publication-type="other" xml:lang="en">Sokolova A.I., Konushin A.S. Metody identifikatsii cheloveka po pokhodke v video [Methods for Identifying a Person by Gait in a Video]. Trudy instituta sistemnogo programmirovaniya RAN [Proceedings of the Institute for System Programming of the RAS], 2019, vol. 31, no. 1, pp. 69-82. DOI:http://dx.doi.org/10.15514/ISPRAS-2019-31(1)-5</mixed-citation></ref><ref id="ref112"><mixed-citation publication-type="other" xml:lang="en">Gorobtsov A.S., Andreev A.E., Skorikov A.V., Tarasov P.S. Upravlenie lokomotsiey antropomorfnogo robota v kvazistaticheskom rezhime [Synthesis of Locomotion Stepping an Anthropomorphic Robotic Systems]. Robototekhnika i iskusstvennyy intellekt [Robotics and Artificial Intelligence]. Krasnoyarsk, Sib. feder. un-t Publ., 2016, pp. 24-28.</mixed-citation></ref><ref id="ref113"><mixed-citation publication-type="other" xml:lang="en">Formalskiy A.M., Klimina L.A. Matematicheskoe modelirovanie povedeniya cheloveka na kachelyakh [Mathematical Modeling of Human Movements on a Swing]. XII Vserossiyskiy syezd po fundamentalnym problemam teoreticheskoy i prikladnoy mekhaniki [The 12th All-Russian Congress on Fundamental Problems of Theoretical and Applied Mechanics]. Ufa, Bashkir State University Publ., 2019, pp. 407-409.</mixed-citation></ref><ref id="ref114"><mixed-citation publication-type="other" xml:lang="en">Formalskiy A.M. Peremeshchenie antropomorfnykh mekhanizmov [Locomotion of Anthropomorphic Mechanisms]. Moscow, Nauka Publ., 1982. 368 p.</mixed-citation></ref><ref id="ref115"><mixed-citation publication-type="other" xml:lang="en">Formalskiy A.M. Upravlenie dvizheniem neustoychivykh obyektov [Motion Control of Unstable Objects]. Moscow, Fizmatlit Publ., 2012. 232 p.</mixed-citation></ref><ref id="ref116"><mixed-citation publication-type="other" xml:lang="en">Chigarev A.V., Borisov A.V. Modelirovanie upravlyaemogo dvizheniya dvunogogo antropomorfnogo mekhanizma [Modeling the Controlled Movement of a Bipedal Anthropomorphic Mechanism]. Rossiyskiy zhurnal biomekhaniki [Russian Journal of Biomechanics], 2010, vol. 15, no. 1 (51), pp. 74-88.</mixed-citation></ref><ref id="ref117"><mixed-citation publication-type="other" xml:lang="en">Avedikov G.E., Zhmakin S.I., Ibragimov V.S., Ivanov A.V., Kobrin A.I., Komarov P.A., Kostenko A.A., Kuznetsov A.S., Martynenko Yu.G., Kuzmichev A.V., Lavrovskiy E.K., Mitrofanov I.E., Pismennaya E.V., Formalskiy A.M. Ekzoskelet: konstruktsiya, upravlenie [Exoskeleton: Design and Control]. XII Vserossiyskoe soveshchanie po problemam upravleniya VSPU-2014 [The 12th All-Russian Congress on Control Problems RCCP-2014]. Moscow, In-t problem upravleniya im. V.A. Trapeznikova RAN Publ., 2014, pp. 84-90.</mixed-citation></ref><ref id="ref118"><mixed-citation publication-type="other" xml:lang="en">Pappas I.P., Popovic M.R., Keller T., Dietz V., Morari M. A Reliable Gait Phase Detection System. IEEE Transactions on Neural Systems and Rehabilitation Engineering: a Publication of the IEEE Engineering in Medicine and Biology Society, 2001, vol. 9, no. 2, pp. 113-125. DOI:http://dx.doi.org/10.1109/7333.928571</mixed-citation></ref><ref id="ref119"><mixed-citation publication-type="other" xml:lang="en">Alem T.T., Lee J.H., Okamoto Sh. A Deep Learning Approach for Biped Robot Locomotion Interface Using a Single Inertial Sensor. Sensors, 2023, vol. 23, article ID: 9841. DOI:http://dx.doi.org/10.3390/s23249841</mixed-citation></ref><ref id="ref120"><mixed-citation publication-type="other" xml:lang="en">DeLuca P.A., Davis R.B., Ounpuu S., Rose S., Sirkin R. Alterations in Surgical Decision Making in Patients with Cerebral Palsy Based on Three-Dimensional Gait Analysis. Journal of Pediatric Orthopaedics, 1997, vol. 17, iss. 5, pp. 608-614. DOI:http://dx.doi.org/10.1097/00004694-199709000-00007</mixed-citation></ref><ref id="ref121"><mixed-citation publication-type="other" xml:lang="en">Aoustin Y., Formalskii A.M. 3D Walking Biped: Optimal Swing of the Arms. Multibody System Dynamics, 2014, vol. 32, no. 1, pp. 55-66. DOI:http://dx.doi.org/10.1007/s11044-013-9378-3</mixed-citation></ref><ref id="ref122"><mixed-citation publication-type="other" xml:lang="en">Aoustin Y., Formalskii A.M. Modeling, Control and Simulation of Upward Jump of a Biped. Multibody System Dynamics, 2013, vol. 29, no. 4, pp. 425-445. DOI:http://dx.doi.org/10.1007/s11044-012-9319-6</mixed-citation></ref><ref id="ref123"><mixed-citation publication-type="other" xml:lang="en">Aoustin Y., Formalskii A.M. On Optimal Swinging of the Biped Arms. 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Nice, IEEE, 2008, pp. 2922-2927. DOI:http://dx.doi.org/10.1109/IROS.2008.4650725</mixed-citation></ref><ref id="ref124"><mixed-citation publication-type="other" xml:lang="en">Aoustin Y., Formalskii A.M. Strategy to Lock the Knee of Exoskeleton Stance Leg: Study in the Framework of Ballistic Walking Model. Mechanisms and Machine Science, 2016, vol. 39, pp. 179-195. DOI:http://dx.doi.org/10.1007/978-3-319-30674-2_14</mixed-citation></ref><ref id="ref125"><mixed-citation publication-type="other" xml:lang="en">Aoustin Y., Formalskii A.M. Upward Jump of a Biped. International Journal of Humanoid Robotics, 2013, vol. 10, no. 4, article ID: 1350032. DOI:http://dx.doi.org/10.1142/S0219843613500321</mixed-citation></ref><ref id="ref126"><mixed-citation publication-type="other" xml:lang="en">Aoustin Y., Formalskii A.M. Walking of Biped with Passive Exoskeleton: Evaluation of Energy Consumption. Multibody System Dynamics, 2018, vol. 43, no. 1, pp. 71-96. DOI:http://dx.doi.org/10.1007/s11044-017-9602-7</mixed-citation></ref><ref id="ref127"><mixed-citation publication-type="other" xml:lang="en">Bae H., Oh J.-H. Biped Robot State Estimation Using Compliant Inverted Pendulum Model. Robotics and Autonomous Systems, 2018, vol. 108, pp. 38-50. DOI:http://dx.doi.org/10.1016/j.robot.2018.06.004</mixed-citation></ref><ref id="ref128"><mixed-citation publication-type="other" xml:lang="en">Bashir K., Xiang T., Gong S. Gait Recognition Using Gait Entropy Image. Proceedings of 3rd International Conference on Imaging for Crime Detection and Prevention (ICDP 2009). London, IET, 2010, pp. 1-6. DOI:http://dx.doi.org/10.1049/ic.2009.0230</mixed-citation></ref><ref id="ref129"><mixed-citation publication-type="other" xml:lang="en">Chambers H.G., Sutherland D.H. A Practical Guide to Gait Analysis. The Journal of the American Academy of Orthopaedic Surgeons, 2002, vol. 10, no. 3, pp. 222-231. DOI:http://dx.doi.org/10.5435/00124635-200205000-00009</mixed-citation></ref><ref id="ref130"><mixed-citation publication-type="other" xml:lang="en">Cho J., Park J.H. Model Predictive Control of Running Biped Robot. Applied Sciences, 2022, vol. 12, article ID: 11183. DOI:http://dx.doi.org/10.3390/app122111183</mixed-citation></ref><ref id="ref131"><mixed-citation publication-type="other" xml:lang="en">Xie Sicheng, Li Xinyu, Lu Shengyu, Li Jingyuan, Hu Chenghao, Gao Liang Compliant Gait Control Method Based on CVSLIP-FF Model for Biped Robot Walking Over Uneven Terrain. ISA Transactions, January 2024. DOI:http://dx.doi.org/10.1016/j.isatra.2023.12.042</mixed-citation></ref><ref id="ref132"><mixed-citation publication-type="other" xml:lang="en">Formalskii A.M. Ballistic Walking Design Via Impulsive Control. Journal of Aerospace Engineering, 2010, vol. 23, no. 2, pp. 129-138. DOI:http://dx.doi.org/10.1061/(ASCE)AS.1943-5525.0000017</mixed-citation></ref><ref id="ref133"><mixed-citation publication-type="other" xml:lang="en">Formalskii A.M. Stabilisation and Motion Control of Unstable Objects. Berlin, Walter de Gruyter GmbH, 2015. 250 p.</mixed-citation></ref><ref id="ref134"><mixed-citation publication-type="other" xml:lang="en">Formalskii A.M., Kruchinin P.A., Voitsitskaya K.L. Stabilization of a Double Inverted Pendulum Installed on a Seesaw. Mechanics of Solids, 2021, vol. 56, no. 8, pp. 1599-1610. DOI:http://dx.doi.org/10.3103/S0025654421080070</mixed-citation></ref><ref id="ref135"><mixed-citation publication-type="other" xml:lang="en">Formalskii A.M. Stabilization of Unstable Mechanical Systems. Journal of Optimization Theory and Applications, 2010, vol. 144, no. 2, pp. 227-253. DOI:http://dx.doi.org/10.1007/s10957-009-9600-x</mixed-citation></ref><ref id="ref136"><mixed-citation publication-type="other" xml:lang="en">Formalskii A.M. Unstable Mechanical Objects: Motion Control, Stabilization. Universal Journal of Mechanical Engineering, 2017, vol. 5, no. 5, pp. 150-169. DOI:http://dx.doi.org/10.13189/ujme.2017.050503</mixed-citation></ref><ref id="ref137"><mixed-citation publication-type="other" xml:lang="en">Gismelseed S., Al Yahmedi A., Zaier R. A Biped Model to Predict a Wide Range of Gait and Posture Results. Franklin Open, May 2023, vol. 3, article ID: 100020. DOI:http://dx.doi.org/10.1016/j.fraope.2023.100020</mixed-citation></ref><ref id="ref138"><mixed-citation publication-type="other" xml:lang="en">Gugayev K.V., Kruchinin P.A., Formalskii A.M. A Model of Maintaining Balance by a Person on the Seesaw. Journal of Applied Mathematics and Mechanics, 2016, vol. 80, no. 4, pp. 316-323. DOI:http://dx.doi.org/10.1016/j.jappmathmech.2016.09.006</mixed-citation></ref><ref id="ref139"><mixed-citation publication-type="other" xml:lang="en">Han J., Bhanu B. Individual Recognition Using Gait Energy Image. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2006, vol. 28, no. 2, pp. 316-322. DOI:http://dx.doi.org/10.1109/TPAMI.2006.38</mixed-citation></ref><ref id="ref140"><mixed-citation publication-type="other" xml:lang="en">Hicks J.L., Schwartz M.H., Delp S.L. Modeling and Simulation of Normal and Pathological Gait. The Identification and Treatment of Gait Problems in Cerebral Palsy. London, UK, Mac Keith Press, 2009, pp. 285-307. DOI:http://dx.doi.org/10.1007/s11832-010-0244-z</mixed-citation></ref><ref id="ref141"><mixed-citation publication-type="other" xml:lang="en">Huan T.T., Anh H.P.H. Advanced Biped Gait Generator Using NARX-MLP Neural Model Optimized by Enhanced Evolutionary Algorithm. Vietnam Journal of Mechanics, 2022, vol. 44, no. 3, pp. 249-265. DOI:http://dx.doi.org/10.15625/0866-7136/17230</mixed-citation></ref><ref id="ref142"><mixed-citation publication-type="other" xml:lang="en">Ivanov A.V., Formalskii A.M. Mathematical Modeling of Crutch Walking. Journal of Computer and Systems Sciences International, 2015, vol. 54, no. 2, pp. 315-329. DOI:http://dx.doi.org/10.1134/S1064230715020082</mixed-citation></ref><ref id="ref143"><mixed-citation publication-type="other" xml:lang="en">Klimina L.A., Formalskii A.M. On the Optimal Swinging of a Swing by a Person Standing on It. Journal of Computer and Systems Sciences International, 2022, vol. 61, no. 6, pp. 944-953. DOI:http://dx.doi.org/10.3103/S0025654421080070</mixed-citation></ref><ref id="ref144"><mixed-citation publication-type="other" xml:lang="en">Klimina L.A., Formalskii A.M. Three-Link Mechanism as a Model of a Person on a Swing. Journal of Computer and Systems Sciences International, 2020, vol. 59, no. 5, pp. 728-744. DOI:http://dx.doi.org/10.1134/S1064230720050081</mixed-citation></ref><ref id="ref145"><mixed-citation publication-type="other" xml:lang="en">Lee L., Grimson W.E.L. Gait Analysis for Recognition and Classification. Proceedings of Fifth IEEE International Conference on Automatic Face Gesture Recognition. Washington, DC, USA, IEEE, 2002, pp. 155-162. DOI:http://dx.doi.org/10.1109/AFGR.2002.1004148</mixed-citation></ref><ref id="ref146"><mixed-citation publication-type="other" xml:lang="en">Che J., Pan Y., Yan W., Yu J. Leg Configuration Analysis and Prototype Design of Biped Robot Based on Spring Mass Model. Actuators, 2022, vol. 11, article ID: 75. DOI:http://dx.doi.org/10.3390/act11030075</mixed-citation></ref><ref id="ref147"><mixed-citation publication-type="other" xml:lang="en">Martinez F., Cifuentes C., Romero E. Simulation of Normal and Pathological Gaits Using a Fusion Knowledge Strategy. Journal of NeuroEngineering and Rehabilitation, 2013, vol. 10, article ID: 73. DOI:http://dx.doi.org/10.1186/1743-0003-10-73</mixed-citation></ref><ref id="ref148"><mixed-citation publication-type="other" xml:lang="en">Martynenko Y.G., Formalskii A.M. Controlled Pendulum on a Movable Base. Mechanics of Solids, 2013, vol. 48, no. 1, pp. 6-18. DOI:http://dx.doi.org/10.3103/S0025654413010020</mixed-citation></ref><ref id="ref149"><mixed-citation publication-type="other" xml:lang="en">Martynenko Y.G., Formalskii A.M. Pendulum on a Movable Base. Doklady Mathematics, 2011, vol. 84, no. 1, pp. 594-599. DOI:http://dx.doi.org/10.1134/S1064562411050115</mixed-citation></ref><ref id="ref150"><mixed-citation publication-type="other" xml:lang="en">Gorobtsov A., Skorikov A., Tarasov P., Markov A., Andreev A. Methods of Increasing Service Minibots Functional Capabilities. Communications in Computer and Information Science, 2019, vol. 1084, pp. 191-202. DOI:http://dx.doi.org/10.1007/978-3-030-29750-3_15</mixed-citation></ref><ref id="ref151"><mixed-citation publication-type="other" xml:lang="en">Liu Ch., Audu M.L., Triolo R.J., Quinn R.D. Neural Networks Trained Via Reinforcement Learning Stabilize Walking of a Three-Dimensional Biped Model with Exoskeleton Applications. Frontiers in Robotics and AI, 2021, vol. 8, article ID: 710999. DOI:http://dx.doi.org/10.3389/frobt.2021.710999</mixed-citation></ref><ref id="ref152"><mixed-citation publication-type="other" xml:lang="en">Gorobtsov A.S., Sychev O.A., Orlova Yu.A., Smirnov E.A., Grigoryeva O.E., Bochkin A.M., Andreeva M.I. Optimal Greedy Control in Reinforcement Learning. Sensors, 2022, vol. 22, no. 22, article ID: 8920. DOI:http://dx.doi.org/10.3390/s22228920</mixed-citation></ref><ref id="ref153"><mixed-citation publication-type="other" xml:lang="en">Gorobtsov A.S., Skorikov A.V., Tarasov P.S., Andreev A.E. Parallel Computing Technologies in the Stability Problem of Humanoid Robot Dynamic Modes. Parallel Computational Technologies (PCT’2021). Chelyabinsk, South Ural State University Publ., 2021, pp. 50-54.</mixed-citation></ref><ref id="ref154"><mixed-citation publication-type="other" xml:lang="en">Gorobtsov A.S., Skorikov A.V., Tarasov P.S., Andreev A.E. Parametric Optimization of Machine Designs Based on Mathematical Models of the Inverse Problem. Parallel Computational Technologies (PCT’2021). Chelyabinsk, South Ural State University Publ., 2021, pp. 55-66.</mixed-citation></ref><ref id="ref155"><mixed-citation publication-type="other" xml:lang="en">Wang S., Piao S., Leng X., He Zh., Bai X., Huazhong L. Real-Time Footprint Planning and Model Predictive Control Based Method for Stable Biped Walking. Computational Intelligence and Neuroscience, 2022, vol. 2022 (6), article ID: 4781747. DOI:http://dx.doi.org/10.1155/2022/4781747</mixed-citation></ref><ref id="ref156"><mixed-citation publication-type="other" xml:lang="en">Ren L., Howard D., Kenney L. Computational Models to Synthesize Human Walking. Journal of Bionic Engineering, 2006, vol. 3, no. 3, pp. 127-138. DOI:http://dx.doi.org/10.1016/S1672-6529(06)60016-4</mixed-citation></ref><ref id="ref157"><mixed-citation publication-type="other" xml:lang="en">Ren L., Jones R.K., Howard D. Predictive Modelling of Human Walking Over a Complete Gait Cycle. Journal of Biomechanics, 2007, vol. 40, no. 7, pp. 1567-1574. DOI:http://dx.doi.org/10.1016/j.jbiomech.2006.07.017</mixed-citation></ref><ref id="ref158"><mixed-citation publication-type="other" xml:lang="en">Wang L., Tan T., Ning H., Hu W. Silhouette Analysis-Based Gait Recognition for Human Identification. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2003, vol. 25, no. 12, pp. 1505-1518. DOI:http://dx.doi.org/10.1109/TPAMI.2003.1251144</mixed-citation></ref><ref id="ref159"><mixed-citation publication-type="other" xml:lang="en">Sivolobov S.V. Deep Neural Network Gait Recognition in Habitoscopy Learning Process. 2022 2nd International Conference on Technology Enhanced Learning in Higher Education (TELE), IEEE Xplore, 2022, pp. 58-61. DOI:http://dx.doi.org/10.1109/TELE55498.2022.9801064</mixed-citation></ref><ref id="ref160"><mixed-citation publication-type="other" xml:lang="en">Sivolobov S.V. Human Gait Feature Extraction Method. Procedia Computer Science, 2021, vol. 193, pp. 220-227. DOI:http://dx.doi.org/10.1016/j.procs.2021.10.022</mixed-citation></ref><ref id="ref161"><mixed-citation publication-type="other" xml:lang="en">Sivolobov S.V. Human Gait Model Optimization for Person Identification. 2022 4th International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency (SUMMA), IEEE Xplore, 2022, pp. 381-384. DOI:http://dx.doi.org/10.1109/SUMMA57301.2022.9973857</mixed-citation></ref><ref id="ref162"><mixed-citation publication-type="other" xml:lang="en">Sivolobov S.V., Khoperskov A.V., Bumagin V.V. Human Gait Modeling Method. IOP Conference Series: Materials Science and Engineering, 2020, vol. 823, article ID: 012024. DOI:http://dx.doi.org/10.1088/1757-899X/828/1/012024</mixed-citation></ref><ref id="ref163"><mixed-citation publication-type="other" xml:lang="en">Surer E., Kose A. Methods and Technologies for Gait Analysis. Computer Analysis of Human Behavior. London, Springer, 2011, pp. 105-123. DOI:http://dx.doi.org/10.1007/978-0-85729-994-9_5</mixed-citation></ref><ref id="ref164"><mixed-citation publication-type="other" xml:lang="en">Gorobtsov A.S., Ryzhov E.N., Andreev A.E., Kohtashvili N.I., Polyanina A.S. The Control System Structure for the Stable Biped Robot Motion. Communications in Computer and Information Ssience, 2017, vol. 754, pp. 231-241. DOI:http://dx.doi.org/10.1007/978-3-319-65551-2_17</mixed-citation></ref><ref id="ref165"><mixed-citation publication-type="other" xml:lang="en">Zhang J., Sun Y., Jing Q., Lu Y., Mi N., Lian X., Dong Sh., Bian J. Walking Stability of Biped Robot Based on Machine Learning Algorithm. Recent Advances in Materials and Manufacturing Technology. Singapore, Springer, 2023, pp. 635-644. DOI:http://dx.doi.org/10.1007/978-981-99-2921-4_58</mixed-citation></ref><ref id="ref166"><mixed-citation publication-type="other" xml:lang="en">Yadav K. Model Analysis and Control of Biped Dynamic Walker with Fault Steps in a Gait Cycle. Proceedings of the Institution of Mechanical Engineers Part C Mechanical Engineering Science. URL:https://journals.sagepub.com/doi/10.1177/09544062231214701. DOI:http://dx.doi.org/10.1177/09544062231214701</mixed-citation></ref></ref-list></back></article>
