<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<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">izvestswsu</journal-id><journal-title-group><journal-title xml:lang="ru">Известия Юго-Западного государственного университета</journal-title><trans-title-group xml:lang="en"><trans-title>Proceedings of the Southwest State University</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2223-1560</issn><issn pub-type="epub">2686-6757</issn><publisher><publisher-name>ЮЗГУ</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.21869/2223-1560-2019-23-4-8-18</article-id><article-id custom-type="elpub" pub-id-type="custom">izvestswsu-573</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>Машиностроение и машиноведение</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>Mechanical engineering and machine science</subject></subj-group></article-categories><title-group><article-title>Использование нейронных сетей для прогнозирования нормальных реакций шагающего робота</article-title><trans-title-group xml:lang="en"><trans-title>Using Neural Networks to Predict the Normal Reactions  of a Walking Robot</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>Савин</surname><given-names>С. И.</given-names></name><name name-style="western" xml:lang="en"><surname>Savin</surname><given-names>S. I.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Савин Сергей Игоревич, кандидат  технических наук, старший научный сотрудник  лаборатории мехатроники, управления  и прототипирования</p><p>ул. Университетская, д.1, г. Иннополис, 420500</p></bio><bio xml:lang="en"/><email xlink:type="simple">s.savin@innopolis.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>Ворочаева</surname><given-names>Л. Ю.</given-names></name><name name-style="western" xml:lang="en"><surname>Vorochaeva</surname><given-names>L. Yu.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Ворочаева Людмила Юрьевна, кандидат  технических наук,  доцент кафедры механики, мехатроники и робототехники</p><p>ул. 50 лет Октября, 94, г. Курск, 305040</p></bio><bio xml:lang="en"/><email xlink:type="simple">mila180888@yandex.ru</email><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Университет Иннополис</institution></aff><aff xml:lang="en"><institution>Innopolis University</institution></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>ФГБОУ ВО «Юго-Западный государственный университет»</institution></aff><aff xml:lang="en"><institution>Southwest State University</institution></aff></aff-alternatives><pub-date pub-type="collection"><year>2019</year></pub-date><pub-date pub-type="epub"><day>22</day><month>10</month><year>2019</year></pub-date><volume>23</volume><issue>4</issue><fpage>8</fpage><lpage>18</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Савин С.И., Ворочаева Л.Ю., 2019</copyright-statement><copyright-year>2019</copyright-year><copyright-holder xml:lang="ru">Савин С.И., Ворочаева Л.Ю.</copyright-holder><copyright-holder xml:lang="en">Savin S.I., Vorochaeva L.Y.</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://izvestswsu.elpub.ru/jour/article/view/573">https://izvestswsu.elpub.ru/jour/article/view/573</self-uri><abstract><sec><title>Цель исследования</title><p>Цель исследования. Данная работа посвящена решению одной из проблем, связанных с управлением шагающими роботами на основе их динамической математической модели, − наличию в ней явных механических связей, обусловленных реакциями связей с опорной поверхностью. Для решения указанной проблемы предлагается использовать полносвязную нейронную сеть для оценки сил нормальных реакций между поверхностью и стопами двуногого шагающего робота во время реализации им одного шага.</p></sec><sec><title>Методы</title><p>Методы. В работе рассмотрены две архитектуры нейронной сети, основанные на полносвязных слоях с ReLU активационными функциями. Архитектура нейронной сети включает в себя пять полносвязных слоев (входной, выходной и три скрытых), а альтернативная архитектура  включает в себя слой прореживания после каждого полносвязного слоя. Входными данными для сети являются состояние робота и требуемые управляющие воздействия, а выходными − предсказанные силы реакции. Обучающая выборка генерируется с помощью моделирования полной динамической модели робота. Сеть построена и обучена с использованием библиотек машинного обучения Keras и TensorFlow.</p></sec><sec><title>Результаты</title><p>Результаты. Описана генерация обучающей выборки для нейронной сети, проведено обучение двух архитектур нейронных сетей. На основании данных моделирования установлено, что обе обученные нейронные сети способны точно предсказывать значения нормальных реакций с использованием значений обобщенных координат и скоростей, а также управляющих воздействий в качестве входных данных, однако при этом наблюдается статическая ошибка предсказания.</p></sec><sec><title>Заключение</title><p>Заключение. Полученные в рамках статьи результаты могут в дальнейшем использоваться для управления движением двуногих шагающих роботов по различным типам поверхностей. </p></sec></abstract><trans-abstract xml:lang="en"><sec><title>Purpose of reseach</title><p>Purpose of reseach. This work is devoted to solving one of the problems associated with the control of walking robots based on their dynamic mathematical model − the presence in it of obvious mechanical bonds due to reactions of bonds with the supporting surface. To solve this problem, it is proposed to use a fully connected neural network to evaluate the forces of normal reactions between the surface and the feet of a bipedal walking machine during its implementation of one step.</p></sec><sec><title>Methods</title><p>Methods. The paper considers two neural network architectures based on fully connected layers with ReLU activation functions. The architecture of the neural network includes five fully connected layers (input, output and three hidden), and an alternative architecture includes a thinning layer after each fully connected layer. The input data for the network are the state of the robot and the required control actions, and the output is the predicted reaction forces. The training sample is generated by modeling a complete dynamic model of the robot. The network is built and trained using machine learning libraries Keras and TensorFlow.</p></sec><sec><title>Results</title><p>Results.The generation of training sample for neural network is described here, and it is carried out the training of two architectures of neural networks. Based on the simulation data, it was established that both trained neural networks are able to accurately predict the values of normal reactions using the values of generalized coordinates and velocities, as well as control actions as input, however, a static prediction error is observed.</p></sec><sec><title>Conclusion</title><p>Conclusion. The results obtained within the framework of the article can be further used to control the movement of bipedal walking machines on various types of surfaces.</p></sec></trans-abstract><kwd-group xml:lang="ru"><kwd>двуногий шагающий робот</kwd><kwd>нейронная сеть</kwd><kwd>архитектура нейронной сети</kwd><kwd>слой прореживания</kwd><kwd>полносвязный слой</kwd><kwd>обучающая и верификационная выборки</kwd><kwd>нормальные реакции</kwd></kwd-group><kwd-group xml:lang="en"><kwd>bipedal walking machine</kwd><kwd>neural network</kwd><kwd>neural network architecture</kwd><kwd>thinning layer</kwd><kwd>fully connected layer</kwd><kwd>training and verification samples</kwd><kwd>normal reactions</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Работа выполнена при поддержке Гранта Президента МК-1537.2019.8, Савин С.И. работал при поддержке РФФИ, проект №18-38-00140\18</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">Werner A., Henze B., Rodriguez D.A., Gabaret J., Porges O., Roa M.A. Multi-contact planning and control for a torque-controlled humanoid robot // Intelligent Robots and Systems (IROS): Proc. IEEE/RSJ Intern. Conf., Daejeon, South Korea. 2016. P. 5708-5715.</mixed-citation><mixed-citation xml:lang="en">Werner A., Henze B., Rodriguez D.A., Gabaret J., Porges O., Roa M.A. Multi-contact planning and control for a torque-controlled humanoid robot. Intelligent Robots and Systems (IROS): Proc. IEEE/RSJ Intern. Conf., Daejeon, South Korea, 2016,pp. 5708-5715.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Posa M., Cantu C., Tedrake R. A direct method for trajectory optimization of rigid bodies through contact // Intern. J. of Robotics Research. 2014. Vol. 33(1). P. 69-81.</mixed-citation><mixed-citation xml:lang="en">Posa M., Cantu C., Tedrake R. A direct method for trajectory optimization of rigid bodies through contact. Intern. J. of Robotics Research, 2014,vol. 33(1),pp. 69-81.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Jatsun S., Savin S., Yatsun A. Parameter optimization for exoskeleton control system using sobol sequences // Symposium on Robot Design, Dynamics and Control. Springer, Cham. 2016. P. 361-368.</mixed-citation><mixed-citation xml:lang="en">Jatsun S., Savin S., Yatsun A. Parameter optimization for exoskeleton control system using sobol sequences. Symposium on Robot Design, Dynamics and Control. Springer, Cham, 2016,pp. 361-368.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Featherstone R. Rigid Body Dynamics Algorithms. Boston, MA: Springer US, 2014. 271 p.</mixed-citation><mixed-citation xml:lang="en">Featherstone R. Rigid Body Dynamics Algorithms. Boston, MA: Springer US, 2014, 271 p.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Mason S., Righetti L., Schaal S. Full dynamics LQR control of a humanoid robot: An experimental study on balancing and squatting // Humanoid Robots: Proc. IEEE-RAS Intern. Conf., Madrid, Spain, 2014. P. 374-379.</mixed-citation><mixed-citation xml:lang="en">Mason S., Righetti L., Schaal  S. Full dynamics LQR control of a humanoid robot: An experimental study on balancing and squatting. Humanoid Robots: Proc. IEEE-RAS Intern. Conf., Madrid, Spain, 2014,pp. 374-379.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Savin S., Jatsun S., Vorochaeva L. Modification of constrained LQR for control of walking in-pipe robots // Dynamics of Systems, Mechanisms and Machines (Dynamics): Proc. IEEE Intern. Conf., Omsk, Russia, 2017. P. 1-6.</mixed-citation><mixed-citation xml:lang="en">Savin S., Jatsun S., Vorochaeva L. Modification of constrained LQR for control of walking in-pipe robots. Dynamics of Systems, Mechanisms and Machines (Dynamics): Proc. IEEE Intern. Conf., Omsk, Russia. 2017,pp. 1-6.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Savin S., Jatsun S., Vorochaeva L. State observer design for a walking in-pipe robot // MATEC Web of Conferences: EDP Sciences. 2018. Vol. 161. P. 03012.</mixed-citation><mixed-citation xml:lang="en">Savin S., Jatsun S., Vorochaeva L. State observer design for a walking in-pipe robot. MATEC Web of Conferences: EDP Sciences. 2018,vol. 161,pp. 03012.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Schmidhuber J. Deep learning in neural networks: An overview // Neural Networks. 2015. Vol. (61). P. 85–117.</mixed-citation><mixed-citation xml:lang="en">Schmidhuber J. Deep learning in neural networks: An overview. Neural Networks, 2015,vol. (61),pp. 85–117.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Srivastava N., Hinton G., Krizhevsky A., Sutskever I., Salakhutdinov R. Dropout: a simple way to prevent neural networks from overfitting // J. of Machine Learning Research. 2014. Vol. 15(1). P. 1929-1958.</mixed-citation><mixed-citation xml:lang="en">Srivastava N., Hinton G., Krizhevsky A., Sutskever I., Salakhutdinov R. Dropout: a simple way to prevent neural networks from overfitting. J. of Machine Learning Research, 2014,vol. 15(1),pp. 1929-1958.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Abadi M., Barham P., Chen J., Chen Z., Davis A., Dean J., … Kudlur M. Tensorflow: A system for large-scale machine learning // Operating Systems Design and Implementation: Proc. 12th Symposium, Savannah, GA, USA, 2016. P. 265-283.</mixed-citation><mixed-citation xml:lang="en">Abadi M., Barham P., Chen J., Chen Z., Davis A., Dean J., … Kudlur M. Tensorflow: A system for large-scale machine learning. Operating Systems Design and Implementation: Proc. 12th Symposium, Savannah, GA, USA, 2016,pp. 265-283.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Glorot X., Bengio Y. Understanding the difficulty of training deep feedforward neural networks // Artificial Intelligence and Statistics: Proc. of the 13-th Intern. Conf., Scottsdale, AZ, USA, 2010. P. 249-256.</mixed-citation><mixed-citation xml:lang="en">Glorot X., Bengio Y. Understanding the difficulty of training deep feedforward neural networks. Artificial Intelligence and Statistics: Proc. of the 13-th Intern. Conf., Scottsdale, AZ, USA,  2010,pp. 249-256.</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>
