{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T17:57:57Z","timestamp":1777658277810,"version":"3.51.4"},"reference-count":22,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2020,2,29]],"date-time":"2020-02-29T00:00:00Z","timestamp":1582934400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Civil-Military Dual-Use Technology \u201cData Collection System with Underwater Glider\u201d","award":["19-SN-MU-01"],"award-info":[{"award-number":["19-SN-MU-01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper focuses on motion analysis of a coupled unmanned surface vehicle (USV)\u2013umbilical cable (UC)\u2013unmanned underwater vehicle (UUV) system to investigate the interaction behavior between the vehicles and the UC in the ocean environment. For this, a new dynamic modeling method for investigating a multi-body dynamics system of this coupling system is employed. Firstly, the structure and hardware composition of the proposed system are presented. The USV and UUV are modeled as rigid-body vehicles, and the flexible UC is discretized using the catenary equation. In order to solve the nonlinear coupled dynamics of the vehicles and flexible UC, the fourth-order Runge\u2013Kutta numerical method is implemented. In modeling the flexible UC dynamics, the shooting method is applied to solve a two-point boundary value problem of the catenary equation. The interaction between the UC and the USV\u2013UUV system is investigated through numerical simulations in the time domain. Through the computer simulation, the behavior of the coupled USV\u2013UC\u2013UUV system is analyzed for three situations which can occur. In particular, variation of the UC forces and moments at the tow points and the configuration of the UC in the water are investigated.<\/jats:p>","DOI":"10.3390\/s20051329","type":"journal-article","created":{"date-parts":[[2020,3,3]],"date-time":"2020-03-03T03:13:28Z","timestamp":1583205208000},"page":"1329","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":77,"title":["Study on Dynamic Behavior of Unmanned Surface Vehicle-Linked Unmanned Underwater Vehicle System for Underwater Exploration"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1645-0957","authenticated-orcid":false,"given":"Mai The","family":"Vu","sequence":"first","affiliation":[{"name":"School of Intelligent Mechatronics Engineering, Sejong University, 98 Gunja-dong, Gwangjin-gu, Seoul 143-747, Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9616-6061","authenticated-orcid":false,"given":"Mien","family":"Van","sequence":"additional","affiliation":[{"name":"School of Electronics, Electrical Engineering and Computer Science, Queen\u2019s University, Belfast BT7 1NN, UK"}]},{"given":"Duc Hong Phuc","family":"Bui","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of Tulsa, Tulsa, OK 74104, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4232-9563","authenticated-orcid":false,"given":"Quang Thang","family":"Do","sequence":"additional","affiliation":[{"name":"Department of Naval Architecture and Ocean Engineering, Nha Trang University, Nha Trang 650000, Vietnam"}]},{"given":"Tuan-Tu","family":"Huynh","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Yuan Ze University, No. 135, Yuandong Road, Zhongli 320, Taoyuan 32003, Taiwan"},{"name":"Department of Electrical Electronic and Mechanical Engineering, Lac Hong University, No. 10, Huynh Van Nghe Road, Bien Hoa, Dong Nai 830000, Vietnam"}]},{"given":"Sang-Do","family":"Lee","sequence":"additional","affiliation":[{"name":"Department of Ship Operation, Korea Maritime and Ocean University, 727 Taejong-ro, Yeongdo-gu, Busan 49112, Korea"}]},{"given":"Hyeung-Sik","family":"Choi","sequence":"additional","affiliation":[{"name":"Division of Mechanical Engineering, Korea Maritime and Ocean University, 727 Taejong-ro, Yeongdo-gu, Busan 49112, Korea"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,29]]},"reference":[{"key":"ref_1","first-page":"705","article-title":"Energy efficient trajectory design for the underwater vehicle with bounded inputs using the global optimal sliding mode control","volume":"25","author":"Vu","year":"2017","journal-title":"J. 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