{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,4]],"date-time":"2026-07-04T15:25:29Z","timestamp":1783178729312,"version":"3.54.6"},"reference-count":39,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,1,22]],"date-time":"2021-01-22T00:00:00Z","timestamp":1611273600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Underwater vehicles (UVs) are subjected to various environmental disturbances due to ocean currents, propulsion systems, and un-modeled disturbances. In practice, it is very challenging to design a control system to maintain UVs stayed at the desired static position permanently under these conditions. Therefore, in this study, a nonlinear dynamics and robust positioning control of the over-actuated autonomous underwater vehicle (AUV) under the effects of ocean current and model uncertainties are presented. First, a motion equation of the over-actuated AUV under the effects of ocean current disturbances is established, and a trajectory generation of the over-actuated AUV heading angle is constructed based on the line of sight (LOS) algorithm. Second, a dynamic positioning (DP) control system based on motion control and an allocation control is proposed. For this, motion control of the over-actuated AUV based on the dynamic sliding mode control (DSMC) theory is adopted to improve the system robustness under the effects of the ocean current and model uncertainties. In addition, the stability of the system is proved based on Lyapunov criteria. Then, using the generalized forces generated from the motion control module, two different methods for optimal allocation control module: the least square (LS) method and quadratic programming (QP) method are developed to distribute a proper thrust to each thruster of the over-actuated AUV. Simulation studies are conducted to examine the effectiveness and robustness of the proposed DP controller. The results show that the proposed DP controller using the QP algorithm provides higher stability with smaller steady-state error and stronger robustness.<\/jats:p>","DOI":"10.3390\/s21030747","type":"journal-article","created":{"date-parts":[[2021,1,22]],"date-time":"2021-01-22T11:13:53Z","timestamp":1611314033000},"page":"747","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":102,"title":["Robust Position Control of an Over-actuated Underwater Vehicle under Model Uncertainties and Ocean Current Effects Using Dynamic Sliding Mode Surface and Optimal Allocation Control"],"prefix":"10.3390","volume":"21","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"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8616-3254","authenticated-orcid":false,"given":"Tat-Hien","family":"Le","sequence":"additional","affiliation":[{"name":"Department of Naval Architecture and Marine System Engineering, Ho Chi Minh City University of Technology (HCMUT), 268 Ly Thuong Kiet Street, District 10, Ho Chi Minh City 700000, Vietnam"},{"name":"Vietnam National University Ho Chi Minh City (VNU-HCM), Linh Trung Ward, Thu Duc District, Ho Chi Minh City 700000, Vietnam"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7896-3139","authenticated-orcid":false,"given":"Ha Le Nhu Ngoc","family":"Thanh","sequence":"additional","affiliation":[{"name":"HUTECH Institute of Engineering, Ho Chi Minh City University of Technology (HUTECH), Ho Chi Minh City 700000, Vietnam"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4575-5952","authenticated-orcid":false,"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"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"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"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Quoc-Dong","family":"Hoang","sequence":"additional","affiliation":[{"name":"Institute of Mechanical Engineering, Vietnam Maritime University, 484 Lachtray Street, Hai Phong City 182582, Vietnam"},{"name":"Department of Mechanical Engineering, Kyung Hee University, Seoul 130-701, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ton Duc","family":"Do","sequence":"additional","affiliation":[{"name":"Department of Robotics and Mechatronics, School Engineering and Digital Sciences, Nazarbayev University, Nur-Sultan Z05H0P9, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/j.oceaneng.2016.09.036","article-title":"A study on an underwater tracked vehicle with a ladder trencher","volume":"127","author":"Vu","year":"2016","journal-title":"Ocean Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/j.oceaneng.2017.02.035","article-title":"A study on hovering motion of the underwater vehicle with umbilical cable","volume":"135","author":"Vu","year":"2017","journal-title":"Ocean Eng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/j.apor.2017.12.005","article-title":"Study on down-cutting ladder trencher of an underwater construction robot for seabed application","volume":"71","author":"Vu","year":"2018","journal-title":"Appl. Ocean Res."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/j.oceaneng.2017.02.006","article-title":"Design of three exponentially convergent robust controllers for the trajectory tracking of autonomous underwater vehicles","volume":"134","author":"Qiao","year":"2017","journal-title":"Ocean Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1016\/j.apor.2019.02.019","article-title":"Analytical design of an underwater construction robot on the slope with an up-cutting mode operation of a cutter bar","volume":"86","author":"Vu","year":"2019","journal-title":"Appl. Ocean Res."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"102180","DOI":"10.1016\/j.apor.2020.102180","article-title":"Docking assessment algorithm for autonomous underwater vehicles","volume":"100","author":"Vu","year":"2020","journal-title":"Appl. Ocean Res."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Cho, H., Jeong, S.-K., Ji, D.-H., Tran, N.-H., Vu, M.T., and Choi, H.-S. (2020). Study on Control System of Integrated Unmanned Surface Vehicle and Underwater Vehicle. Sensors, 20.","DOI":"10.3390\/s20092633"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Vu, M.T., Van, M., Bui, D.H.P., Do, Q.T., Huynh, T.T., Lee, S.D., and Choi, H.S. (2020). Study on Dynamic Behavior of Unmanned Surface Vehicle-Linked-Unmanned Underwater Vehicle System for Underwater Exploration. Sensors, 20.","DOI":"10.3390\/s20051329"},{"key":"ref_9","first-page":"767","article-title":"Experimental study of dynamic stability of underwater vehicle-manipulator system using zero moment point","volume":"25","author":"Kang","year":"2017","journal-title":"J. Mar. Sci. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"107567","DOI":"10.1016\/j.oceaneng.2020.107567","article-title":"Glider performance analysis and intermediate-fidelity modelling of underwater vehicles","volume":"210","author":"Deutsch","year":"2020","journal-title":"Ocean Eng."},{"key":"ref_11","first-page":"1575","article-title":"Navigation and Control of Underwater Tracked Vehicle Using Ultrashort Baseline and Ring Laser Gyro Sensors","volume":"31","author":"Ji","year":"2019","journal-title":"Sens. Mater."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"39432","DOI":"10.1109\/ACCESS.2019.2907193","article-title":"Modeling and Control of Underwater Mine Explorer Robot UX-1","volume":"7","author":"Fernandez","year":"2019","journal-title":"IEEE Access"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"S137","DOI":"10.1016\/S1672-6529(09)60227-4","article-title":"Better Endurance and Load Capacity: An Improved Design of Manta Ray Robot (RoMan-II)","volume":"7","author":"Zhou","year":"2010","journal-title":"J. Bionic Eng."},{"key":"ref_14","first-page":"283","article-title":"A study on an up-milling rock crushing tool operation of an underwater tracked vehicle","volume":"233","author":"Vu","year":"2019","journal-title":"Proc. Inst. Mech. Eng. M J. Eng. Marit. Environ."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Fernandez, R.A.S., Parra, R.E.A., Milosevic, Z., Dominguez, S., and Rossi, C. (2019). Nonlinear Attitude Control of Spherical Underwater Vehicle. Sensors, 19.","DOI":"10.3390\/s19061445"},{"key":"ref_16","unstructured":"Vu, M.T., Choi, H.S., Nhat, T.Q.M., Ji, D.H., and Son, H.J. (2017, January 18\u201321). Study on the dynamic behaviors of an USV with a ROV. Proceedings of the OCEANS 2017, Anchorage, AK, USA."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Antonelli, G., Fossen, T.I., and Yoerger, D.R. (2008). Underwater Robotics, Springer.","DOI":"10.1007\/978-3-540-30301-5_44"},{"key":"ref_18","first-page":"17","article-title":"A Study on Unmanned Surface Vehicle Combined with Remotely Operated Vehicle System","volume":"9","author":"Jung","year":"2019","journal-title":"Proc. Eng. Technol. Innov."},{"key":"ref_19","unstructured":"Farrell, J.A., Pang, S., Li, W., and Arrieta, R.M. (2004, January 10\u201313). Biologically inspired chemical plume tracing demonstrated on an autonomous underwater vehicle. Proceedings of the 2004 IEEE International Conference on Systems, Man and Cybernetics, Hague, The Netherlands."},{"key":"ref_20","unstructured":"Yildiz, \u00d6., G\u00f6kalp, R.B., and Yilmaz, A.E. (2009, January 5\u20138). A review on motion control of the underwater vehicles. Proceedings of the 2009 International Conference on Electrical and Electronics Engineering-ELECO 2009, Bursa, Turkey."},{"key":"ref_21","unstructured":"Jun, S.W., and Lee, H.J. (2011, January 26\u201329). Design of TS fuzzy-model-based controller for depth control of autonomous underwater vehicles with parametric uncertainties. Proceedings of the 2011 11th International Conference on Control, Automation and Systems, Gyeonggi-do, Korea."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1080\/00423114.2011.642806","article-title":"Road curvature estimation for vehicle lane departure detection using a robust Takagi\u2013Sugeno fuzzy observer","volume":"51","author":"Dahmani","year":"2013","journal-title":"Veh. Syst. Dyn."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Thanh, H.L.N.N., Vu, M.T., Mung, N.X., Nguyen, N.P., and Phuong, N.T. (2020). Perturbation Observer-Based Robust Control Using a Multiple Sliding Surfaces for Nonlinear Systems with Influences of Matched and Unmatched Uncertainties. Mathematics, 8.","DOI":"10.3390\/math8081371"},{"key":"ref_24","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. Mar. Sci. Technol."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Medagoda, L., and Williams, S.B. (2012, January 21\u201324). Model predictive control of an autonomous underwater vehicle in an in situ estimated water current profile. Proceedings of the 2012 Oceans-Yeosu, Yeosu, Korea.","DOI":"10.1109\/OCEANS-Yeosu.2012.6263604"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"6855","DOI":"10.1109\/ACCESS.2020.3048706","article-title":"Station-Keeping Control of a Hovering Over-Actuated Autonomous Underwater Vehicle Under Ocean Current Effects and Model Uncertainties in Horizontal Plane","volume":"9","author":"Vu","year":"2021","journal-title":"IEEE Access"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1889","DOI":"10.1016\/j.mcm.2011.01.014","article-title":"Neural network-based nonlinear tracking control of kinematically redundant robot manipulators","volume":"53","author":"Kumar","year":"2011","journal-title":"Math. Comput. Model."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1080\/20464177.2005.11020190","article-title":"Multivariable PID tuning of dynamic ship positioning control systems","volume":"4","author":"Martin","year":"2005","journal-title":"J. Mar. Eng. Technol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1016\/j.oceaneng.2018.03.086","article-title":"Nonlinear adaptive fuzzy output-feedback controller design for dynamic positioning system of ships","volume":"158","author":"Lin","year":"2018","journal-title":"Ocean Eng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1121","DOI":"10.1016\/j.conengprac.2010.06.007","article-title":"Dynamic positioning systems: An experimental analysis of sliding mode control","volume":"18","author":"Tannuri","year":"2010","journal-title":"Control Eng. Pract."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.apor.2015.07.005","article-title":"Adaptive fuzzy controller design for dynamic positioning system of vessels","volume":"53","author":"Hu","year":"2015","journal-title":"Appl. Ocean Res."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1016\/j.neucom.2012.11.027","article-title":"A robust adaptive neural networks controller for maritime dynamic positioning system","volume":"110","author":"Du","year":"2013","journal-title":"Neurocomputing"},{"key":"ref_33","unstructured":"Subcommittee, S.H. (1950, January 11\u201314). Nomenclature for Treating the Motion of a Submerged Body through a Fluid. Proceedings of the American Towing Tank Conference, New York, NY, USA."},{"key":"ref_34","unstructured":"Fossen, T.I. (1994). Guidance and Control of Ocean Vehicles, John Wiley & Sons."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Fossen, T.I. (2011). Handbook of Marine Craft Hydrodynamics and Motion Control, John Wiley & Sons.","DOI":"10.1002\/9781119994138"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1109\/JOE.1993.236372","article-title":"Multivariable Sliding Mode Control for Autonomous Diving and Steering of Unmanned Underwater Vehicles","volume":"18","author":"Healey","year":"1993","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Xu, H., Zhang, G.C., Sun, Y.S., Pang, S., Ran, X.R., and Wang, X.B. (2019). Design and Experiment of a Plateau Data-Gathering AUV. J. Mar. Sci. Eng., 7.","DOI":"10.3390\/jmse7100376"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/j.arcontrol.2011.03.008","article-title":"A survey of dynamic positioning control systems","volume":"35","author":"Soresen","year":"2011","journal-title":"Annu. Rev. Control."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/S0005-1098(98)00121-6","article-title":"Passive nonlinear observer design for ships using Lyapunov methods: Full-scale experiments with a supply vessel","volume":"35","author":"Fossen","year":"1999","journal-title":"Automatica"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/3\/747\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:14:11Z","timestamp":1760159651000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/3\/747"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,22]]},"references-count":39,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,2]]}},"alternative-id":["s21030747"],"URL":"https:\/\/doi.org\/10.3390\/s21030747","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,22]]}}}