{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,20]],"date-time":"2025-11-20T06:37:36Z","timestamp":1763620656602,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2019,11,15]],"date-time":"2019-11-15T00:00:00Z","timestamp":1573776000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Equipment Pre-Research Project","award":["41412030201"],"award-info":[{"award-number":["41412030201"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51779057, 51709061, 51609047"],"award-info":[{"award-number":["51779057, 51709061, 51609047"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The three-dimensional (3D) path following problem of an underactuated autonomous underwater vehicle with ocean currents disturbances is addressed in this paper. Firstly, the motion equation under the ocean currents disturbance is established, and the dynamic model of 3D tracking error is constructed based on virtual guidance method. Then, a finite-time control scheme based on super-twisting observer and command filtered backstepping technology is proposed. We adopt super-twisting observer based on finite-time theory to observe the ocean currents disturbances for improving the system robust. A command filtered backstepping is proposed to replace the differential process in the conventional backstepping method for avoiding the differential expansion problem. The filter compensation loop is designed to ensure the accuracy of the filtered signal, and the anti-integration saturation link is designed considering the influence of integral saturation. Lyapunov stability theory is used to prove the stability of the underactuated AUV. Simulation studies are conducted to show the effectiveness and robustness of the controller.<\/jats:p>","DOI":"10.3390\/s19224987","type":"journal-article","created":{"date-parts":[[2019,11,15]],"date-time":"2019-11-15T11:25:56Z","timestamp":1573817156000},"page":"4987","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Underactuated AUV Nonlinear Finite-Time Tracking Control Based on Command Filter and Disturbance Observer"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8149-4609","authenticated-orcid":false,"given":"Hao","family":"Xu","sequence":"first","affiliation":[{"name":"Science and Technology on Underwater Vehicle Laboratory, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guo-cheng","family":"Zhang","sequence":"additional","affiliation":[{"name":"Science and Technology on Underwater Vehicle Laboratory, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jian","family":"Cao","sequence":"additional","affiliation":[{"name":"Science and Technology on Underwater Vehicle Laboratory, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuo","family":"Pang","sequence":"additional","affiliation":[{"name":"Science and Technology on Underwater Vehicle Laboratory, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu-shan","family":"Sun","sequence":"additional","affiliation":[{"name":"Science and Technology on Underwater Vehicle Laboratory, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,11,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/j.conengprac.2018.10.004","article-title":"Pipeline following by visual servoing for Autonomous Underwater Vehicles","volume":"82","author":"Allibert","year":"2019","journal-title":"Control Eng. Pract."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.arcontrol.2006.08.003","article-title":"Autonomous underwater vehicles for scientific and naval operations","volume":"30","author":"Bovio","year":"2006","journal-title":"Annu. Rev. Control"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1016\/j.margeo.2014.03.012","article-title":"Autonomous Underwater Vehicles (AUVs): Their past, present and future contributions to the advancement of marine geoscience","volume":"352","author":"Wynn","year":"2014","journal-title":"Mar. Geol."},{"key":"ref_4","unstructured":"Allen, B., Stokey, R., Austin, T., Forrester, N., Goldsborough, R., Purcell, M., and von Alt, C. (1997, January 6\u20139). REMUS: A small, low cost AUV; system description, field trials and performance results. Proceedings of the Oceans \u201897. MTS\/IEEE Conference Proceedings, Halifax, NS, Canada."},{"key":"ref_5","unstructured":"Stokey, R.P., Roup, A., von Alt, C., Allen, B., Forrester, N., Austin, T., Goldsborough, R., Purcell, M., Jaffre, F., and Packard, G. (2005, January 17\u201323). Development of the REMUS 600 autonomous underwater vehicle. Proceedings of the OCEANS 2005 MTS\/IEEE, Washington, DC, USA."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"572","DOI":"10.1007\/s40815-017-0401-3","article-title":"Survey on fuzzy-logic-based guidance and control of marine surface vehicles and underwater vehicles","volume":"20","author":"Xiang","year":"2018","journal-title":"Int. J. Fuzzy Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/j.ins.2015.04.025","article-title":"Containment control of networked autonomous underwater vehicles with model uncertainty and ocean disturbances guided by multiple leaders","volume":"316","author":"Peng","year":"2015","journal-title":"Inf. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"820","DOI":"10.1109\/TCST.2014.2338354","article-title":"Line-of-Sight Path Following for Dubins Paths With Adaptive Sideslip Compensation of Drift Forces","volume":"23","author":"Fossen","year":"2014","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1623","DOI":"10.1109\/TCST.2015.2504838","article-title":"Integral Line-of-Sight Guidance and Control of Underactuated Marine Vehicles: Theory, Simulations, and Experiments","volume":"24","author":"Caharija","year":"2016","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1109\/TSMC.2017.2697447","article-title":"Output-feedback path-following control of autonomous underwater vehicles based on an extended state observer and projection neural networks","volume":"48","author":"Peng","year":"2017","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1423","DOI":"10.1109\/TCST.2018.2834518","article-title":"Trajectory Tracking and Path Following for Underactuated Marine Vehicles","volume":"27","author":"Paliotta","year":"2019","journal-title":"IEEE Trans. Contr. Syst. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.oceaneng.2019.02.017","article-title":"Fuzzy unknown observer-based robust adaptive path following control of underactuated surface vehicles subject to multiple unknowns","volume":"176","author":"Wang","year":"2019","journal-title":"Ocean Eng."},{"key":"ref_13","unstructured":"Encarnacao, P., and Pascoal, A. (2000, January 12\u201315). 3D path following for autonomous underwater vehicle. Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No. 00CH37187), Sydney, Australia."},{"key":"ref_14","unstructured":"Breivik, M., and Fossen, T.I. (2005, January 17\u201323). Guidance-based path following for autonomous underwater vehicles. Proceedings of the OCEANS 2005 MTS\/IEEE, Washington, DC, USA."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1016\/j.oceaneng.2017.10.001","article-title":"Nonlinear guidance and fuzzy control for three-dimensional path following of an underactuated autonomous underwater vehicle","volume":"146","author":"Yu","year":"2017","journal-title":"Ocean Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1016\/j.oceaneng.2015.06.034","article-title":"Study of 3 dimension trajectory tracking of underactuated autonomous underwater vehicle","volume":"105","author":"Li","year":"2015","journal-title":"Ocean Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"706","DOI":"10.1109\/TMECH.2004.839034","article-title":"Disturbance Observer Based Control for Nonlinear Systems","volume":"9","author":"Chen","year":"2004","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1222","DOI":"10.1109\/TIE.2019.2898585","article-title":"Disturbance Observer Design for Nonlinear Systems Represented by Input\u2013Output Models","volume":"67","author":"Ding","year":"2019","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2545","DOI":"10.1109\/TAC.2018.2867163","article-title":"A New Second-Order Sliding Mode and Its Application to Nonlinear Constrained Systems","volume":"64","author":"Ding","year":"2019","journal-title":"IEEE Trans. Automat. Contr."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"640","DOI":"10.1007\/s40815-017-0386-y","article-title":"Three-Dimensional Path Following of an Underactuated AUV Based on Fuzzy Backstepping Sliding Mode Control","volume":"20","author":"Liang","year":"2018","journal-title":"Int. J. Fuzzy Syst."},{"key":"ref_21","unstructured":"Borhaug, E., and Pettersen, K.Y. (2005, January 15). Cross-track control for underactuated autonomous vehicles. Proceedings of the 44th IEEE Conference on Decision and Control, Seville, Spain."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Caharija, W., Pettersen, K.Y., Gravdahl, J.T., and B\u00f8rhaug, E. (2012, January 10\u201313). Path following of underactuated autonomous underwater vehicles in the presence of ocean currents. Proceedings of the 2012 IEEE 51st IEEE Conference on Decision and Control (CDC), Maui, HI, USA.","DOI":"10.1109\/CDC.2012.6427007"},{"key":"ref_23","first-page":"631","article-title":"Underactuated AUV 3D path tracking control based filter backstepping method","volume":"41","author":"Wang","year":"2015","journal-title":"Acta Autom. Sin."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/j.isatra.2016.07.013","article-title":"Finite-time sliding surface constrained control for a robot manipulator with an unknown deadzone and disturbance","volume":"65","author":"Han","year":"2016","journal-title":"ISA Trans."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1016\/j.oceaneng.2017.09.062","article-title":"Finite-time observer based accurate tracking control of a marine vehicle with complex unknowns","volume":"145","author":"Wang","year":"2017","journal-title":"Ocean Eng."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Zhang, J., Yu, S., and Yan, Y. (2019). Fixed-time output feedback trajectory tracking control of marine surface vessels subject to unknown external disturbances and uncertainties. ISA Trans.","DOI":"10.1016\/j.isatra.2019.03.007"},{"key":"ref_27","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_28","unstructured":"Fossen, T.I. (2002). Guidance, Navigation, and Control of Ships, Rigs and Underwater Vehicles, Marine Cybernetics."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1734","DOI":"10.1016\/j.oceaneng.2006.10.019","article-title":"Nonlinear path-following control of an AUV","volume":"34","author":"Lapierre","year":"2007","journal-title":"Ocean Eng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1109\/JOE.2013.2278891","article-title":"AUV Navigation and Localization: A Review","volume":"39","author":"Paull","year":"2014","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.ast.2014.08.009","article-title":"Disturbance observer based finite-time attitude control for rigid spacecraft under input saturation","volume":"39","author":"Hu","year":"2014","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1016\/j.cja.2014.02.017","article-title":"Adaptive finite-time backstepping control for attitude tracking of spacecraft based on rotation matrix","volume":"27","author":"Guo","year":"2014","journal-title":"Chin. J. 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