{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T14:14:11Z","timestamp":1764080051137,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,8,28]],"date-time":"2024-08-28T00:00:00Z","timestamp":1724803200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Education Equipment Development Fund","award":["8091B032259","62273165","2023T160493","2021M702505"],"award-info":[{"award-number":["8091B032259","62273165","2023T160493","2021M702505"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["8091B032259","62273165","2023T160493","2021M702505"],"award-info":[{"award-number":["8091B032259","62273165","2023T160493","2021M702505"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"China Postdoctoral Science Foundation","award":["8091B032259","62273165","2023T160493","2021M702505"],"award-info":[{"award-number":["8091B032259","62273165","2023T160493","2021M702505"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>To achieve precise control of the symmetrical unmanned surface vehicle (USV) under strong external disturbances, we propose a disturbance estimation and conditional disturbance compensation control (CDCC) scheme. First, the differential flatness method is applied to convert the underactuated model into a fully actuated one, simplifying the controller design. Then, a nonlinear disturbance observer (NDOB) is designed to estimate the lumped disturbance. Subsequently, a continuous disturbance characterization index (CDCI) is proposed, which not only indicates whether the disturbance is beneficial to the system stability but also makes the controller switch smoothly and suppresses the chattering phenomenon greatly. Indicated by the CDCI, the proposed CDCC method can not only utilize the beneficial disturbance but also compensate for the detrimental disturbance, which improves the USV\u2019s control performance under strong external disturbances. Moreover, a trajectory-planning method is designed to generate an obstacle avoidance reference trajectory for the controller. Finally, simulations verify the feasibility of applying the proposed control method to USV.<\/jats:p>","DOI":"10.3390\/sym16091118","type":"journal-article","created":{"date-parts":[[2024,8,28]],"date-time":"2024-08-28T07:52:08Z","timestamp":1724831528000},"page":"1118","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Differential Flatness Based Unmanned Surface Vehicle Control: Planning and Conditional Disturbance-Compensation"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1121-0420","authenticated-orcid":false,"given":"Xing","family":"Fang","sequence":"first","affiliation":[{"name":"Key Laboratory of Advanced Process Control for Light Industry of the Ministry of Education, Institute of Automation, Jiangnan University, Wuxi 214000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chengxu","family":"Zhang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Advanced Process Control for Light Industry of the Ministry of Education, Institute of Automation, Jiangnan University, Wuxi 214000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3130-6497","authenticated-orcid":false,"given":"Chengxi","family":"Zhang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Advanced Process Control for Light Industry of the Ministry of Education, Institute of Automation, Jiangnan University, Wuxi 214000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7764-0258","authenticated-orcid":false,"given":"Yu","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0035-5701","authenticated-orcid":false,"given":"Gaofei","family":"Xu","sequence":"additional","affiliation":[{"name":"Institute of Deep-Sea Science and Engineering, Chinese Academy of Sciences, 28 Luhuitou Rd., Sanya 572000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yujia","family":"Shang","sequence":"additional","affiliation":[{"name":"Instrumentation Technology and Economy Institute, 397A Guanganmenwai St., Beijing 100054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.arcontrol.2016.04.018","article-title":"Unmanned surface vehicles: An overview of developments and challenges","volume":"41","author":"Liu","year":"2016","journal-title":"Annu. Rev. Control"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3847","DOI":"10.1109\/TII.2023.3316256","article-title":"Trajectory Tracking Control for Differential-Driven Unmanned Surface Vessels Considering Propeller Servo Loop","volume":"20","author":"Xu","year":"2023","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Jiang, K., Mao, L., Su, Y., and Zheng, Y. (2021). Trajectory Tracking Control for Underactuated USV with Prescribed Performance and Input Quantization. Symmetry, 13.","DOI":"10.3390\/sym13112208"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"110475","DOI":"10.1016\/j.oceaneng.2021.110475","article-title":"Robust trajectory tracking with adjustable performance of underactuated surface vessels via quantized state feedback","volume":"246","author":"Park","year":"2022","journal-title":"Ocean Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"115298","DOI":"10.1016\/j.oceaneng.2023.115298","article-title":"An adaptive error constraint line-of-sight guidance and finite-time backstepping control for unmanned surface vehicles","volume":"285","author":"Tong","year":"2023","journal-title":"Ocean Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1080\/00207179.2011.638328","article-title":"The trajectory tracking problem for an unmanned four-rotor system: Flatness-based approach","volume":"85","year":"2012","journal-title":"Int. J. Control"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"6300","DOI":"10.1016\/j.jfranklin.2018.06.018","article-title":"Flatness-based adaptive sliding mode tracking control for a quadrotor with disturbances","volume":"355","author":"Ma","year":"2018","journal-title":"J. Frankl. Inst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2214","DOI":"10.1002\/acs.3315","article-title":"Trajectory planning and tracking for four-wheel steering vehicle based on differential flatness and active disturbance rejection controller","volume":"35","author":"Xia","year":"2021","journal-title":"Int. J. Adapt. Control Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1368","DOI":"10.1109\/TIV.2022.3186280","article-title":"Trajectory Tracking of Autonomous Vehicle: A Differential Flatness Approach With Disturbance-Observer-Based Control","volume":"8","author":"Wang","year":"2023","journal-title":"IEEE Trans. Intell. Veh."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Rigatos, G., Siano, P., and Zervos, N. (2016, January 16\u201319). A nonlinear H-infinity control approach for autonomous navigation of underactuated vessels. Proceedings of the International Conference on Control, Automation and Systems (ICCAS), Gyeongju, Republic of Korea.","DOI":"10.1109\/ICCAS.2016.7832456"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"7879","DOI":"10.1002\/rnc.6249","article-title":"Extended bounded real lemma based sum of squares for static output feedback H-infinity heading control","volume":"32","author":"Huang","year":"2022","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"114781","DOI":"10.1016\/j.oceaneng.2023.114781","article-title":"A novel non-fragile H\u221e fault-tolerant course-keeping control for uncertain unmanned surface vehicles with rudder failures","volume":"280","author":"Xiong","year":"2023","journal-title":"Ocean Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"6950","DOI":"10.1109\/TII.2022.3142323","article-title":"Filtered Probabilistic Model Predictive Control-Based Reinforcement Learning for Unmanned Surface Vehicles","volume":"18","author":"Cui","year":"2022","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1109\/MCS.2015.2408011","article-title":"Disturbance Observer-Based Control: Methods and Applications","volume":"35","author":"Zolotas","year":"2015","journal-title":"IEEE Control Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1205","DOI":"10.1016\/j.jprocont.2009.02.004","article-title":"Disturbance observer-based multi-variable control of ball mill grinding circuits","volume":"19","author":"Chen","year":"2009","journal-title":"J. Process Control"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.oceaneng.2019.01.043","article-title":"Improved decentralized finite-time formation control of underactuated USVs via a novel disturbance observer","volume":"174","author":"Huang","year":"2019","journal-title":"Ocean Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"111868","DOI":"10.1016\/j.oceaneng.2022.111868","article-title":"Predictive compensator based event-triggered model predictive control with nonlinear disturbance observer for unmanned surface vehicle under cyber-attacks","volume":"259","author":"Feng","year":"2022","journal-title":"Ocean Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1109\/TVT.2019.2955020","article-title":"Asymptotic Stabilization of USVs With Actuator Dead-Zones and Yaw Constraints Based on Fixed-Time Disturbance Observer","volume":"69","author":"Guo","year":"2020","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"113203","DOI":"10.1016\/j.oceaneng.2022.113203","article-title":"Composite trajectory tracking of a ship-borne manipulator system based on full-order terminal sliding mode control under external disturbances and model uncertainties","volume":"267","author":"Er","year":"2023","journal-title":"Ocean Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"106603","DOI":"10.1016\/j.jfranklin.2024.01.004","article-title":"Fault-tolerant control of underactuated MSVs based on neural finite-time disturbance observer: An Event-triggered Mechanism","volume":"361","author":"Meng","year":"2024","journal-title":"J. Frankl. Inst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1016\/j.jfranklin.2023.11.030","article-title":"An improved predictor LOS-based global fixed-time prescribed performance controller for the path following of underactuated marine surface vehicles with input saturation","volume":"361","author":"Liu","year":"2024","journal-title":"J. Frankl. Inst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1279","DOI":"10.1109\/TAES.2019.2928605","article-title":"Robust Tracking for Hypersonic Reentry Vehicles via Disturbance Estimation-Triggered Control","volume":"56","author":"Guo","year":"2020","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_23","first-page":"6327","article-title":"Appointed-Time Control for Flexible Hypersonic Vehicles with Conditional Disturbance Negation","volume":"59","author":"Sun","year":"2023","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"5641","DOI":"10.1002\/rnc.4696","article-title":"Trajectory tracking control for manned submersible system with disturbances via disturbance characterization index approach","volume":"29","author":"Fang","year":"2019","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1007\/s11768-022-00124-9","article-title":"Trajectory tracking anti-disturbance control for unmanned aerial helicopter based on disturbance characterization index","volume":"21","author":"Chen","year":"2023","journal-title":"Control Theory Technol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"502","DOI":"10.1007\/s11424-022-2037-0","article-title":"Trajectory Tracking Control for Under-Actuated Hovercraft Using Differential Flatness and Reinforcement Learning-Based Active Disturbance Rejection Control","volume":"35","author":"Xiangyu","year":"2022","journal-title":"J. Syst. Sci. Complex."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"114403","DOI":"10.1016\/j.oceaneng.2023.114403","article-title":"Finite time course keeping control for unmanned surface vehicles with command filter and rudder saturation","volume":"280","author":"He","year":"2023","journal-title":"Ocean Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1177\/0278364910385586","article-title":"Differential flatness-based robust control of mobile robots in the presence of slip","volume":"30","author":"Ryu","year":"2011","journal-title":"Int. J. Rob. Res."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1083","DOI":"10.1109\/TIE.2015.2478397","article-title":"Disturbance-Observer-Based Control and Related Methods\u2014An Overview","volume":"63","author":"Chen","year":"2016","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Li, X., Zhu, Z., Shen, G., and Tang, Y. (2021). Wire Tension Coordination Control of Electro-Hydraulic Servo Driven Double-Rope Winding Hoisting Systems Using a Hybrid Controller Combining the Flatness-Based Control and a Disturbance Observer. Symmetry, 13.","DOI":"10.3390\/sym13040716"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1979","DOI":"10.1109\/TSMC.2017.2700433","article-title":"Composite Learning Control of Flexible-Link Manipulator Using NN and DOB","volume":"48","author":"Xu","year":"2018","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1109\/LCSYS.2017.2778313","article-title":"Optimal Motion Planning for Differentially Flat Systems Using Bernstein Approximation","volume":"2","author":"Cichella","year":"2018","journal-title":"IEEE Contr. Syst. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"3655","DOI":"10.1109\/TRO.2022.3187296","article-title":"Adaptive Bezier Degree Reduction and Splitting for Computationally Efficient Motion Planning","volume":"38","author":"Arslan","year":"2022","journal-title":"IEEE Trans. Robot."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1109\/MCS.2013.2258758","article-title":"Matlab Tricks and Tips [Focus on Education]","volume":"33","author":"Leang","year":"2013","journal-title":"IEEE Control Syst. Mag."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/9\/1118\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:44:16Z","timestamp":1760111056000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/9\/1118"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,28]]},"references-count":34,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2024,9]]}},"alternative-id":["sym16091118"],"URL":"https:\/\/doi.org\/10.3390\/sym16091118","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2024,8,28]]}}}