{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,20]],"date-time":"2026-07-20T16:13:32Z","timestamp":1784564012896,"version":"3.55.0"},"reference-count":31,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2018,2,23]],"date-time":"2018-02-23T00:00:00Z","timestamp":1519344000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Nature Science Foundation of China","award":["51679057"],"award-info":[{"award-number":["51679057"]}]},{"name":"Science Foundation for Distinguished Young Scholars of Heilongjiang Province of China","award":["J2016JQ0052"],"award-info":[{"award-number":["J2016JQ0052"]}]},{"name":"Natural Science Foundation of Heilongjiang Province of China","award":["E2017014"],"award-info":[{"award-number":["E2017014"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Unmanned underwater vehicles (UUVs) have rapidly developed as mobile sensor networks recently in the investigation, survey, and exploration of the underwater environment. The goal of this paper is to develop a practical and efficient formation control method to improve work efficiency of multi-UUV sensor networks. Distributed leader-follower formation controllers are designed based on a state feedback and consensus algorithm. Considering that each vehicle is subject to model uncertainties and current disturbances, a second-order integral UUV model with a nonlinear function is established using the state feedback linearized method under current disturbances. For unstable communication among UUVs, communication failure and acoustic link noise interference are considered. Two-layer random switching communication topologies are proposed to solve the problem of communication failure. For acoustic link noise interference, accurate representation of valid communication information and noise stripping when designing controllers is necessary. Effective communication topology weights are designed to represent the validity of communication information interfered by noise. Utilizing state feedback and noise stripping, sufficient conditions for design formation controllers are proposed to ensure UUV formation achieves consensus under model uncertainties, current disturbances, and unstable communication. The stability of formation controllers is proven by the Lyapunov-Razumikhin theorem, and the validity is verified by simulation results.<\/jats:p>","DOI":"10.3390\/s18020662","type":"journal-article","created":{"date-parts":[[2018,2,23]],"date-time":"2018-02-23T12:41:40Z","timestamp":1519389700000},"page":"662","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":46,"title":["Leader-Follower Formation Control of UUVs with Model Uncertainties, Current Disturbances, and Unstable Communication"],"prefix":"10.3390","volume":"18","author":[{"given":"Zheping","family":"Yan","sequence":"first","affiliation":[{"name":"College of Automation, Harbin Engineering University, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Da","family":"Xu","sequence":"additional","affiliation":[{"name":"College of Automation, Harbin Engineering University, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tao","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Automation, Harbin Engineering University, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wei","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Automation, Harbin Engineering University, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yibo","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Automation, Harbin Engineering University, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,2,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"899","DOI":"10.1109\/JSAC.2012.120606","article-title":"Underwater data collection using robotic sensor networks","volume":"30","author":"Hollinger","year":"2012","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1599","DOI":"10.3390\/s17071599","article-title":"Polar grid navigation algorithm for unmanned underwater vehicles","volume":"17","author":"Yan","year":"2017","journal-title":"Sensors"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Rodriguez-Molina, J., Bilbao, S., Martinez, B., Frasheri, M., and Curuklu, B. (2017). An optimized, data distribution service-based solution for reliable data exchange among autonomous underwater vehicles. Sensors, 17.","DOI":"10.3390\/s17081802"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Al-Khatib, H., Antonelli, G., Caffaz, A., Caiti, A., Casalino, G., de Jong, I.B., Duarte, H., Indiveri, G., Jesus, S., and Kebkal, K. (2015, January 18\u201321). The widely scalable Mobile Underwater Sonar Technology (WiMUST) project: An overview. Proceedings of the Oceans 2015, Genova, Italy.","DOI":"10.1109\/OCEANS-Genova.2015.7271688"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Li, N., Curuklu, B., Bastos, J., Sucasas, V., Fernandez, J.A.S., and Rodriguez, J. (2017). A probabilistic and highly efficient topology control algorithm for underwater cooperating AUV networks. Sensors, 17.","DOI":"10.3390\/s17051022"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1950","DOI":"10.1049\/iet-cta.2013.0072","article-title":"A decoupled controller design approach for formation control of autonomous underwater vehicles with time delays","volume":"7","author":"Yang","year":"2013","journal-title":"IET Control Theory Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1190","DOI":"10.1109\/TCST.2010.2076388","article-title":"Can a simple control scheme work for a formation control of multiple autonomous underwater vehicles?","volume":"19","author":"Hou","year":"2011","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Edwards, D., Bean, T., Odell, D., and Anderson, M. (2004, January 17\u201318). A leader\u2013follower algorithm for multiple AUV formations. Proceedings of the IEEE\/OES Autonomous Underwater Vehicles, Sebasco, ME, USA.","DOI":"10.21236\/ADA461848"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1491","DOI":"10.1016\/j.oceaneng.2010.07.006","article-title":"Leader\u2013follower formation control of underactuated autonomous underwater vehicles","volume":"37","author":"Cui","year":"2010","journal-title":"Ocean Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1177\/0142331215590010","article-title":"Cooperative control coordination of a team of underwater vehicles with communication constraints","volume":"38","author":"Das","year":"2016","journal-title":"Trans. Inst. Meas. Control"},{"key":"ref_11","first-page":"327","article-title":"Leader-following consensus of nonlinear multi agent systems with stochastic sampling","volume":"47","author":"He","year":"2015","journal-title":"IEEE Trans. Cybern."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1109\/TCST.2009.2016428","article-title":"Distributed cooperative attitude synchronization and tracking for multiple rigid bodies","volume":"18","author":"Ren","year":"2010","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"5025","DOI":"10.1109\/TIE.2016.2587858","article-title":"Adaptive output consensus with saturation and deadzone and its application","volume":"64","author":"Shen","year":"2017","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2668","DOI":"10.1109\/TCSI.2013.2244322","article-title":"A unified approach to practical consensus with quantized data and time delay","volume":"60","author":"Li","year":"2013","journal-title":"IEEE Trans. Circuits Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1109\/TAC.2005.846556","article-title":"Consensus seeking in multi agent systems under dynamically changing interaction topologies","volume":"50","author":"Ren","year":"2005","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1089","DOI":"10.1016\/j.automatica.2010.03.006","article-title":"Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems","volume":"46","author":"Yu","year":"2010","journal-title":"Automatica"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1496","DOI":"10.1016\/j.automatica.2011.02.027","article-title":"Second-order consensus in multi-agent dynamical systems with sampled position data","volume":"47","author":"Yu","year":"2011","journal-title":"Automatica"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3359","DOI":"10.1016\/j.automatica.2013.08.003","article-title":"Finite-time consensus and collision avoidance control algorithms for multiple AUVs","volume":"49","author":"Li","year":"2013","journal-title":"Automatica"},{"key":"ref_19","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_20","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.oceaneng.2014.08.019","article-title":"Adaptive coordinated tracking control of multiple autonomous underwater vehicles","volume":"91","author":"Xue","year":"2014","journal-title":"Ocean Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1007\/s12555-009-0412-4","article-title":"An efficient underwater coverage method for multi-AUV with sea current disturbances","volume":"7","author":"Jung","year":"2009","journal-title":"Int. J. Control Autom. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1109\/TCST.2015.2420636","article-title":"Range-Based underwater vehicle localization in the presence of unknown ocean currents: theory and experiments","volume":"24","author":"Bayat","year":"2016","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1109\/JOE.2014.2323492","article-title":"State estimation and compression method for thenavigation of multiple autonomous underwater vehicles with limited communication traffic","volume":"40","author":"Matsuda","year":"2015","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Tsiogkas, N., Papadimitriou, G., Saigol, Z., and Lane, D. (2014, January 14\u201319). Efficient Multi-AUV Cooperation using Semantic Knowledge Representation for Underwater Archaeology Missions. Proceedings of the OCEANS 2014, St. Johns, QC, Canada.","DOI":"10.1109\/OCEANS.2014.7003085"},{"key":"ref_25","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_26","doi-asserted-by":"crossref","first-page":"3831","DOI":"10.1109\/TIE.2017.2652346","article-title":"Distributed Containment Maneuvering of Multiple Marine Vessels via Neurodynamics-Based Output Feedback","volume":"64","author":"Peng","year":"2017","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1264","DOI":"10.1049\/iet-cta.2014.0472","article-title":"On the neuro-adaptive feedback linearising control of underactuated autonomous underwater vehicles in three-dimensional space","volume":"9","author":"Shojaei","year":"2015","journal-title":"IET Control Theory Appl."},{"key":"ref_28","unstructured":"Khalil, H.K. (2002). Nonlinear Systems, Printice Hall. [3rd ed.]."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Osborn, J., Qualls, S., Canning, J., Anderson, M., Edwards, D., and Wolbrecht, E. (2015, January 19\u201322). AUV State Estimation and Navigation to Compensate for Ocean Currents. Proceedings of the OCEANS 2015, Washington, DC, USA.","DOI":"10.23919\/OCEANS.2015.7401906"},{"key":"ref_30","unstructured":"Zhao, X.R., and Peng, X.Y. (2007). The Basis of Random Process and Its Application, Harbin Engineering University Press."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1165","DOI":"10.1137\/S0363012903434753","article-title":"A unified approach for stochastic and mean square stability of continuous-time linear systems with Markovian jumping parameters and additive disturbances","volume":"44","author":"Fragoso","year":"2005","journal-title":"SIAM J. Control Optim."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/2\/662\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T14:56:07Z","timestamp":1760194567000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/2\/662"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,2,23]]},"references-count":31,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,2]]}},"alternative-id":["s18020662"],"URL":"https:\/\/doi.org\/10.3390\/s18020662","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,2,23]]}}}