{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T10:07:43Z","timestamp":1760609263419,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2020,3,30]],"date-time":"2020-03-30T00:00:00Z","timestamp":1585526400000},"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\u2019 coordination and formation have attracted increasing attention since they have great potential for real-world applications. However, such vehicles are usually under-actuated and with very limited communication capabilities. On the basis of the multibody system concept, a multiple autonomous underwater vehicle formation and communication link framework has been established with an adaptive and radial basis function (RBF) strategy. For acoustic communication, a packets transmission scheme with topology and protocol has been investigated on the basis of an acoustic communication framework and transmission model. Moreover, the cooperative localization errors caused by packet loss are estimated through reinforcement learning radial basis function neural networks. Furthermore, in order to realize formation cruising, an adaptive RBF formation scheme with magnitude reduced multi-layered potential energy functions has been designed on the basis of a time-delayed network framework. Finally, simulations and experiments have been extensively performed to validate the effectiveness of the proposed methods.<\/jats:p>","DOI":"10.3390\/s20071943","type":"journal-article","created":{"date-parts":[[2020,4,1]],"date-time":"2020-04-01T03:44:13Z","timestamp":1585712653000},"page":"1943","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Multibody System-Based Adaptive Formation Scheme for Multiple Under-Actuated AUVs"],"prefix":"10.3390","volume":"20","author":[{"given":"Hai","family":"Huang","sequence":"first","affiliation":[{"name":"National Defense Key Laboratory of Underwater Vehicles Technology, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qirong","family":"Tang","sequence":"additional","affiliation":[{"name":"Laboratory of Robotics and Multibody System, Tongji University, Shanghai 201804, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guocheng","family":"Zhang","sequence":"additional","affiliation":[{"name":"National Defense Key Laboratory of Underwater Vehicles Technology, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tiedong","family":"Zhang","sequence":"additional","affiliation":[{"name":"National Defense Key Laboratory of Underwater Vehicles Technology, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lei","family":"Wan","sequence":"additional","affiliation":[{"name":"National Defense Key Laboratory of Underwater Vehicles Technology, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongjie","family":"Pang","sequence":"additional","affiliation":[{"name":"National Defense Key Laboratory of Underwater Vehicles Technology, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Mohammad Pourmahmood Aghababa (2012). 3D path planning for underwater vehicles using five evolutionary optimization algorithms avoiding static and energetic obstacles. 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