{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T10:19:19Z","timestamp":1784715559533,"version":"3.55.0"},"reference-count":37,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,3,10]],"date-time":"2023-03-10T00:00:00Z","timestamp":1678406400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Guangdong Major Project of Basic and Applied Basic Research","award":["2019B030302001"],"award-info":[{"award-number":["2019B030302001"]}]},{"name":"Guangdong Major Project of Basic and Applied Basic Research","award":["2022YFB3902800"],"award-info":[{"award-number":["2022YFB3902800"]}]},{"name":"National Key R&amp;D Program of China","award":["2019B030302001"],"award-info":[{"award-number":["2019B030302001"]}]},{"name":"National Key R&amp;D Program of China","award":["2022YFB3902800"],"award-info":[{"award-number":["2022YFB3902800"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A distributed six-degree-of-freedom (6-DOF) cooperative control for multiple spacecraft formation is investigated considering parametric uncertainties, external disturbances, and time-varying communication delays. Unit dual quaternions are used to describe the kinematics and dynamics models of the 6-DOF relative motion of the spacecraft. A distributed coordinated controller based on dual quaternions with time-varying communication delays is proposed. The unknown mass and inertia, as well as unknown disturbances, are then taken into account. An adaptive coordinated control law is developed by combining the coordinated control algorithm with an adaptive algorithm to compensate for parametric uncertainties and external disturbances. The Lyapunov method is used to prove that the tracking errors converge globally asymptotically. Numerical simulations show that the proposed method can realize cooperative control of attitude and orbit for the multi-spacecraft formation.<\/jats:p>","DOI":"10.3390\/s23063003","type":"journal-article","created":{"date-parts":[[2023,3,10]],"date-time":"2023-03-10T03:02:08Z","timestamp":1678417328000},"page":"3003","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Adaptive Control for Gravitational Wave Detection Formation Considering Time-Varying Communication Delays"],"prefix":"10.3390","volume":"23","author":[{"given":"Yu","family":"Zhang","sequence":"first","affiliation":[{"name":"MOE Key Laboratory of TianQin Mission, TianQin Research Center for Gravitational Physics & School of Physics and Astronomy, Frontiers Science Center for TianQin, CNSA Research Center for Gravitational Waves, Sun Yat-Sen University (Zhuhai Campus), Zhuhai 519082, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0701-6171","authenticated-orcid":false,"given":"Yuan","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Aeronautics and Astronautics, Sun Yat-Sen University, Shenzhen 518107, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Juzheng","family":"Zhang","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of TianQin Mission, TianQin Research Center for Gravitational Physics & School of Physics and Astronomy, Frontiers Science Center for TianQin, CNSA Research Center for Gravitational Waves, Sun Yat-Sen University (Zhuhai Campus), Zhuhai 519082, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhenkun","family":"Lu","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of TianQin Mission, TianQin Research Center for Gravitational Physics & School of Physics and Astronomy, Frontiers Science Center for TianQin, CNSA Research Center for Gravitational Waves, Sun Yat-Sen University (Zhuhai Campus), Zhuhai 519082, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jikun","family":"Yang","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of TianQin Mission, TianQin Research Center for Gravitational Physics & School of Physics and Astronomy, Frontiers Science Center for TianQin, CNSA Research Center for Gravitational Waves, Sun Yat-Sen University (Zhuhai Campus), Zhuhai 519082, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"061102","DOI":"10.1103\/PhysRevLett.116.061102","article-title":"Observation of gravitational waves from a binary black hole merger","volume":"116","author":"Abbott","year":"2016","journal-title":"Phys. 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