{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T03:47:51Z","timestamp":1772423271668,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2024,8,31]],"date-time":"2024-08-31T00:00:00Z","timestamp":1725062400000},"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>Accurate sensing and control are important for high-performance formation control of spacecraft systems. This paper presents a strategy of disturbance estimation and distributed predefined-time control for the formation of multi-spacecraft systems with uncertainties based on a disturbance observer. The process begins by formulating a kinematics model for the relative motion of spacecraft, with the formation\u2019s communication topology represented by a directed graph for the formation system of the spacecraft. A disturbance observer is then developed to estimate the disturbances, and the estimation errors can be convergent in fixed time. Following this, a disturbance-estimation-based sliding mode control is proposed to guarantee the predefined-time convergence of the multi-spacecraft formation system, regardless of initial conditions. It allows each spacecraft to reach its desired position within a set time frame. The results of the analysis of the multi-spacecraft formation system are also provided. Finally, an example simulation of a five-spacecraft formation flying system is provided to demonstrate the presented formation control method.<\/jats:p>","DOI":"10.3390\/s24175671","type":"journal-article","created":{"date-parts":[[2024,9,2]],"date-time":"2024-09-02T12:54:42Z","timestamp":1725281682000},"page":"5671","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Disturbance Estimation and Predefined-Time Control Approach to Formation of Multi-Spacecraft Systems"],"prefix":"10.3390","volume":"24","author":[{"given":"Zhicheng","family":"Zhang","sequence":"first","affiliation":[{"name":"College of Engineering, Peking University, Beijing 100871, China"},{"name":"China Academy of Aerospace Science and Innovation, Beijing 100871, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weimin","family":"Bao","sequence":"additional","affiliation":[{"name":"School of Aerospace Science and Technology, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qimin","family":"Hou","sequence":"additional","affiliation":[{"name":"School of Astronautics, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yinhao","family":"Ju","sequence":"additional","affiliation":[{"name":"School of Astronautics, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4344-4600","authenticated-orcid":false,"given":"Yabin","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Astronautics, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1109\/JPROC.2018.2794879","article-title":"A survey on formation control of small satellites","volume":"106","author":"Liu","year":"2018","journal-title":"Proc. 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