{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T09:04:24Z","timestamp":1770973464327,"version":"3.50.1"},"reference-count":39,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2022,7,6]],"date-time":"2022-07-06T00:00:00Z","timestamp":1657065600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ho Chi Minh City University of Technology and Education","award":["IITP-2022-2018-0-01423"],"award-info":[{"award-number":["IITP-2022-2018-0-01423"]}]},{"name":"Ho Chi Minh City University of Technology and Education","award":["2020R1A6A1A03038540"],"award-info":[{"award-number":["2020R1A6A1A03038540"]}]},{"name":"MSIT (Ministry of Science and ICT)","award":["IITP-2022-2018-0-01423"],"award-info":[{"award-number":["IITP-2022-2018-0-01423"]}]},{"name":"MSIT (Ministry of Science and ICT)","award":["2020R1A6A1A03038540"],"award-info":[{"award-number":["2020R1A6A1A03038540"]}]},{"name":"IITP (Institute for Information &amp; Communications Technology Planning &amp; Evaluation)","award":["IITP-2022-2018-0-01423"],"award-info":[{"award-number":["IITP-2022-2018-0-01423"]}]},{"name":"IITP (Institute for Information &amp; Communications Technology Planning &amp; Evaluation)","award":["2020R1A6A1A03038540"],"award-info":[{"award-number":["2020R1A6A1A03038540"]}]},{"name":"Ministry of Education","award":["IITP-2022-2018-0-01423"],"award-info":[{"award-number":["IITP-2022-2018-0-01423"]}]},{"name":"Ministry of Education","award":["2020R1A6A1A03038540"],"award-info":[{"award-number":["2020R1A6A1A03038540"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A trajectory tracking control for quadcopter unmanned aerial vehicle (UAV) based on a nonlinear robust backstepping algorithm and extended state\/disturbance observer (ESDO) is presented in this paper. To obtain robust attitude stabilization and superior performance of three-dimension position tracking control, the construction of the proposed algorithm can be separated into three parts. First, a mathematical model of UAV negatively influenced by exogenous disturbances is established. Following, an extended state\/disturbance observer using a general second-order model is designed to approximate undesirable influences of perturbations on the UAVs dynamics. Finally, a nonlinear robust controller is constructed by an integration of the nominal backstepping technique with ESDO to enhance the performance of attitude and position control mode. Robust stability of the closed-loop disturbed system is obtained and guaranteed through the Lyapunov theorem without precise knowledge of the upper bound condition of perturbations. Lastly, a numerical simulation is carried out and compared with other previous controllers to demonstrate the great advantage and effectiveness of the proposed control method.<\/jats:p>","DOI":"10.3390\/s22145082","type":"journal-article","created":{"date-parts":[[2022,7,6]],"date-time":"2022-07-06T21:15:52Z","timestamp":1657142152000},"page":"5082","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Quadcopter UAVs Extended States\/Disturbance Observer-Based Nonlinear Robust Backstepping Control"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7896-3139","authenticated-orcid":false,"given":"Ha Le Nhu Ngoc","family":"Thanh","sequence":"first","affiliation":[{"name":"Department of Mechatronics Engineering, Ho Chi Minh City University of Technology and Education (HCMUTE), Ho Chi Minh City 71307, Vietnam"}]},{"given":"Tuan Tu","family":"Huynh","sequence":"additional","affiliation":[{"name":"Faculty of Mechatronics and Electronics, Lac Hong University, Bien Hoa 810000, Vietnam"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1645-0957","authenticated-orcid":false,"given":"Mai The","family":"Vu","sequence":"additional","affiliation":[{"name":"School of Intelligent Mechatronics Engineering, Sejong University, Seoul 05006, Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5632-9399","authenticated-orcid":false,"given":"Nguyen Xuan","family":"Mung","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical and Aerospace Engineering, Sejong University, Seoul 05006, Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5100-6264","authenticated-orcid":false,"given":"Nguyen Ngoc","family":"Phi","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical and Aerospace Engineering, Sejong University, Seoul 05006, Korea"}]},{"given":"Sung Kyung","family":"Hong","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical and Aerospace Engineering, Sejong University, Seoul 05006, Korea"},{"name":"Department of Convergence Engineering for Intelligent Drone, Sejong University, Seoul 05006, Korea"}]},{"given":"Truong Nguyen Luan","family":"Vu","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, Ho Chi Minh City University of Technology and Education (HCMUTE), Ho Chi Minh City 71307, Vietnam"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1109\/TII.2015.2397878","article-title":"Quaternion-Based Robust Attitude Control for Uncertain Robotic Quadrotors","volume":"11","author":"Hao","year":"2015","journal-title":"IEEE Trans. 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