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Simultaneously, a prominent feature of these systems is the unknown time-varying control direction. To stabilize such systems, Nussbaum gain technique is constructively framed to overcome the unknown control direction problem. To prevent that the constraints are overstepped, the time-varying asymmetric barrier Lyapunov functions are employed in each step of the backstepping design. The design involves an adaptive-based online approximator to cope with unknown dynamics of the system. A simulation example on aircraft skin inspection robot with three-dimensional trajectory is given to show the effectiveness of the proposed control scheme.<\/jats:p>","DOI":"10.1177\/09596518231222038","type":"journal-article","created":{"date-parts":[[2024,2,12]],"date-time":"2024-02-12T00:28:31Z","timestamp":1707697711000},"page":"1153-1165","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Adaptive tracking control-based Nussbaum gain for a class of multi-input and multi-output nonlinear systems with time-varying state constraints"],"prefix":"10.1177","volume":"238","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3741-2813","authenticated-orcid":false,"given":"Xingkai","family":"Feng","sequence":"first","affiliation":[{"name":"Department of Automatic Control, College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 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