<p>This article investigates the event-triggered adaptive fuzzy finite-time formation of the multiple quadrotor unmanned aerial vehicles (QUAVs) under time-varying asymmetric state constraints and disturbances. Firstly, the unknown continuous nonlinearities of the QUAVs are approximated by the fuzzy logic systems (FLSs), and the distributed estimators with adaptive parameters are constructed to estimate and compensate the composite disturbances. Secondly, the command filters are introduced into the controller design process to eliminate complexity explosion problem, and the errors compensation mechanism based on communication network is introduced to compensate the filtering errors. Thirdly, by building the communication mechanism between the QUAVs and the virtual leader, the event-triggered finite-time tracking scheme is established to reduce unnecessary transmission of network resources. The stability of the proposed finite-time distributed formation scheme is analyzed, and it is verified that all the signals of QUAVs are bounded without exceeding the preset time-varying state constraints. The event trigger interval has a positive lower bound and the tracking errors converge to a small origin neighborhood in a finite time. Finally, simulation results are carried out to verify the superiority and effectiveness of the presented formation algorithm.</p>