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This article presents a robust adaptive control based on Immersion and Invariance (I&I) method for a class of quadrotors subject to disturbances. The nonlinear model of the considered quadrotor including position subsystem and attitude subsystem is established, which has the characteristics of high nonlinearity, underactuation and strong coupling between the subsystems. To achieve satisfying position tracking performance, an I&I adaptive control approach is proposed for the uncertain position subsystem. To enhance the robustness of the attitude subsystem subject to disturbances, a robust adaptive control law based on disturbance observer (DO) is developed to stabilize the subsystem. The DO for the attitude subsystem is constructed to accommodate unknown external disturbances and a robust adaptive bounding law is designed to dominate the modelling errors. The ultimate boundedness of all the signals in the closed-loop system is proved by Lyapunov-based stability analysis. Experimental results performed on an actual indoor micro quadrotor indicate a better performance of the proposed controller compared with the nominal controller without robust and adaptive parts.