This work proposes a feedback control strategy capable of controlling the dynamics of an under-actuated Vertical Take-Off and Landing (VTOL) aerial vehicle to track a desired trajectory globally with respect to the initial conditions. The novelty of the proposed design is the idea of considering a cascade control paradigm in which the attitude dynamics, which are governed by means of a hybrid controller capable of overcoming the well-known topological constraints, and the position dynamics of the vehicle play respectively the role of the inner and of the outer loop. The stability properties of the proposed controller are then derived by analyzing the interconnection between a hybrid system, namely the closed-loop attitude dynamics, and a continuous time system, given by the closed-loop position dynamics. The proposed algorithms are then demonstrated by means of simulations obtained considering a miniature quadrotor prototype.
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