The actual paper presents an in-depth study and experimental development of a class of rotorcraft, named as x-tilt, that features four tilting rotors. Initially, the equations of motion modeling the aerial robot are presented based on the Euler-Lagrange formulation. The model includes the aerodynamic effects induced by the rotorcraft's relative motion and propellers. For control purposes the aforementioned model is split into a nominal model and lumped disturbance terms, the latter encompassing endogenous and exogenous uncertainties. In this vein, the actual work propose a robust navigation strategy targeting a specific performance profile whose problem is formulated through the model predictive control (MPC) framework. To this end, two schemes are proposed, (i) an integral MPC and a (ii) MP sliding-mode Control (MPSMC). Both control schemes are linked to a extended-state Linear Kalman Filter (ES-LKF) that furnishes the states and lumped disturbance estimates. Moreover, a high-fidelity simulation is presented in detail to validate the effectiveness of the proposed controller within a realistic scenario. We finally present the experimental stage to validate the tilting-rotor configuration as well as the integral MPC.