This paper focuses on the design, implementation and experimental validation of a Tube-Based Model Predictive Control (TBMPC) law for the stabilization of the horizontal dynamics of an Unmanned Aerial Vehicle (UAV) quadrotor. These dynamics are modelled by a discrete-time linear system subject to additive disturbance and polytopic constraints, which model is derived through an identification strategy from experimental flight data that is adapted to the subsequent design of invariant sets. The results obtained from a validation flight with the TBMPC law are presented to illustrate the robust state and control input constraints satisfaction.