In this paper the design and the experimental verification of a Constrained Finite Time Optimal (CFTO) control scheme for the attitude control of an Unmanned Quadrotor Helicopter (UqH) subject to wind gusts is being presented. In the proposed design the UqH has been modeled by a set of Piecewise Affine (PWA) linear equations while the wind gusts effects are embedded in the system model description as the affine terms. In this approach the switching among the PWA model descriptions are ruled by the rate of the rotation angles. In the design of the stabilizing CFTO-controller both the magnitude of external disturbances (worst case applied wind gust), and the mechanical constraints of the UqH such as maximum thrust in the rotors and UqH's angles rate are taken under consideration in order to design an off-line controller that could rapidly be applied to a UqH in a form of a look-up table. The proposed control scheme is applied in experimental studies and multiple test-cases are presented that prove the efficiency of the proposed scheme.