The aim of this article is to present a novel quaternion based control scheme for the attitude control problem of a quadrotor equipped with variable pitch propellers. A variable pitch propeller is a type of propeller system utilizes a mechanical mechanism to change the pitch of the rotor blades, while when applied to quadrotors it results in an over-actuated control system. The novelty of the article stems from: a) the proposal of an experimental model for variable pitch propellers and b) the novel proposed thrust and power consumption optimisations for the over-actuated quadrotor. Throughout the article, the merits of the proposed novel approach are being analyzed and discussed, while the efficiency of the variable pitch propellers are being evaluated by extended simulation and experimental results.