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This work proposes a flatness-based trajectory planning for a quadrotor Unmanned Aerial Vehicle (UAV) system. The objective is to drive the system as fast as possible from an initial position to a final position without violating system constraints. These constraints can be the actuator limits or the maximal allowable pitch and roll angles. By deriving the extrema of the nominal control inputs to be applied along the reference trajectories as well as the nominal angles that the system will achieve, the solutions to the trajectory planning are obtained by using simple equations. The proposed approach is applied to the quadrotor UAV test-bed of the Networked Autonomous Vehicles (NAV) Laboratory of Concordia University where sliding mode controller and linear quadratic regulator are implemented, tested and compared.