This paper deals with the problem of trajectory planning and tracking of a quadcopter system based on the property of differential flatness. First, B-spline characterisations of the flat output allow for optimal trajectory generation subject to waypoint constraints, thrust and angle constraints while minimising the trajectory length. Second, the proposed tracking control strategy combines feedback linearisation and nested saturation control via flatness. The control strategy provides bounded inputs (thrust, roll and pitch angles) while ensuring the overall stability of the tracking error dynamics. The control parameters are chosen based on the information of the a priori given reference trajectory. Moreover, conditions for the existence of these parameters are presented. The effectiveness of the trajectory planning and the tracking control design is analysed and validated through simulation and experimental results over a real nano-quadcopter platform, the Crazyflie 2.0.