State of the art trajectory generation schemes for quadrotors assume a simple dynamic model. They neglect aerodynamic effects such as induced drag and blade flapping and assume that no wind is present. In order to overcome this limitation, this thesis investigates a trajectory optimization scheme based upon Differential Dynamic Programming (DDP). There are various software-implementations of the DDP scheme. For future deployment on robotic hardware the software is required to be computationally efficient, written in C++ and to be open-source. A library named GCOP, which was developed at the John Hopkins University, fulfills these requirements and is used. Before implementing the solver, a full model of the Crazyflie Nano Quadcopter is identified experimentally. The solver is validated, normalized and the performance is benchmarked. This method yields reliable minimum control-effort trajectories. A control scheme is proposed and studied in Monte-Carlo simulations. Itis robust and able to handle large modelling errors in mass and moment of inertia while ensuring minimal error on the final state.