The use of Quadrotor UAVs has been widely well known. It has capability to hover, vertical take-off and landing (VTOL) with having less complexity in vehicle dynamics compared with small helicopter. It is basically an unstable system and exhibits nonlinear behavior. This book describes the development of nonlinear model of quadrotor dynamics derived from Newton-Euler formulation and presented under Matlab/Simulink environment. The Model is equipped by Stability Augmentation System (SAS) to maintain the quadrotor level flight (attitude stability). The autonomous mission for this vehicle is fixed for trajectory following. LQR Optimal control was chosen to accomplish this mission.