Book excerpt: The use of quadrotor or quadcopter type aerial vehicles has increased greatly in many industries and continues to be expanded. Many of the uses for the vehicle involve autonomously following a desired trajectory. More specifically there is a need for a control system that automatically executes a predetermined desired trajectory. This is often called the trajectory tracking problem and has been solved in a variety of different ways. In this thesis an LQR controller with time varying gains is designed, that is able to eliminate tracking error, by evaluating the linear time varying estimation of the quadcopter dynamics about a predetermined trajectory. This is done by obtaining the reference states and inputs in terms of a so called “flat output”. The performance of the LQR is evaluated via numerical simulation of various trajectories. To obtain realistic use cases some consideration is paidto the development of trajectories and the feasibility conditions needed to execute the desired trajectories. This is then compared to simplified dynamic models and variations of optimal control law for steady state cases. It is determined that the performance of a simplified LQR and dynamic model is acceptable for certain classes of the trajectories attempted. This control structure is then put onto an AR.Drone 2.0 and tested for altitude, pitch, roll, and yaw stability using MATLAB/Simulink with embedded coder. In doing so comparisons are made between different sensor fusion techniques for attitude estimation from an onboard inertial measurement unit (IMU). Comparisons between the AR.Drone 2.0 performance and the simulation results in altitude control show a possible discrepancy between the dynamic model and the real system. The addition of an integrator is used to achieve stable altitude control and correct error. This is done without full position and orientation feedback and uses only onboard sensors from the AR.Drone 2.0.