This paper deals with the trajectory tracking problem for a quadrotor unmanned aerial vehicle (UAV). For this purpose, two control strategies are proposed. First, a flight controller with a hierarchical structure is designed, whereby the complete closed-loop system is divided into two blocks. The system has an inner block for attitude control and an outer block for position stabilization, for a total of six proportional-derivative/proportional-integral-derivative (PD/PID) controllers. The second new trajectory tracking strategy is based on attitude stabilization. In addition to a direct stabilization of yaw and altitude, the x and y positions are stabilized by choosing an appropriate control of roll and pitch angles. The relations between positions (x, y) and rotations (roll, pitch) are derived from the natural flight of the quadcopter. In this second approach, with only four controllers, the quadrotor UAV is able to follow any trajectory. In both approaches, the PD/PID controllers are synthesized using the genetic algorithm method, and compared with those obtained by the reference model method. Furthermore, a comparison between PD and PID controller performance is performed. Thereafter, the robustness of the proposed controllers is tested for trajectory tracking in a disturbed environment. Simulation results demonstrate that for the two approaches, PD controllers show a better behavior with respect to quadcopter stabilization than in trajectory tracking under different conditions.