Quadrotors are coming up as an attractive platform for unmanned aerial vehicle (UAV) research, due to the simplicity of their structure and maintenance, their ability to hover, and their vertical take-off and landing (VTOL) capability. With the vast advancements in small-size sensors, actuators, and processors, researchers are now focusing on developing mini UAV’s to be used in both research and commercial applications. This work presents a detailed mathematical nonlinear dynamic model of the quadrotor which is formulated using the Newton-Euler method. Although the quadrotor is a 6 DOF under-actuated system, the derived rotational subsystem is fully actuated, while the translational subsystem is under-actuated. The derivation of the mathematical model was followed by the development of the controller to control the altitude, attitude, heading and position of the quadrotor in space, which is, based on the linear Proportional-Derivative- Integral (PID) controller; thus, a simplified version of the model is obtained. The gains of the controllers will be tuned using optimization techniques to improve the system's dynamic response. The standard Imperialist Competitive Algorithm (ICA) was applied to tune the PID parameters and then it was compared to Cultural Exchange Imperialist Competitive algorithm (CEICA) tuning, and the results show improvement in the proposed algorithm. The objective function results were enhanced by (23.91%) in the CEICA compared with ICA.