This paper presents a model-based control design for trajectory tracking of two-wheeled mobile robots based on Linear Quadratic Regulator (LQR) optimal control. The model proposed in this article has been implemented on a computational model which is obtained from kinematic and dynamic relations of KHEPERA IV. The purpose of control is to track a predefined reference trajectory with the best possible precision considering the dynamic limits of the robot. Applying several challenging paths to the system showed that the control design is able to track applied reference paths with an acceptable tracking error. Manuscript profile