In this paper, a new navigating method for a non-holonomic wheeled moving robot in a dynamic environment with the moving obstacles is proposed. This method is indeed the combination of the nonlinear optimal controller based on State-Dependent Riccati Equation (SDRE) and an obstacle avoidance algorithm named artificial potential field (APF). The corresponding cost function of the SDRE is obtained of APF algorithm. APF algorithm forces the robot to approach the target as an attracting (low-potential) point and to get away from the obstacle as a repulsing (high-potential) point. This method calculates the best path from origin to destination which also implicitly guaranties the stability. The obtained path is the best according to the both amount of traveled distance and input energy. Moreover, this approach not only avoid both fixed and moving obstacle, but also create a smooth path in presence of them. Keeping the nonlinear structure of the system instead of eliminating them during the linearization process is the advantage of SDRE method. Here, the robot navigation is done in the presence of the three different movements of obstacle: (1) fixed speed, (2) fixed acceleration and (3) non-uniform circular. The represented simulation results indicate a suitable performance of the proposed algorithm.