The path planning of a mobile robots refers to the process of finding the path to be arrived at without colliding with an obstacle to the destination of the desired robot. For obstacle avoidance, we need to information about precise location of obstacle and safe distance for avoiding collision with obstacle and an algorithm to calculate the navigation of the mobile robot.

Usually, the path planning need to a separated for navigation of the robot, but in this paper, we omit the process of path planning, and use the algorithm that can navigate the mobile robot directly in real time. since there is no path planning, it is impossible to obstacle avoidance algorithms that are widely know and existing. So we suggest a new obstacle avoidance algorithm that is use optimal solution defined as an optimization problem with constraints, and use the algorithm for obstacle avoidance movement.

In this paper, we defined the destination, positions of the robots and position errors of the robot as the cost function of a quadratic form, and defined navigation of the mobile robot as optimization problem which is minimize the cost function. The cost function is linearized by Taylor Series Expanded Method. Gauss-Newton method is used to determine the position of the wheel. the From wheel position, we obtained a speed of left and right wheel of the differential driven robot. The current position of the robot is calculated by Jacobian matrix of the kinematic model and the wheel speed. Using the calculated current position, we drove the robot directly to reach the destination without path planning.

When an obstacle is recognized in the path, we converted optimization problem, between an obstacle with the mobile robot, with constraints to minimization problem without constraints, using Exterior Penalty method(barrier method). Since the object function, converted minimization problem without constraints, is also cost function, we repeat same manner which is described above. We integrating such methods, and verified the algorithm though Experiments and simulations.