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nonholonomic mobile robots are widely used in industrial environments due to their extended workspace. Also, to increase the productivity and efficiency of the mobile robot, their path planning is an important task, and is attracted attention of many of robotic scientists. In this paper, the optimal path planning of the wheeled mobile robots are performed considering their nonlinear dynamic equations and the nonholonomic constraints. Problem of the trajectory optimization is formulated, and conditions of the optimality are derived as a set of nonlinear differential equations by means of indirect method of optimal control method. Then, the optimality equations are solved numerically, and variant simulations are executed. To verify the simulation study, some experimental analysis are done for the Scout mobile robot and compared to the simulation results. The experimental analysis verifies the simulation results, and demonstrates the applicability of the proposed method for the optimal path planning of the mobile robots.