A novel open-loop control method is presented for mobile robots based on an asymptotic inverse dynamic solution and trajectory planning. The method is based on quantification of sliding by a small nondimensional parameter. Asymptotic expansion of the equations yields the dominant nonslip solution along with a first-order correction for sliding. A trajectory planning is then introduced based on transitional circles between the robot initial states and target reference trajectory. The transitional trajectory ensures smooth convergence of the robot states to the target reference trajectory, which is essential for open-loop control. Experimental results with a differential drive mobile robot demonstrate the significant improvement of the controller performance when the first-order correction is included.