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This paper presents navigation function (NF) based control for differentially driven mobile robots in which performance in transient state was significantly improved in comparison to previously known methods. The gradient of the navigation function is used to generate direction of motion but the velocity is computed as a function of position and orientation error. It makes the system converge faster to desired values. Convergence analysis is performed to show the relationship between location of the eigenvalues of linearized system and the convergence of the coordinates to desired values. The improvement of the performance is illustrated with simulation and experimental results.