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The purpose of this paper is to investigate the trajectory tracking problem of the mobile robot. The method integrates a kinematic controller and a torque controller into the dynamic model using backstepping techniques. First, the analytic B-spline function is used to generate a smoothly feasible trajectory between the initial and desired configuration so that the motion path can pass through desired intermediate points and satisfy the kinematic constraints and curvature restrictions. Second, a set of sufficient conditions and a systematic transform procedure are presented for determining if a nonlinear kinematic model can be converted to the integrator chained form which significantly reduced the complexity of designing the privileged velocity. Finally, an adaptive tracking control is developed for the hierarchical model based on backstepping methodology and computed-torque techniques to achieve global asymptotically stable. Simulation results are utilized to illustrate the effectiveness of the proposed control architecture.