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In this paper, we deal with the problem of global tracking and stabilization control of internally damped mobile robots with unknown parameters, and subject to input torque saturation and external disturbances. To overcome the difficulties due to these factors, a new adaptive scheme is proposed to ensure the bounds of the control torques as functions of only design parameters and reference trajectories and thus computable in advance. Then suitable design parameters are determined so that such bounds are within the given saturation limits. To compensate for the disturbances, we estimate their unknown bounds and employ the estimates in controller design. System stability, perfect tracking and stabilization to the origin are established. Simulation studies conducted also verify the effectiveness of the proposed scheme.