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In this paper, we propose a computed torque controller for a dynamic model of nonholonomic mobile manipulator with bounded external disturbances in order to treat the adaptive tracking control. Firstly, a velocity controller is designed for the kinematic steering system. Secondly, a computed torque controller is designed such that the mobile manipulator velocity converges to the desired velocity controller deduced from the first step. In particular, the mobile manipulator can globally follow any path such as a straight line or a circle. Simulation results are given to demonstrate the effectiveness of the proposed controller.