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The problem of controlling a rigid manipulator driven by induction motors operating in the current-command mode to follow a desired trajectory is considered in this paper. Based on a fourth-order reduced model of an induction motor, a current controller is proposed using only measurements of link positions and velocities as well as stator currents of induction motors. The rotor flux is estimated through a closed-loop observer. Provided that the flux observer is properly initialized, this controller is singularity-free and ensures the global exponential tracking to the desired trajectory. Simulations are presented to illustrate the performance of this controller.