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In this paper, a new class of finite-dimensional repetitive controllers for robot manipulators is proposed. The global asymptotic stability is proved for the unperturbed system. The passivity-based design of the proposed repetitive controller avoids the problem of tight stability conditions and slow convergence of the conventional, internal model-based, repetitive controllers. The passive interconnection of the controller and the nonlinear mechanical systems provides the same stability conditions as the controller with the exact feed-forward compensation of robot dynamics. The simulation results on a three degrees of freedom spatial manipulator illustrate the performances of the proposed controller.