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A model-free control scheme with the elasto-plastic friction observer is presented for robust and high-precision positioning of a robot manipulator. The traditional model-based adaptive controller requires information on the robotic dynamics in advance and thus undergoes robustness problem because of complex dynamics and non-linear frictions of a robot system. This problem is overcome by an employed model-free recurrent cerebellar model articulation controller (RCMAC) system and friction estimator for friction and uncertainty compensation of a robot manipulator. The adaptive laws of the RCMAC networks to approximate an ideal equivalent sliding mode control law and adaptive friction estimation laws based on the elasto-plastic friction model are derived based on the Lyapunov stability analysis. To guarantee stability and increase convergence speed of the RCMAC network, the optimal learning rates are obtained by the fully informed particle swarm (FIPS) algorithm. The robust positioning performance of the proposed control scheme is verified by simulation and experiment for the Scorbot robot in the presence of the joint dynamic friction and uncertainty.