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This study deals with the trajectory tracking controller design of a wheeled mobile robot subject to delayed measurements. Using the flatness properties of the unicycle-type mobile robot, an output feedback approach based on a non-linear predictor to estimate the state variables is proposed. It enables one to guarantee the exponential stability of the tracking errors. A finite-time observer based on sliding mode theory is applied for the estimation of the delay whose value is assumed to be constant but unknown. The stability property of the closed-loop system with delayed outputs is studied using the Lyapunov theory. Numerical simulations in a realistic environment show the efficiency of the proposed approach.