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The authors present a robust adaptive control approach using model reference adaptive control (MRAC) for autonomous robot systems with random friction. First, a non-linear model of the robot system is approximated by feedback linearisation to derive a nominal control law. Next, a least square observer is constructed for the online estimation of friction dynamics. The authors derive a perturbed system model governing the friction estimation error and design an MRAC control to mitigate its effect. Also, stability conditions for the perturbed system model using the Lyapunov stability theory are derived. The authors demonstrate the success of the proposed control methodology through computer simulation, including a comparison to a traditional controller based on nominal dynamics.