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In this paper, we consider a robust controller design for a two-wheeled inverted pendulum mobile robot driving on uniform slopes. For stabilizing the body posture of the mobile robot on slopes, we use a 2 degree-of-freedom (DOF) model which is obtained by restricting the spinning motion in a 3 DOF motion dynamic equation. In order to design the robust controller guaranteeing stability of the robot driving on slopes, we propose a sliding mode control based on the theory of variable structure systems and design a sliding surface using the theory of the linear quadratic regulation (LQR). From simulation results, we show that the proposed controller effectively controls the robot driving on slopes.