This paper proposes an optimal ARS control of a two-wheel mobile inverted pendulum robot. Conventional researches are highly concentrated on the robust control of a mobile inverted pendulum on the flat ground, $i.e.$, mostly focus on the compensation of gyroscope signals. This newly proposed algorithm deals with a climbing control of a slanted surface based on the dynamic modeling using the conventional structure. During the climbing control of the robot, unexpected disturbance forces are essentially caused by the irregular contact force which comes from the irregular contact angle between the wheel and the terrain. The disturbances have effects on the optimal posture of the mobile robot to compensate the slanted angle. Therefore the dynamics equations through physical interpretation are derived for the selection of optimum climbing posture through ARS. Also using the ultrasonic sensor the slope information is obtained to compensate for the force of gravity. The control inputs are dynamically adjusted to climb up the slanted surface effectively. The proposed algorithm is demonstrated through the real experiments.