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Because the obstacle-avoidance function is indispensable for providing the safe and easy operation of human-operated robotic systems, this paper deals with the obstacle-avoidance control for a human-operated mobile robot in unknown environments. A general type of two-wheeled mobile robot with inexpensive distance sensors to detect obstacles is considered. Because the robot cannot move in arbitrary directions due to a nonholonomic constraint, we propose a model-reference control approach, in which a reference model generates the desired trajectory to satisfy the nonholonomic constraint, and the robot follows the desired trajectory. The reference model has the steering-like and brake-like functions that are adjusted according to the distance-sensor information. The stability of the proposed control system is analyzed with a linear model. The effectiveness of the proposed method is confirmed by experiments in which several operators handle the robot in an environment with obstacles.