© 2020 Elsevier B.V. This paper proposes a novel control system design for a two-wheeled service robot that follows a person as an assistant without knowing the person's destination. For this kind of service robot, the key skill is to realize human-friendly movement. However, appropriate motion always changed depending on the situation. For instance, when the robot is close and person turns toward it, it is important to suppress the robot's acceleration. Likewise, if the person turns away from the robot, the robot should maintain its position within an appropriate area. Therefore, to deal with various required movements, our control system is able to change its properties automatically and suitably depending on the situation by using weights of the cost function in nonlinear model predictive control (NMPC) as a function of the relative distance between the person and the robot. Unlike previous methods, our design includes only one controller. Consequently, we are able to take into account system stability. Moreover, owing to proposing in NMPC framework, it is easy to extend our method by adopting other recognition or goal-setting methods. We conducted simulations using actual human walking data taken by the robot's laser range sensors. The experiments demonstrate that the robot can follow a person who performs U-turn, confirming that our method can produce human-friendly robot movement in a practical scene.