We have constructed a car type personal mobility (a robot cart) that moves around autonomously to help people transfer their luggage and to bring people to their target location. For an autonomous mobility, it is important to avoid making passengers uncomfortable or anxious, as well as to provide safety for the people around them. One reason of the anxious feeling is movements by autonomous navigation that is unexpected for passengers, and it can be reduced by taking a navigation algorithm that is similar to a human way of steering. Based on this concept, focusing on the human way of steering by changing gaze points depending on curvature of the path, we developed an algorithm of look-ahead path tracking for autonomous robot carts according to change the target point from the curvature of the path. First, we formulated the geometrical relationship among the curvature of a path, the position of target points, and the trajectory of a robot, and then, proposed the algorithm to control a robot using the relationship. We implemented the algorithm on the robot cart we constructed, and conducted experiments to evaluate it.