In the research of underactuated control, there are limited results that are for the controlled object with three and more inputs and are based on an invariant manifold theory. For example, there is a switching control method based on an invariant manifold. However, such a control method generates sudden changes of inputs when switching the controllers. In this paper, a control method is proposed by using the concept of quasi-continuous exponential stabilization. This method need not switch controllers, so that it suppresses the sudden changes of inputs, because the first and second steps in the conventional switching control based on an invariant manifold can be represented by one summarized form. Therefore, loads applied to the actuators can be considered to be reduced. It is shown through simulation experiments that the proposed method can suppress sudden changes of inputs, compared to the conventional switching control method, where the controlled object is a fire truck robot to be an underactuated system with three inputs and six outputs.