This paper presents a shape transformation control method of a mobile robot with wheel-arms. The proposed method aims at transformation from a four-wheeled mode for high-speed mobility to an inverted pendulum mode, which has advantages of high viewing position and small turning radius. The transformation starts with lifting up the wheel-arms to raise the center of gravity of the whole robot including the main body and arms. From such initial states, the body is lifted up and controlled to the target angle by partial linearization, while returning the arms to the initial angle. Then, the robot position is controlled by manipulating the target body angle. Unlike existing methods, we take into account the effects of the body angular velocity and the tracking error of the body angle by constructing a model set, which is composed of a single nominal model and its polytopic uncertainty for the system matrices. In order to derive the model set, we assume that the target body angle is constrained to a prescribed range. Therefore, the target body angle is manipulated using a model predictive control method, such that the closed-loop system is asymptotically stabilized, while the given constraint is satisfied, for all systems in the model set. The effectiveness of the proposed method is demonstrated in both simulations and real robot experiments.