A rigid planar space robot is represented as a Caplygin system and its base attitude can be stabilized by means of geometric phase. However, in cases when flexible arms are used for control of the base attitude, inherent resonance modes are excited and instability is resulted. In this study, we propose to synthesize a stabilizing controller as adaptive tracking control system combined with sliding mode control to track to the arm trajectories derived from the geometric phase of the Caplygin system. Usefulness of the proposed controller is demonstrated by numerical simulations and Laboratory experiments.