In this paper we address the feedback control of a planar space robot. Such a system has a nonholonomic constraint due to the conservation of its angular momentum. A previous work presents a feedback control system using 'a radically isometric orientation'. But the convergence is inefficient when the desired point is placed near the zero-holonomy curve. This study proposes to adopt 'a virtual desired point', which is at first placed in a region far apart from the zero-holonomy curve, and moves to the real desired point automatically. The main contribution of this 'virtual desired point' is that the establishment of an uniquely effective controller for any desired point, and the improvement of the convergence speed to a desired point.