In this paper we address the problem of reconfiguration of a freely floating planar space robot. Such a system is nonholonomic in nature due to the conservation of its angular momentum. This paper presents a smooth and time-invariant feedback control strategy that asymptotically converges the system states from practically any configuration to the desired configuration. The controller does not render the desired configuration asymptotically stable in the sense of Lyapunov but suffers from no convergence problem. The control strategy, though time-invariant, uses a nonlinear oscillator and extends the concept of geometric phase to control. In certain situations the controller has a slow rate of convergence but this problem can be easily rectified by simple modifications, as suggested in this paper. A stability analysis of the closed loop system using the original controller is only presented but results of numerical simulation indicate that both the modified controllers as well as the original controller can converge the system states to their desired values satisfactorily.