This study deals with feedback control of reorientation of a planar space robot. Mukherjee and Kamon propose to define 'a radially isometric orientation' and successfully establish a smooth time invariant control system. However the proposed controller suffers from slow rate of convergence for a desired configuration being placed on or near a zero-holonomy curve. They also propose two modified controllers for such configurations, but stability problem for the modified controllers remains future work and a criterion for choosing the original or modified controller is not discussed for general configurations. This paper proposes to adopt a 'moving desired configuration' for convergence to any desired configuration. The moving desired configuration is designed to move to a 'real' desired configuration with the system states close to an invariant manifold. The paper describes how to define the invariant manifold and how to move the moving desired point to the real one.