Modelling and control of rigid-flexible multibody systems is studied in this paper. As a specified application, a space robotic system with flexible appendages during a cooperative object manipulation task is considered. This robotic system necessitates delicate force exertion by several end-effectors to move an object along a desired path. During such maneuvers, flexible appendages like solar panels may get stimulated and vibrate. This vibrating motion will cause some oscillatory disturbing forces on the spacecraft, which in turn produces error in the motion of the end-effectors of the cooperative manipulating arms. In addition, vibration control of these flexible members to protect them from fracture is another challenging problem in an object manipulation task for the stated systems. Therefore, the multiple impedance control algorithm is extended to perform an object manipulation task by such complicated rigid-flexible multibody systems. This extension in the control algorithm considers the modification term which compensates the disturbing forces due to vibrating motion of flexible appendages. Finally, a space free-flying robotic system which contains two 2-DOF planar cooperative manipulators, appended with two highly flexible solar panels, is simulated. Obtained results reveal the merits of the developed model-based controller which will be discussed.