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Multiple impedance control (MIC) is a new algorithm which enforces a designated impedance on both a manipulated object, and all cooperating manipulators. In this paper, the MIC is applied to a space robotic system in which robotic arms, mounted on a free-flying-base, manipulate an object. The general formulation of the MIC is extended to include the dynamic coupling between the arms and the base. It is shown that under the MIC law, all participating manipulators, the free-flyer base, and the manipulated object exhibit the same designated impedance behavior. This guarantees good tracking of system manipulators and the object, in performing a manipulation task. A system of two cooperating two-link manipulators is simulated, in which a remote centre compliance is attached to the second end-effector. The object is grabbed with a pivoted grasp condition, i.e. both the translational and rotational motions of the …