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The multiple impedance control (MIC) is a model-based algorithm for cooperative object manipulation. Computation of the system dynamics even if perfectly known, may require considerable process time at each step for implementing the control law. The non-model-based multiple impedance control (NMIC) has been recently proposed for fixed base robots to eliminate the need to system dynamic model in implementation of the MIC algorithm. In this paper, the NMIC law is extended to coordinated object manipulation by a space free flying robot (SFFR) that consists a moving spacecraft and a number of manipulators mounted on it. To improve the precise tracking characteristics of the manipulated object and the SFFR, the butter-worth filter is also exploited. Next, the proposed NMIC law is applied on a SFFR with 20 DOF that manipulates an object on a desired path that deliberately includes impacts due to contact with an obstacle. The obtained results show good tracking performance that reveal the merits of NMIC law as a non-model-based algorithm for object manipulation tasks, which can be implemented with reasonable limited on-line computations.