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Mobile robotic systems, which include a mobile platform with one or more manipulators, are of great interest in most applications, e.g. planet explorations, rescuing operations, nursing, book keeping, storing and many others. To manipulate an object with two or more cooperating manipulators, the Multiple Impedance control (MIC) as a model-based algorithm enforces a desired impedance law on each manipulator, the manipulated object, and the moving base itself. However, to apply model-based control laws, it is needed to extract explicit system dynamic model, which of course for such systems may lead to very complicated nonlinear equations of motions. To this end, non-holonomic constraint of a wheeled system is derived, and the obtained dynamics model is reformatted to become a more concise one using natural orthogonal complement method. Next, the MIC law is applied to manipulate an object by two 6-dof cooperating manipulators mounted on a wheeled platform while the moving base is driven with two differentially driver wheels. Obtained results reveal a good tracking performance of the system, i.e. a coordinated smooth motion of the object, manipulators and the moving base, even in the presence of impacts due to contact with an obstacle, and system flexibility.