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In this paper, the optimal nonholonomic motion planning of free-floating space robot system with dual-arms is discussed. Base on the linear and angular momentum conservations of the system, the system state equations for control design are established, so the nonholonomic motion planning objective of attitude control of space robot system is translated as the solution of a canonical nonlinear control problem. The optimal control scheme of the system proposed is studied, and an adaptive genetic algorithm for computing approximate optimal control of the system proposed is developed. The optimal motion planning approach proposed above possesses the advantages that it can obtain the desired angles of the base's attitude and arms' joints only by controlling the arms' joints motion. A planar free-floating space robot system with dual-arms is simulated to verify the proposed approach.