Abstract: The tracking control for coordinated motion of a free-floating dual-arm space robot system in task space is developed. Aiming at the case that external disturbances exist and system inertial parameters are unknown, an adaptive tuning control scheme based on a fuzzy basis function (FBF) network is designed. A fuzzy basis function network is used to build the unknown dynamic model of dual-arm space robot and a robust technique is applied to deal with uncertainties associated with modeling errors and external disturbances. The control scheme needs neither to linearly parameterize the dynamic equations of the system, nor to require a priori knowledge of system inertial parameters. Meanwhile, all weights and parameters of the FBF network can be adaptively tuned online with a learning rule, and consequently the control scheme is flexible. Stability analysis guarantees global stability and tracking performance. A simulation example illustrates that the proposed control scheme can effectively control the base’s attitude, and the end-effector of the dual-arm space robot is able to track desired trajectories synchronously.