Aiming at the problem of cooperation between multi manipulators of a free-floating spacecraft in space, a collaborative control method based on consistency theory is proposed. This method combines the directed graph communication topology with the generalized Jacobian matrix to realize the cooperation between multiple manipulators of the free-floating spacecraft. Firstly, the directed graph of communication relationship between multiple manipulators is established to determine the master arm and slave arm under the ``leader-follower'' system. Secondly, based on the directed communication topology, the planning of master and slave manipulators' motion is carried out to realize the transmission of master arm's motion to the slave arms. Thirdly, the generalized Jacobian matrix is used to map the end motion to joint motion under the condition of momentum conservation, and the multi-arms' collaborative motion controller in the joint space is designed based on consistency theory. Finally, the stability of the controller is proved based on the Lyapunov stability theory, and the position control error is analyzed. The simulation results show that the proposed control method can realize the aggregation, tracking and position coordination of each manipulator in the space control task of the multi-arm spacecraft system.