Analogy to the definition of Human-robot Interaction (HRI), the case of multiple manipulators with shared workspace, non-simultaneous manufacturing tasks and separate objects is named as multi-manipulator cooperation, which is becoming more widely employed in modern industrial manufacturing system and requiring non-collision path planning as a key issue in terms of safety and efficiency. In this paper, a novel method called Sampling based Position Space Map Search (SbPSMS) method which combines the map search method with the time-sampling based method will be proposed, including a minimum distance prediction method based on PSO-BP neural network for collision detection and two candidate position determination methods for search map establishing of all manipulators. After the specific search map simplification process, the local path fragments during each sampling time interval can be determined via cost function, which will be glued together to generate the final collision-free paths. The simulation results not only show that the PSO-BP hybrid algorithm has more accurate of nearly 2mm than the standard BP neural network in minimum distance prediction, but also demonstrated that our proposal can successfully achieve collision avoidance of dual manipulators system whilst meeting the real-time requirements for multi-manipulator cooperate assembling scenarios. The further satisfactory simulation results of triple manipulators suggesting our algorithm can be extended to applications of multiple manipulators cooperate manufacturing.