Construction work should be simplified by introducing modularity into both structural components and means of assembly. Based on this idea, we have proposed a novel concept of fully automated construction system called Automatic Modular Assembly System (AMAS), which drastically reduces the difficulty of automated construction task. In this paper, we focus on distributed control method of the assembler robots. The area on which the assembler robots can move dynamically expand during the construction process. We introduce a gradient field to indicate the directions based on current map to the assembler robots. The structure modules generate the gradient field by using neighbor-to-neighbor communication. We assume large number of modules and robots; therefore we need to organize the motion paths of these robots to avoid collision among them. An algorithm which is based on blackboard algorithm allows robots to search their paths in the spatiotemporal space.