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To enable efficient transportation in semiconductor fabrication bays, it is necessary to generate route planning of multiple automated guided vehicles (AGVs) efficiently to minimize the total transportation time without collision among AGVs. In this paper, we propose a distributed route-planning method for multiple mobile robots using an augmented Lagrangian decomposition and coordination technique. The proposed method features a characteristic that each AGV individually creates a near-optimal routing plan through repetitive data exchange among the AGVs and local optimization for each AGV. Dijkstra's algorithm is used for local optimization. The optimality of the solution generated by the proposed method is evaluated by comparing the solution with an optimal solution derived by solving integer linear programming problems. A near-optimal solution, within 3% of the average gap from the optimal solution for an example transportation system consisting of 143 nodes and 14 AGVs, can be derived in less than 5 s of computation time for 100 types of requests. The proposed method is implemented in an experimental system with three AGVs, and the routing plan is derived in the configuration space, taking the motion of the robot into account. It is experimentally demonstrated that the proposed method is effective for various problems, despite the fact that each route for an AGV is created without minimizing the entire objective function.