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Based on the dynamic window approach (DWA) for robot navigation, this paper presents a local reactive method, called DWA*, for mobile robots to characterize unknown indoor environments for achieving high-speed, smooth, and local-minima-free navigation. The original DWA utilizes only a small part of environmental information to search for a proper motion command in the robot's motion space. Hence, the robot can be easily driven into a local-minima area and trapped in complex environments. In order to escape from the local-minima area, the proposed DWA* applies a region analysis technique to filter improper commands, and uses the A* search algorithm with the look-ahead verification to determine the optimal command that can lead the robot to the best consequence after a designated number of steps. Finally, related simulation and experimental results using laser- and sonar-based mobile robots are presented to illustrate the excellent performance of using DWA* compared with that of using the original DWA.