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For a robot to move autonomously in an unknown dynamic environment, a real-time motion generation is necessary. Especially, safety motion generations are important. There are a lot of methods for making safe motion. For example, it is popular to check only around the robot with additional sensors and avoid obstacles detected by the sensors, though, the coordination problem between global trajectory making and local obstacle avoidance should be accrued in this way. It is also popular to estimate the size of obstacles to be large, though adequate width of the dilatation is different by environment. Another approach would be to determine candidates of the safe trajectory from the layout of obstacles as a generalized Voronoi diagram and then randomly search for an appropriate trajectory. This approach can acutualize the global trajectory making and local obstacle avoidance at the same time. However, it may be sufficient if a local generalized Voronoi diagram is available for limiting the sampling area. Based on this idea, this paper explains Voronoi-based StRRT composed of an StRRT subjected to biasing extraction of sample points toward the border of a generalized Voronoi diagram and proposes the efficient method of applying StRRT to the omnidirectional mobile robots. Finally, it shows the possibilities of this method for practical situations.