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Recently various autonomous mobile robots are developed for practical use. For coexistence with the robots and human in the real environment, the consideration of safety is very important. We should consider a region with a limitation of a maximum velocity of a mobile robot for the safety. In this paper, we propose path planning and trajectory generation methods for a mobile robot which moves in the environment with predetermined velocity constraints. In order to demonstrate the validity of the proposed methods, numerical simulations and experiments have been carried out.