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This paper proposes an end-to-end deep reinforcement learning approach for mobile robot navigation with dynamic obstacles avoidance. Using experience collected in a simulation environment, a convolutional neural network (CNN) is trained to predict proper steering actions of a robot from its egocentric local occupancy maps, which accommodate various sensors and fusion algorithms. The trained neural network is then transferred and executed on a real-world mobile robot to guide its local path planning. The new approach is evaluated both qualitatively and quantitatively in simulation and real-world robot experiments. The results show that the map-based end-to-end navigation model is easy to be deployed to a robotic platform, robust to sensor noise and outperforms other existing DRL-based models in many indicators.