To enable mobile robots to successfully avoid static and dynamic obstacles and safely and rapidly navigate to their destinations, this study proposes an autonomous collision avoidance and navigation algorithm for mobile robots based on Point Cloud Library (PCL) and imitation learning. Building upon the Cartographer algorithm, this approach integrates 2D LiDAR and stereo cameras to achieve mobile robot localization and map building. Based on this integration, a path planning algorithm for mobile robots is designed using an improved Dynamic Window Approach (DWA) via fuzzy reinforcement learning to ensure navigation safety in the environment. Simulation results demonstrate that the Cartographer algorithm, which integrates LiDAR and stereo information, significantly enhances the localization accuracy of the original Cartographer algorithm, providing higher-precision localization performance for mobile robots. The improved DWA based on fuzzy reinforcement learning can plan a relatively optimal path with a shorter trajectory length and higher operational efficiency.