As the complexity of modern library management tasks increases, it is difficult for traditional mobile robots to meet the task of moving and classifying books. In order to design a mobile robot that can autonomously classify and transport books, the study realizes the tasks of book classification and transportation in libraries by fusing the differential speed algorithm and the robot motion model algorithm. First, the robot operating system is utilized to scan the books, classify the books, and obtain the category information of the books. Then, the differential speed algorithm is used to control the motion of the robot to ensure that the robot can accurately transport the books to the designated location. At the same time, combined with the robot motion model algorithm, the motion trajectory of the robot is planned to ensure that the robot can avoid obstacles and stably complete the book transportation task. Finally, the deep reinforcement learning algorithm is used to train the decision-making model of the robot to improve the intelligence level of the robot. The results of simulation experiments show that the research method has the highest accuracy, with an average accuracy of 99.98%, and the robot is able to accurately categorize the books and quickly avoid obstacles with strong stability. The results of the application experiments show that the research method has the shortest moving distance, with an average moving distance of 132 m and an average completion time of 34 seconds, which are lower than the remaining three types of robots. The research robot showed high accuracy in the task of returning books in four time periods within 10 days in the library, with an average accuracy of 99.58%. The experimental results validate the superiority of the research methodology and show that the robots are capable of accurately recognizing and classifying books and can autonomously perform transportation tasks in libraries. The research results help to improve the automation level and management efficiency of libraries and have important application value.