With the development of automation technologies, autonomous robots are increasingly used in many important applications. However, precise self-navigation and accurate path planning remain a significant challenge, particularly for the robots operating in complex circumstances such as city centers. In this paper, a nonholonomically constrained robot with high-precision navigation and path planning capability was designed based on the Robot Operating System (ROS), and an improved hybrid A* algorithm was developed to increase the processing efficiency and accuracy of the global path planning and navigation of the robot. The performance and effectiveness of the algorithm were evaluated by using randomly constructed maps in MATLAB and validated in a practical circumstance. Local path planning and obstacle avoidance were carried out based on the model predictive control (MPC) theory. Compared with the conventional A* + DWA (dynamic window approach) method, the average searching time was reduced by 12.62~24.5%, and the average search length was reduced by 9.25~9.5%. In practical navigating tests, the average search time was reduced by 18~24%, and the average search length was reduced by 10.3~12%, while the overall path was smoother. The results demonstrate that the improved algorithm can enable precise and efficient navigation and path planning of the robot in complex circumstances.