A navigation system based on the Nav2 behavior tree was proposed to address the inapplicability of traditional algorithm for single-steering-wheel automated guided vehicle (AGV) and the high-orderliness requirement of warehouse logistics operation. An overall operational directed graph was constructed, and an improved global path planning algorithm based on site and heading constraints was developed using a modified Dijkstra approach. A gradient-guided dynamic window approach (DWA) enhanced through multi-objective optimization was introduced, while an improved A* algorithm with a separated-axis and tri-neighborhood expansion strategy was employed to plan obstacle avoidance paths. These two methods operated cooperatively to achieve local path planning, and an obstacle avoidance strategy was constructed within the Nav2 behavior tree framework. The simulation results showed that the proposed Dijkstra algorithm reduced the number of traversed nodes by up to 81.6% and the pathfinding time by up to 42.1% compared with traditional algorithms. The improved DWA achieved a maximum reduction of 73.78% in the root mean square error (RMSE) during obstacle-free path following compared with the traditional DWA, maintaining control accuracy within 50 mm. Real-vehicle experiments demonstrated that the improved DWA algorithm reduced the tracking error by up to 50.26% compared with the traditional DWA. The improved DWA algorithm can accurately identify and respond to both static and dynamic obstacles, exhibiting high flexibility and precision.