The work aims to address the difficulty of ensuring smooth following trajectories and obstacle avoidance at the same time when unmanned transport vehicles are travelling along a global path in the packaging workshop. The Frenet coordinate frame was constructed to describe the relative relationship between the vehicle pose and the global path. A quintic polynomial was adopted to generate multiple local paths to be selected. The obstacle profile of the packaging workshop was fuzzy processed by the obstacle potential field method, and the expansion interval was set. Combined with the collision values calculated for the sampling points of the path to be selected in the obstacle expansion interval, and the deviation values of the sampling points from the globally planned paths, the obstacle avoidance quality of the local paths was comprehensively evaluated to filter out the optimal obstacle avoidance path. According to the size of obstacles, the algorithm could dynamically calculate the local obstacle avoidance path with small offset from the global path and coherent motion. The proposed algorithm makes the vehicle complete the transport task with better effect and higher efficiency.