In complex environments characterized by multiple obstacles, the traditional A* algorithm in path planning presents the problem of redundant turning nodes. This not only increases path length and complexity but also hinders the smooth navigation of the AGV. To address these challenges, this study introduces an improved A* algorithm predicated on the tensile mechanism of a flexible rope, aimed at diminishing path nodes and augmenting trajectory smoothness. First, the mechanism of flexible rope stretching was analyzed, and critical nodes were extracted from the paths generated by the A* algorithm. Subsequently, the degeneration of non-obstacle force points was executed to minimize redundant steering nodes, followed by the sequential stretching of paths between force points, thereby streamlining the trajectory and enhancing smoothness. Ultimately, the refined A* algorithm underwent simulation experiments and was applied to AGVs for autonomous navigation path planning experiments. The simulation outcomes demonstrated that the A* algorithm, refined with the flexible rope stretching mechanism, achieved a 59.2% reduction in turning angles, a 54.2% decrease in the number of turning points, and an 11% reduction in path length, significantly simplifying and smoothing the trajectory. In the AGV navigation experiments, the optimized A* algorithm, when compared to the traditional A* algorithm, registered a 16% decrease in average angular velocity and a 33% reduction in driving turning angles, with average travel trajectory length and time reduced by 2.4% and 4%, respectively. Additionally, the average travel trajectory length and time spent are reduced by 2.4% and 4%, respectively. The experiments results show that the AGV experiences smaller node transformations and posture adjustments while following the paths planned by the improved A* algorithm, leading to smoother and more efficient movement.