Facility agricultural robots operating in greenhouse environments often encounter narrow passages, dense obstacle distributions, and frequent path-direction changes, which increase the difficulty of achieving efficient and smooth autonomous navigation. Conventional A* algorithms usually suffer from redundant node expansion, dense turning-point distributions, and insufficient path continuity under such constrained conditions. To address these issues, this study proposes an improved A*-based path-planning framework that integrates adaptive heuristic weighting, dynamic corner correction, and Bézier-curve-based path smoothing. Rather than introducing an entirely new planning paradigm, the proposed method coordinates several existing optimization strategies within a unified framework to improve search efficiency, path regularity, and path continuity for facility agricultural scenarios. The adaptive heuristic weighting strategy dynamically adjusts the contribution of the heuristic term according to the relative distance between the current node and the target node, thereby improving global search guidance while reducing unnecessary exploration. Dynamic corner correction is introduced to suppress zigzag path structures and reduce redundant turning nodes in obstacle-dense regions, while Bézier-curve-based smoothing is employed to improve path continuity and compatibility with the kinematic characteristics of agricultural mobile robots. Simulation experiments were conducted on grid maps and greenhouse-like environments with different obstacle distributions, and comparative evaluations were performed against Dijkstra, RRT, and conventional A* algorithms. Under representative simulation scenarios, the proposed framework reduced the number of turning points by up to 53.7% and decreased computation time by approximately 19.4% compared with the conventional A* algorithm, based on the average results of repeated trials under identical conditions. In addition, physical platform experiments on a ROS2-based agricultural robot demonstrated that the planned trajectories maintained relatively stable navigation performance and smoother directional transitions in constrained greenhouse-like environments. The results indicate that the proposed framework achieves a more balanced trade-off between computational efficiency, path compactness, and path smoothness than the benchmark methods considered in this study. Nevertheless, the current validation remains limited to structured or semi-structured greenhouse environments under static obstacle conditions. Future work will focus on improving adaptability to dynamic agricultural scenarios and integrating the framework with real-time perception and motion-control systems for practical greenhouse deployment.