Aiming to address the challenges posed by the natural growth of asparagus branches and leaves obstructing pathways and the limited working space in raised beds, which result in significant map construction noise, large localization errors, and low mapping accuracy during the autonomous navigation of asparagus harvesting robots, an autonomous navigation system was presented based on 3D LiDAR SLAM for greenhouse asparagus harvesting robots. Initially, 3D point cloud data from the greenhouse environment were acquired by using a Velodyne 16-line 3D LiDAR sensor combined with an N100 inertial measurement unit (IMU). An adaptive point cloud filtering method was employed to preprocess the point cloud data, removing noise caused by the asparagus branches and leaves, thereby reducing the computational burden on the navigation system. Subsequently, a global re-localization process was performed by using the Cartographer pure localization algorithm based on extended Kalman filtering (EKF). For path planning, the Dijkstra algorithm was utilized for global path planning, while the dynamic window approach (DWA) was applied for local path planning. Experimental results demonstrated that the optimal parameter combination for the adaptive point cloud filtering method was k1=6.912, s1=0.334, and s2=0.918. The integration of adaptive point cloud filtering with the Cartographer algorithm enabled high-precision mapping in the greenhouse environment, with a maximum absolute error of 0.056m, a maximum relative error of 9.3%, and a root mean square error of 0.035m. The improved localization algorithm achieved lateral deviation no greater than 0.196m and longitudinal deviation no greater than 0.082m in the greenhouse environment. During autonomous navigation at speeds of 0.10m/s, 0.20m/s, and 0.30m/s, the lateral, longitudinal, and heading mean deviations were no greater than 0.082m, 0.091m, and 7.562°, respectively, while their corresponding standard deviations did not exceed 0.078m, 0.092m, and 6.561°. The proposed navigation framework satisfied the high-precision mapping, localization, and navigation requirements for autonomous systems in greenhouse environments, providing a theoretical and technical foundation for the deployment of harvesting robots in agricultural settings.