Natural rubber is widely used in human life because of its excellent quality. At present, manual tapping is still the main way to obtain natural rubber. There is a sore need for intelligent tapping devices in the tapping industry, and the autonomous navigation technique is of great importance to make rubber-tapping devices intelligent. To realize the autonomous navigation of the intelligent rubber-tapping platform and to collect information on a rubber forest, the sparse point cloud data of tree trunks are extracted by the low-cost LiDAR and a gyroscope through the clustering method. The point cloud is fitted into circles by the Gauss–Newton method to obtain the center point of each tree. Then, these center points are threaded through the Least Squares method to obtain the straight line, which is regarded as the navigation path of the robot in this forest. Moreover, the Extended Kalman Filter (EKF) algorithm is adopted to obtain the robot’s position. In a forest with different row spacings and plant spacings, the heading error and lateral error of this robot are analyzed and a Fuzzy Controller is applied for the following activities: walking along one row with a fixed lateral distance, stopping at fixed points, turning from one row into another, and collecting information on plant spacing, row spacing, and trees’ diameters. Then, according to the collected information, each tree’s position is calculated, and the geometric feature map is constructed. In a forest with different row spacings and plant spacings, three repeated tests have been carried out at an initial speed of 0.3 m/s. The results show that the Root Mean Square (RMS) lateral errors are less than 10.32 cm, which shows that the proposed navigation method provides great path tracking. The fixed-point stopping range of the robot can meet the requirements for automatic rubber tapping of the mechanical arm, and the average stopping error is 12.08 cm. In the geometric feature map constructed by collecting information, the RMS radius errors are less than 0.66 cm, and the RMS plant spacing errors are less than 11.31 cm. These results show that the method for collecting information and constructing a map recursively in the process of navigation proposed in the paper provides a solution for forest information collection. The method provides a low-cost, real-time, and stable solution for forest navigation of automatic rubber tapping equipment, and the collected information not only assists the automatic tapping equipment to plan the tapping path, but also provides a basis for the informationization and precise management of a rubber plantation.