## 1 Introduction  
Soybean and maize are two of the most important staple and oilseed crops in China. The strip intercropping of soybean and maize has been widely adopted across the country, offering a mutually beneficial growth environment by leveraging the edge-row advantages of maize [1, 2, 3, 4]. However, current machinery operations in soybean-maize strip intercropping systems still largely depend on manual intervention, often resulting in issues such as seedling damage caused by wheel traffic. To address these challenges, enabling autonomous operation of agricultural machinery has become a research focus [5, 6]. In strip intercropping systems, soybean and maize are typically sown in rows using precision seeding techniques, which makes it feasible to plan inter-row wheel paths by extracting the central lines of the crop rows. At present, two primary approaches are used for crop row identification and navigation line extraction: machine vision and LiDAR-based techniques. Research on crop row detection and navigation line extraction began relatively early in foreign countries. Many studies have employed machine vision and deep learning models to identify crop rows and extract navigation paths [7; 8; 9; 10; 11]. For example, [PERSON] et al. [12] utilized binocular vision techniques to detect soybean crop rows by integrating multiple image processing algorithms. However, the performance of their approach requires further validation in complex environments with dense weeds or heavy shadows. [PERSON] et al. [13] proposed an improved UNet-based model for detecting the central lines of maize crop rows. Their method achieved promising results, significantly reducing both the average fitting time and angular error compared to traditional vertical projection methods, reaching 66 ms and 4.37\({}^{\circ}\), respectively. Similarly, [PERSON] et al. [14] applied a convolutional neural network (CNN) to detect rice seedlings and accurately determine inter-row spacing in paddy fields. However, machine vision techniques still face numerous challenges in complex and variable field environments. Factors such as shadows, fluctuating lighting conditions, and lengthy image processing times can adversely affect the accuracy of crop row detection and navigation line extraction. To address these issues, [PERSON] et al. [15] employed an improved YOLOv8 model for the detection of multiple crop types. The experimental results demonstrated the model's exceptional performance, with mean average precision (mAP) values consistently exceeding 96.4%, highlighting its robustness and stability in diverse agricultural scenarios. Although machine vision and deep learning techniques have achieved significant progress in capturing crop image features, the variability of field environments and differences in agronomic traits pose substantial challenges to image processing. The complexity of field conditions often introduces large amounts of redundant information into the captured images, which not only increases the computational burden and prolongs processing time but also complicates stereo matching. These factors collectively degrade the accuracy of crop row detection and navigation line extraction [16; 17]. In contrast, LiDAR technology determines the distance to a target by emitting laser pulses, enabling the direct acquisition of spatial information [18; 19; 20]. Moreover, LiDAR is inherently robust to variations in shadow and lighting conditions [21; 22], which gives it a significant advantage in complex and highly occluded environments. With continuous technological advancements and declining hardware costs, LiDAR is becoming increasingly promising for agricultural applications. In recent years, both domestic and international researchers have made notable progress in applying LiDAR to crop row detection. For instance, [PERSON] et al. [23] successfully integrated two-dimensional LiDAR with the Hough transform algorithm to achieve accurate navigation of autonomous vehicles in real-world environments, such as orchards. Similarly, [PERSON] et al.