# An Intelligent Measurement Method and System for Vehicle Passing Angles
## 1 Introduction and Background  
Vehicle passing angles are important parameters in vehicle measurement standards [1]. The vehicle passing angles are the geometric parameters of a vehicle that determine a vehicle's ability to pass on different terrains; the larger the passing angle, the better the ability to pass on steep roads. The stability- and quality-related measurements of vehicles' passing angles affect the quality of acceptance in the industrial production of vehicles, and they also play an important role in the planning of transportation systems [2] and military deployment in complex terrains [3]. During the vehicle manufacturing process, the actual parameters often deviate from the designed vehicle model. Accurate measurements of these parameters are of significant importance for guiding production processes and determining competitive bidding. The vehicle passing angle diagram shown in Figure 1, which includes the approach angle, departure angle and ramp breakover angle [1], are still commonly measured manually in practice [4]. The staff must select the target points on the vehicle and estimate the position of the line tangent to the tire manually and then measure them and calculate the passing angles using trigonometric functions. However, this manual measurement method introduces multiple sources of error, making it inefficient and difficult to quantify and guarantee the consistency of the data and thus causing this method to be prone to controversy in both product acceptance and competitive bidding. Existing automated non-contact measurement methods for vehicle contours are gradually maturing. A method for traversability assessment planning was proposed in the research of [PERSON], [PERSON] et al. [5], which was based on the computation of a specific vehiclemodel considering the geometric information of a rough terrain surface obtained from laser scanning with LIDAR. However, this method mainly assesses the passability for a specific vehicle model and thus cannot be universally applied to vehicles easily or provide specific measurement parameters. [PERSON], [PERSON] et al. [6] presented a measuring system that analyzes the wheels of passing vehicles using a horizontal LIDAR in a plane close and nearly parallel to the road surface. However, only the wheels were considered in the paper, and no data were collected from the chassis of the vehicle; thus, this method cannot be applied to calculate vehicle-related geometric parameters. In 2019, [PERSON], [PERSON] et al. [7] proposed another method to measure vehicle passing angles using a measuring plate and an improved tool instead of manual measurement. However, different models of modified lifting plates were required to fit the widely varying vehicle requirements, meaning that it is still a contact measurement method that needs to be more convenient. Some automated methods are available to measure the geometric parameters of vehicles [8; 9; 10; 11]. However, these methods cannot be directly applied to the measurement of passing parameters. The methods proposed in [8; 9; 10] employ various image segmentation techniques combined with vehicle morphology [8], neural networks [9], or prior knowledge [10] to extract vehicle contour boundaries and calculate their dimensions. Although these single-view methods are fast, they tend to have larger errors, and they struggle to capture information about the vehicle's bottom side using a single perspective. The method presented in [11] is a multi-view 3D imaging and detection approach that uses unmanned aerial vehicles to capture vehicle images from different angles and reconstruct them in 3D. However, these multi-view methods require comprehensive information from multiple angles to ensure robustness and accuracy. When capturing images of the vehicle's bottom side, the angles of acquisition are limited, and factors such as lighting conditions and image quality can significantly affect the imaging quality and completeness.