###### Abstract  
When traversing soft and rugged terrain, a planetary rover is susceptible to slipping and sinking, which impedes its movement. The real-time detection of wheel sinkage in the planetary wheel-on-limb system is crucial for enhancing motion safety and passability on such terrain. Initially, this study establishes a measurement of wheel sinkage under complex terrain conditions. Subsequently, a monocular vision-based wheel sinkage detection method is presented by combining the wheel-terrain boundary with the wheel center position (WTB-WCP). The method enables the efficient and accurate detection of wheel sinkage through two-stage parallel computation of the wheel-terrain boundary fitting and wheel center localization. Finally, this study establishes an experimental platform based on a monocular camera and the planetary rover wheel-on-limb system to experimentally validate and comparatively analyze the proposed method. The experimental results demonstrate that the method effectively provides information on the wheel sinkage of the planetary rover wheel-on-limb system, and the relative errors of the method do not exceed 4%. The method has high accuracy and reliability and is greatly significant for the safety and passability of planetary rovers in soft and rugged terrain. s +
Footnote †: journal: Applied  
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Footnote †: journal: Applied  
in grayscale. Despite its computational efficiency and simplicity, it is notably affected by variations in lighting and shading. [PERSON] et al. introduced the visual sinkage estimation (VSE) algorithm in 2006 [16]. The algorithm first converts the image of the wheel-ground contact surface into a grayscale map and then determines the contact angle and sink value using equally spaced black concentric circles on the wheel and edge detection. [PERSON] and colleagues implemented [PERSON]'s principles for sinkage detection and employed robust image processing techniques to identify contact points, thereby enhancing the VES algorithm. However, despite its simplicity, feasibility, and efficiency, this method does not consider image noise, which can result in lower precision when calculating sinking [17]. These methods only work well if the difference in grayscale between the wheel and the terrain is large enough. To overcome the limitations of high grayscale differences, [PERSON] et al. [18] proposed a method to detect wheel sinking based on the Normalized Cuts image segmentation method. This method recognizes the wheel-soil boundary line by segmenting the wheel-soil image and thus determines the wheel sinkage value. The method mentioned offers the benefits of providing highly accurate and detailed data. However, its main limitations include noise insensitivity and high image quality requirements. In 2015, [PERSON] [19] introduced a wheel-soil boundary extraction method based on machine vision and saturation. The method extracts the wheel contour by transforming the image space and image binary processing. The algorithm enhances traditional image enhancement by considering the interaction between the wheel and soil. Additionally, a calculation model has been developed for wheel sinkage under complex ground conditions. Combining the wheel contour and the morphological features of the wheel-terrain contact, the wheel sinkage depth, entry angle, and departure angle are effectively calculated based on the wheel sinkage model. This method requires high image illumination and exhibits low accuracy at small values of wheel sinkage. In order to avoid the influence of environmental factors such as illumination, some scholars have begun to use methods other than image processing for wheel sinkage detection. [PERSON] et al. [20] acquire the depth information of the soil area beside the wheel by placing a TOF camera on the side of the wheel and subsequently calculating the wheel sinkage. Unlike image processing methods, this method is minimally affected by the conditions of the target environment, such as lighting or reflectance. In 2017, [PERSON] et al.