## 5 Conclusions  
This article presents a monocular visual sinkage detection method combining WTB and WCP for the planetary rover wheel-on-limb system. The wheel sinkage is captured using a single camera, and the original image is transformed into a frontal view of the wheel surface through a perspective transformation. Subsequently, the Hough circle detection algorithm is employed to obtain the pixel coordinates and radius of the wheel center in pixels. The Canny edge detection algorithm is utilized to capture image information at the wheel-terrain boundary. Next, the least squares fitting method is employed to obtain the best-fit straight line representing the boundary at the intersection. Finally, the settlement of the wheel should be calculated using the wheel settlement calculation model. The algorithm was ultimately validated using a soil tank experimental platform. The results indicated that the pixel coordinate error of the Hough circle detection result is below 10 pixels, and the actual error is less than 2 mm. The error as a percentage of radius does not exceed 2% when compared to the actual wheel size, which has a diameter of 160 mm. The relative errors of the monocular vision sinkage detection method do not exceed 4%, which exhibits a higher level of accuracy and reliability compared to the conventional visual sinkage estimation algorithm.  
This method is able to work with the wheel-on-limb system to determine the passability of the planetary rover's traveling area, which is greatly significant for the driving safety of the planetary rover during exoplanet exploration. Similarly, the method can be  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Test**} & **Reference Sinkage** & **Sinkage Value Detected** & **Sinkage Value Detected** & **Relative Error** & **Relative Error** \\  & **Value (mm)** & **by MVSD (mm)** & **by VSE (mm)** & **of MVSD** & **of VSE** \\ \hline
1 & 0.00 & 0.00 & 0.00 & 0.00\% & 0.00\% \\
2 & 8.10 & 8.25 & 8.30 & 1.85\% & 2.47\% \\
3 & 16.06 & 16.30 & 15.62 & 1.49\% & 2.74\% \\
4 & 20.43 & 20.05 & 19.86 & 1.86\% & 2.79\% \\
5 & 25.42 & 24.91 & 24.01 & 2.01\% & 5.55\% \\
6 & 30.12 & 29.28 & 28.56 & 2.79\% & 5.18\% \\
7 & 32.83 & 31.79 & 30.32 & 3.17\% & 7.65\% \\
8 & 36.16 & 34.77 & 33.03 & 3.84\% & 8.66\% \\ \hline \hline \end{tabular}
\end{table}
Table 4: Wheel sinkage detection results.  
Figure 9: Comparative analysis test results.  
used for sinkage detection of wheeled vehicles in unknown terrain in the field, which is important for passability detection and vehicle traveling safety in the forward area. In addition, this sinkage detection method can be prepared for the study of terrain mechanics in rugged terrain to realize the calculation of wheel-soil interaction forces moving over rugged terrain.  
Conceptualization, B.L. and D.W.; methodology, B.L. and L.F.; validation, B.L. and D.W.; investigation, B.L. and D.W.; resources, D.W.; writing--original draft preparation, B.L.; writing--review and editing, L.F. and D.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant number 62103184.  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors acknowledge [PERSON] for his contributions to the process of equipment debugging and field testing.  
The authors declare no conflicts of interest.