# Riverbank Following Planner (RBFP) for USVs Based on Point Cloud Data
## 4 Experiments
### Statistics  
The boxplot in Figure 9 shows a five-digit visual representation of the distance between the USV and the riverbank under four wind conditions and three different riverbank shapes of straight, convex, and concave banks. The five-number summary is the mean (and 50% quartile), 25% quartile, 75% quartile, maximum, and minimum. The median of relative distance in the three scenarios is closely distributed at 21 m. The box plot is comparatively short, suggesting that overall relative distances have a stable performance with each other. In the straight case, the interquartile range (IQR) is the smallest compared with the other two cases. This renders that the proposed method has achieved the best performance doing straight bank following. The IQR in the straight case has a minimum IQR of about 0.5 m. The IQR for convex and concave cases are about 3 and 4 m, respectively. It means that the USV encounters a convex or concave shape on the path, when the error in the desired heading suddenly becomes larger, while the USV maintains the linear speed of the previous timestamp due to inertia. Therefore, the riverbank distance is suddenly larger when compensating for the heading error. In engineering practice, the PID controllers we use are based on the compensation of errors to achieve control. Their delay leads to large errors but within acceptable limits.  
Table 2 shows the observations in all the tests. We take \(\pm\)15% of the relative distance between the USV and the riverbank as the interval for high precision following the riverbank, which is called the following performance. We established a margin of 15%, which is grounded on extensive testing and evaluation, ensuring the reliability and robustness of our following algorithm. The following performance is assessed based on the ability to maintain a 20 m distance from the riverbank, allowing a \(\pm\)15% error margin. This criterion was not arbitrarily chosen but is a result of comprehensive analysis and experimentation, reinforcing the credibility and feasibility of our method in real-world applications. We can see that the USV achieved 96.92% following the performance average of those 4 values in different wind speeds in the straight riverbank, perfectly achieving the desired results. At the same time, its mean is minimal, which proves that the oscillation amplitude of USV is small and the path is smooth. In convex banks, the shape of the bank drops rapidly after the raised vertex, so it takes time for the USV to complete the scanning and following of the bank. At the same time, when the relative distance between the USV and the riverbank increases, the USV will gradually approach the direction of the riverbank through PID control, increasing the mean value and variance of the relative distance between the USV and the riverbank, the results show that the following performance can reach 67.30%. In the concave bank, the minimum value of the USV and riverbank is smaller than that in the convex bank. This is because in the concave scenario, the dynamic of the USV causes it to  
Figure 9: Boxplot of Relative Distance. (**a**) Straight Riverbank. (**b**) Convex Riverbank. (**c**) Concave Riverbank.  
deviate from the planned path when approaching the riverbank, and the PID controller helps the USV return to the original path. However, the decreased variance demonstrates that the USV has a high level of precision in following the planned path in this scenario. The result shows that the following performance can reach 60.90%. Because the RBFP takes into account that the wind affects the path planning and corrects the path in time when deviations occur, we obtain similar results with very few deviations when we set different wind speeds in the simulation.