## 3 Performance Analysis of Modified Algorithm
### Analysis of Algorithm Robustness  
To test the optimization of the modified Hybrid A* algorithm under random conditions, we have conducted thousand planning experiments in two scenes with randomly given start position and goal position. We are moreover repeat the experiment at three different terrain resolutions scenes (0.1 m, 0.5 m, 1.0 m). Figure 16 is the schematic diagram of two scenes with lower resolution.  
With the decrease of terrain resolution, C-MAP loses a lot of surface roughness information. As a result, in the planning of low-resolution maps, the optimization rate is more concentrated in the 0% to 10% range, as shown in Figure 16(c)-f. Significantly, when the resolution is from 0.1 m to 0.5 m, the average optimization rate of two scenes decreases rapidly, while the latter decreases slowly from 0.5 m to 1.0 m, as shown in Figure 18. The result shows that the planning algorithm cannot optimize the trajectory well when the terrain resolution (grid accuracy) is reduced from high to low.  
Based on the results of the random test, we consider several factors that affect the optimization rate:  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Path Length (m)** & **Accumulative Cost** & **Total Score** & **Optimization Rate (\%)** \\ \hline Scene 1 & OCM & 40 & 1124.4 & 1113.8 & 5.93 \\ Start I & C-MAP & 43 & 1057.7 & 1047.8 & 5.93 \\ Scene 1 & OCM & 39 & 926.9 & 918.2 & 5.26 \\ Start II & C-MAP & 37 & 878.1 & 869.9 & 5.26 \\ Scene 1 & OCM & 41 & 316.4 & 313.7 & 6.87 \\ Start III & C-MAP & 39 & 294.6 & 292.1 & 6.87 \\ Scene 2 & OCM & 57 & 386.2 & 382.9 & \\ Start I & C-MAP & 61 & 315.7 & 313.1 & 18.23 \\ Scene 2 & OCM & 54 & 1174.8 & 1163.6 & 9.82 \\ Start II & C-MAP & 58 & 1059.4 & 1049.3 & \\ Scene 2 & OCM & 62 & 1096.8 & 1086.4 & \\ Start III & C-MAP & 59 & 1020.1 & 1010.5 & 6.99 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Planning Path Evaluation Table in Two Scene.  
1. The influence of planning map construction, including the DSM accuracy and filter threshold. The accuracy of DSM directly affects the recognition ability of the construction algorithm for surface roughness. However, the improvement of accuracy will result in more computational work and the program needs to process more data units. Therefore, 0.1 m is an appropriate accuracy value.
2. For the filter threshold, it affects the ability of the construction algorithm to distinguish obstacles from the surface. Moreover, it is difficult to construct a surface roughness model if the terrain is flat.
3. The influence is caused by the parameter setting of Hybrid A* algorithm. The setting of parameters will directly affect the quality of the final path. To illustrate, if the ReverseCost setting is greater than ForwardCost, the algorithm will consider the backward situation more. If the Extension Interval setting is too large, it will cause extra computation. Switch Cost penalizes the direction change of a vehicle. However, in this paper, since Tire Cost is a dynamic value, the static value of Switch Cost will weaken its effect so that it can be considered as an adaptive value.
4. Caused by statistics of path cost. The entropy method may not be able to integrate the path length and the accumulative cost on the surface very well, which makes the calculation error.  
Figure 16: Two scenes with different terrain resolution. (**a**,**c**) are the 0.5 m terrain resolution scenes; (**b**,**d**) are the 1.0 m terrain resolution scenes.  
Figure 17: Optimization rate of the random path in two scenes with different terrain resolutions. (**a**,**c**,**e**) are the random tests in scene 1; (**b**,**d**,**f**) are the tests in scene 2. (**a**,**b**) are tested in the 0.1 m terrain resolution scenes; (**c**,**d**) are tested in the 0.5 m terrain resolution scenes; (**e**,**f**) are tested in the 1.0 m terrain resolution scenes.