## 3 Experiments
### Parametric Experiments for the Number of Segments \(m\)  
SPA* shows excellent performance in static navigation path planning experiments, but the number of segments \(m\) of SPA * is only set to 7. If the \(m\) of SPA * is changed, will the performance of SPA * be greatly affected? Or how to set the \(m\) of SPA* to make SPA* show better performance? In order to obtain answers to the above questions, we designed an adequate parametric experiment on \(m\) for SPA*. It is based on Section 3.1, adjusting \(m\) for different map size cases: 6-70 for 100 \(\times\) 100, 6-100 for 200 \(\times\) 200, and 6-200 for 400 \(\times\) 400. And the changes in the running times of the algorithms \(f_{1}\) and \(f_{2}\) are observed (the R-VIMO of SPA* is always 0). We also added an additional indicator, namely the same ratio as the generated path (SR-GP). SR-GP is calculated by the following Equation (13). \[\frac{ismember(Path_{SPA*},Path_{gp})}{length(Path_{SPA*})}, \tag{13}\]  
where \(ismember(a,b)\) represents the number of the same components of vectors \(a\) and \(b\); \(length(\cdot)\) is a function that counts the length of the vectors inside the brackets. A larger SR-GP means a higher degree of identity with the generated path. SR-GP equal to 1 means that the generated path has no new information after SPA*. Hence, we want the SR-GP to be as small as possible. In this way, the path is expected to have better risk-control ability. The experimental results are shown in Figure 6. The x and y axes of Figure 6a,d,g indicate the SR-GP and the running time, respectively, and the size of the bubble indicates the number of segments \(m\). The blue markers on Figure 6b,e,h indicate \(f_{1}\); the yellow markers on Figure 6c,f,i indicate \(f_{2}\); where 100 \(\times\) 100 is represented by a circular marker; 200 \(\times\) 200 is represented by a diamond marker; and 400 \(\times\) 400 is represented by a triangular marker. For 100 \(\times\) 100, the SPA* algorithm time and SR-GP both show an increasing trend as the number of segments increases (the yellow curve is the trend line). And at this time, both \(f_{1}\) and \(f_{2}\) show a tendency to rise first and then stabilize around a certain value to fluctuate, and the threshold at which they tend to stabilize is around \(m\) = 40. Therefore, we believe that in the case of 100 \(\times\) 100, the lower the number of segments, the better, but not less than 6. For 200 \(\times\) 200, as the number of segments increases, the SR-GP of SPA* continues to rise, while the overall SPA* algorithm running time tends to fluctuate downward. And at this time, both \(f_{1}\) and \(f_{2}\) show the trend of first rising and then stabilizing around a certain value fluctuating, and the threshold at which they tend to stabilize is around \(m\) = 30. Sowe think that \(m\) that makes SR-GP maintain between 0.2 and 0.3 is preferable in the case of 200 \(\times\) 200. The range of \(m\) satisfying the above condition is 10-20. For 400 \(\times\) 400, the SR-GP of SPA* continues to rise as the number of segments increases, while the running time of SPA* first decreases rapidly and then the rate of decrease tends to level off. Finally, the running time of SPA* stabilizes at a certain value. And at this time, both \(f_{1}\) and \(f_{2}\) show a trend of first rising and then stabilizing around a certain value fluctuating, and the threshold at which they tend to stabilize is around \(m\) = 60. So, we think that \(m\) that makes SR-GP maintain between 0.1 and 0.2 is preferable in the case of 400 \(\times\) 400. The range of \(m\) satisfying the above condition is 15-30. Figure 6: Experiments on the sensitivity of \(m\) for different map sizes.