# RJA-Star Algorithm for UAV Path Planning Based on Improved RSDOS Model
## 2 Materials and Methods
### Improved Path Planning Algorithm
From the results, we can get the mean and variance of RJA star algorithm and A-star algorithm under each size map, as shown in Table 3.

It can be concluded from Table 3 that the RJA star algorithm has smaller variance and mean value in both running time and nodes, which means that the RJA star algorithm is more stable and excellent in running time and nodes performance. The RJA star algorithm considers the safety distance, so the mean value of path is less than A-star algorithm, but the variance is greater than A-star algorithm. Regression analysis was conducted for our data. As shown in Figure 12a-c. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Map Size** & **Path Parameters** & **Traditional** & **RJA-Star** & **RJA-Star** \\  & & **A-Star** & **RJA-Star** & **Reduced** \\  & & & & **Proportion** \\ \hline \multirow{6}{*}{\(80\times 80\)} & Average running time/s & 221.547 & 8.858 & 96.00\% \\  & Average number of nodes & 64,183 & 55 & 99.91\% \\  & Total distance/s & 121.645 & 120.178 & 1.21\% \\  & Max turning & 90\({}^{\circ}\) & 56.85\({}^{\circ}\) & 36.83\% \\  & Number of turns & 41 & 4 & 90.24\% \\  & Average running time/s & 475.785 & 11.184 & 97.65\% \\  & Average number of nodes & 100,609 & 81 & 99.96\% \\
100 \(\times\) 100 & Total distance/s & 150.335 & 146.839 & 2.53\% \\  & Max turning & 90\({}^{\circ}\) & 33.024\({}^{\circ}\) & 63.31\% \\  & Number of turns & 56 & 2 & 96.08\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._ \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Map Size** & **Map ID** & **Evaluating Indicator** & **Estimated Parameters** & **A-Star** & **RJA-Star** \\ \hline \multirow{6}{*}{\(20\times 20\)} & \multirow{3}{*}{1–20} & Average running time/s & mean & 1.194 & 0.501 \\  & & Average running time/s & variance & 0.106 & 0.031 \\  & & mean & 1937.950 & 12.300 \\  & & variance & 3,139,070.892 & 85.484 \\  & & Total distance/s & mean & 34.729 & 34.007 \\  & & variance & 0.293 & 1.181 \\  & & mean & 33.634 & 2.900 \\  & & variance & 619.427 & 0.352 \\
50 \(\times\) 50 & 21–40 & Average number of nodes & mean & 23,298.050 & 19.050 \\  & & variance & 57,624,445.210 & 96.787 \\  & & Total distance/s & mean & 77.010 & 74.192 \\  & & variance & 0.275 & 0.624 \\  & & mean & 119.688 & 4.893 \\  & & variance & 308.581 & 0.844 \\
50 \(\times\) 50 & 41–60 & Average number of nodes & mean & 48,848.400 & 37.550 \\  & & variance & 23,670,949.090 & 350.892 \\  & & mean & 119.351 & 117.597 \\  & & variance & 0.020 & 15.461 \\  & & mean & 323.165 & 2.900 \\  & & variance & 50,306.815 & 0.352 \\
100 \(\times\) 100 & 61–80 & Average number of nodes & mean & 79,975.700 & 40.900 \\  & & variance & 829,201,538.100 & 526.937 \\  & & mean & 147.947 & 145.607 \\  & & variance & 0.454 & 12.160 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mean and variance of different indexes of two algorithms. Figure 12: (a) Regression analysis of computing time of two algorithms. (b) Regression analysis of two algorithms’ access nodes. (c) Regression analysis of path length of two algorithms. We can see that the number of nodes and path moving length of the two algorithms show a linear regression trend. The regression accuracy of their path lengths can reach 93.02% and 92.64% respectively. The running time of A-star algorithm is exponential regression, with an accuracy of 83.69%. The running time of RJA star algorithm is linear regression, with an accuracy of 76.63%. [PERSON] et al. proposed the geometric A-star algorithm [31]. To compare the advantages and disadvantages of A-star algorithm, geometric A-star algorithm and improved RJA algorithm, we simulated 100 experiments in scenario 9, and took the average value to Table 4.

Overall, the RJA-star algorithm performs better in terms of computing time and detecting nodes. ## 4 Conclusions

This paper proposes a new path planning algorithm, namely RJA star algorithm.