# Research on Path Planning for Robots with Improved A* Algorithm under Bidirectional JPS Strategy
## 4 Simulation Analysis and Experimental Validation
### Simulation Analysis
Specifically, the improved algorithm demonstrates greater efficiency in improving the search speed with larger maps. Conversely, with smaller maps, the efficiency of the improved algorithm in enhancing the search speed diminishes. When the ratio of obstacles in the map varies, due to the introduction of environmental constraints, if the percentage of obstacles is low, the improved algorithm shows less noticeable improvement in path length, and in some cases, the path length may even worsen. However, the improvement in search time is significant. Conversely, when the percentage of obstacles is higher, the improved algorithm demonstrates more pronounced improvement in path length, but the improvement in search time deteriorates compared to the scenario with a lower obstacle percentage. However, in \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Map Size**} & **Experimental** & **Number of Nodes** & **Path Length** & **Number of Turns** & **Search Time** & **Percentage of** \\  & **Algorithms** & **Traversed (Number)** & **(Meters)** & **(Times)** & **(Seconds)** & **Obstacles** \\ \hline \multirow{4}{*}{\(20\times 20\)} & A* & 77 & 24.7279 & 7 & 0.233068 & \\  & JPS algorithm & 20 & 24.7279 & 7 & 0.157325 & \\  & Improved algorithm & 26 & 24.1381 & 6 & 0.115842 & \\ \hline \multirow{4}{*}{\(40\times 40\)} & A* & 326 & 61.0122 & 17 & 0.707153 & \\  & JPS algorithm & 39 & 61.0122 & 17 & 0.386459 & \\  & Improved algorithm & 32 & 58.0070 & 10 & 0.268241 & \\ \hline \multirow{4}{*}{\(60\times 60\)} & A* & 290 & 88.3259 & 11 & 1.101714 & \\  & JPS algorithm & 38 & 88.3259 & 11 & 0.549135 & \\  & Improved algorithm & 30 & 93.5291 & 6 & 0.345265 & \\ \hline \multirow{4}{*}{\(80\times 80\)} & A* & 836 & 131.6396 & 21 & 3.334070 & \\  & JPS algorithm & 51 & 131.6396 & 21 & 1.585116 & \\ \cline{1-1}  & Improved algorithm & 52 & 134.3342 & 15 & 0.912868 & \\ \hline \multirow{4}{*}{\(100\times 100\)} & A* & 876 & 160.5097 & 23 & 5.128762 & \\ \cline{1-1}  & JPS algorithm & 55 & 160.5097 & 23 & 2.237949 & \\ \cline{1-1}  & Improved algorithm & 48 & 159.7931 & 16 & 1.109351 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of three algorithms on grid maps with low proportions of obstacles. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Map Size**} & **Experimental** & **Number of Nodes** & **Path Length** & **Number of Turns** & **Search Time** & **Percentage of** \\  & **Algorithms** & **Traversed (Number)** & **(Meters)** & **(Times)** & **(Seconds)** & **Obstacles** \\ \hline \multirow{4}{*}{\(20\times 20\)} & A* & 131 & 29.3137 & 12 & 0.448762 & \\  & JPS algorithm & 40 & 30.7279 & 9 & 0.379653 & \\  & Improved algorithm & 57 & 30.2587 & 9 & 0.331437 & \\ \hline \multirow{4}{*}{\(40\times 40\)} & A* & 183 & 62.6274 & 25 & 1.247487 & \\  & JPS algorithm & 79 & 62.6274 & 25 & 0.956823 & \\  & Improved algorithm & 125 & 60.3749 & 18 & 0.757804 & \\ \hline \multirow{4}{*}{\(60\times 60\)} & A* & 280 & 100.7696 & 34 & 2.161697 & \\  & JPS algorithm & 86 & 100.7696 & 32 & 1.513218 & \\ \cline{1-1}  & Improved algorithm & 128 & 99.3118 & 29 & 1.027475 & \\ \hline \multirow{4}{*}{\(80\times 80\)} & A* & 694 & 136.9117 & 31 & 4.919608 & \\ \cline{1-1}  & JPS algorithm & 113 & 136.9117 & 31 & 3.414556 & \\ \cline{1-1}  & Improved algorithm & 132 & 134.7762 & 24 & 2.055904 & \\ \hline \multirow{4}{*}{\(100\times 100\)} & A* & 791 & 173.3970 & 35 & 7.117738 & \\ \cline{1-1}  & JPS algorithm & 127 & 173.3970 & 35 & 4.593951 & \\ \cline{1-1}  & Improved algorithm & 144 & 169.9316 & 27 & 2.378748 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of three algorithms on grid maps with high proportions of obstacles. general, compared to the other two algorithms, the improved A* algorithm has significantly enhanced both the efficiency of pathfinding and algorithm optimization.