# Path Planning of a Mobile Robot Based on the Improved RRT Algorithm
## 4 Simulation and Analysis
### Simulation of Fast Planning  
In the fast planning experiment, we focused on the algorithm's ability to quickly find paths in different scenarios. The running time and the number of nodes are important evaluation metrics, and the quality of the path is not considered. In order to verify the effectiveness of the proposed adjustable probability and sampling area strategies, the performance of the proposed APS-RRT planner is compared with that of the RRT and Bias-RRT algorithms. Statistical data based on the experiment results are presented in Table 2.  
Map1 is a simple environment for testing the performance of algorithms in a scenario with fewer obstacles. All three algorithms can achieve good results, but the APS-RRT planner makes considerable improvement in terms of the time cost and memory usage. Compared with the RRT and Bias-RRT algorithms, the APS-RRT planner reduces the running time by 57.1% and 40%, respectively. The APS-RRT planner also reduces the average number of nodes by 71.4% and 46.6%, respectively. Map2 is a complex environment with multiple obstacles; it is used to test the performance of algorithms in the cluttered scenario. The Bias-RRT algorithm exhibit poor performance in Map2 and almost degenerates into the RRT algorithm, because the density of obstacles is high in this environment and the fixed goal bias probability makes the algorithm easily fall into a local minimum. However, the performance of the APS-RRT planner is not affected by this environment. The APS-RRT planner still maintains the efficient exploration capabilities, because it can adaptively adjust the goal bias probability and sampling area according to the growth status of the search tree, leading the planner to reach the target effectively. Compared with the RRT and Bias-RRT algorithms, in terms of the planning time, the APS-RRT planner reduces the average time cost by about 56.5%; the average number of nodes is reduced by 71.4% and 63%, respectively. Map3 simulates an indoor scenario that contains many trap regions. The third row of Figure 7 shows that the nodes of the RRT and Bias-RRT algorithms fill almost the entire configuration space, but many nodes have no influence on the final path. The node redundancy \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \(\lambda,r\) & 30 \\ \(p_{\text{max}}\) & 0.9 \\ \(P_{\text{min}}\) & 0.1 \\ _threshold_ & 100 \\ Maximum iteration & 3000 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the experiments. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Environment** & **Algorithm** & **Time (s)** & **Std** & **Nodes (n)** & **Std** & **Success Rate** \\ \hline \multirow{3}{*}{Map1} & RRT & 0.21 & 0.05 & 141.72 & 37.97 & 1 \\  & Bias-RRT (\(p\) = 0.5) & 0.15 & 0.03 & 75.84 & 19.87 & 1 \\  & APS-RRT & 0.09 & 0.02 & 40.5 & 7.95 & 1 \\ \hline \multirow{3}{*}{Map2} & RRT & 0.23 & 0.11 & 176.9 & 81.02 & 1 \\  & Bias-RRT (\(p\) = 0.5) & 0.23 & 0.15 & 136.7 & 83.41 & 1 \\  & APS-RRT & 0.1 & 0.02 & 50.64 & 12.14 & 1 \\ \hline \multirow{3}{*}{Map3} & RRT & 0.72 & 0.6 & 466.23 & 277.57 & 0.96 \\  & Bias-RRT (\(p\) = 0.5) & 0.64 & 0.51 & 338.82 & 209.68 & 0.88 \\  & APS-RRT & 0.13 & 0.06 & 80.98 & 43.19 & 1 \\ \hline \multirow{3}{*}{Map4} & RRT & 0.34 & 0.36 & 213.88 & 143.34 & 0.68 \\  & Bias-RRT (\(p\) = 0.5) & 0.32 & 0.17 & 165.23 & 71.59 & 0.6 \\ \cline{1-1}  & APS-RRT & 0.17 & 0.14 & 76.95 & 51.37 & 0.88 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The statistical data for the simulation of fast planning. of the two algorithms is a serious issue, because two of the planners have difficulty avoiding the trap regions, meaning that they consume a lot of computing resources. However, the APS-RRT planner can avoid unnecessary explorations in unimportant regions, where the solutions probably do not exist.