# Path Planning of Intelligent Mobile Robots with an Improved RRT Algorithm
## 3 Experimental Validation
### Multi-Map Environment Path Planning Simulation Experiment
As shown in Figure 8a-d and Table 3, in the multi-channel map scenario, the optimal average path length planned by the improved algorithm is reduced by 21.07% and the average number of samples is reduced by 72.98% compared with the traditional RRT algorithm; the significant reduction of samples indicates that the randomness of the algorithm is reduced, the redundant points are reduced, the average planning time is reduced by 54.49%, and the number of effective points is reduced by a small margin. The comparison of the above two sets of experiments illustrates the path planning ability of the improved algorithm in multi-channel maps. From Figure 10a-d and Table 4, it can be seen that in a narrow single-channel environment, the RRT algorithm experiences a large degree of collisions and backward growth, as shown in Figure 10b,c. A particle will undergo repetitive collisions in almost the same orientation, which makes it difficult to accurately find the correct path, and the time complexity becomes high in 40 groups of experiments, with only 3 groups finding the correct path, as shown in Figure 10a. In contrast, the improved algorithm in this paper utilizes the variable steering angle strategy to redefine the direction of travel when the node particles grow against the grain; when multiple collisions occur at a node, the particle is filtered using Kalman filtering to avoid redundancy of collisions and improve efficiency. The  
Figure 8: Multi-channel map simulation results. In this figure, the blue triangle represents the starting point, the pink triangle represents the target point, the black dashed circle represents the target point area, the four black rectangles represent obstacles, which include three channels that lead to the target point area, and the red solid line represents the final path from the starting point to the target point. (**a**) RRT-Channel 1; (**b**) RRT-Channel 2; (**c**) RRT-Channel 3; (**d**) improvement of the RRT-KF algorithm. Figure 9: Map channel numbering. The numbers 1, 2, and 3 represent three paths from the starting point to the target point. optimized algorithm reduces the average path length by 13.50% and the average planning time by 59.31% compared with the traditional algorithm, and nearly half of the average sampling points are due to collisions, the optimized average sampling points are reduced by 62.74%, and the effective point utilization rate is increased by 11.36%. The above two sets of experiments illustrate the path planning ability of the improved algorithm under narrow single channel. The simulation results for the single-channel map are shown in Figure 10.  
Next, by simulating the path planning in a real environment, constructing a raster map in the 2D plane--with black rectangles indicating obstacles--and comparing the path planning ability of the traditional RRT algorithm with the improved algorithm, the simulation results are shown in Figure 11. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & **Average Path** & **Average** & **Average** & **Average** & **Average** & **Average** \\  & **Path** & **Planning** & **Collision** & **Collision** & **Number of** & **Number of** & **Number of** \\  & **Length** & **Time** & **Collision** & **Spamling** & **Scampling** & **Active** \\  & & & & **Points** & **Points** & **Points** \\ \hline RRT & 49.723 & 0.765 & 334 & 738 & 44 \\ Improved algorithm & 43.021 & 0.319 & 5 & 275 & 39 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of single-channel map simulation data. Figure 10: Simulation results of the single-channel map. In this figure, the blue triangle represents the starting point, the pink triangle represents the target point, the black dashed circle represents the target point area, the four black rectangles represent obstacles, there is exactly one channel that leads to the target point area, and the red solid line represents the final path from the starting point to the target point.