# Efficient Path Planning Based on Dynamic Bridging Rapidly Exploring Random Tree
## 5 Simulation and Experimental Results
### Real-World Experiment II  
To test the effectiveness of the proposed algorithm in path planning over long periods of time, an environment full of obstacles was designed. In this experimental site, as shown in Figure 16, four rectangular obstacles of 20 \(\times\) 20 \(\times\) 30 cm, one L-shaped obstacle consisting of two long rectangles of 100 \(\times\) 6 \(\times\) 30 cm, and two L-shaped obstacles consisting of 85 \(\times\) 6 \(\times\) 30 cm and 60 \(\times\) 6 \(\times\) 30 cm were placed. The parameters and environmental parameters set by the robot are consistent with Experiment 1. The starting point was anchored in the map's bottom right corner. To enhance the evaluation of the robot's performance in the real environment, goal commands were issued at strategic points on the map to enable the robot to navigate once in the complex environment.  
The actual mobile robot's going and returning using the two algorithms are shown in Figure 17, respectively. Given the overlap between the robot's outbound and return paths, to prevent any visual confusion within a singular image, the decision was made to separate the actual trajectories of the two path-planning methods. These are represented in two distinct images, showcased through frame extraction and overlay. An optimal selection of 80 frames was made to authentically depict the robot's movement trajectory.  
In Figure 18, the robot's movement trajectory is displayed on the Rviz visualization platform. The actual motion path of the DBR-RRT robot is represented by green lines, while the actual motion path of the RRT-Connect robot is represented by red lines.  
Figure 16: Experiment environment.  
Figure 17: One-time path planning using the RRT-Connect and DBR-RRT algorithm. (**a**) RRT-Connect to planned outbound; (**b**) RRT-Connect planned return trip; (**c**) DBR-RRT to planned outbound; (**d**) DBR-RRT planned return trip.  
Upon close examination of the red trajectory, it was discerned that a judgment error occurred at the first turn. Rather than making a left at the intersection, the robot chose to proceed straight, causing an unnecessary path extension. In addition, at the point where the robot is about to enter a turn, its trajectory shows a series of obvious twists and turns, revealing that the path planning is not smooth enough. And being too close to the obstacle in the upper right corner may cause potential safety issues.  
As can be seen in Figure 19, after mapping the robot's speed onto the trajectory for depth comparison, the traditional RRT-Connect algorithm exhibits significant speed fluctuations in multiple key areas. Particularly in areas requiring turns, a marked difference in robot speed was observed. Moreover, on sections devoid of significant turns, the speed presented unstable fluctuation characteristics. The speed parameters used in this experiment are as follows:  
Following the experimental verification, Table 2 shows that the proposed DBR-RRT shows higher efficiency than the traditional RRT-Connect algorithm. Firstly, its average completion time is 9 s faster than the traditional RRT-Connect algorithm. Secondly, the average running speed of the DBR-RRT algorithm is also higher than that of the traditional algorithms, indicating that the robot can maintain higher operating efficiency throughout the entire operation process. Finally, it is worth noting that the standard deviation of the DBR-RRT algorithm is relatively low, which means that the robot's operating speed changes are more stable and less susceptible to sudden factors, thus maintaining a good driving performance in different environments and conditions.  
Figure 19: Speed–trajectory curves of RRT\(-\)Connect and DBR\(-\)RRT. (**a**) RRT\(-\)Connect (**b**) DBR-RRT.  
Figure 18: The trajectory generated by the RRT- Connect and DBR-RRT algorithms are displayed in Rviz: (**a**) RRT-Connect. (**b**) DBR-RRT.