# Efficient Path Planning Based on Dynamic Bridging Rapidly Exploring Random Tree
## 5 Simulation and Experimental Results
### Simulation I  
To validate the simulation experiment, a series of simulation experiments were conducted using the above-mentioned navigation architecture on the TurtuleBot3 Waffle mobile robot platform. These experiments aim to verify whether the robot can still maintain a fast path planning speed and robustness in different obstacle environments. Simulation experiments were crafted based on the Ubuntu 20.04-ROS-Neotic system, with the establishment of a densely populated obstacle environment to simulate point-to-point navigation tasks. In simulation I, the simulation environment was 13.2 \(\times\) 10.8 m in size, and two rectangular obstacles of 4.8 \(\times\) 1.2 \(\times\) 2 m and an L-shaped obstacle composed of two rectangular obstacles were placed, with dimensions of 8.4 \(\times\) 0.2 \(\times\) 2 m and 1.8 \(\times\) 0.3 \(\times\) 2 m, respectively. There were also a number of irregularly shaped obstacles in the environment. We used a TurtuleBot3 Waffle Pi robot with dimensions of 281 \(\times\) 306 \(\times\) 141 mm, \(v_{\text{max}}\) = 0.26 m/s, and \(w_{\text{max}}\) = 1.82 rad/s. The model of the laser ranging sensor used is LDS-01; the scanning range of the laser radar is set to 3.0 m, the expansion radius is set to 1.0 m, and the cost scaling factor is set to 3.0. By comparing the traditional RRT-Connect algorithm with our improved algorithm, and recording the speed curve, motion trajectory, and time consumption of the mobile robot, a deeper understanding of the convergence speed and robustness of our improved algorithm emerges. The simulation experiment platform used was Gazebo, as shown in Figure 9a,b. Figure 9 shows that the physical platform is built in Gazebo; the map was constructed by the Gmapping algorithm and visualized using Rviz to simulate a real environment with different shapes of obstacles in the scene, forming a large concave obstacle. The robot had to bypass the obstacles and move to the target location in the lower left corner. Pre-designed scripts were employed to establish and publish the target coordinates of the mobile robot, replacing the process of manually selecting the target point through the Rviz visualization tool. This ensures the consistency of the target point's position in each experiment, thereby reducing the error within the experimental results. In this experiment, our script set the target point in the lower left corner of the image. A total of 30 simulation experiments were conducted this time, and the statistical indicators used for the comparative evaluation are as follows:  
Four different global path planning algorithms are thoroughly evaluated in Simulation 1: Informed-RRT*, RRT-Connect, RRT*, and the modified DBR-RRT. To ensure the fairness and accuracy of the comparison, all algorithms were run in the same test environment, and their running times and standardized speed deviation calculations are meticulously documented in Table 1, and Figure 10 shows a detailed record of each of the four speed profiles. Figure 9: Under the L-shaped obstacle environment. (**a**) Gazebo environment in simulation I; (**b**) RVIZ environment in simulation I. In Table 1 and Figure 10, it is shown that DBR-RRT shows an improvement of 15.95% in average speed and a 27.45% improvement in speed standard deviation compared to Informed-RRT*. Compared to RRT-Connect, DBR-RRT shows a 22.73% improvement in average speed and a 13.95% improvement in speed standard deviation. In addition, DBR-RRT results in 20.38% improvement in average speed and 5.13% improvement in standard deviation compared to RRT*. These results indicate that the proposed algorithm exhibits a high consistency and low speed fluctuations over multiple runs. In addition, DBR-RRT achieves a maximum speed of 0.301 m/s, which is slightly higher than the 0.276 m/s of RRT-Connect, indicating that the proposed algorithm maintains stability without sacrificing navigation performance.