# Efficient Path Planning Based on Dynamic Bridging Rapidly Exploring Random Tree
## 5 Simulation and Experimental Results
### Simulation II  
In simulation II, the simulation environment is 12 \(\times\) 10.8 m in size, with three rectangular obstacles of 4.8 \(\times\) 1.2 \(\times\) 2 m and five circular obstacles with a diameter of 0.5 m. The robot and other environmental parameters are the same as in simulation I. Five smaller obstacles were strategically placed to surround the robot in a dense environment. The robot's task was to move to the bottom right corner of the image while avoiding these obstacles. To better simulate obstacles that may suddenly appear in the real environment, these hindrances were intentionally excluded from grid maps constructed using SLAM technology.  
Figure 11 shows a path planning process using the DBR-RRT algorithm. This design makes the robot unaware of these obstacles at the beginning of the initial navigation task. However, when the robot approaches these obstacles, its internal LiDAR can effectively detect them and successfully use our algorithm to plan new paths to avoid these obstacles. Real-time robot planning trajectories were acquired and visualized by subscribing to pertinent topics, offering a clear perspective of the robot's current state. In this experiment, the target point was set in the lower right corner. In this case, the robot had to detour around five \"suddenly appearing\" obstacles. By incorporating such challenges, the robot was predisposed to encounter obstacles early on, positioning itself in potentially hazardous zones surrounded by impediments. This setting allows us to visually observe and compare the robustness and planning efficiency of the two algorithms.  
RBG color mapping was employed to vividly convey the robot's speed information on its travel path. As shown in Figure 12b, the proposed algorithm enabled the robot to have a faster average speed compared to the RT-Connect algorithm, and the speed could be smoothly transitioned during the overall path planning process. In Figure 12a, there are meanders in the robot path and there are multiple instances of sudden velocity mutations. The traditional RRT-Connect algorithm exhibits serious problems when dealing with local optimal solutions, causing the robot to fall into a state of spinning in place. In this case, the  
Figure 11: One experiment of DBR-RRT algorithm for path planning.  
robot's speed exhibits an extremely unstable acceleration and deceleration process, even approaching zero. Therefore, the repeated rotation of the robot resulted in a significant increase in the overall path planning time.  
Figure 13 shows a comparison of the trajectories generated by the two algorithms. The robot using the RRT-Connect algorithm for path planning had three detours in the trajectory from (1.7, 1.3) to (3.5, 1.0), and there was a large slewing behavior at (3.5, 1.0), which greatly increased the path length. For unknown obstacles in a known environment, traditional algorithms perform inefficient mass collision detection and inefficiently generate paths in real time. In contrast, the algorithm proposed in this paper will first perform a Bridging Test for obstacles, select the points surrounded by obstacles, and generate a virtual node set in the iterative process to quickly guide the robot away from the dangerous area surrounded by obstacles.  
Figure 12: Trajectory velocity curves of two algorithms: (**a**) RRT\(-\)Connect and (**b**) DBR\(-\)RRT.  
Figure 13: Comparison of trajectories of the two algorithms.  
Therefore, the algorithm proposed in this paper performs better in this trap environment and can quickly plan a new path when a sudden obstacle is detected. In addition, the overall planning process maintains a stable speed, allowing for stable acceleration and deceleration even during unavoidable steering processes. As shown in Figures 12 and 13, the robot's movement trajectory is a smooth curve that remains stable after turning, and the final trajectory approaches a straight line.