## 3 Simulation  
### Simulation Environment  
To evaluate the effectiveness of the improved algorithm, a simulation experiment was conducted using the Gazebo simulation environment. In this experiment, dynamic obstacles, representing personnel vehicles, were simplified, while static obstacles included goods and other items. Multiple path planning algorithms were tested to assess their efficiency and the quality of their path planning in various environments. The simulation experiment employed the following hardware configuration: CPU with a frequency of 2.9 GHz and a dynamic acceleration frequency of 4.2 GHz, 16 GB of memory, GPU with a default frequency of 1365 MHz, and a maximum Boost frequency of 1680 MHz. The software platform consisted of the Ubuntu 18.04 operating system, Visual Studio Code development environment, Python and C++ programming languages, Robot Operating System (ROS) Melodic, Gazebo simulation platform, TensorFlow 1.12.0 deep learning framework, CUDA 9.0, cuDNN, and the OpenCV 3.1.0.0 computer vision library, among others.  
To fully verify the algorithm, obstacle-free environments, wide obstacle environments, and complex dynamic environments were built separately, as shown in Figure 4a-c.  
In all environments, the dimensions of the vehicle are 0.42 m in length, 0.31 m in width, and 0.184 m in height. Specifically, the obstacle-free environment has a size of 20 m \(\times\) 20 m, and, at the beginning of each round, the starting position of the autonomous vehicle is randomly determined, as is the target position. The obstacle environment consists of an infinitely large map with a 20 m \(\times\) 20 m obstacle area. It includes five static squares with dimensions of 1 m \(\times\) 1 m \(\times\) 1 m as obstacles, along with ten dynamic squares representing people, vehicles, and other moving obstacles in an open environment. The size of static squares is 1 m \(\times\) 1 m \(\times\) 1 m. The complex dynamic environment is 15 m \(\times\) 15 m in size, with three square cubes with wheels of 1 m \(\times\) 1 m \(\times\) 1 m as dynamic obstacles, and two static obstacles with a length of 0.54 m, a width of 0.31 m, and a height of 0.019 m. Black and wooden squares are simulation models of dynamic obstacles and static obstacles, respectively. The simulation also includes blue dots representing the autonomous vehicle, green dots representing the target points (transparent non-obstacles), red paths representing the driving paths of the autonomous vehicle, and blue, green, and yellow paths representing the driving paths of dynamic obstacles. At the start of each round, the starting position of the static obstacle is randomly determined, whereas the dynamic obstacle has a fixed starting point but follows a random walking path. The maximum linear speed of the dynamic obstacles is 0.5 m/s. In traditional algorithms, the maximum linear speed of the autonomous vehicle is set to 1 m/s, and the angular speed is 0.5 rad/s. The experiment utilizes Jackal autonomous vehicles for path planning, which are equipped with a single-line lidar, a binocular camera, an odometer, and two drive wheels. The point cloud information dimension of the single-line lidar is 360\({}^{\circ}\), and its detection distance is between 0.1 m and 3.5 m. The binocular camera captures RGB image information with a resolution of 768 \(\times\) 1024 \(\times\) 3.  
Figure 4: Simulation experiment environment. (**a**) Non-obstruction environment; (**b**) obstruction environment; (**c**) complex dynamic environment.