## 2 BIT* Algorithm Procedure
### Algorithm Steps
The TD3 algorithm, grounded in the Actor-Critic framework, dynamically adjusts and optimizes the initial path by refining its policy and value networks. Specifically, TD3 employs a comprehensive reward function designed to minimize turning angles within the path, smooth speed transitions, and shorten the overall path length, ultimately generating a trajectory that is smoother, shorter, and more conducive to USV execution. Path Planning Problem and Environmental Setup for Unmanned Surface Vehicles in Hybrid Intelligent Systems Based on the A*+DKN Deep Reinforcement Learning Algorithm  
This research introduces a hybrid strategy integrating TD3 and BIT* to plan the shortest path for Unmanned Surface Vehicles (USVs) while ensuring the most time-efficient navigation. Through an end-to-end approach, reward design, and deep learning, the model can learn environmental features, output navigation strategies, avoid obstacles, and achieve efficient path planning. The BIT* algorithm serves as pre-processing and an initialization step for TD3, generating initial paths in static environments to provide TD3 with a reference trajectory and state information, thus expediting its learning process. TD3 then dynamically adjusts and optimizes the path provided by BIT*. In the environment setup phase, this research utilizes a grid-based method to construct a map model. The grid method divides the entire map environment into grid cells, with the dimensions of the Unmanned Surface Vehicle (USV) serving as the unit. Free space is recorded as 0, and obstacles are marked as 1. Figure 1 is a rasterized training map. As depicted in Figure 1, the map dimensions are 300 \(\times\) 300 pixels. White areas denote navigable regions devoid of obstacles, while black areas represent obstacle regions. We assign a value of 1 to black areas, representing  
obstacles, and a value of 0 to white areas, representing navigable space. The rasterized map used in this study (as shown in Figure 1) was generated by a random algorithm. Specifically, we first created a blank 300 \(\times\) 300 pixel image and then used Python 3.9's PIL library and random library to randomly place 3000 black squares of 2 \(\times\) 2 pixels in size on the image as obstacles. To prevent the obstacles from overlapping, we used a set called occupied to record the areas that have been occupied by obstacles. The upper-left corner coordinates of the obstacles are randomly generated within the image range. If the generated area overlaps with existing obstacles, it is regenerated until an unoccupied area is found. This method of randomly generating obstacles simulates the randomness and uncertainty of the distribution of obstacles. To verify the performance of the algorithm on different maps, we used the above method to generate multiple random maps with different obstacle distributions and conducted tests. The experimental results show that the proposed BIT*+TD3 hybrid algorithm exhibits good path planning performance on these random maps, and the indicators such as success rate, path length, and computation time have good consistency between different maps. This shows that the algorithm has strong robustness to the randomness of the map and can adapt to environments with different obstacle distributions. Nevertheless, it should be noted that the density and size of obstacles may affect the performance of the algorithm. In the case of extremely high obstacle density or excessively large obstacle size, the algorithm may take longer to find a feasible path or even fail to find a feasible path. Therefore, the results of this study are mainly applicable to the case where the obstacle density is moderate and the size is small. We define the following two-dimensional vector mathematical model:  
\[\mathrm{f}(x,y)= \begin{cases}0,&\text{if no obstacle exists}\\ 1,&\text{if an obstacle exists'}\end{cases}  \tag{3}\]  
where \(x\) represents the abscissa corresponding to the center of the grid cell, and \(y\) represents the ordinate corresponding to the center of the grid cell.