## 4 Experimental Validation
### Improved BIT* Algorithm with Adaptive Parameter Optimization for Optimal Path Planning
#### 4.1.2 Improved BIT* Algorithm  
This experiment aims to comprehensively evaluate the performance of the implemented BIT* algorithm. The experiments will be developed and tested using the Python programming language within the PyCharm IDE environment and simulated on a single-channel grayscale image of 300 \(\times\) 300 pixels. The BIT* algorithm is implemented based on the original study with several optimizations, primarily including employing the Euclidean distance as the heuristic function, incorporating a combination of uniform and Gaussian sampling strategies, and utilizing the KD-Tree data structure for efficient nearest neighbor search. To enhance the algorithm's efficiency, the edge rewiring process of the original BIT* algorithm is optimized to be performed only when it can significantly improve the path quality. The experiments will utilize libraries such as OpenCV, matplotlib, and numpy for image processing, graphical plotting, and numerical computations. Key algorithmic parameters, including the initial sampling radius, connection radius, and the parameter controlling the probability of Gaussian sampling, will be detailed in the subsequent experimental parameter settings section. The experiments will primarily assess the effectiveness, efficiency, path quality, and robustness of the BIT* algorithm, and performance metrics such as success rate, computation time, path length, and the number of expanded nodes will be recorded and analyzed. As depicted in Figures 5-8, after the simulation of the enhanced BIT* algorithm, the smoothness of its path is significantly improved compared to the original BIT* algorithm. To comprehensively evaluate the performance of the enhanced BIT* algorithm and validate  
Figure 4: Results of the traditional BIT* algorithm. its superiority in path planning, this research conducted comparative experiments with A*, RRT*, and the original BIT* algorithm. The comparative data in Table 1 clearly demonstrates that, in terms of optimal path length, the enhanced BIT* algorithm achieved the best result, at only 430.75, representing a reduction of approximately 6.1% in path length compared to the original BIT* algorithm's 460.23. More notably, compared to the RRT* algorithm (507.17) and the A* algorithm (600), the enhanced BIT* algorithm reduced the path length by approximately 12.1% and 25.7%, respectively, indicating a significant advantage in exploring superior paths. Regarding path smoothness, we employed two metrics, the number of turns and turning cost, for quantitative evaluation. The number of turns directly reflects the tortuosity of the path, while the turning cost, under hydrodynamic model constraints, represents the cost incurred by the vessel for turning operations during path tracking. This metric comprehensively considers both turning angle and energy consumption. The data in Table 1 shows that the enhanced BIT* algorithm has only 24 turns, significantly lower than the original BIT* algorithm's 26 turns, the RRT* algorithm's 47 turns, and the A* algorithm's 447 turns. In terms of turning cost, the enhanced BIT* algorithm exhibits an even more overwhelming advantage, at only 40.95, far lower than the original BIT* algorithm's 75.43, the RRT* algorithm's 473.62, and the A* algorithm's 8586.00. This series of data powerfully demonstrates the superior performance of the enhanced BIT* algorithm in generating smoother paths. By reducing unnecessary turns, it not only decreases the energy consumption of the Unmanned Surface Vehicle (USV) but also enhances the stability and execution efficiency of its motion (Table 2). Combining with the iterative results in Figure 5, it can be observed that the enhanced BIT* algorithm obtains the optimal path after only 19 iterations. Furthermore, at the 15 th iteration, the difference in optimal path length compared to the previous iteration is less than 0.092, indicating a very fast convergence speed of the algorithm.