## 1 Introduction
### The Current State of Research on the BIT* Algorithm  
Path planning, as one of the core problems in robotics and automation, has consistently garnered widespread attention from researchers. Among the numerous path planning algorithms, sampling-based algorithms are highly favored due to their effectiveness in addressing motion planning problems in high-dimensional spaces and complex environments. To further enhance the performance of sampling algorithms, particularly in terms of ensuring path quality and planning efficiency, researchers are continuously exploring new methods and strategies to achieve faster and higher-quality path planning. [PERSON] et al. [3] proposed the BIT* (Batch Informed Trees) algorithm, which combines the advantages of RRT* and FMT* and optimizes the search process through heuristic methods. The algorithm gradually constructs an implicit random geometric graph (RGG) in batches and uses dynamic programming to search for the optimal path in the graph. The BIT* algorithm has shown significant computational advantages in high-dimensional spaces and can quickly find feasible solutions in complex environments and gradually optimize them to the optimal solution. [PERSON] et al. [6] proposed the RABIT* (Regionally Accelerated Batch Informed Trees) algorithm, which further extends the BIT* algorithm. RABIT* accelerates the search process by introducing a local optimizer (such as CHOMP), especially in environments with narrow passages. This algorithm can significantly improve search efficiency while maintaining asymptotic optimality, especially in high-dimensional spaces. [PERSON] et al. [7] proposed the FIT* (Flexible Informed Trees) algorithm, which further optimizes the BIT* algorithm through an adaptive batch size strategy. The FIT* algorithm dynamically adjusts the batch size according to the dimension of the configuration space and the hypervolume of the hyperellipsoid, thereby increasing the sampling density in the initial path discovery phase and reducing the sampling density in the optimization phase, improving the overall efficiency of the algorithm. Experiments show that FIT* outperforms existing algorithms in spaces from two to eight dimensions. [PERSON] et al. [8] analyzed the theoretical basis of the BIT* algorithm in another study, proving its probabilistic completeness and asymptotic optimality. By viewing the BIT* algorithm as a search over a series of implicit random geometric graphs, the authors demonstrate the efficiency of the algorithm in high-dimensional spaces and propose its potential future applications. [PERSON] [9] proposed the et-BIT* (error tolerance batch informed tree) algorithm, which is optimized for path planning in dynamic environments. et-BIT* increases the diversity of paths by generating error-tolerant points around the robot's end effector, enabling rapid avoidance of sudden obstacles in dynamic environments. Experiments show that et-BIT* exhibits good real-time performance and robustness in dynamic path planning tasks in six-dimensional space. [PERSON] and [PERSON] [10] proposed the ISBT (Informed Batch Belief Trees) algorithm, which extends the BIT* algorithm to path planning problems in uncertain environments. ISBT constructs a nominal trajectory graph and searches in the belief space to find the optimal path considering motion and control uncertainties. Experiments show that ISBT can find non-trivial path planning solutions in complex environments and is computationally more efficient than existing similar methods.