# Efficient Path Planning Based on Dynamic Bridging Rapidly Exploring Random Tree
## 2 Related Work  
To address these challenges, researchers have gradually introduced more sophisticated strategies. In [23], [PERSON] et al. employed the strategy of the directed expansion of new nodes, making the algorithm more efficient, combined with curvature constraints for path smoothing. However, this method's drawback is the excessive path search time. Other researchers also offered their solutions. Based on the RRT method, in [24], [PERSON] et al. introduced a rewire process and path cost function to improve the nodes in the existing search tree and their connections. This adjustment made RRT achieve an asymptotically optimal performance, but the process of finding the optimal path can greatly increase the time required for path planning. [PERSON] et al. proposed the improved algorithm Informed-RRT* in [25], which utilizes an elliptical heuristic search for optimal sampling. This approach addresses the strong randomness inherent in the traditional RRT algorithm. However, it tends to encounter local extremum issues in complex scenarios. Subsequently,in [26], [PERSON] et al. introduced Bi-RRT*, which constrains the sampling range and employs dual trees between the start and goal points to communicate information, thereby further enhancing the overall convergence speed, but this method still suffers from the problems of a low success rate for path planning under small samples, and the planning efficiency still needs to be improved under large samples. In [27], [PERSON] effectively reduces the number of mobility simulations required for path planning by combining the RRT algorithm with adaptive surrogate modeling. Using the surrogate model to guide the exploration of random trees under mobility reliability constraints, and then employing these exploration trees and reliability assessments to refine the surrogate model. However, a high dependence on the accuracy of the agent model can generate problems such as, for example, insufficient preparation of the initial agent model or the inability to update it efficiently during the exploration process. [PERSON] et al. proposed RRT*-Smart in [28], which, after generating the initial path, improves RRT*'s convergence speed by removing redundant nodes and optimizing sampling. In [29], [PERSON] proposed a novel algorithm based on bidirectional Rapidly Exploring Random Trees and direct connection. Initially, an expansion strategy based on artificial potential fields was designed in the joint space, which was then integrated with the GB-RRT algorithm. Additionally, a direct connection strategy was developed to enhance the efficiency of expansion, ensuring larger safety margins between the obstacles and the system. In specific environments such as narrow spaces or areas with dense obstacles issues like difficulty in node expansion and generation of convoluted paths arise. [PERSON] proposed the Ellipsoidal Rapidly exploring Random Tree (E-RRT*) in [30]. This approach replaces line segments with ellipsoids to connect adjacent nodes and introduces a slow informed guidance method to optimize the sampling process, effectively addressing path planning challenges in confined spaces. In [31], [PERSON] made distinct optimizations to the sampling and proposed a flow-based VF-RRT* algorithm. This method quantifies the process of feasible path countercurrent using a parameter called the up-flow coefficient, constructs a heuristic space based on the flow function, and adaptively rejects sampling nodes outside the flow value range with an adjustable probability. Another noteworthy method is the Fast-Marching Tree (FMT*) method [32], which combines probabilistic roadmap and RRT approaches by using a set + of sample points for tree expansion. However, the FMT method has the particular issue of redundant exploration, which leads to a decline in its path-searching performance. To solve this problem, [PERSON] et al. proposed a direction-selective heuristic function that can evaluate the cost gradient of the samples, adjust the ordering of samples, and guide the expansion of FMT.