# RJ-RRT: Improved RRT for Path Planning in Narrow Passages
## 1 Introduction
In [17], the authors propose a Voronoi bias-based planner and improve the sampling strategy according to the visibility of the regions by nodes in the tree. In [18], the authors regress the sampling points located on the obstacle so that the tree can expand around the edge of the obstacle, thus ensuring the exploration inside the passages. In [19], the author reduces the total number of samples by rejecting nodes located in the repeated sampling area and proposes a random steer strategy for the narrow passage area, as well as the fusion and adjustment of the path to make the path close to the optimal path. In [20], the authors use a simple heuristic to generate additional subtrees in the configuration space and control the expansion of the subtrees through parameters. In [21], a modified bridge test is used to identify narrow passages and relies on multiple subtrees to explore narrow passages. In [22], the author balances the exploration of global and local random trees through Markov chains. In [23], the authors use PRM globally and rely on special sampling points to activate RRT and use RRT to explore the complex environment. Based on this idea, RRT can be combined with various variants of PRM. In particular, with the development of machine learning methods in recent years, learning-based path-planning methods have been extensively developed. In [24], for dynamically changing environments, the authors build a predictive model using Support Vector Machine (SVM) to capture the connectivity of narrow passages. In [25], the authors learn by analyzing the density of samples around special regions, using semantic information to guide the distribution of sampling points in random sampling. In [26], the authors model the expansion of random trees as a multi-armed bandit problem and learn action values through reinforcement learning. In [27], the author uses a large number of asymptotically optimal paths planned by A* as a dataset to train convolutional neural network (CNN) model, which can predict the optimal path on the map and guide the distribution of sampling points. In [28], the authors perform local sampling around the sampling point that are difficult to expand, and by performing principal component analysis (PCA) on these local sampling points, the local surrounding environment is divided into narrow passage entrances, narrow passage interiors, and obstacle edges, so random trees can climb obstacles in different environments like vines to expand. This method has achieved good results in the environment with narrow passages. However, due to its dependence on the environment, the performance is slightly worse than RRT in an environment with many obstacles but no narrow passages. In addition, when solving the problem of narrow passages, the above methods mostly ignore the randomness of whole configuration space sampling, which often leads to part of sampling points in space that are not helpful for the final path construction so that increasing the total planning time and wasting memory resources. This paper proposes a new planning algorithm based on the RRT named Reduce-Judge RRT (RJ-RRT). Specifically, the new algorithm includes two improvements: firstly, based on the greedy idea, a sampling strategy is proposed to reduce the sampling space to the goal area gradually. Secondly, a new method of environment judgment is proposed, when a narrow passage is identified, it can be explored by subtrees expansion inside the passages. The improved environment judgment method only needs a straightforward calculation to determine the environment around the current sampling point. Both strategies improve planning efficiency. On the one hand, random sampling points are used to reduce the sampling space to avoid random tree expansion in space that does not help with path planning. On the other hand, random sampling points are used to detect the surrounding environment, and the subtree of narrow passages helps the random tree expand in the configuration space that is difficult to explore.