**2. Related Work**

The RRT algorithm has been widely used in the field of robot motion and path planning. However, the paths obtained are not optimal, mainly because of several aspects such as path planning time, the number of points, and the path length. To solve these shortcomings, many improved algorithms based on the RRT algorithm have been proposed to promote the path-planning efficiency. LaValle and Kuffner proposed a bidirectional extended random tree algorithm [14] that generated two random trees from the starting point and the target point simultaneously, expanding them in space separately. This algorithm used a greedy strategy to reduce the number of iterations in the path generation process. Sertac and Emilio proposed an asymptotically optimal RRT\* algorithm (an improved algorithm for progressively optimizing path length by reselecting parent point) [15], which changed the selection of the parent point and used a cost function to select the point with the smallest cost in the neighborhood of the extended point as the parent point, thus reducing the cost of path generation and improving the search efficiency. Jordan et al. borrowed the RRT-Connect (bidirectional extended random tree) algorithm idea and proposed a bidirectional extended RRT\* algorithm, namely B-RRT\* (bidirectional version of RRT\*) algorithm [16]. Wang Kun et al. proposed a two-way extended RRT\* algorithm for heuristic search, which reduced the number of iterations to a certain extent [17]. Jordan proposed the B-RRT\* algorithm [18], which used the strategy of reselecting the parent point and rewiring two trees to speed up the algorithm convergence. Qureshi et al. added the heuristic strategy to the B-RRT\* algorithm and proposed the IB-RRT\* (Intelligent

bidirectional-RRT\*) algorithm [16]. Qureshi et al. combined the artificial potential field method with the RRT\* algorithm to improve the convergence speed of the algorithm [19]. Barfoot proposed the Inform-RRT\* algorithm [20] to narrow the search range and speed up the convergence of the algorithm on the basis of obtaining feasible paths. Mashayekhi et al. proposed the Informed-RRT\*-Connect algorithm [21], which used a bidirectional tree to quickly find the initial path before using a subset of heuristics to directly sample to accelerate convergence, and the heuristic algorithm performed better in the improved RRT\*-Connect algorithm. While the RRT\* algorithm and its improved algorithm helped to reduce the path length, their planning times were several times longer than that of the RRT algorithm. Although the RRT-Connect algorithm and its improved algorithm had a slight reduction in the number of redundant points and planning time, the optimization effect was not significant and the path length was much longer than that of the RRT algorithm.

The above improvement algorithms have different advantages. In this paper, we focused on both the path planning time and the number of redundant points. Two different improved strategies for each of the two aspects combined are proposed.

#### **3. Methods**

#### *3.1. The Rapidly-Exploring Random Tree Algorithm (RRT)*

The rapidly-exploring random tree algorithm is a probability-complete global path planning algorithm that obtains path points by random sampling in the search space and then achieving a feasible path from the start point to the goal point. The specific process is shown in Algorithm 1.

#### **Algorithm 1.** RRT algorithm.


The random tree expansion diagram for the RRT algorithm is shown in Figure 1. The RRT algorithm generates new points by random sampling in the workspace. In the random tree expansion process, searching *Pparent* requires traversing the entire random tree, a process that takes a lot of time when the random tree grows relatively large, which in turn leads to a slow path-planning speed of the algorithm. The sampling method of the RRT algorithm is highly random, which results in a large number of redundant points. For these problems, two improved strategies are proposed in this paper.

**Figure 1.** Random tree expansion diagram for the RRT algorithm. The red circle indicates the starting point and the green circle indicates the target point. Black circle indicates the path point, black solid line indicates the path, and black dashed line with arrow indicates the current expansion direction of the random tree. *Prand* denotes the randomly sampled point, *Pparent* denotes the parent point, and *Pnew* denotes the new point.
