*Article* **An Improved Rapidly-Exploring Random Trees Algorithm Combining Parent Point Priority Determination Strategy and Real-Time Optimization Strategy for Path Planning**

**Lijing Tian, Zhizhuo Zhang, Change Zheng \*, Ye Tian, Yuchen Zhao, Zhongyu Wang and Yihan Qin**

School of Technology, Beijing Forestry University, Beijing 100083, China; T7190221@bjfu.edu.cn (L.T.); zhangzhizhuo@bjfu.edu.cn (Z.Z.); tytoemail@bjfu.edu.cn (Y.T.); zhaoyuchen@bjfu.edu.cn (Y.Z.); wangzhongyu@bjfu.edu.cn (Z.W.); linxinyi031@bjfu.edu.cn (Y.Q.)

**\*** Correspondence: zhengchange@bjfu.edu.cn

**Abstract:** In order to solve the problems of long path planning time and large number of redundant points in the rapidly-exploring random trees algorithm, this paper proposed an improved algorithm based on the parent point priority determination strategy and the real-time optimization strategy to optimize the rapidly-exploring random trees algorithm. First, in order to shorten the path-planning time, the parent point is determined before generating a new point, which eliminates the complicated process of traversing the random tree to search the parent point when generating a new point. Second, a real-time optimization strategy is combined, whose core idea is to compare the distance of a new point, its parent point, and two ancestor points to the target point when a new point is generated, choosing the new point that is helpful for the growth of the random tree to reduce the number of redundant points. Simulation results of 3-dimensional path planning showed that the success rate of the proposed algorithm, which combines the strategy of parent point priority determination and the strategy of real-time optimization, was close to 100%. Compared with the rapidly-exploring random trees algorithm, the number of points was reduced by more than 93.25%, the path planning time was reduced by more than 91.49%, and the path length was reduced by more than 7.88%. The IRB1410 manipulator was used to build a test platform in a laboratory environment. The path obtained by the proposed algorithm enables the manipulator to safely avoid obstacles to reach the target point. The conclusion can be made that the proposed strategy has a better performance on optimizing the success rate, the number of points, the planning time, and the path length.

**Keywords:** rapidly-exploring random trees; manipulator; priority determination; real-time optimization; path planning

### **1. Introduction**

Whether for mobile robots such as AGV (automated guided vehicle) carts working in automated workshops, or robotic arms such as agricultural manipulators in the field, the core of automation for autonomous robots is path planning. Path planning is the process of finding an obstacle-free path from an initial position to a target position in a known or partially known environment [1].

Path planning is one of the most important research focuses of robots. Chinthaka Premachandra et al. completed the robot's path planning in an indoor environment by a self-localization method through baseboard recognition and image processing [2]. Wenzhou Chen et al. used distributed sonar sensors to calculate the distance between the receiver and the generator in real time to control the moving path of the robot [3]. Chinthaka Premachandra et al. proposed a hybrid aerial-terrestrial robot system to help UAVs avoid obstacles during the movement [4]. Path planning algorithms can usually be divided into three types. The first type is the bionic-based path planning algorithm [5], of which the ant colony algorithm is a common one and has the advantages of robustness and

**Citation:** Tian, L.; Zhang, Z.; Zheng, C.; Tian, Y.; Zhao, Y.; Wang, Z.; Qin, Y. An Improved Rapidly-Exploring Random Trees Algorithm Combining Parent Point Priority Determination Strategy and Real-Time Optimization Strategy for Path Planning. *Sensors* **2021**, *21*, 6907. https://doi.org/ 10.3390/s21206907

Academic Editor: Baochang Zhang

Received: 22 September 2021 Accepted: 14 October 2021 Published: 18 October 2021

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environmental adaptability, but its convergence speed is slow and very easy to fall into the local optimum. The second type is the map-based path planning algorithm, of which the A\* algorithm (Optimal A-algorithm), with the optimal surrogate and prognostic functions, is a commonly used one and has the advantages of heuristic search and the obtained path is optimal, but its planning time is long and not applicable to high-dimensional space [6]. The third type is the sampling-based path planning algorithm [7], of which the most commonly used one is the RRT (rapidly-exploring random trees) algorithm [8]. As an efficient pathplanning method in a multi-dimensional space, the RRT algorithm uses an initial point as the root point and generates a random extended tree by randomly sampling and adding leaf points. When a leaf point in the random tree contains a target point or enters a target region, a path from the initial point to the target point, consisting of tree points, can be found in the random tree. The RRT algorithm is the most popular path planning algorithm due to the rapidness, probabilistic completeness, and good scalability [9–13].

However, the RRT algorithm also has many disadvantages. Among the main disadvantages of the RRT algorithm, one is that the whole random tree needs to be traversed to search the parent point in the process of new point generation, which consumes a lot of computation time. The other is the large number of redundant points generated during the path generation process. To address the above problems, this paper proposes an improved RRT algorithm based on the PPD strategy (the strategy of parent point priority determination) to speed up the path planning, and further optimizes the efficiency of the algorithm by incorporating the RO strategy (real-time optimization) on this basis. The PPD strategy would shorten the path planning time and the RO strategy would reduce the number of redundant points. Finally, MATLAB-based three-dimensional comparison simulation experiments were conducted, and the experimental results showed that the proposed algorithm has a faster planning speed and can generate fewer redundant points, which has a better performance compared with other improved algorithms.

The rest of this paper is organized as follows. Section 2 introduces the related work and Section 3 presents the proposed RRT algorithm in three parts including the RRT algorithm, the PPD strategy, and the RO strategy. Section 4 shows the simulation results of the proposed algorithm in three-dimensional space and the experiments using IRB1410 in the laboratory. In the following, a discussion is presented in Section 5. Finally, Section 6 presents the conclusions of this paper.
