#### Article
###### Abstract  
Sampling-based methods are popular in the motion planning of robots, especially in high-dimensional spaces. Among the many such methods, the Rapidly-exploring Random Tree (RRT) algorithm has been widely used in multi-degree-of-freedom manipulators and has yielded good results. However, existing RRT planners have low exploration efficiency and slow convergence speed and have been unable to meet the requirements of the intelligence level in the Industry 4.0 mode. To solve these problems, a general autonomous path planning algorithm of Node Control (NC-RRT) is proposed in this paper based on the architecture of the RRT algorithm. Firstly, a method of gradually changing the sampling area is proposed to guide exploration, thereby effectively improving the search speed. In addition, the node control mechanism is introduced to constrain the extended nodes of the tree and thus reduce the extension of invalid nodes and extract boundary nodes (or near-boundary nodes). By changing the value of the node control factor, the random tree is prevented from falling into a so-called \"local trap\" phenomenon, and boundary nodes are selected as extended nodes. The proposed algorithm is simulated in different environments. Results reveal that the algorithm greatly reduces the invalid exploration in the configuration space and significantly improves planning efficiency. In addition, because this method can efficiently use boundary nodes, it has a stronger applicability to narrow environments compared with existing RRT algorithms and can effectively improve the success rate of exploration. R Rapidly-exploring Random Tree (RRT); manipulator; motion planning; obstacle avoidance; complex environment +
Footnote †: journal: Applied  
methods mainly seek a collision-free path from the start point to the goal point by sampling in the Configuration space (C-space). It is unnecessary to model the entire space, and the methods have a probabilistic completeness [1; 2; 3]. Therefore, sampling-based methods are widely used in the motion planning of high-dimensional spaces owing to their unique advantages. For example, the Rapidly-exploring Random Tree (RRT) [4] and Probabilistic Roadmap Method (PRM) [5; 6] are the most popular and commonly used techniques. Basic-RRT, as shown in Algorithm 1, has been widely used in many fields, including robot motion planning, as a single-query planner since it was proposed by [PERSON] et al. in 1998. A large number of algorithms derived from RRT have been proposed to solve different problems. Improvements in RRT have mainly focused on sampling strategies and their guidance for exploring areas, the selection of extension nodes, the directions and step sizes of extensions, selection of metrics, and the collision detection algorithm and local connection method, all of which have many studies available for reference [7]. These improved methods enhance the performance of Basic-RRT from various aspects, but the obtained solutions are still highly suboptimal in most cases. Therefore, various methods of pruning and smoothing [8; 9; 10; 11] have been proposed to implement path post processing. ```
1:\(T\leftarrow\text{InitTree(}q_{start}\text{)}\);
2:for\(i=1\)to n do
3:\(q_{rand}\leftarrow\text{RandomSample(}i\text{)}\);
4:\(q_{near}\leftarrow\text{NearestNeighbor(}q_{rand},T\text{)}\);
5:\(q_{new}\leftarrow\text{Extend(}q_{rand},q_{near},\epsilon\text{)}\);
6:if CollisionFree(\(q_{near},q_{new}\)) then
7: AddNewNode(\(T,q_{new}\));
8:endif
9:if Distance(\(q_{new},q_{goal}\)) \(<\rho_{min}\) then
10:return\(T\);
11:endif
12:endfor
13:return\(Failed\);
```  
**Algorithm 1** Basic-RRT algorithm. Algorithm improvement, regardless of the method, has only two purposes: to reduce the path cost and to reduce the running time of the algorithm. For the former, the typical method is RRT*, which is an optimal planning method based on RRT and proposed by [PERSON] and [PERSON] [12]. It guarantees the asymptotic optimality of the algorithm by adding two processes to Basic-RRT: \"near vertices\" and \"rewire\".