## 3 Path-Planning Design and Dynamic-Obstacle Avoidance Strategy
### Trajectory Optimization Based on the Resultant Path of 3D JPS Algorithm
#### 3.2.1 An Any-Angle Path-Planning Strategy Based on the Parent Node Transfer Law  
In the traditional JPS algorithm for path planning, the expansion direction of the current node is determined by the neighbor-pruning law. The selection of the neighbor-pruning rule, on the other hand, relies on the position relationship of the parent node with respect to the current node. In general, the final path result set generated by the JPS algorithm contains a chain of parent-child node relationships. After the JPS algorithm completes the search, it is also necessary to infer the final path based on the chain of parent-child node relationships. The parent-child node relationship chains obtained by the JPS algorithm and the A* algorithm are different. The relational chain of the A* algorithm is complete, and it completely covers every grid node in the result path searched by the A* algorithm. As for the JPS algorithm, it is obvious that the chain of relations consists of jump points and the redundant nodes between every two jump points are removed, as shown in Figure 10.  
From the complete chain of relations, it can be found that the parent of any node \(x\) can only be a visible neighbor node of \(x\), as shown by \(parent(x)_{old}\) in Figure 10. The JPS algorithm, however, breaks this rule. It can be seen that the parent node in the parent-child node relationship chain obtained by the JPS algorithm is not a neighbor of the parent node, but has direct visibility between the two nodes, that is, the line of sight (LOS) has direct accessibility [17]. When two nodes have a parent-child relationship, the redundant nodes in their middle can be deleted, as is the case with the 3D JPS algorithm. Therefore, in this  
Figure 10: JPS algorithm parent–child node relationship chain. Figure 9: Trajectory optimization framework. paper, the way of passing the parent node to the forward node in the parent-child node relationship chain is called the parent-node-passing law, and it is further improved and expanded on this basis. The JPS algorithm and the 3D JPS algorithm still have a gap between the obtained paths compared to the shortest paths in the actual space. The fundamental reason for this is the limitation of the search direction, as shown in Figure 11.  
As we can see in Figure 11, there are still redundant steering points in the set of nodes for both JPS algorithms resulting in paths that are not the shortest. Therefore, how to delete these redundant nodes becomes the key to path optimization. The core of the parent-passing rule is that if there is LOS reachability between two nodes, all nodes between these two nodes are considered redundant, and any unnecessary path transitions caused by them can be replaced by the direct connection of the two nodes. It would be unwise to use the strategy of combining every two nodes to verify the LOS reachability in the parent-node-passing rule. As the number of path nodes grows, the number of such verifications will increase significantly to affect the overall computational efficiency of the algorithm. For this reason, an inert strategy is used in this paper in the specific implementation of the parent-node-passing law. By default, all nodes have LOS reachability with the parent node of the current detection point, and LOS authenticity is considered when a specific verification of a node in the path is needed. The specific way of the parent-node-passing law used in this paper is as follows. 1. First of all, the path nodes of the 3D JPS algorithm are complemented so that each raster through which the path of the 3D JPS algorithm passes is included in the set of nodes. Let the set of nodes be \(pathlist=\textlessdot x_{end},x_{n},x_{n-1},\ldots,x_{i},\ldots,x_{1},x_{start}\textgreater\). 2. Set the parent node of all nodes in the node collection to be the initial node. That is, all nodes have direct visibility with the initial node by default. 3.