## 3 Four-Dimensional Dynamic Cooperative Path Planning Algorithm
### Dynamic Priority RRT* Algorithm
In the simulation, an improved repulsive force function was added to solve the problem of the unreachability of the target. The traditional artificial potential field was compared with HAPF in the path collision avoidance planning of obstacles near the target. In order to verify the effectiveness of the algorithm and ensure the optimal performance of the traditional algorithm, the traditional algorithm was simulated using the best parameters. At the same time, in order to intuitively show the superiority of the improved potential field function, this simulation used the radar threat as the environment model for verification. The potential field parameters of the HAPF algorithm are \(k_{att}\)= 8, \(k_{rep}\)= 30, \(\rho_{o}=2\) km, \(l=0.2\) km, and \(n=0.7\). According to the simulation data, the generation node of the repulsion potential field corresponding to the last path node is [7.1654, 9.9636, 1.9927] km. The relative distance between this node and the target node is 1.0541 km, which is less than the obstacle influence distance, so obstacle threat near the target node is extant. Figure 18 shows the comparison between the two algorithms. It can be seen in Figure 18 that HAPF reaches the target node, while the traditional potential field method has the problem of target unreachability. The relative distances between different path nodes and target nodes of UAVs in the two algorithms are recorded separately. It can be seen that when there is an obstacle threat near the target, the traditional artificial potential field method oscillates near the target node and cannot reach the target node. The improved potential field method is able to reach the target node, which shows that the improved algorithm can solve the problem of the unreachable target. Figure 6:1 Comparison results of the cooperative path planning layers under different scenarios. Regarding the problem of the traditional artificial potential field method easily falling into the local minimum, this paper proposes a strategy to set heuristic target nodes in order to escape the local minimum. In the simulation, HAPF is compared with the traditional artificial potential field method. The potential field parameters are set as \(k_{att}=8\), \(k_{rep}=20\), \(n=0.7\), \(\rho_{o}=2\) km, and \(l=0.2\) km in the simulation. The starting node of the UAV is [0,0,0] km, and the goal is [22,22,5] km. In order to fully verify the effectiveness of the algorithm, five combined obstacles with different obstacle threats are established in the simulation, and the five obstacles constitute the local minimum area. Figure 19a shows the traditional artificial potential field method and Figure 19b shows the HAPF algorithm. It can be seen in Figure 19a that when the UAV reaches the path node [13.9930, 14.5990, 4.7578] km, it falls into the local minimum value and oscillates back and forth near it, unable to escape it. In Figure 19b after the UAV has been trapped in the local minimum area, it successfully escapes and finally flies to the target node due to the guidance of heuristic sub-target nodes. The virtual spherical radius of the selected sub-target node is 3.1370 km, and the heuristic sub-target node coordinates are [13.1161, 17.5908, 4.9435] km. According to Figure 19 and the simulation data, after adding heuristic sub-target nodes, the UAV is able to escape the local minimum region, which solves the problem of the traditional potential field model easily falling into the local minimum. In this paper, regarding the problem of the improved potential field easily generating local path vibrations when avoiding obstacles and planning trajectory collision avoidance, a memory resultant force strategy was proposed to improve this problem. In the simulation, by comparing the traditional artificial method with the potential field method, the effect of

Figure 6:2 A comparison of escaping from local minima. (**a**) Classical APF. (**b**) HAPF. Figure 6:3 A comparison of solving the problem of target unreachability. (**a**) Is the complete view.