## 3 Four-Dimensional Dynamic Cooperative Path Planning Algorithm
### Dynamic Priority RRT* Algorithm
(**b**) Is the enlarged view of the goal region. resultant force memory on improving the local vibration is verified. In the simulation, the potential field simulation parameters are set as \(k_{att}=8\), \(k_{rep}=20\), \(n=0.7\), \(\rho_{o}=2\) km, and \(l=0.2\) km. In the HAPF algorithm with a memory factor, the value of the memory factor is set to \(\lambda_{1}=0.7\) and \(\lambda_{2}=0.3\). Figure 20 simulates the flight path of the two algorithms. It can be seen in Figure 20 that the UAV flight path was significantly improved after adding the memory resultant force without the local path oscillation. It can also be seen in Figure 20 that after adding the memory resultant force, the variations of resultant force angle between adjacent path nodes of the UAV become significantly smaller and there is no significant angle oscillation. This shows that the introduction of this strategy satisfies the flight constraints of UAVs, does not cause large angle changes between adjacent path nodes, makes the flight path smoother, and is suitable for the collision avoidance trajectory planning of UAVs. ## 5 Conclusions and Future Work

In this paper, a 4D dynamic cooperative path planning algorithm is proposed to solve the cooperative path planning problem under the 4D cooperative constraints of multiple UAVs. Each UAV shares the same arrival time. There is no conflict between them and they are able to successfully implement threat avoidance. The algorithm proposed in this paper adopts a hierarchical architecture; namely, a 4D cooperative path planning layer and a local anti-collision planning layer. First, the DPRRT* algorithm was used to complete the 4D cooperative preplanning based on the initially known environment before UAV flights. Later, if a UAV encounters sudden threats while in flight, the HAPF algorithm of the local anti-collision planning layer is used to avoid these sudden threats. Simultaneously, UAVs not affected by sudden threats continue to fly along their planned paths. It should be noted that the 4D cooperation constraint cannot be satisfied after the sudden threat avoidance. Therefore, after the sudden threat avoidance has been completed, the DPRRT* algorithm in the 4D cooperative path planning layer is used to replan the 4D cooperative path. Whenever a new threat appears, local obstacle avoidance planning and 4D coordinated path replanning of the threat are required until all UAVs reach the target at the same time. The simulation and comparison experiments show that the proposed algorithm is able to plan a cooperative path, thus satisfying the 4D cooperative constraints for UAVs, and the algorithm has high efficiency, stability, and robustness. In future work, we plan to extend the proposed algorithm to other application levels; that is, we aim to use multiple UAVs for the actual experimental verification of the proposed algorithm. In addition, considering that the swarm intelligence cooperation composed of a large number of UAVs may be a hot topic in the near future, we plan to improve the

Figure 6:4 A comparison of local shocks. (**a**) Is the complete view. (**b**) Is the enlarged view of the goal region. algorithm proposed in this paper and explore a 4D cooperative planning algorithm that can be synchronized, so that the algorithm is able to achieve efficient and robust cooperative path planning for 50 or even 100 UAVs. Conceptualization, Y.G. and X.L. ; methodology, Y.G. ; software, Y.G. ; validation, Y.G. ; formal analysis, Y.G. ; investigation, Y.G. and W.J. ; resources, Y.G. and X.L. ; data curation, Y.G. and W.J. ; writing--original draft preparation, Y.G. ; writing--review and editing, Y.G. ; visualization, Y.G. ; supervision, Y.G., X.L., W.J. and W.Z. ; project administration, X.L. and W.Z. ; funding acquisition, X.L. and W.Z. All authors have read and agreed to the published version of the manuscript. This research work was funded by the National Natural Science Foundation of China, grant No. 62073266, and the Aeronautical Science Foundation of China, grant No. 201905053003. Not applicable.