## 4 Simulation Results  
### Path Planning for 2-D Formation Rendezvous  
When all are UAVs flying at the same and constant altitude, the problem is simplified to the 2-D formation rendezvous and there is no need to consider the terrain, namely \(J_{i,\text{terr}}\equiv 0\). Only two obstacles and two no-fly zones exist in the environment, which are modeled as circles and rectangles. The initial poses of UAVs and the formation pose are given in Table 1 and the desired formation configuration is given in Table 2. The safety radius and maximum curvature of all UAVs are 0.1 km and \(\kappa_{\text{max}}=2\text{km}^{-1}\). Other parameters of the DCPSO are as follows: \(M=20\),\(T=50\),\(w_{1}=0.5\), and \(N_{\text{p}}=N_{\text{ph}}=50\). The results are depicted in Figures 4 and 5. In Figure 4, the paths of UAVs for formation rendezvous are given, which are generated by the DCPSO without cooperation, the DCPSO with cooperation, and the conventional CCGA, respectively. The curvature variations with respect to path length of all three UAVs are given in Figure 5. In Figure 4, \"\(\blacksquare\)\" denotes the initial location of UAV, \"\(\bullet\)\" is the formation rendezvous point, and \"\(\circ\)\" shows the desired formation configuration at the rendezvous point. The lengths of the three paths and their minimum separation distances with the different algorithms are given in Table 3.  
From Figures 4a and 5a, all three paths generated by DCPSO without cooperation between UAVs avoid the obstacles and no-fly zones in the environment and the curvature changes continuously while meeting the maximum-curvature constraint. However, from Table 3 we can see that the lengths differ significantly because of no cooperation between UAVs. Thus, UAVs cannot arrive at the rendezvous point simultaneously while flying at the same constant speed and the desired configuration cannot be achieved. For DCPSO with cooperation proposed in this paper, as shown in Figures 4b and 5b, the generated paths can also satisfy the safety requirements and the kinematic constraints of UAVs. Furthermore, the lengths of the three paths are almost the same from Table 3, with a maximum difference of 0.0028 km and no collision occurs between UAVs. This means the UAVs can achieve simultaneous arrival and form the desired configuration at the rendezvous point. On the contrary, paths generated by the conventional CCGA can almost achieve simultaneous arrival collision-free between UAVs, as well as satisfying the safety requirements and the kinematic constraints of UAVs, as shown in Figure 4c, Figure 5c, and Table 3. The maximum difference of lengths is about 0.1 km, which cannot be ignored and needs to be diminished by slightly increasing the parameters \((m_{0},\quad m_{1})\) of paths with the smaller lengths. On the other hand, the largest length is about 0.55 km larger than that produced by DCPSO with cooperation, which means the conventional CCGA has trapped the local optimum. To analyze the performance comparison between the conventional CCGA and the DCPSO proposed in this paper, 30 experiments in the same environment for both algorithms are conducted. The statistical results of these experiments are given in Table 4. Assume that, if the maximum difference of lengths in an experiment is larger than 0.35 km (about 1% of the path length), this corresponding experiment is considered to have failed. According to Table 4, the success rate of the proposed DCPSO is up to 0.9, while the CCGA only has a value of 0.433. Taking only the successful experiments into consideration, the mean length and standard deviation of each path are given in Table 4. With the proposed DCPSO, the maximum mean length is 35.0611 km and the mean maximum difference of lengths is about 0.0301 km, while the values are 35.2982 km and 0.1515 km with CCGA. This means by using the conventional CCGA, it is easier to trap the local optimum.