**5. Experimental Results and Discussion**

The performance comparison of the path planning and tracking control strategy is presented in this section. Firstly, the path planning performance of the quadcopter is examined on three different maps. Generating the shortest and safest path of quadcopter on all three maps is performed with the PSO, GWO, and hybrid HHO–GWO algorithms. The quadcopter at origin point (0, 0, 0) rises by 15 m along the *Z*-axis in all 3 maps. Afterwards, the payload holds the path from the first to the fifth waypoints, and the payload release path from the fifth to ninth waypoints are generated by metaheuristic optimization algorithms such as PSO, GWO, and hybrid HHO–GWO. The mass of payload is 1 kg. Therefore, the total mass of quadcopter has been changed from 3 kg to 4 kg in all missions. The root mean squared error (*RMSE*) performance criterion in path planning and tracking is denoted as:

$$RMSE = \frac{1}{N\_m} \sum\_{i=1}^{N\_m} \sqrt{(Xref\_i - X\_i)^2 + (Yref\_i - Y\_i)^2 + (Zref\_i - Z\_i)^2} \tag{52}$$

where *Xrefi*, *Yrefi*, and *Zrefi* are reference positions of the quadcopter; *Xi*, *Yi*, and *Zi* are measured positions of the quadcopter in *X*, *Y*, and *Z* axes, respectively; and the total number of measurements is expressed with *Nm*. The energy efficiency can be calculated as:

$$E\_{eff} = \frac{E\_b - E\_t}{E\_b} \times 100\tag{53}$$

where *Eb* is the total energy of the battery, and *Et* is the total energy consumed by the quadcopter. The generated waypoints are presented for Scenario 1 in Table 2. The distances of the paths created are 37.53 m, 36.26 m, 35.68 m in Scenario 1 for the PSO, GWO, and hybrid HHO–GWO, respectively. The performance of the payload hold and release path is demonstrated in Figure 6. The path generated by metaheuristic optimization algorithms is illustrated on Scenario 1 with obstacles in Figure 7. When the convergence rate and minimum point are investigated, the maximum convergence rate and minimum point has been obtained for the proposed hybrid HHO–GWO algorithm. The shortest distance path is obtained with the hybrid HHO–GWO on Scenario 1.

The generated waypoints are introduced for Scenario 2 in Table 3. The distances of the paths created are 37.47 m, 40.72 m, and 36.73 m in Scenario 2 for the PSO, GWO, and hybrid HHO–GWO, respectively. The performance of the payload hold-and-release path is displayed in Figure 8. The paths generated by the metaheuristic optimization algorithms are indicated in Scenario 2 with obstacles in Figure 9. When the convergence rate and minimum point are investigated, the maximum convergence rate and minimum point has been obtained for the proposed hybrid HHO–GWO algorithm. The generated minimum path distance is obtained for the hybrid HHO–GWO in Scenario 2.

**Figure 6.** The optimized payload hold (**a**) and release (**b**) path performance of metaheuristic optimization algorithms for Map 1.


**Table 2.** Optimized waypoints for Scenario 1.

**Table 3.** Optimized waypoints for Scenario 2.


The generated waypoints are demonstrated for Scenario 3 in Table 4. The distances of the paths created are 31.32 m, 32.24 m, and 29.59 m on Map 3 for the PSO, GWO, and hybrid HHO–GWO, respectively. The performance of the payload hold-and-release path is displayed in Figure 10. The paths generated by the metaheuristic optimization algorithms are shown in Scenario 3 with obstacles in Figure 11. The numbers on Figures 7, 9 and 11 are used to label the waypoints obtained by the optimization algorithms. When the convergence rate and minimum point are investigated, the maximum convergence rate and minimum point were obtained for the proposed hybrid HHO–GWO algorithm. The generated minimum path distance is obtained for hybrid HHO–GWO in Scenario 3. To summarize, the path planning on all three maps is obtained for the proposed hybrid HHO–GWO algorithm for minimum distance and the maximum converge rate. The PSO algorithm is run 500 times for Scenarios 1–3, and the average running times for each scenario are determined as 66.14 s, 66.16 s, and 66.01 s, respectively. The GWO algorithm is run 500 times for Scenarios 1–3, and the average running times for each scenario are 65.12 s, 65.25 s, and 65.11 s, respectively. The proposed hybrid HHO–GWO algorithm is run 500 times for Scenarios 1–3, and the average running times for each scenario are measured as 64.09 s, 64.68 s, and 64.71 s, respectively. Note that all algorithms mentioned in the study are run on a PC device, which has an Intel i7-10750H, 6 cores, 2.6 GHz Turbo, and 32 GB RAM. All codes are compiled with MATLAB 2020b.

**Figure 7.** The optimized path for Map 1 (**a**) using PSO, (**b**) using GWO, and (**c**) using hybrid HHO–GWO.

**Figure 8.** The optimized payload hold (**a**) and release (**b**) path performance of metaheuristic optimization algorithms for Map 2.

**Figure 9.** The optimized path for Map 2 (**a**) using PSO, (**b**) using GWO, and (**c**) using hybrid HHO–GWO.

**Table 4.** Optimized waypoints for Scenario 3.


**Figure 10.** The optimized payload hold (**a**) and release (**b**) path performance of metaheuristic optimization algorithms for Map 3.

**Figure 11.** The optimized path for Map 3 (**a**) using PSO, (**b**) using GWO, and (**c**) using hybrid HHO–GWO.

The path tracking performance of the quadcopter is analyzed with these generated waypoints. The payload hold and release are carried out in waypoints 5 and 9, respectively. The performance of the quadcopter under both path tracking and sudden payload change is examined. The path tracking in a payload hold–release mission is illustrated in Figures 12–14 for Scenarios 1, 2, and 3, respectively. The total path, RMSE, target time, and energy efficiency performance criteria of metaheuristic algorithms are presented in Table 5. The total measured paths are 53.025 m, 51.631 m, and 50.7 m, and the mean square errors are 21.76 m, 19.98 m, and 19.57 m for PSO, GWO, and hybrid HHO–GWO, respectively, in Scenario 1. The total times of the payload hold–release mission in Scenario

(**c**)

1 are 66.15 s, 65.01 s, and 64.12 s for the PSO, GWO, and hybrid HHO–GWO, respectively. The energy efficiencies of the quadcopter in Scenario 1 are obtained as 64.51%, 67.42%, and 68.08% for the PSO, GWO, and hybrid HHO–GWO respectively. The total measured paths are 52.92 m, 56.52 m, and 52.51 m, and the mean square errors are 19.86 m, 22.7 m, and 19.35 m for the PSO, GWO, and hybrid HHO–GWO, respectively, in Scenario 2. The total mission times are 66.18 s, 65.24 s, and 64.76 s, and the energy efficiencies obtained are 67.92%, 63.33%, and 68.74% for the PSO, GWO, and hybrid HHO–GWO, respectively, in Scenario 2. The total measured paths are 46.87 m, 47.80 m, and 44.72 m, and the mean square errors are 17.65 m, 18.49 m, and 16.92 m for the PSO, GWO, and hybrid HHO–GWO, respectively, in Scenario 3. The total mission times are 65.99 s, 65.01 s, and 64.71 s, and the energy efficiencies are 66.74%, 65.5%, and 68.81% for the PSO, GWO, and hybrid HHO– GWO, respectively, in Scenario 3. The minimum total path, mean square error, target time, and energy efficiency are obtained for the hybrid HHO–GWO in all Scenarios. When the path tracking performance of the quadcopter in Figure 14 for Scenario 3, which has the highest environmental difficulty level, is evaluated, it is seen that the least change in the *Z*-axis occurs with the proposed algorithm. This shows that the energy is used optimally. The results show that the hybrid HHO–GWO algorithm has the highest energy efficiency.

**Table 5.** Performance criteria of metaheuristic optimization algorithms for path planning and tracking.


To summarize, the path planning and tracking control strategy of the quadcopter have been proposed in this study. The path planning has been achieved via PSO, GWO, and the proposed hybrid HHO–GWO algorithms. The results of path planning show that the shortest and safest paths are obtained for all scenarios. After this, the path-tracking performance of the quadcopter in a payload hold–release mission is investigated for all scenarios. The path-tracking results express that the minimum total path, mean square error, target time and energy efficiency of quadcopter in payload transportation mission have been obtained for all scenarios. The path-tracking error due to the mass uncertainty of the quadcopter has been minimized in all scenarios with obstacles. The contributions of this study are the following:


**Figure 12.** The path-tracking performance of the quadcopter for Map 1 (**a**) using PSO, (**b**) using GWO, and (**c**) using hybrid HHO–GWO.

**Figure 13.** The path-tracking performance of quadcopter for Map 2 (**a**) using PSO, (**b**) using GWO, and (**c**) using hybrid HHO–GWO.

**Figure 14.** The path-tracking performance of quadcopter for Map 3 (**a**) using PSO, (**b**) using GWO, and (**c**) using hybrid HHO–GWO.
