## 5 Conclusions  
In this paper, we have addressed a long-standing problem related to the tuning of compensated PD and PID controllers for path tracking of the QUAV vehicle modeled with six different dynamics. We compared eight metaheuristic algorithms ( PSO, GWO, HGS, LSHADE, LSPACMA, MPA, SMA and WOA), finding optimal parameters to select the most accurate algorithm. The HGS algorithm was the most suitable of the eight evaluated, as it obtained the lowest RMSE for the compensated PD and PID controls. The trajectory used was a square with an elevation change, with 40 individuals and 20 evolutions for the compensated PD control, \(RMSE=0.03724725237912\), and the number of optimized parameters is twelve. For the compensated PID control with 100 individuals and 40 evolutions, the \(RMSE=0.032594309723623\), the number of optimized parameters is eighteen. For the case of compensated PD control, the following best algorithms are GWO, MPA and SMA, with an RMSE close to HGS. This case corresponds to when 40 individuals are used, and for the case of compensated PID control, only the HGS, GWO, MPA and SMA were simulated. On the other hand, the algorithm LSPACMA was the most limited in optimization scope. We also found those optimized gains for the square path could take the QUAV to a different trajectory like the sinewave and step paths, resulting in the most suitable tuning for the compensated PD and PID controllers for QUAV trajectory tracking. This modeling approach is now ready and suited for implementation at an experimental level.  
Conceptualization, N.S.Z.-P., N.H.-R. and J.C.S.-T.-M.; methodology, N.S.Z.-P., N.H.-R. and J.C.S.-T.-M.; software, N.S.Z.-P. and N.H.-R; validation, N.S.Z.-P., N.H.-R. and I.B.-V.; formal analysis, N.S.Z.-P., [PERSON]-R. and [PERSON]-T.-M.; investigation, N.S.Z.-P., [PERSON]-R. and [PERSON]-T.-M.; resources, J.M.-M. and J.C.S.-T.-M.; data curation, N.S.Z.-P.; writing--original draft preparation, N.S.Z.-P. and I.B.-V.; writing--review and editing, N.S.Z.-P. and I.B.-V.; visualization, N.S.Z.-P. and I.B.-V.; supervision, [PERSON]-M. and [PERSON]-T.-M.; project administration, J.M.-M. and J.C.S.-T.-M.; funding acquisition, J.M.-M. and J.C.S.-T.-M. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Council for Science and Technology (CONACYT) with project number CB- 2017-2018-A1-S-43008. [PERSON] was supported by CONACYT grant number 785376.  
Not applicable.  
Desired trajectories and dynamic performance data are publicly available at [[https://github.com/[PERSON]/Metaheuristics-enabled-path-tracking-Optimization-in-Unmanned-Aerial-Vehicles](https://github.com/[PERSON]/Metaheuristics-enabled-path-tracking-Optimization-in-Unmanned-Aerial-Vehicles)]([https://github.com/[PERSON]/Metaheuristics-enabled-path-tracking-Optimization-in-Unmanned-Aerial-Vehicles](https://github.com/[PERSON]/Metaheuristics-enabled-path-tracking-Optimization-in-Unmanned-Aerial-Vehicles)), accessed on 26 October 2021.  
The authors declare that they have no known competing financial interest or personal relationships that could have appeared to influence the work reported in this paper.