## 5 Conclusions  
In this study, the control of the quadcopter was carried out by using an SDCS controller and an FOPID controller supported by the tested MH algorithms. The performance of the tested MH algorithms varied significantly with changes in population size and maximum iterations. Adjustments to these parameters directly impact the optimization results, influencing the effectiveness of the controller. Larger populations may explore the solution space more thoroughly, while more iterations can refine solutions further. Balancing these parameters is crucial for achieving optimal controller performance. Fine-tuning may lead to better convergence and improved results in specific applications. A new study can be performed by changing the maximum iteration number and population size of the PO, which provided the best results among the MH algorithms. In addition, to prove the success of MH algorithms, new research including other recently developed MH algorithms can be carried out. In this study, FOPID, which is one of the simplest and most common controllers, was used. Other control methods can be used to compare the success of the algorithms used in this study. Additionally, academic and industrial research on multibody and digital twin models has gained significant traction. The methods tested in this study are intended to control a quadcopter modeled in environments like Simscape. Simulations using a solid model of the quadcopter are expected to better reflect the system's response to disturbances compared to purely mathematical models. Future studies could focus on comparing the performance of the model reference adaptive controller, commonly used in quadcopter control, with the SDCS method. This comparison will provide valuable insights into the effectiveness of both approaches. Noise and disturbance were not taken into account in this study, highlighting an area for future research. Many existing studies on quadcopter control, both in simulations and real environments, report transient and steady-state errors that differ from the findings of this paper. To validate the effectiveness of the SDCS controller, it is crucial to conduct tests using a real quadcopter. This will provide a more comprehensive evaluation of the controller's performance under realistic conditions. Environmental factors such as wind, along with the challenges of modeling unidentified scenarios, create a complex landscape for future work. While it is possible to identify and extensively model primary factors, this process can be intricate and prone to errors in the parameters. To enhance accuracy and reliability in controller synthesis, incorporating external world dynamics as an input can be effective. This serves as an input in the proposed system model and undergoes a series of computations before being integrated, as discussed in other studies [28; 29]. This approach helps mitigate uncertainties and improves overall system performance. This study presents the integration of the SDCS technique for optimizing quadcopter paths to enhance energy-efficient navigation. The proposed approach involves constructing an objective function based on route lengths and minimizing this cost function using the SDCS method. As a result, the controller effectively reduces route lengths, leading to time savings and improved energy efficiency. Additionally, a comparative evaluation of the proposed SDCS method with the MH optimization algorithms, including FFO, FHO,and PO, is reported. In contrast to the tested MH algorithms, which are among the first used in the literature to optimize quadcopter paths, the proposed method ensures the optimal solution, not the near-optimal solution. The results demonstrate that the SDCS method significantly outperforms the tested MH algorithms, highlighting its effectiveness in optimizing quadcopter navigation. The proposed modeling framework details how the SDCS method can be integrated into energy-saving-focused path planning applications and validates this adaptation through various case studies.