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Simultaneous design of morphing hexarotor and autopilot system by using deep neural network and SPSA

Oguz Kose (Gümüşhane Üniversitesi, Gumushane, Turkey)
Tugrul Oktay (Faculty of Aeronautics and Astronautics, Erciyes University, Kayseri, Turkey)

Aircraft Engineering and Aerospace Technology

ISSN: 0002-2667

Article publication date: 13 February 2023

Issue publication date: 2 May 2023




The purpose of this paper is to optimize the simultaneous flight performance of a hexarotor unmanned aerial vehicle (UAV) by using simultaneous perturbation stochastic approximation (i.e. SPSA), deep neural network and proportional integral derivative (i.e. PID) according to varying arm length (i.e. morphing).


In this paper, proper PID gain coefficients and morphing ratio were obtained using the stochastic optimization method, also known as SPSA to maximize flight efficiency. Because it is difficult to establish an analytical connection between the morphing ratio and hexarotor moments of inertia, the deep neural network was used to obtain the moments of inertia according to the morphing ratio. By using SPSA and deep neural network, the best performance indexes were obtained and both longitudinal and lateral flight simulations were performed with the obtained data.


With SPSA, the best PID coefficients and morphing ratio are obtained for both longitudinal and lateral flight. Because the hexarotor solid body model changes according to the morphing ratio, the moment of inertia values used in the simulations also change. According to the morphing ratio, the moment of inertia values was obtained with the deep neural network over a created data set.

Research limitations/implications

It takes a long time to obtain the morphing ratio suitable for the hexarotor model and the PID gain coefficients suitable for this morphing ratio. However, this situation can be overcome with the proposed SPSA. In addition, it takes a long time to obtain the appropriate moments of inertia according to the morphing ratio. However, in this case, it was overcome using the deep neural network.

Practical implications

Determining the morphing ratio and PID gain coefficients using the optimization method, as well as determining the moments of inertia using the deep neural network, is very useful as it can increase the efficiency of hexarotor flight and flight efficiently with different arm lengths. With the proposed method, the hexarotor design performance criteria (i.e. rise time, settling time and overshoot) values were significantly improved compared to similar studies.

Social implications

Determining the hexarotor flight parameters using SPSA and deep neural network provides advantages in terms of time, cost and applicability.


The hexarotor flight efficiency is improved with the proposed SPSA and deep neural network approaches. In addition, the desired flight parameters can be obtained more quickly and reliably with the proposed approaches. The design performance criteria were also improved, enabling the hexarotor UAV to follow the given trajectory in the best way and providing convenience for end users. SPSA was preferred because it converged faster than other methods. While other methods perform 2n operations per iteration, SPSA only performs two operations. To obtain the moment of inertia, many physical parameter values of the UAV are required in the existing methods. In the proposed method, by creating a date set, only arm length and moment of inertia were estimated without the need to obtain physical parameters with the deep neural network structure.



Kose, O. and Oktay, T. (2023), "Simultaneous design of morphing hexarotor and autopilot system by using deep neural network and SPSA", Aircraft Engineering and Aerospace Technology, Vol. 95 No. 6, pp. 939-949.



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