Quadrotor Modeling Approaches and Trajectory Tracking Control Algorithms: A Review

(1) * Abitha M.A. Mail (APJ Abdul Kalam Technological University, India)
(2) Abdul Saleem Mail (APJ Abdul Kalam Technological University, India)
*corresponding author


Quadrotor unmanned aerial vehicles are utilized in basically every sector of society, including the business, civil, and military industries. Popular applications include delivery, agriculture, target-acquisition, surveying, surveillance, and rescue. They are widely used due to their exceptional features such as accuracy, capability to perform swift inspections, simplicity in deploying perilous and uncertain missions, and additional praiseworthy attributes. This article presents a comprehensive analysis of the theoretical frameworks that have been proposed for the purpose of quadrotor modelling and control. Detailed examinations are conducted on every methodology that underpins the control algorithms, spanning from traditional linear to modern. The analysis looks at hybrid control technique models, which incorporate adaptive components across multiple controllers to improve overall performance and resilience by addressing individual algorithm shortcomings. This analysis also delves deeper into potential future research avenues. These include the development of learning-based or hybrid methodologies that employ machine learning and artificial intelligence to optimize performance and adaptability. For instance, model reference adaptive control systems can learn adaptation laws through machine learning techniques, as opposed to depending on predefined adaptation laws. By training neural networks or fuzzy logic controllers to forecast optimal adaptation parameters based on sensor data, the quadrotor can adjust to fluctuating conditions more effectively. A comparison table is provided to elaborate on the advantages, disadvantages, and hybrid versions of each control algorithm. This will serve as a concise guide that will promote innovation, facilitate the selection and integration of appropriate control algorithms, and enhance the functionality of quadrotor control systems.


Quadrotor UAV; PID Controller; LQR Controller; MPC Controller; SMC Control




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[1] M. DeGarmo and G. Nelson, “Prospective unmanned aerial vehicle operations in the future national airspace system,” AIAA 4th Aviation Technology, Integration and Operations (ATIO), p. 6243, 2004, https://doi.org/10.2514/6.2004-6243.

[2] M. Idrissi, M. Salami and F. Annaz, “A review of quadrotor unmanned aerial vehicles: Applications, architectural design and control algorithms,” Journal of Intelligent & Robotic Systems, vol. 104, no. 22, pp. 1–33, 2022, https://doi.org/10.1007/s10846-021-01527-7.

[3] L. R. G. Carrillo et al., “Modeling the quad-rotor mini-rotorcraft,” Quad Rotorcraft Control: Vision Based Hovering and Navigation 2013, pp. 23–34, 2013, https://doi.org/10.1007/978-1-4471-4399-4_2.

[4] T. Luukkonen, “Modelling and control of quadcopter,” Independent research project in applied mathematics, vol. 22, no. 22, pp. 1–22, 2011, https://sal.aalto.fi/publications/pdf-files/eluu11public.pdf.

[5] P. Bibik, J. Narkiewicz, M. Zasuwa and M. Zugaj, “Quadrotor Dynamics and Control for Precise Handling,” Innovative Simulation Systems, pp. 335–351, 2015, https://doi.org/10.1007/978-3-319-21118-3_19.

[6] F. Sabatino, “Quadrotor control: modeling, nonlinear control design, and simulation,” KTH Electrical Engineering, 2015, https://www.kth.se/polopolyfs/1.588039.1600688317!/Thesis%20KTH%20-%20Francesco%20Sabatino.pdf.

[7] H. C. T. E. Fernando, A. T. A. De Silva, M. D. C. De Zoysa, K. A. D. C. Dilshan and S. R. Munasinghe, “Modelling, simulation and implementation of a quadrotor UAV,” 2013 IEEE 8th International Conference on Industrial and Information Systems, pp. 207-212, 2013, https://doi.org/10.1109/ICIInfS.2013.6731982.

[8] C. Zhang, X. Zhou, H. Zhao, A. Dai and H. Zhou, “Three-dimensional fuzzy control of mini quadrotor UAV trajectory tracking under impact of wind disturbance,” 2016 International Conference on Advanced Mechatronic Systems (ICAMechS), pp. 372-377, 2016, https://doi.org/10.1109/ICAMechS.2016.7813477.

[9] P. E. I. Pounds, D. R. Bersak, and A. M. Dollar, “Stability of smallscale uav helicopters and quadrotors with added payload mass under pid control,” Autonomous Robots, vol. 33, no. 1, pp. 129–142, 2012, https://doi.org/10.1007/s10514-012-9280-5.

[10] A. L. Salih, M. Moghavvemi, H. A. Mohamed et al., “Flight pid controller design for a uav quadrotor,” Scientific research and essays 2010, vol. 5, no. 23, pp. 3660–3667, 2010, https://www.researchgate.net/publication/230633819.

[11] H. Bolandi, M. Rezaei, R. Mohsenipour et al., “Attitude control of a quadrotor with optimized pid controller,” Intelligent Control and Automation, vol. 4, no. 3, pp. 335–342, 2013, https://doi.org/10.4236/ica.2013.43039.

[12] A. A. Najm and I. K. Ibraheem, “Nonlinear pid controller design for a 6-dof uav quadrotor system,” Engineering Science and Technology, an International Journal, vol. 22, no. 4, pp. 1087–1097, 2019, https://doi.org/10.1016/j.jestch.2019.02.005.

[13] J. Dong and B. He, “Novel fuzzy pid-type iterative learning control for quadrotor uav,” Sensors, vol. 19, no. 1, 2019, https://doi.org/10.3390/s19010024.

[14] A. Ghasemi and M. M. Azimi, “Adaptive fuzzy pid control based on nonlinear disturbance observer for quadrotor,” Journal of Vibration and Control, vol. 29, no. 13-14, pp. 2965–2977, 2022, https://doi.org/10.1177/10775463221089734.

[15] A. Noordin, M. A. M. Basri, and Z. Mohamed, “Real-time implementation of an adaptive pid controller for the quadrotor mav embedded flight control system,” Aerospace, vol. 10, no. 1, 2023, https://doi.org/10.3390/aerospace10010059.

[16] C. Zhang, J. Li, and Z. Gao, “Attitude control of quadrotor uav based on fuzzy pid control under small disturbance,” Highlights in Science, Engineering and Technology, vol. 53, pp. 199–207, 2023, https://doi.org/10.54097/hset.v53i.9725.

[17] A. Fekik, A. T. Azar, M. L. Hamida et al., “Modeling and simulation of quadcopter using self-tuningfuzzy-pi controller,” Mobile Robot: Motion Control and Path Planning, vol. 1090, pp. 231–251, 2023, https://doi.org/10.1007/978-3-031-26564-8_8.

[18] F. Behrooz, N. Mariun, M. H. Marhaban et al., “Review of control techniques for hvac systems—nonlinearity approaches based on fuzzy cognitive maps,” Energies vol. 11, no. 3, 2018, https://doi.org/10.3390/en11030495.

[19] C. B. Jabeur, and H. Seddik, “Optimized neural networks pid controller with wind rejection strategy for a quad-rotor,” Journal of Robotics and Control, vol. 3, no. 1, pp. 62–72, 2022, https://doi.org/10.18196/jrc.v3i1.11660.

[20] M. O. Efe, “Neural Network Assisted Computationally Simple ¨ piλd µ Control of a Quadrotor UAV,” IEEE Transactions on Industrial Informatics, vol. 7, no. 2, pp. 354-361, 2011, https://doi.org/10.1109/TII.2011.2123906.

[21] M. G. Abdolrasol, S. Hussain, T. S. Ustun et al., “Artificial neural networks based optimization techniques: A review,” Electronics, vol. 10, no. 21, 2021, https://doi.org/10.3390/electronics10212689.

[22] N. H. Sahrir, and M. A. M. Basri, “Pso–pid controller for quadcopter uav: index performance comparison,” Arabian Journal for Science and Engineering, vol. 48, pp. 15241–15255, 2023, https://doi.org/10.1007/s13369-023-08088-x.

[23] Z. Qin, “Pid control algorithm based on particle swarm optimization for quadrotor uav with tip defect,” Academic Journal of Science and Technology, vol. 7, no. 2, pp. 101–105, 2023, https://doi.org/10.54097/ajst.v7i2.11951.

[24] S. E. I. Hasseni, L. Abdou and H. E. Glida, “Parameters tuning of a quadrotor pid controllers by using nature-inspired algorithms,” Evolutionary Intelligence, vol. 14, no. 1, pp. 61–73, 2019, https://doi.org/10.1007/s12065-019-00312-8.

[25] B. E. Demir, and F. Demir, “Comparison of metaheuristic optimization algorithms for quadrotor pid controllers,” Tehnicki vjesnik, vol. 30, no. 4, pp. 1096–1103, 2023, https://doi.org/10.17559/TV-20221108150435.

[26] A. G¨un, “Attitude control of a quadrotor using pid controller based on differential evolution algorithm,” Expert Systems with Applications, vol. 229, 2023, https://doi.org/10.1016/j.eswa.2023.120518.

[27] T. Nuchkrua and M. Parnichkun, “Identification and optimal control of quadrotor,” Thammasat International Journal of Science and Technology, vol. 17, no. 4, pp. 36–53, 2012, https://www.thaiscience.info/Article%20for%20ThaiScience/Article/62/10028406.pdf.

[28] S. Bouabdallah, “Design and control of quadrotors with application to autonomous flying,” EPFL scientific publications, pp. 1–155, 2007, https://doi.org/10.5075/epfl-thesis-3727.

[29] S. Durand, B. Boisseau, J. J. Martinez-Molina, N. Marchand and T. Raharijaona, “Event-based LQR with integral action,” Proceedings of the 2014 IEEE Emerging Technology and Factory Automation, pp. 1-7, 2014, https://doi.org/10.1109/ETFA.2014.7005067.

[30] J. Lin, Z. Miao, Y. Wang, G. Hu, X. Wang and H. Wang, “Error-State LQR Geofencing Tracking Control for Underactuated Quadrotor Systems,” IEEE/ASME Transactions on Mechatronics, pp. 1–12, 2023, https://doi.org/10.1109/TMECH.2023.3292893.

[31] O. A. Dhewa, A. Dharmawan and T. Priyambodo, “Model of linear quadratic regulator (lqr) control method in hovering state of quadrotor,” Journal of Telecommunication, Electronic and Computer Engineering, vol. 9, pp. 135–143, 2017, https://jtec.utem.edu.my/jtec/article/view/1589/1891.

[32] N. A. Ismail, N. L. Othman, Z. Zain et al., “Attitude control of quadrotor,” ARPN Journal of Engineering and Applied Sciences, vol. 10, no. 22, pp. 1726–1731, 2015, http://www.arpnjournals.org/jeas/researchpapers/rp2015/jeas 1215 3152.pdf.

[33] E. Okyere, A. Bousbaine, G. T. Poyi et al., “Lqr controller design for quad-rotor helicopters,” The Journal of Engineering, vol. 2019, no. 17, pp. 4003–4007, 2019, https://doi.org/10.1049/joe.2018.8126.

[34] H. Jafari, M. Zareh, J. Roshanian et al., “An optimal guidance law applied to quadrotor using lqr method,” Transactions of the Japan Society for Aeronautical and Space Sciences, vol. 53, no. 179, pp. 32–39, 2010, https://doi.org/10.2322/tjsass.53.32.

[35] S. Rauniyar, S. Bhalla, D. Choi et al., “Ekf-slam for quadcopter using differential flatness-based lqr control,” Electronics, vol. 12, no. 5, 2023, https://doi.org/10.3390/electronics12051113.

[36] L. M. Argentim, W. C. Rezende, P. E. Santos and R. A. Aguiar, “PID, LQR and LQR-PID on a quadcopter platform,” 2013 International Conference on Informatics, Electronics and Vision, pp. 1-6, 2013, https://doi.org/10.1109/ICIEV.2013.6572698.

[37] T. Zhao and W. Li, “Lqr-based attitude controllers design for a 3-dof helicopter system with comparative experimental tests,” International Journal of Dynamics and Control, pp. 1–10, 2023, https://doi.org/10.1007/s40435-023-01242-1.

[38] H. B. Khamseh, and F. J. Sharifi, “Ukf–based lqr control of a manipulating unmanned aerial vehicle,” Unmanned Systems, vol. 5, no. 3, pp. 131–139, 2017, https://doi.org/10.1142/S2301385017400015.

[39] G. G. Garrido, O. J. S. S´anchez, H. R. Trejo et al., “Discrete integral optimal controller for quadrotor attitude stabilization: Experimental results,” Applied Sciences, vol. 13, no. 16, 2023, https://doi.org/10.3390/app13169293.

[40] E. V. Kumar, G. S. Raaja, and J. Raaja, “Adaptive pso for optimal lqr tracking control of 2 dof laboratory helicopter,” Applied Soft Computing, vol. 41, pp. 77–90, 2016, https://doi.org/10.1016/j.asoc.2015.12.023.

[41] A. Bansal and V. Sharma, “Design and analysis of robust h∞ controller,” Control theory and informatics, vol. 3, no. 2, pp. 7–14, 2013, https://app.cafeprozhe.com/storage/files/project/GrF1guX35maoJ9NEvT4XKOIAeRhP0MzhE4170DYj.pdf.

[42] Y. Zuo, Y. T. Liu and A. Ahmad, “Autonomous Blimp Control via H∞ Robust Deep Residual Reinforce[1]ment Learning,” 2023 IEEE 19th International Conference on Automation Science and Engineering, pp. 1-8, 2023, https://doi.org/10.1109/CASE56687.2023.10260561.

[43] O. Araar and N. Aouf, “Full linear control of a quadrotor UAV, LQ vs H∞,” 2014 UKACC International Conference on Control, pp. 133-138, 2014, https://doi.org/10.1109/CONTROL.2014.6915128.

[44] C. MASSE, O. GOUGEON, D. -T. NGUYEN and D. SAUSSI E, “Modeling and Control of a Quadcopter Flying in a Wind Field: A Comparison Between LQR and Structured H∞ Control Techniques,” 2018 International Conference on Unmanned Aircraft Systems, pp. 1408-1417, 2018, https://doi.org/10.1109/ICUAS.2018.8453402.

[45] Z. Bellahcene, M. Bouhamida, M. Denai et al., “Adaptive neural network-based robust h∞ trackingcontrol of a quadrotor uav under wind disturbances,” International Journal of Automation and Control, vol. 15, no. 1, pp. 28–57, 2020, https://doi.org/10.1504/IJAAC.2021.111747.

[46] G. V. Raffo, M. G. Ortega and F. R. Rubio, “Backstepping/nonlinear H∞ control for path tracking of a quadrotor unmanned aerial vehicle,” 2008 American Control Conference, pp. 3356-3361, 2018, https://doi.org/10.1109/ACC.2008.4587010.

[47] K. Ghasemi, and G. Alizadeh, “Control of quadrotor using sliding mode disturbance observer and nonlinear H∞,” International Journal of Robotics, Theory and Applications, vol. 4, no. 1, pp. 38-46, 2015, https://ijr.kntu.ac.ir/article_12496_2124.html.

[48] M. Schwenzer, M. Ay, T. Bergs et al., “Review on model predictive control: An engineering perspective,” The International Journal of Advanced Manufacturing Technology, vol. 117, no. 5, pp. 1327–1349, 2021, https://doi.org/10.1007/s00170-021-07682-3.

[49] D. R. Guevara, A. F. Contreras and O. J. G. Villarreal, “A qlpv-mpc control strategy for trajectory tracking of quadrotors,” Machines, vol. 11, no. 7, 2023, https://doi.org/10.3390/machines11070755.

[50] M. Bangura and R. Mahony, “Real-time model predictive control for quadrotors,” IFAC Proceedings Volumes, vol. 47, no. 3, pp. 11773–11780, 2014, https://doi.org/10.3182/20140824-6-ZA-1003.00203.

[51] S. Jalili, B. Rezaie and Z. Rahmani, “A novel hybrid model predictive control design with applicationto a qu adrotor helicopter,” Optimal Control Applications and Methods, vol. 39, no. 4, pp. 1301–1322, 2018, https://doi.org/10.1002/oca.2411.

[52] K. Alexis, G. Nikolakopoulos and A. Tzes, “Model predictive quadrotor control: attitude, altitude and position experimental studies,” IET Control Theory & Applications, vol. 6, no. 12, pp. 1812–1827, 2012, https://doi.org/10.1049/iet-cta.2011.0348.

[53] M. H. Jaffery, L. Shead, J. L. Forshaw et al., “Experimental quadrotor flight performance using computationally efficient and recursively feasible linear model predictive control,” International Journal of Control, vol. 86, no. 12, pp. 2189–2202, 2013, https://doi.org/10.1080/00207179.2013.804256.

[54] D. Wang, Q. Pan, Y. Shi, J. Hu and C. Zhao, “Efficient Nonlinear Model Predictive Control for Quadrotor Trajectory Tracking: Algorithms and Experiment,” IEEE Transactions on Cybernetics, vol. 51, no. 10, pp. 5057-5068, 2021, https://doi.org/10.1109/TCYB.2020.3043361.

[55] K. Zhang, Y. Shi and H. Sheng, “Robust Nonlinear Model Predictive Control Based Visual Servoing of Quadrotor UAVs,” IEEE/ASME Transactions on Mechatronics, vol. 26, no. 2, pp. 700-708, 2021, https://doi.org/10.1109/TMECH.2021.3053267.

[56] M. Elhesasy, T. N. Dief, M. Atallah et al., “Non-linear model predictive control using casadi package for trajectory tracking of quadrotor,” Energies, vol. 16, no. 5, 2023, https://doi.org/10.3390/en16052143.

[57] Y. T. Chen, C. S. Yu and P. N. Chen, “Feedback linearization based robust control for linear permanent magnet synchronous motors,” Energies, vol. 13, no. 20, 2020, https://doi.org/10.3390/en13205242.

[58] A. Ruiz, D. Rotondo and B. Morcego, “Design of shifting state-feedback controllers for constrained feedback linearized systems: Application to quadrotor attitude control,” International Journal of Robust and Nonlinear Control, vol. 34, no. 4, pp. 2614–2638, 2023, https://doi.org/10.1002/rnc.7098.

[59] I. M. Lazim, A. R. Husain, Z. Mohamed et al., “Disturbance observer-based formation tracking control of multiple quadrotors in the presence of disturbances,” Transactions of the Institute of Measurement and Control, vol. 41, no. 14, pp. 4129–4141, 2019, https://doi.org/10.1177/014233121985192.

[60] A. Mahmood and Y. Kim, “Decentrailized formation flight control of quadcopters using robust feedback linearization,” Journal of the Franklin Institute, vol. 354, no. 2, pp. 852–871, 2017, https://doi.org/10.1016/j.jfranklin.2016.10.039.

[61] I. M. Lazim, A. R. Husain, M. A. M. Basri, and N. A. M. Subha, “Feedback linearization with intelligent disturbance observer for autonomous quadrotor with time-varying disturbance,” International Journal of Mechanical and Mechatronics Engineering, vol. 18, no. 5, pp. 47–55, 2018, https://oarep.usim.edu.my/jspui/bitstream/123456789/11848/1/Feedback%20Linearization%20with%20Intelligent%20Disturbance%20Observer%20for%20Autonomous%20Quadrotor%20with%20Time-varying%20Disturbance.pdf.

[62] Z. Yaou, Z. Wansheng, L. Tiansheng, and L. Jingsong, “The attitude control of the four–rotor unmanned helicopter based on feedback linearization control,” WSEAS Transactions on Systems, vol. 12, no. 4, pp. 229–239, 2013, https://www.wseas.org/multimedia/journals/systems/2013/5702-117.pdf.

[63] W. Zhou, K. Yin, R. Wang and Y. E. Wang, “Design of attitude control system for uav based on feedback linearization and adaptive control,” Mathematical Problems in Engineering, vol. 2014, 2014, https://doi.org/10.1155/2014/492680.

[64] D. Zhang, H. Qi, X. Wu, Y. Xie, and J. Xu, “The quadrotor dynamic modeling and indoor target tracking control method,” Mathematical problems in engineering, Mathematical Problems in Engineering, vol. 2014, pp. 1–9, 2014, http://dx.doi.org/10.1155/2014/637034.

[65] J. R. S. Benevides, M. A. D. Paiva, P. V. G. Simplício, R. S. Inoue and M. H. Terra, "Disturbance Observer-Based Robust Control of a Quadrotor Subject to Parametric Uncertainties and Wind Disturbance," in IEEE Access, vol. 10, pp. 7554-7565, 2022, https://doi.org/10.1109/ACCESS.2022.3141939.

[66] M. Ghanifar, M. Kamzan and M. Tayefi, “Different intelligent methods for coefficient tuning of quadrotor feedbacklinearization controlle,” Journal of Aerospace Science and Technology, vol. 16, no. 1, pp. 56–65, 2023, https://doi.org/10.22034/jast.2023.355914.1123.

[67] M. A. M. Basri, A. R. Husain and K. A. Danapalasingam, “Enhanced backstepping controller design with application to autonomous quadrotor unmanned aerial vehicle,” Journal of Intelligent & Robotic Systems, vol. 79, no. 2, pp. 295–321, 2015, https://doi.org/10.1007/s10846-014-0072-3.

[68] M. Karahan, C. Kasnakoglu and A. N. Akay, “Robust backstepping control of a quadrotor uav under pink noise and sinusoidal disturbance,” Studies In Informatics And Control, 2023, https://doi.org/10.24846/v32i2y202302.

[69] M. A. M. Basri, A. R. Husain and K. A. Danapalasingam, “Intelligent adaptive backstepping control for mimo uncertain non-linear quadrotor helicopter systems,” Transactions of the Institute of Measurement and Control, vol. 37, no. 3, pp. 345–361, 2014, https://doi.org/10.1177/014233121453890.

[70] L. Zhou, J. Zhang, H. She and H. Jin, “Quadrotor uav flight control via a novel saturation integral backstepping controller,” Automatika, vol. 60, no. 2, pp. 193–206, 2019, https://doi.org/10.1080/00051144.2019.1610838.

[71] R. Babaei and A. F. Ehyaei, “Robust backstepping control of a quadrotor uav using extended kalman bucy filter,” International Journal of Mechatronics, Electrical and Computer Technology, vol. 5, no. 16, pp. 2276–2291, 2015, https://www.aeuso.org/includes/files/articles/Vol5Iss162276-2291RobustBacksteppingControlofaQu.pdf.

[72] C. Ha, Z. Zou, F. B. Choi and D. Lee, “Passivity-based adaptive backstepping control of quadrotor-type uavs,” Robotics and Autonomous Systems, vol. 62, no. 9, pp. 1305–1315, 2014, https://doi.org/10.1016/j.robot.2014.03.019.

[73] Y. Liu, J. Ma and H. Tu, “Robust command filtered adaptive backstepping control for a quadrotor aircraft,” Journal of Control Science and Engineering, vol. 2018, pp. 1–9, 2018, https://doi.org/10.1155/2018/1854648.

[74] Z. Fang and W. Gao, “Adaptive backstepping control of an indoor micro-quadrotor,” Research Journal of Applied Sciences, Engineering and Technology, vol. 4, pp. 4216–4226, 2012, https://maxwellsci.com/print/rjaset/v4-4216-4226.pdf.

[75] X. Zheng, X. Yang, H. Zhao and Y. Chen, “Saturated Adaptive-Law-Based Backstepping and Its Applications to a Quadrotor Hover,” IEEE Transactions on Industrial Electronics, vol. 69, no. 12, pp. 13473-13482, 2022, https://doi.org/10.1109/TIE.2021.3139235.

[76] O. Zekry, M. Ashry, A. Hafez, and T. Attia, “Modeling and analysis of nonlinear backstepping controller for the crazyflie quadrotor trajectory tracking,” Journal of Physics: Conference Series, vo. 2616, 2023, https://doi.org/10.1088/1742-6596/2616/1/012031.

[77] L. H. Chu and N. H. Nguyen, “Adaptive Sliding Mode Control for the Quadrotor with unknown Disturbance and Uncertain Parameters,” 2023 International Conference on System Science and Engineering, pp. 320-326, 2023, https://doi.org/10.1109/ICSSE58758.2023.10227184.

[78] H. Lu, C. Liu, M. Coombes, L. Guo and W. H. Chen, “Online optimisation-based backstepping control design with application to quadrotor,” IET Control Theory & Applications, vol. 10, no. 14, pp. 1–29, 2016, https://doi.org/10.1049/iet-cta.2015.0976.

[79] M. Wang, B. Chen and C. Lin, “Fixed-TimeBackstepping Control of Quadrotor Trajectory Tracking Based On Neural Network,” IEEE Access, vol. 8, pp. 177092-177099, 2020, https://doi.org/10.1109/ACCESS.2020.3027052.

[80] Y. Zou and Z. Zheng, “A Robust Adaptive RBFNN Augmenting Backstepping Control Approach for a Model-Scaled Helicopter,” IEEE Transactions on Control Systems Technology, vol. 23, no. 6, pp. 2344-2352, 2015, https://doi.org/10.1109/TCST.2015.2396851.

[81] M. Maaruf, W. M. Hamanah and M. A. Abido, “Hybrid backstepping control of a quadrotor using a radial basis function neural network,” Mathematics, vol. 11, no. 4, 2023, https://doi.org/10.3390/math11040991.

[82] A. Kapnopoulos, C. Kazakidis and A. Alexandridis, “Quadrotor trajectory tracking based on backstepping control and radial basis function neural networks,” Results in Control and Optimization, vol. 14, 2024, https://doi.org/10.1016/j.rico.2023.100335.

[83] V. Utkin, J. Guldner and J. Shi, “Sliding mode control in electromechanical systems,” Systems & Controls, 2009, https://doi.org/10.1201/9781420065619.

[84] H. Asharioun, E. Davoudi, M. Mazare et al., “Real-time fault tolerant attitude stabilization control of a quadrotor in the presence of actuator fault,” Modares Mechanical Engineering, vol. 23, no. 7, pp. 424–437, 2023, https://doi.org/10.22034/mme.23.7.424.

[85] V. I. Utkin, “Sliding mode control in dynamic systems,” Proceedings of 32nd IEEE Conference on Decision and Control, vol.3, pp. 2446-2451, 1993, https://doi.org/10.1109/CDC.1993.325637.

[86] A. Medjghou, N. Slimane and K. Chafaa, “Fuzzy sliding mode control based on backstepping synthe[1]sis for unmanned quadrotors,” Advances in Electrical and Electronic Engineering, vol. 16, no. 2 pp. 135–146, 2018, https://doi.org/10.15598/aeee.v16i2.2231.

[87] C. Bensalah, N. K. M’sirdi and A. Naamane, “Full modelling and sliding mode control for a quadrotor uav in visual servoing task,” IMAACA2019, pp. 1–10, 2019, https://hal.archives-ouvertes.fr/hal-02471653.

[88] G. Perozzi, D. Efimov, J. M. Biannic and L. Planckaert, “Trajectory tracking for a quadrotor under wind perturbations: sliding mode control with state-dependent gains,” Journal of the Franklin Institute, vol. 355, no. 12, pp. 4809–4838, 2018, https://doi.org/10.1016/j.jfranklin.2018.04.042.

[89] A. -W. A. Saif, K. B. Gaufan, S. El-Ferik and M. Al-Dhaifallah, “Fractional Order Sliding Mode Control of Quadrotor Based on Fractional Order Model,” IEEE Access, vol. 11, pp. 79823-79837, 2023, https://doi.org/10.1109/ACCESS.2023.3296644.

[90] M. A, Dhaifallah, F. M. A. Qahtani, S. Elferik, and A. W. A. Saif, “Quadrotor robust fractional-order sliding mode control in unmanned aerial vehicles for eliminating external disturbances,” Aerospace, vol. 10, no. 8, p. 665, 2023, https://doi.org/10.3390/aerospace10080665.

[91] B. Liu, Y. Wang, O. Mofid, S. Mobayen and M. H. Khooban, “Barrier Function-Based Backstepping Fractional-Order Sliding Mode Control for Quad-Rotor Unmanned Aerial Vehicle Under External Disturbances,” IEEE Transactions on Aerospace and Electronic Systems, vol. 60, no. 1, pp. 716-728, 2024, https://doi.org/10.1109/TAES.2023.3328801.

[92] M. Labbadi, M. Defoort, G. P. Incremona and M. Djemai, “Fractional-order integral terminal sliding mode control for perturbed nonlinear systems with application to quadrotors,” International Journal of Robust and Nonlinear Control, vol. 33, no. 17, pp. 10278–10303, 2023, https://doi.org/10.1002/rnc.6608.

[93] Z. Jia, J. Yu, Y. Mei et al., “Integral backstepping sliding mode control for quadrotor helicopter under external uncertain disturbances,” Aerospace Science and Technology, vol. 68, pp. 299–307, 2017, https://doi.org/10.1016/j.ast.2017.05.022.

[94] M. Labbadi and M. Cherkaoui, “Robust integral terminal sliding mode control for quadrotor uav withexternal disturbances,” International Journal of Aerospace Engineering, vol. 2019, 2019, https://doi.org/10.1155/2019/2016416.

[95] S. Nadda and A. Swarup, “On adaptive sliding mode control for improved quadrotor tracking,” Journal of Vibration and Control, vol. 24, no. 14, pp. 3219–3230, 2017, https://doi.org/10.1177/107754631770354.

[96] A. Moya, H. Castaneda and H. Wang, “Fixed-time extended observer-based adaptive sliding mode control for a quadrotor uav under severe turbulent wind,” Drones, vol. 7, no. 12, 2023, https://doi.org/10.3390/drones7120700.

[97] H. Hassani, A. Mansouri and A. Ahaitouf, “Robust trajectory tracking control of an uncertain quadrotor via a novel adaptive nonsingular sliding mode control,” Arabian Journal for Science and Engineering, pp. 1–25, 2023, https://doi.org/10.1007/s13369-023-08455-8.

[98] N. Hamdadou, H. Bouadi, N. Hebablia and M. Yazid, “Stochastic estimator based adaptive sliding mode control for a quadrotor in rainy flight conditions,” Unmanned Systems, vol. 12, no. 1, pp. 133–148, 2023, https://doi.org/10.1142/S2301385024500092.

[99] H. Ahn, M. Hu, Y. Chung and K. You, “Sliding-mode control for flight stability of quadrotor drone using adaptive super-twisting reaching law,” Drones, vol. 7, no. 8, 2023, https://doi.org/10.3390/drones7080522.

[100] S. Mobayen, F. F. M. E. Sousy, K. A. Alattas, O. Mofid, A. Fekih and T. Rojsiraphisal, “Adaptive fastreaching nonsingular terminal sliding mode tracking control for quadrotor uavs subject to model uncertainties and external disturbances,” Ain Shams Engineering Journal, vol. 14, no. 8, 2023, https://doi.org/10.1016/j.asej.2022.102059.

[101] J. Baek and M. Kang, “A Synthesized Sliding-Mode Control for Attitude Trajectory Tracking of Quadrotor UAV Systems,” IEEE/ASME Transactions on Mechatronics, vol. 28, no. 4, pp. 2189-2199, 2023, https://doi.org/10.1109/TMECH.2022.3230755.

[102] G. Zhu, S. Wang, L. Sun, W. Ge and X. Zhang, “Output feedback adaptive dynamic surface slidingmode control for quadrotor uavs with tracking error constraints,” Complexity, vol. 2020, 2020, https://doi.org/10.1155/2020/8537198.

[103] J. Pan, B. Shao, J. Xiong and Q. Zhang, “Attitude control of quadrotor uavs based on adaptive sliding mode,” International Journal of Control, Automation and Systems, vol. 21, pp. 2698–27070, 2023, https://doi.org/10.1007/s12555-022-0189-2.

[104] H. H. Hady, E. M. N., A. A. B. and S. N. Makhtar, "Development of Quadrotor Control under Wind Disturbance," 2021 5th International Symposium on Multidisciplinary Studies and Innovative Technologies (ISMSIT), pp. 498-504, 2021, https://doi.org/10.1109/ISMSIT52890.2021.9604649.

[105] R. Mathewson and F. Fahimi, “Nonlinear adaptive sliding mode control with application to quadcopters,” Nonlinear Engineering, vol. 12, no. 1, 2023, https://doi.org/10.1515/nleng-2022-0268.

[106] L. L. Vega, B. C. Toledo and A. G. Loukianov, “Robust block second order sliding mode control for a quadrotor,” Journal of the Franklin Institute, vol. 349, no. 2, pp. 719–739, 2012, https://doi.org/10.1016/j.jfranklin.2011.10.017.

[107] S. Jiang, C. Liu and Y. Gao, “Mimo adaptive high-order sliding mode control for quadrotor attitude tracking,” Journal of Aerospace Engineering, vol. 34, no. 4, 2021, https://doi.org/10.1061/(ASCE)AS.1943-5525.0001271.

[108] G. E. M. Abro, S. A. B. M. Zulkifli, V. S. Asirvadam and Z. A. Ali, “Model-freebased single-dimension fuzzy smc design for underactuated quadrotor uav,” Actuators, vol. 10, no. 8, 2021, https://doi.org/10.3390/act10080191.

[109] G. E. M. Abro, S. A. B. M. Zulkifli and V. S. Asirvadam, “Dual-loop single dimension fuzzy-based sliding mode control design for robust tracking of an underactuated quadrotor craft,” Asian Journal of Control, vol. 25, no. 1, pp. 144–169, 2022, https://doi.org/10.1002/asjc.2753.

[110] H. Luo and S. Zhang, “Control of quadrotor based on rbf neural network adaptive fast terminal sliding mode strategy,” Journal of Physics: Conference Series, vol. 2437, 2023, https://doi.org/10.1088/1742-6596/2437/1/012120.

[111] N. Jennan and E. M. Mellouli, “New optimal fast terminal sliding mode control combined with neuralnetworks for modelling and controlling a drone quadrotor,” International Journal of Automation and Control, vol. 17, no. 6, pp. 595–612, 2023. https://doi.org/10.1504/ijaac.2023.10054839.

[112] S. Shen, J. Xu, P. Chen and Q. Xia, “Adaptive Neural Network Extended State Observer-Based Finite-Time Convergent Sliding Mode Control for a Quad Tiltrotor UAV,” IEEE Transactions on Aerospace and Electronic Systems, vol. 59, no. 5, pp. 6360-6373, 2023, https://doi.org/10.1109/TAES.2023.3274733.

[113] Q. T. Dam, R. E. H. Thabet, S. A. Ali, F. Guerin and Y. Tang, “Adaptive neural networkbased sliding mode controller for trajectory tracking of a quadrotor uav,” IEEE Transactions on Industrial Electronics, 2023, https://doi.org/10.36227/techrxiv.24174771.v1.

[114] G. Yu, J. Reis and C. Silvestre, “Quadrotor Neural Network Adaptive Control: Design and Experimental Validation,” IEEE Robotics and Automation Letters, vol. 8, no. 5, pp. 2574-2581, 2023, https://doi.org/10.1109/LRA.2023.3254450.

[115] O. Bing ¨ ol and H. M. G ¨ uzey, “Fixed-time neuro-sliding mode controller design for quadrotor uav transporting a suspended payload,” European Journal of Control, vol. 73, 2023, https://doi.org/10.1016/j.ejcon.2023.100879.

[116] E. Kayacan and R. Maslim, “Type-2 Fuzzy Logic Trajectory Tracking Control of Quadrotor VTOL Aircraft With Elliptic Membership Functions,” IEEE/ASME Transactions on Mechatronics, vol. 22,no. 1, pp. 339-348, 2017, https://doi.org/10.1109/TMECH.2016.2614672.

[117] T. Abdollahi, S. Salehfard, C. H. Xiong and J. F. Ying, “Simplified fuzzypad ´e controller for attitude control of quadrotor helicopters,” IET Control Theory & Applications, vol. 12, no. 2, pp. 310–317, 2018, https://doi.org/10.1049/iet-cta.2017.0584.

[118] E. Kayacan and M. A. Khanesar, “Fundamentals of Type-1 Fuzzy Logic Theory,” Fuzzy Neural Networks for Real Time Control Applications, pp. 13–24, 2016, https://doi.org/10.1016/B978-0-12-802687-8.00002-5.

[119] Y. Ju, Y. Zhang and G. Zhu, “Fuzzy Adaptive Linear Active Disturbance Rejection Control for Quadrotor Load UAV Based on Kalman Filter,” IEEE Access, vol. 11, pp. 104253-104269, 2023, https://doi.org/10.1109/ACCESS.2023.3317171.

[120] B. Erginer and E. Altug, “Design and implementation of a hybrid fuzzy logic controller for a quadrotor vtol vehicle,” International Journal of Control, Automation and Systems, vol. 10, no. 1, pp. 61–70, 2012, https://doi.org/10.1007/s12555-012-0107-0.

[121] Z. Liu, C. Yuan, Y. Zhang and J. Lou, “A learning-based fault tolerant tracking control of an unmanned quadrotor helicopter,” Journal of Intelligent & Robotic Systems, vol. 84, no. 1, pp. 145– 162, 2016, https://doi.org/10.1007/s10846-015-0293-0.

[122] F. Torres, A. Rabhi, D. Lara et al., “Fuzzy state feedback for attitude stabilization of quadrotor,” International Journal of Advanced Robotic Systems, vol. 13, no. 1, 2016, https://doi.org/10.5772/61934.

[123] B. N. AbdulSamed, A. A. Aldair and A. Al-Mayyahi, “Robust trajectory tracking control and obstacles avoidance algorithm for quadrotor unmanned aerial vehicle,” Journal of Electrical Engineering & Technology, vol. 15, no. 2, pp. 855–868, 2020, https://doi.org/10.1007/s42835-020-00350-8.

[124] F. Santoso, M. A. Garratt and S. G. Anavatti, “Hybrid PD-Fuzzy and PD Controllers for Trajectory Tracking of a Quadrotor Unmanned Aerial Vehicle: Autopilot Designs and Real-Time Flight Tests,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 51, no. 3, pp. 1817-1829, 2021, https://doi.org/10.1109/TSMC.2019.2906320.

[125] A. Dorzhigulov, B. Bissengaliuly, B. F. Spencer et al., “Anfis based quadrotor drone altitude control implementation on raspberry pi platform,” Analog Integrated Circuits and Signal Processing, vol. 95, no. 3, pp. 435–445, 2018, https://doi.org/10.1007/s10470-018-1159-8.

[126] S. Khatoon, I. Nasiruddin and M. Shahid, “Design and simulation of a hybrid pd-anfis controller for attitude tracking control of a quadrotor uav,” Arabian Journal for Science and Engineering, vol. 42, no. 12, pp. 5211–5229, 2017, https://doi.org/10.1007/s13369-017-2586-z.

[127] A. M. E. R. Mendoza and W. Yu, “Fuzzy adaptive control law for trajectory tracking based on a fuzzy adaptive neural pid controller of a multi-rotor unmanned aerial vehicle,” International Journal of Control, Automation and Systems, vol. 21, no. 2, pp. 658–670, 2023, https://doi.org/10.1007/s12555-021-0299-2.

[128] A. Eltayeb, M. F. Rahmat, M. A. M. Basri, M. A. M. Eltoum and S. El-Ferik, “An Improved Design of an Adaptive Sliding Mode Controller for Chattering Attenuation and Trajectory Tracking of the Quadcopter UAV,” IEEE Access, vol. 8, pp. 205968-205979, 2020, https://doi.org/10.1109/ACCESS.2020.3037557.

[129] J. Rao, B. Li, Z. Zhang et al., “Position control of quadrotor uav based on cascade fuzzy neural network,” Energies, vol. 15, no. 5, 2023, https://doi.org/10.3390/en15051763.

[130] B. Selma, S. Chouraqui and B. Selma, “A genetic algorithmbased neuro-fuzzy controller for unmanned aerial vehicle control,” International Journal of Applied Metaheuristic Computing, vol. 13, no. 1, pp. 1–23, 2022, https://doi.org/10.4018/IJAMC.292505.

[131] D. Korkmaz, H. Acikgoz and M. Ustundag, “Altitude and attitude control of a quadcopter based on neurofuzzy controller,” Proceedings of the 11th International Conference on Robotics, Vision, Signal Processing and Power Applications: Enhancing Research and Innovation through the Fourth Industrial Revolution, pp. 1009–1015, 2022, https://doi.org/10.1007/978-981-16-8129-5_154.

[132] Z. Yang, B. Cheng, C. Lv, Y. Wang and P. Lu, “Fuzzy neural network dynamic inverse control strategy for quadrotor uav based on atmospheric turbulence,” Applied Sciences, vol. 12, no. 23, 2022, https://doi.org/10.3390/app122312232.

[133] A. A. F. A. Ghaffar, T. Richardson and C. Greatwood, “A combined model reference adaptive control law for multirotor uavs,” IET Control Theory & Applications, vol. 15, no. 11, pp. 1474–1487, 2021, https://doi.org/10.1049/cth2.12137.

[134] Glushchenko A and Lastochkin K, “Quadrotor trajectory tracking using model reference adaptive control, neural network-based parameter uncertainty compensator, and different plant parameterizations,” Computation, vol. 11, no. 8, 2023, https://doi.org/10.3390/computation11080163.

[135] A. A. Ghaffar and T. Richardson, “Model reference adaptive control and lqr control for quadrotor with parametric uncertainties,” International Journal of Mechanical and Mechatronics Engineering, vol. 9, no. 2, pp. 244–250, 2015, https://publications.waset.org/10000466/pdf.

[136] M. Mohammadi and A. M. Shahri, “Adaptive nonlinear stabilization control for a quadrotor uav: Theory, simulation and experimentation,” Journal of Intelligent & Robotic Systems, vol. 72, no. 1, pp. 105–122, 2013, https://doi.org/10.1007/s10846-013-9813-y.

[137] M. Orsag, C. M. Korpela, S. Bogdan and P. Y. Oh., “Hybrid adaptive control for aerial manipulation,” Journal of intelligent & robotic systems, vol. 73, no. 1, pp. 693–707, 2014, https://doi.org/10.1007/s10846-013-9936-1.

[138] X. Liang, G. Chen, J. Wang, Z. Bi and P. Sun, “An adaptive control system for variable mass quad-rotor uav involved in rescue missions,” International Journal of Simulation: Systems, Science and Technology, vol. 17, no. 29, 2016, https://ijssst.info/Vol-17/No-29/paper22.pdf.

[139] T. E. Fraire, A. Saenz, F. Salas, R. Juarez and W. Giernacki, “Trajectory tracking with adaptive robust control for quadrotor,” Applied Sciences, vol. 11, no. 18, 2021, https://doi.org/10.3390/app11188571.

[140] G. Joshi, J. Virdi and G. Chowdhary, “Asynchronous deep model reference adaptive control,” ArXiv, 2020, https://arxiv.org/pdf/2011.02920.pdf.

[141] A. Glushchenko and K. Lastochkin, “Quadrotor trajectory tracking using model reference adaptive control, neural network-based parameter uncertainty compensator, and different plant parameterizations,” Computation, vol. 11, no. 8, pp. 1–18, 2023, https://doi.org/10.3390/computation11080163.

[142] E. Capello, A. Scola, G. Guglieri and F. Quagliotti, “Mini quadrotor uav: design and experiment,” Journal of Aerospace Engineering, vol. 25, no. 4, pp. 559–573, 2012, https://doi.org/10.1061/(ASCE)AS.1943-5525.0000171.

[143] P. Kotaru, R. Edmonson and K. Sreenath, “Geometric L1 adaptive attitude control for a quadrotor unmanned aerial vehicle,” Journal of Dynamic Systems, Measurement, and Control, vol. 142, no. 3, 2020, https://doi.org/10.1115/1.4045558.

[144] Z. Wu, S. Cheng, P. Zhao et al., “L1 quad: L1 adaptive augmentation of geometric control for agile quadrotors with performance guarantees,” ArXiv, 2023, https://arxiv.org/pdf/2302.07208.pdf.

[145] J. Zhong, W. Chen and H. Zhang, “Transition control of a tail-sitter unmanned aerial vehicle with l1 neural network adaptive control,” Chinese Journal of Aeronautics, vol. 36, no. 7, pp. 460–475, 2023, https://doi.org/10.1016/j.cja.2023.04.002.

[146] T. Souanef, “Multiple model l 1 adaptive fault-tolerant control of small unmanned aerial vehicles,” Journal of Aerospace Engineering, vol. 37, no. 1, 2024, https://doi.org/10.1061/JAEEEZ.ASENG-4427.

[147] Z. Zuo and P. Ru, “Augmented L1 adaptive tracking control of quad-rotor unmanned aircrafts,” IEEE Transactions on Aerospace and Electronic Systems, vol. 50, no. 4, pp. 3090-3101, 2014, https://doi.org/10.1109/TAES.2014.120705.

[148] A. C. Satici, H. Poonawala and M. W. Spong, “Robust Optimal Control of Quadrotor UAVs,” IEEE Access, vol. 1, pp. 79-93, 2013, https://doi.org/10.1109/ACCESS.2013.2260794.

[149] P. D. Monte and B. Lohmann, “Position trajectory tracking of a quadrotor based on l1 adaptive control,” at– Automatisierungstechnik, vol. 62, no. 3, pp. 188–202, 2014, https://doi.org/10.1515/auto-2013-1035.

[150] K. Srakaew, V. Sangveraphunsiri, S. Chantranuwathana and R. Chancharoen, “Design of narma-l2 neurocontroller for nonlinear dynamical system,” 29th International Conference on Modeling Identification, and Control, pp. 210–215, 2010, https://doi.org/10.2316/P.2010.675-044.

[151] K. S. Narendra and S. Mukhopadhyay, “Adaptive control using neural networks and approximate models,” Proceedings of 1995 American Control Conference, vol. 1, pp. 355-359, 1995, https://doi.org/10.1109/ACC.1995.529269.

[152] El Hamidi K, Mjahed M, E. K. A, et al., “Design of hybrid neural controller for nonlinear mimo system based on narmal2 model,” IETE Journal of Research, vol. 69, no. 5, pp. 3038–3051, 2023, https://doi.org/10.1080/03772063.2021.1909507.

[153] K. El. Hamidi, M. Mjahed, A. El. Kari and H. Ayad, “Adaptive control using neural networks and approximate models for nonlinear dynamic systems,” Modelling and Simulation in Engineering, vol. 2020, 2020, https://doi.org/10.1155/2020/8642915.

[154] N. S. Al. Fallooji and M. Abbod, “Helicopter control using fuzzy logic and narma-l2 techniques,” International Journal of Intelligent Systems & Applications, vol. 12, no. 5, 2020, https://doi.org/10.5815/ijisa.2020.05.01.

[155] K. Ucak and G. O. Gunel, “Online support vector regression based adaptive narma-l2 controller for nonlinear systems,” Neural Processing Letters, vol. 53, no. 1, pp. 405–428, 2021, https://doi.org/10.1007/s11063-020-10403-8.


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