Hostname: page-component-76c49bb84f-c7tcl Total loading time: 0 Render date: 2025-07-03T21:06:33.206Z Has data issue: false hasContentIssue false

Adaptive robust trajectory tracking control with states-estimation for DJI-F450 quadrotor under multiple unknown disturbances

Published online by Cambridge University Press:  30 June 2025

Nigar Ahmed
Affiliation:
Institute of Artificial Intelligence and Mobile Robotics, Dalian, China College of Marine Electrical Engineering, Dalian Maritime University, Dalian, China
Meng Joo Er*
Affiliation:
Institute of Artificial Intelligence and Mobile Robotics, Dalian, China College of Marine Electrical Engineering, Dalian Maritime University, Dalian, China
*
Corresponding author: Meng Joo Er; Email: mjer@dlmu.edu.cn

Abstract

A quadrotor unmanned aerial vehicle (UAV) must achieve desired flight missions despite internal uncertainties and external disturbances. This paper proposes an adaptive trajectory tracking control method that attenuates unknown uncertainties and disturbances. Although the quadrotor is underactuated, a fully actuated controller is designed using backstepping control. To avoid repeated derivatives of control inputs, a dynamic surface method introduces a filter and auxiliary controller. Lyapunov criteria guide adaptive laws for tuning controller gain and filters. A low-power observer is integrated for state estimation. Additionally, a disturbance observer is developed and combined with the control scheme to handle unknown disturbances. Simulations on a DJI F450 quadrotor demonstrate that the proposed control algorithm offers strong trajectory-tracking performance and system stability under multiple uncertainties and external disturbances during flight.

Information

Type
Research Article
Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Royal Institute of Navigation

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Ahmed, N. and Ali Shah, S. A. (2022). Adaptive output-feedback robust active disturbance rejection control for uncertain quadrotor with unknown disturbances. Engineering Computations, 39(4), 14731491.10.1108/EC-02-2021-0098CrossRefGoogle Scholar
Ahmed, N. and Er, M. J. (2024). Command-filtered robust trajectory tracking control for aggressive maneuvers of quadrotor UAV with multiple unknown disturbances. Engineering Science and Technology, an International Journal, 59, 101858.10.1016/j.jestch.2024.101858CrossRefGoogle Scholar
An, S., Yuan, S. and Li, H. (2016). Self-tuning of PID controllers design by adaptive interaction for quadrotor UAV. In: 2016 IEEE Chinese Guidance, Navigation and Control Conference (CGNCC), IEEE, 15471552.Google Scholar
Astolfi, D., Marconi, L., Praly, L. and Teel, A. R. (2018). Low-power peaking-free high-gain observers. Automatica, 98, 169179.10.1016/j.automatica.2018.09.009CrossRefGoogle Scholar
Atassi, A. N. and Khalil, H. K. (1999). A separation principle for the stabilization of a class of nonlinear systems. IEEE Transactions on Automatic Control, 44(9), 16721687.10.1109/9.788534CrossRefGoogle Scholar
Bouabdallah, S., Noth, A. and Siegwart, R. (2004). PID vs LQ control techniques applied to an indoor micro quadrotor. In: 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE Cat. No. 04CH37566), Vol. 3, IEEE, 2451–2456.10.1109/IROS.2004.1389776CrossRefGoogle Scholar
Chen, F., Jiang, R., Zhang, K., Jiang, B. and Tao, G. (2016). Robust backstepping sliding-mode control and observer-based fault estimation for a quadrotor UAV. IEEE Transactions on Industrial Electronics, 63(8), 50445056.Google Scholar
Chen, F., Lei, W., Zhang, K., Tao, G. and Jiang, B. (2016). A novel nonlinear resilient control for a quadrotor UAV via backstepping control and nonlinear disturbance observer. Nonlinear Dynamics, 85, 12811295.10.1007/s11071-016-2760-yCrossRefGoogle Scholar
Chen, M., Xiong, S. and Wu, Q. (2021). Tracking flight control of quadrotor based on disturbance observer. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 51(3), 14141423.10.1109/TSMC.2019.2896891CrossRefGoogle Scholar
Dierks, T. and Jagannathan, S. (2009). Output feedback control of a quadrotor uav using neural networks. IEEE Transactions on Neural Networks, 21(1), 5066.10.1109/TNN.2009.2034145CrossRefGoogle ScholarPubMed
Elkhatem, A. S. and Engin, S. N. (2022). Robust LQR and LQR-PI control strategies based on adaptive weighting matrix selection for a UAV position and attitude tracking control. Alexandria Engineering Journal, 61(8), 62756292.10.1016/j.aej.2021.11.057CrossRefGoogle Scholar
Flores, G., González-Huitron, V. and Rodrguez-Mata, A. (2020). Output feedback control for a quadrotor aircraft using an adaptive high gain observer. International Journal of Control, Automation and Systems, 18(6), 14741486.10.1007/s12555-019-0944-6CrossRefGoogle Scholar
Gao, Q., Wei, X.-T., Li, D.-H., Ji, Y.-H. and Jia, C. (2022). Tracking control for a quadrotor via dynamic surface control and adaptive dynamic programming. International Journal of Control, Automation and Systems, 20(1), 349363.10.1007/s12555-020-0812-zCrossRefGoogle Scholar
Gharib, M. R. and Moavenian, M. (2016). Full dynamics and control of a quadrotor using quantitative feedback theory. International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, 29(3), 501519.10.1002/jnm.2101CrossRefGoogle Scholar
Gong, X., Hou, Z.-C., Zhao, C.-J., Bai, Y. and Tian, Y.-T. (2012). Adaptive backstepping sliding mode trajectory tracking control for a quad-rotor. International Journal of Automation and Computing, 9, 555560.10.1007/s11633-012-0679-4CrossRefGoogle Scholar
Hou, Z., Yu, X. and Lu, P. (2022). Terminal sliding mode control for quadrotors with chattering reduction and disturbances estimator: Theory and application. Journal of Intelligent & Robotic Systems, 105(4), 71.10.1007/s10846-022-01679-0CrossRefGoogle Scholar
Jiao, Q., Liu, J., Zhang, Y. and Lian, W. (2018). Analysis and design the controller for quadrotors based on PID control method. In 2018 33rd Youth Academic Annual Conference of Chinese Association of Automation (YAC), IEEE, 8892.10.1109/YAC.2018.8406352CrossRefGoogle Scholar
Jung, S. and Kim, Y. (2022). Low-power peaking-free extended-observer-based pitch autopilot for morphing unmanned aerial vehicle. Journal of Guidance, Control, and Dynamics, 45(2), 362371.10.2514/1.G005998CrossRefGoogle Scholar
Kang, B., Miao, Y., Liu, F., Duan, J., Wang, K. and Jiang, S. (2021). A second-order sliding mode controller of quad-rotor UAV based on PID sliding mode surface with unbalanced load. Journal of Systems Science and Complexity, 34, 520536.10.1007/s11424-020-9306-6CrossRefGoogle Scholar
Khalil, H. K. (2017), High-Gain Observers in Nonlinear Feedback Control. SIAM.10.1137/1.9781611974867CrossRefGoogle Scholar
Kristic, M., Kanellakopoulis, I., Kokotovic, P. and Mayne, D. (1996). Nonlinear and adaptive control design. IEEE Transactions on Automatic Control, 41(12), 18491852.Google Scholar
Lee, D., Burg, T. C., Xian, B. and Dawson, D. M. (2007). Output feedback tracking control of an underactuated quad-rotor UAV. In: 2007 American Control Conference, IEEE, 1775–1780.10.1109/ACC.2007.4282556CrossRefGoogle Scholar
Li, S., Duan, N. and Min, H. (2024). Trajectory tracking control for quadrotor unmanned aerial vehicle with input delay and disturbances. Asian Journal of Control, 26(1), 150161.10.1002/asjc.3192CrossRefGoogle Scholar
Liu, B., Wang, Y., Sepestanaki, M. A., Pouzesh, M., Mobayen, S., Rouhani, S. H. and Fekih, A. (2024). Event-trigger-based adaptive barrier function higher-order global sliding mode control technique for quadrotor UAVs. IEEE Transactions on Aerospace and Electronic Systems, 60 (5), 56745684.10.1109/TAES.2024.3394461CrossRefGoogle Scholar
Liu, J., Gai, W., Zhang, J. and Li, Y. (2019). Nonlinear adaptive backstepping with ESO for the quadrotor trajectory tracking control in the multiple disturbances. International Journal of Control, Automation and Systems, 17, 27542768.10.1007/s12555-018-0909-9CrossRefGoogle Scholar
Lopez-Sanchez, I., Rossomando, F., Pérez-Alcocer, R., Soria, C., Carelli, R. and Moreno-Valenzuela, J. (2021). Adaptive trajectory tracking control for quadrotors with disturbances by using generalized regression neural networks. Neurocomputing, 460, 243255.10.1016/j.neucom.2021.06.079CrossRefGoogle Scholar
Ma, H.-J., Liu, Y., Li, T. and Yang, G.-H. (2018). Nonlinear high-gain observer-based diagnosis and compensation for actuator and sensor faults in a quadrotor unmanned aerial vehicle. IEEE Transactions on Industrial Informatics, 15(1), 550562.10.1109/TII.2018.2865522CrossRefGoogle Scholar
Meng, R., Chen, S., Hua, C., Qian, J. and Sun, J. (2020). Disturbance observer-based output feedback control for uncertain QUAVs with input saturation. Neurocomputing, 413, 96106.10.1016/j.neucom.2020.06.096CrossRefGoogle Scholar
Mofid, O. and Mobayen, S. (2024). Robust fractional-order sliding mode tracker for quad-rotor UAVs: Event-triggered adaptive backstepping approach under disturbance and uncertainty’, Aerospace Science and Technology, 146, 108916.10.1016/j.ast.2024.108916CrossRefGoogle Scholar
Nettari, Y., Labbadi, M. and Kurt, S. (2023). Adaptive robust finite-time tracking control for quadrotor subject to disturbances. Advances in Space Research, 71(9), 38033821.10.1016/j.asr.2022.09.016CrossRefGoogle Scholar
Nguyen, N. P. and Hong, S. K. (2018). Sliding mode Thau observer for actuator fault diagnosis of quadcopter UAVs. Applied Sciences 8(10), 1893.10.3390/app8101893CrossRefGoogle Scholar
Niu, Y., Ban, H., Zhang, H., Gong, W. and Yu, F. (2021). Nonsingular terminal sliding mode based finite-time dynamic surface control for a quadrotor UAV. Algorithms, 14(11), 315.10.3390/a14110315CrossRefGoogle Scholar
Pan, J., Shao, B., Xiong, J. and Zhang, Q. (2023). Attitude control of quadrotor UAVs based on adaptive sliding mode. International Journal of Control, Automation and Systems, 21, 26982707.10.1007/s12555-022-0189-2CrossRefGoogle Scholar
Shao, X., Liu, J. and Wang, H. (2018). Robust back-stepping output feedback trajectory tracking for quadrotors via extended state observer and sigmoid tracking differentiator. Mechanical Systems and Signal Processing, 104, 631647.10.1016/j.ymssp.2017.11.034CrossRefGoogle Scholar
Shi, D., Wu, Z. and Chou, W. (2018). Generalized extended state observer based high precision attitude control of quadrotor vehicles subject to wind disturbance. IEEE Access, 6, 3234932359.10.1109/ACCESS.2018.2842198CrossRefGoogle Scholar
Siddiqui, M. N., Zhu, X., Rasool, H., Afzal, M. B. and Ahmed, N. (2024). Model-free low-power observer based robust trajectory tracking control of UAV quadrotor with unknown disturbances. Aircraft Engineering and Aerospace Technology, 96(2), 316328.10.1108/AEAT-08-2023-0212CrossRefGoogle Scholar
Tayebi, A. and McGilvray, S. (2006). Attitude stabilization of a VTOL quadrotor aircraft. IEEE Transactions on Control Systems Technology, 14(3), 562571.10.1109/TCST.2006.872519CrossRefGoogle Scholar
Wan, M., Chen, M. and Lungu, M. (2023). Integral backstepping sliding mode control for unmanned autonomous helicopters based on neural networks. Drones, 7(3), 154.10.3390/drones7030154CrossRefGoogle Scholar
Wang, D. and Huang, J. (2005). Neural network-based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict-feedback form. IEEE Transactions on Neural Networks, 16(1), 195202.10.1109/TNN.2004.839354CrossRefGoogle ScholarPubMed
Wang, H. and Chen, M. (2016). Trajectory tracking control for an indoor quadrotor UAV based on the disturbance observer. Transactions of the Institute of Measurement and Control, 38(6), 675692.10.1177/0142331215597057CrossRefGoogle Scholar
Wang, H., Li, N., Wang, Y. and Su, B. (2021). Backstepping sliding mode trajectory tracking via extended state observer for quadrotors with wind disturbance. International Journal of Control, Automation and Systems, 19, 32733284.10.1007/s12555-020-0673-5CrossRefGoogle Scholar
Wang, H., Ye, X., Tian, Y., Zheng, G. and Christov, N. (2016). Model-free–based terminal SMC of quadrotor attitude and position. IEEE Transactions on Aerospace and Electronic Systems, 52(5), 25192528.10.1109/TAES.2016.150303CrossRefGoogle Scholar
Wang, J., Alattas, K. A., Bouteraa, Y., Mofid, O. and Mobayen, S. (2023). Adaptive finite-time backstepping control tracker for quadrotor UAV with model uncertainty and external disturbance. Aerospace Science and Technology, 133, 108088.10.1016/j.ast.2022.108088CrossRefGoogle Scholar
Wang, Q., Namiki, A., Asignacion, A. Jr, Li, Z. and Suzuki, S. (2023). Chattering reduction of sliding mode control for quadrotor uavs based on reinforcement learning. Drones, 7(7), 420.10.3390/drones7070420CrossRefGoogle Scholar
Wang, X., Sun, S., van Kampen, E.-J. and Chu, Q. (2019). Quadrotor fault tolerant incremental sliding mode control driven by sliding mode disturbance observers. Aerospace Science and Technology, 87, 417430.10.1016/j.ast.2019.03.001CrossRefGoogle Scholar
Wu, C., Yan, J., Lin, H., Wu, X. and Xiao, B. (2021). Fixed-time disturbance observer-based chattering-free sliding mode attitude tracking control of aircraft with sensor noises. Aerospace Science and Technology, 111, 106565.10.1016/j.ast.2021.106565CrossRefGoogle Scholar
Zhao, B., Xian, B., Zhang, Y. and Zhang, X. (2014). Nonlinear robust adaptive tracking control of a quadrotor UAV via immersion and invariance methodology. IEEE Transactions on Industrial Electronics, 62(5), 28912902.10.1109/TIE.2014.2364982CrossRefGoogle Scholar
Zhao, B., Xian, B., Zhang, Y. and Zhang, X. (2015). Nonlinear robust sliding mode control of a quadrotor unmanned aerial vehicle based on immersion and invariance method. International Journal of Robust and Nonlinear Control, 25(18), 37143731.10.1002/rnc.3290CrossRefGoogle Scholar
Zheng, X., Yang, X., Zhao, H. and Chen, Y. (2022). Saturated adaptive-law-based backstepping and its applications to a quadrotor hover. IEEE Transactions on Industrial Electronics, 69(12), 1347313482.10.1109/TIE.2021.3139235CrossRefGoogle Scholar
Zhu, G., Wang, S., Sun, L., Ge, W. and Zhang, X. (2020). Output feedback adaptive dynamic surface sliding-mode control for quadrotor UAVs with tracking error constraints. Complexity, 2020, 123.Google Scholar
Zhu, Z. and Cao, S. (2019). Back-stepping sliding mode control method for quadrotor uav with actuator failure. The Journal of Engineering, 2019(22), 83748377.10.1049/joe.2019.1084CrossRefGoogle Scholar
Zou, Y. and Meng, Z. (2018). Immersion and invariance-based adaptive controller for quadrotor systems. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 49(11), 22882297.10.1109/TSMC.2018.2790929CrossRefGoogle Scholar
Zuo, Z. (2010). Trajectory tracking control design with command-filtered compensation for a quadrotor. IET Control Theory & Applications, 4(11), 23432355.10.1049/iet-cta.2009.0336CrossRefGoogle Scholar