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Barrier Lyapunov function and adaptive backstepping-based control of a quadrotor UAV

Published online by Cambridge University Press:  05 June 2023

Adel Khadhraoui Open the ORCID record for Adel Khadhraoui [Opens in a new window] ,
Amir Zouaoui  and
Mohamad Saad
Adel Khadhraoui*
Affiliation:
School of Engineering, University of Quebec in Abitibi-Temiscamingue, Rouyn-Noranda, QC, J9X5E4, Canada
Amir Zouaoui
Affiliation:
School of Engineering, University of Quebec in Abitibi-Temiscamingue, Rouyn-Noranda, QC, J9X5E4, Canada
Mohamad Saad
Affiliation:
School of Engineering, University of Quebec in Abitibi-Temiscamingue, Rouyn-Noranda, QC, J9X5E4, Canada
*
Corresponding author: Adel Khadhraoui; Email: adel.khadhraoui@uqat.ca
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Abstract

This paper presents backstepping control and backstepping constraint control approaches for a quadrotor unmanned aerial vehicle (UAV) control system. The proposed methods are applied to a Parrot Mambo drone model to control rotational motion along the $x$, $y$, and $z$ axes during hovering and trajectory tracking. In the backstepping control approach, each state of the system controls the previous state and is called “virtual control.” The last state is controlled by the real control input. The idea is to compute, in several steps, a control law that ensures the asymptotic stability of the system. The backstepping constraint control method, based on barrier Lyapunov functions (BLFs), is designed not only to track the desired trajectory but also to guarantee no violation of the position and angle constraints. Symmetric BLFs are introduced in the design of the controller. A nonlinear mathematical model is considered in this study. Based on Lyapunov stability theory, it can be concluded that the proposed controllers can guarantee the stability of the UAV system and the state converges asymptotically to the desired trajectory. To make the control robust, an adaptation law is applied to the backstepping control that estimates the unknown parameters and ensures their convergence to their respective values. Validation of the proposed controllers was performed by simulation on a flying UAV system.

Keywords

flying robotUAVquadrotortracking trajectorybacksteppingadaptative controlbarrier functionconstraintsLyapunov methods

Information

Type
Research Article
Information
Robotica , Volume 41 , Issue 10 , October 2023 , pp. 2941 - 2963
Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

Lee, D., Kim, H. J. and Sastry, S., “Feedback linearization vs. adaptive sliding mode control for a quadrotor helicopter,” Int J. Cont. Autom. Syst. 7(3), 419–428 (2009).10.1007/s12555-009-0311-8CrossRefGoogle Scholar
Chung-Cheng, C. and Yen-Ting, C., “Feedback linearized optimal control design for quadrotor with multi-performances,” IEEE Access 9, 26674–26695 (2021).Google Scholar
Hossny, M., El-Badawy, A. and Hassan, R.. “Fuzzy Model Predictive Control of a Quadrotor Unmanned Aerial Vehicle,” In: Proceedings of International Conference on Unmanned Aircraft Systems, Athens, Greece (2020) pp. 1–4.Google Scholar
Mueller, K., Fennel, M. and Trommer, F. G.. “Model Predictive Control for Vision-Based Quadrotor Guidance,” In: Proceedings of IEEE/ION Position, Location and Navigation Symposium, Portland, OR, USA (2020) pp. 50–61.Google Scholar
Wang, J., Alattas, K., Bouteraa, Y., Mofid, O. and Mobayen, S., “Adaptive finite-time backstepping control tracker for quadrotor UAV with model uncertainty and external disturbance,” Aerosp. Sci. Technol. 133, 108088 (2023).CrossRefGoogle Scholar
Liu, Y., Jiang, B., Lu, J., Cao, J. and Lu, G., “Event-triggered sliding mode control for attitude stabilization of a rigid spacecraft,” IEEE Trans. Syst., Man, Cybern. Syst. 50(9), 3290–3299 (2020).CrossRefGoogle Scholar
Khebbache, H., “Fault Tolerance via the Backstepping Method of Nonlinear Systems: Quadrotor-like UAV System Application,” In: Master’s Degree Project  (University Ferhat Abbas of Setif (UFAS), Algeria, 2018).Google Scholar
Mahmoud, M. S. and Saad, M., “Robust adaptive multilevel control of a quadrotor,” IEEE Access 8, 167684–167692 (2020).10.1109/ACCESS.2020.3022724CrossRefGoogle Scholar
Labbadi, M. and Cherkaoui, M., “Robust adaptive nonsingular fast terminal sliding-mode tracking control for an uncertain quadrotor UAV subjected to disturbances,” ISA Trans. 99, 290–304 (2020).Google Scholar
Das, A., Lewis, F. and Subbaro, K., “A modified backstepping control of quadrotor,” J. Itell. Robot. Syst. 56(1-2), 127–151 (2009).CrossRefGoogle Scholar
Liu, J., Gai, W., Zhang, J. and Li, Y., “A nonlinear adaptive backstepping with ESO for the quadrotor trajectory tracking control in the multiple disturbances,” Int. J. Control, Autom. Syst. 17(11), 2754–2768 (2019).CrossRefGoogle Scholar
Martins, L., Cardeira, C. and Oliveira, P., “Feedback linearization with zero dynamics stabilization for quadrotor control,” J. Intell. Robotic Syst. 101(1), 1–a17 (2021).Google Scholar
Alexis, K., Nikolakopoulos, G. and Tzes, A., “Model predictive quadrotor control: Attitude, altitude and position experimental studies,” IET Control Theory Appl. 6(12), 1812–1827 (2012).CrossRefGoogle Scholar
Yang, J. and Zheng, W. X., “Offset-free nonlinear MPC for mismatched disturbance attenuation with application to a static var compensator,” IEEE Trans. Circuits Syst. II, Exp. Briefs 61(1), 49–53 (2014).Google Scholar
Sihao, S., Angel, R., Philipp, F., Elia, K. and Scaramuzza, D., “A comparative study of nonlinear mpc and differential-flatness-based control for quadrotor agile flight,” IEEE Trans. Robot., 1–17 (2022).Google Scholar
Gupta, N. and Kothari, M., “Modeling and control of inverted flight of a variable-pitch quadrotor,” (2017).Google Scholar
Yang, Y. and Yan, Y., “Attitude regulation for unmanned quadrotors using adaptive fuzzy gain-scheduling sliding mode control,” Aerosp. Sci. Technol. 54, 208–217 (2016).CrossRefGoogle Scholar
Ríos, H., Falcón, R., González, O. A. and Dzul, A., “Continuous sliding mode control strategies for quadrotor robust tracking: Real-time application,” IEEE Trans. Ind. Electron. 66(2), 1264–1272 (2019).CrossRefGoogle Scholar
Hou, Z., Lu, P. and Tu, Z., “Nonsingular terminal sliding mode control for a quadrotor UAV with a total rotor failure,” Aerosp. Sci. Technol. 98, 105716 (2020).10.1016/j.ast.2020.105716CrossRefGoogle Scholar
Basri, M., Abidin, M. and Subha, N., “Simulation of backstepping-based nonlinear control for quadrotor helicopter,” Appl. Model. Simul. 2(1), 34–40 (2018).Google Scholar
Wang, M., Chen, B. and Lin, C., “Fixed-timeBackstepping control of quadrotor trajectory tracking based on neural network,” IEEE Access 8, 177092–177099 (2020).10.1109/ACCESS.2020.3027052CrossRefGoogle Scholar
Fuyang, C., Rongqiang, J., Kangkang, Z., Bin, J. and Gang, T., “Robust backstepping sliding-mode control and observer-based fault estimation for a quadrotor UAV,” IEEE Trans. Ind. Electron. 63(8), 5044–5056 (2016).Google Scholar
Brahmi, B., Saad, M., El-Bayeh, C., Rahman, M. and Brahmi, A., “Novel adaptive backstepping control for uncertain manipulator robots using state and output feedback,” Robotica 40(5), 1326–1344 (2022).10.1017/S0263574721001132CrossRefGoogle Scholar
Wei, Y., Li, C., Sun, Y. and Ma, G., “Backstepping Approach for Controlling a Quadrotor Using Barrier Lyapunov Functions,” In: Proceedings of the 2017 Chinese Control Conference(2017) pp. 6235–6239.Google Scholar
Zhongjun, H., Qiang, C., Yi, H. and Cong, C., “Barrier Lyapunov Function Based Finite-Time Backstepping Control of Quadrotor with Full State Constraints,” In: Proceedings of the 37th Chinese Control Conference, Wuhan, China (July 25-27, 2018).Google Scholar
Peng, T. K., Sam, G. S. and Hock, T. E., “Barrier Lyapunov Functions for the control of output-constrained nonlinear systems,” Automatica 45(4), 918–927 (2009).Google Scholar
Han, S. I., Cheong, J. Y. and Lee, J. M., “Barrier Lyapunov function based sliding mode control for guaranteed tracking performance of robot manipulator,” Math. Prob. Eng. 2013, 1–9 (2013).Google Scholar
Rauh, A. and Senkel, L., “Interval Methods for Robust Sliding Mode Control Synthesis of High-temperature Fuel Cells with State and Input Constraints,” In: Variable-Structure Approaches. Springer (2016), pp. 53–85.Google Scholar
Fu, C., Hong, W., Lu, H., Zhang, L., Guo, X. and Tian, Y., “Adaptive robust backstepping attitude control for a multi-rotor unmanned aerial vehicle with time-varying output constraints,” Aerosp. Sci. Technol. 78, 593–603 (2018).CrossRefGoogle Scholar
Jiang, T., Lin, D. and Song, T., “Finite-time backstepping control for quadrotors with disturbances and input constraints,” IEEE Access 6, 62037–62049 (2018).CrossRefGoogle Scholar
Liu, N., Shao, X., Li, J. and Zhang, W., “Attitude restricted back-stepping anti-disturbance control for vision based quadrotors with visibility constraint,” ISA Trans. 100, 109–125 (2020).CrossRefGoogle ScholarPubMed
Nguyen, A. T., Xuan-Mung, N. and Hong, S. K., “Quadcopter adaptive trajectory tracking control: A new approach via backstepping technique,” Appl. Sci. 9(18), 3873 (2019).10.3390/app9183873CrossRefGoogle Scholar
Shihong, D., P.Ju, H. and Chih-Chiang, C., “Second-order sliding mode controller design with output constraint,” Automatica, 112(Art no. 108704) (2020).Google Scholar
Francesco, S., “Quadrotor Control: Modeling, Nonlinear Control Design, and Simulation,” In: Master’s Degree Project,Stockholm, Sweden (June 2015).Google Scholar
Hu, T., Lin, Z. and Chen, B., “An analysis and design method for linear systems subject to actuator saturation and disturbance,” Automatica 38(2), 351–359 (2020).CrossRefGoogle Scholar
Li, W. and Slotine, J.-J. E., Applied Nonlinear Control. Englewood Cliffs, NJ: Prentice Hall, vol. 199 (1991).Google Scholar
Zhang, Y., Wang, W., Huang, P. and Jiang, Z., “Monocular vision-based sense and avoid of UAV using nonlinear model predictive control,” Robotica 37(9), 1582–1594 (2019).CrossRefGoogle Scholar
Garcia, O., Rojo-Rodriguez, E., Sanchez, A., Saucedo, D. and Munoz-Vazquez, A., “Robust geometric navigation of a quadrotor UAV on SE(3,” Robotica 38(6), 1019–1040 (2020).10.1017/S0263574719001231CrossRefGoogle Scholar
Tripathi, V. K., Kamath, A. K., Behera, L., Verma, N. K. and Nahavandi, S., “Finite-time super twisting sliding mode controller based on higher-order sliding mode observer for real-time trajectory tracking of a quadrator,” IET Cont. Theory Appl 14(16), 2359–2371 (2020).Google Scholar
Villanueva, A., Luque-Vega, L., González-Jiménez, L. and Arellano-Muro, C., “Robust multimode flight framework based on sliding mode control for a rotary UAV,” Robotica 39(4), 699–717 (2021).10.1017/S0263574720000673CrossRefGoogle Scholar
Xiangyu, S., Guanghui, S., Weiran, Y., Jianxing, L. and Ligang, W., “Adaptive sliding mode control for quadrotor UAVs with input saturation,” IEEE/ASME Trans. Mechatron. 27(3), 1498–1509 (2022).Google Scholar
Ye, H., Jiang, H., Ma, S., Tang, B. and Wahab, L., “Linear model predictive control of automatic parking path tracking with soft constraints,” Int. J. Adv. Robot. Syst. 16(3), 172988141985220 (2019).CrossRefGoogle Scholar
Wong, C. K. and Lee, Y. Y., “Lane-based traffic signal simulation and optimization for preventing overflow,” Mathematics 8(1368), 1368 (2020).CrossRefGoogle Scholar
Qin, W., “Unit sliding mode control for disturbed crowd dynamics system based on integral barrier Lyapunov function,” IEEE Access 8, 257–264 (2020).CrossRefGoogle Scholar
Dong, C., Liu, Y. and Wang, Q., “Barrier Lyapunov function based adaptive finite-time control for hypersonic flight vehicles with state constraints,” ISA Trans. 96, 163–176 (2020).10.1016/j.isatra.2019.06.011CrossRefGoogle ScholarPubMed