Model-assisted extended state observer and dynamic surface control–based trajectory tracking for quadrotors via output-feedback mechanism
Corresponding Author
Xingling Shao
Key Laboratory of Instrumentation Science and Dynamic Measurement, Ministry of Education, North University of China, Taiyuan, China
National Key Laboratory for Electronic Measurement Technology, School of Instrument and Electronics, North University of China, Taiyuan, China
Correspondence
Xingling Shao, Key Laboratory of Instrumentation Science and Dynamic Measurement, Ministry of Education; National Key Laboratory for Electronic Measurement Technology, School of Instrument and Electronics, North University of China, Taiyuan 030051, China.
Email: [email protected]
Search for more papers by this authorNing Liu
Key Laboratory of Instrumentation Science and Dynamic Measurement, Ministry of Education, North University of China, Taiyuan, China
National Key Laboratory for Electronic Measurement Technology, School of Instrument and Electronics, North University of China, Taiyuan, China
Search for more papers by this authorJun Liu
Key Laboratory of Instrumentation Science and Dynamic Measurement, Ministry of Education, North University of China, Taiyuan, China
National Key Laboratory for Electronic Measurement Technology, School of Instrument and Electronics, North University of China, Taiyuan, China
Search for more papers by this authorHonglun Wang
School of Automation Science and Electrical Engineering, Beihang University, Beijing, China
Search for more papers by this authorCorresponding Author
Xingling Shao
Key Laboratory of Instrumentation Science and Dynamic Measurement, Ministry of Education, North University of China, Taiyuan, China
National Key Laboratory for Electronic Measurement Technology, School of Instrument and Electronics, North University of China, Taiyuan, China
Correspondence
Xingling Shao, Key Laboratory of Instrumentation Science and Dynamic Measurement, Ministry of Education; National Key Laboratory for Electronic Measurement Technology, School of Instrument and Electronics, North University of China, Taiyuan 030051, China.
Email: [email protected]
Search for more papers by this authorNing Liu
Key Laboratory of Instrumentation Science and Dynamic Measurement, Ministry of Education, North University of China, Taiyuan, China
National Key Laboratory for Electronic Measurement Technology, School of Instrument and Electronics, North University of China, Taiyuan, China
Search for more papers by this authorJun Liu
Key Laboratory of Instrumentation Science and Dynamic Measurement, Ministry of Education, North University of China, Taiyuan, China
National Key Laboratory for Electronic Measurement Technology, School of Instrument and Electronics, North University of China, Taiyuan, China
Search for more papers by this authorHonglun Wang
School of Automation Science and Electrical Engineering, Beihang University, Beijing, China
Search for more papers by this authorSummary
In this paper, an output-feedback trajectory tracking controller for quadrotors is presented by integrating a model-assisted extended state observer (ESO) with dynamic surface control. The quadrotor dynamics are described by translational and rotational loops with lumped disturbances to promote the hierarchical control design. Then, by exploiting the structural property of the quadrotor, a model information–assisted high-order ESO that relies only on position measurements is designed to estimate not only the unmeasurable states but also the lumped disturbances in the rotational loop. In addition, to account for the problem of “explosion of complexity” inherent in hierarchical control, the output feedback–based trajectory tracking and attitude stabilization laws are respectively synthesized by utilizing dynamic surface control and the corresponding estimated signals provided by the ESO. The stability analysis is given, showing that the output-feedback trajectory tracking controller can ensure the ultimate boundedness of all signals in the closed-loop system and make the tracking errors arbitrarily small. Finally, flight simulations with respect to an 8-shaped trajectory command are performed to verify the effectiveness of the proposed scheme in obtaining the stable and accurate trajectory tracking using position measurements only.
REFERENCES
- 1Lee H, Kim HJ. Trajectory tracking control of multirotors from modeling to experiments: a survey. Int J Control Autom Syst. 2017; 15(1): 281-292.
- 2Sinan ON, Mert O, Onder EM. Feedback control strategies for quadrotor-type aerial robots: a survey. Trans Inst Meas Control. 2016; 38(5): 529-554.
- 3Tomic T, Schmid K, Phillip L, et al. Towards a fully autonomous UAV: research platform for indoor and outdoor urban search and rescue. IEEE Robot Autom Mag. 2012; 19(3): 46-56.
- 4Raza SA, Sutherland M, Etele J, et al. Experimental validation of quadrotor simulation tool for flight within building wakes. Aerosp Sci Technol. 2017; 67: 169-180.
- 5Voos H. Nonlinear control of quadrotor micro-UAV using feedback linearization. Paper presented at: IEEE International Conference on Mechatronics; 2009; Malaga, Spain.
- 6Madani T, Benallegue A. Control of a quadrotor Mini-Helicopter via full state back-stepping technique. Paper presented at: 2006 IEEE Conference on Decision & Control; 2006; Paris, France.
- 7Chen FY, Lei W, Zhang K, Tao G, Jiang B. A novel nonlinear resilient control for a quadrotor UAV via back-stepping control and nonlinear disturbance observer. Nonlinear Dynamics. 2016; 85(2): 1281-1295.
- 8Yacef F, Bouhail O, Hamerlain M, Rizoug N. Observer-based adaptive fuzzy back-stepping tracking control of quadrotor unmanned aerial vehicle powered by li-ion battery. J Intell Robot Syst. 2016; 84(1-4): 179-197.
- 9Chen FY, Jiang RQ, Zhang KK, et al. Robust back-stepping sliding-mode control and observer-based fault estimation for a quadrotor UAV. IEEE Trans Ind Electron. 2016; 63(8): 5044-5056.
- 10Chiheb Ben R, Farhani F, Zaafouri A, Chaari A. A novel adaptive control method for induction motor based on back-stepping approach using dSpace DS1104 control board. Mech Syst Signal Process. 2018; 100: 466-481.
- 11Yangming Z, Peng Y, Zhen Z. Robust adaptive back-stepping control for piezoelectric nano-manipulating systems. Mech Syst Signal Process. 2017; 83: 130-148.
- 12Zapateiro M, Luo N, Karimi HR, Vehi J. Vibration control of a class of semiactive suspension system using neural network and back-stepping techniques. Mech Syst Signal Process. 2009; 23(6): 1946-1953.
- 13Jia ZY, Jianqiao Y, Yuesong M, Yongbo C, Yuanchuan S, Xiaolin A. Integral back-stepping sliding mode control for quadrotor helicopter uncer external uncertain disturbances. Aerosp Sci Technol. 2017; 68: 299-307.
- 14Xiong JJ, Zheng EH. Position and attitude tracking control for a quadrotor UAV. ISA Trans. 2014; 53(3): 725-731.
- 15Zheng EH, Xiong JJ, Luo JL. Second order sliding mode control for a quadrotor UAV. ISA Trans. 2014; 53(4): 1350-1356.
- 16Bambang S, Naoki U, Shigenori S. Least square based sliding mode control for a quadrotor helicopter and energy saving by chattering reduction. Mech Syst Signal Process. 2016; 66-67: 769-784.
- 17Yang YN, Yan Y. Attitude regulation for unmanned quadrotors using adaptive fuzzy gain-scheduling sliding mode control. Aerosp Sci Technol. 2016; 54: 208-217.
- 18Rooh ul A, Li AJ, Khan MU, Shamshirband S, Kamsin A. An adaptive trajectory tracking control of four rotor hover vehicle using extended normalized radial basis function network. Mech Syst Signal Process. 2017; 83: 53-74.
- 19Szanto N, Narayanan V, Jagannathan S. Event-sampled control of quadrotor unmanned aerial vehicle using neural networks. Paper presented at: 2017 American Control Conference (ACC); 2017; Seattle, WA.
- 20Dierks T, Jagannathan S. Output feedback control of a quadrotor UAV using neural networks. IEEE Trans Neural Netw. 2010; 21(1): 50-66.
- 21Lee D, Burg T, Xian B, Dawson D. Output feedback tracking control of an underactuated quad-rotor UAV. Paper presented at: 2007 American Control Conference (ACC); 2007; New York, NY.
- 22Kendoul F. Nonlinear hierarchical flight controller for unmanned rotorcraft: design, stability, and experiments. J Guid Control Dynam. 2009; 32(6): 1954-1958.
- 23Zhao B, Xian B, Zhang Y, et al. Nonlinear robust sliding mode control of a quadrotor unmanned aerial vehicle based on immersion and invariance method. Int J Robust Nonlinear Control. 2015; 25(18): 3714-3731.
- 24Raffo GV, Ortega MG, Rubio FR. An integral predictive/nonlinear H infinity control structure for a quadrotor helicopter. Automatica. 2010; 46(1): 29-39.
- 25Li SS, Wang YN, Tan JH, et al. Adaptive RBFNN/integral sliding mode control for a quadrotor aircraft. Neurocomputing. 2016; 216: 126-134.
- 26Zhou ZB, Li Y, Zhang JF, et al. Integrated navigation system for a low-cost quadrotor aerial vehicle in the presence of rotor influences. J Surv Eng. 2017; 143(1): 1-13.
- 27Abdessameud A, Tayebi A. Global trajectory tracking control of VTOL-UAVs without linear velocity measurements. Automatica. 2010; 46(6): 1053-1059.
- 28Bertrand S, Guenard N, Hamel T, et al. A hierarchical controller miniature VTOL UAVs: design and stability analysis using singular perturbation theory. Control Eng Pract. 2011; 19(10): 1099-1108.
- 29Zou Y. Trajectory tracking controller for quadrotors without velocity and angular velocity measurements. IET Control Theory Appl. 2017; 11(1): 101-109.
- 30Gao Z. Scaling and bandwidth-parameterization based controller tuning. Paper presented at: American Control Conference; 2003; Denver, CO.
- 31Yao J, Jiao Z, Ma D. Extended-state-observer-based output feedback nonlinear robust control of hydraulic systems with back-stepping. IEEE Trans Ind Electron. 2014; 24(6): 993-1015.
- 32Guo Q, Zhang Y, Celler BG, et al. Back-stepping control of electro-hydraulic system based on extended-state-observer with plant dynamics largely unknown. IEEE Trans Ind Electron. 2016; 63(11): 6909-6920.
- 33Shao X, Wang H. Active disturbance rejection based trajectory linearization control for hypersonic reentry vehicle with bounded uncertainties. ISA Trans. 2015; 54(1): 27-38.
- 34Shao X, Wang H. Back-stepping active disturbance rejection control design for integrated missile guidance and control system via reduced-order ESO. ISA Trans. 2015; 57: 10-22.
- 35Swaroop D, Hedrick JK, Yeip PP, et al. Dynamic surface control for a class of nonlinear systems. IEEE Trans Autom Control. 2000; 45(10): 1893-1899.
- 36Liu YH, Huang LP, Xiao DM. Adaptive dynamic surface control for uncertain nonaffine nonlinear systems. Int J Robust Nonlinear Control. 2017; 27(4): 535-546.
- 37Wang D, Huang J. Neural network-based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict-feedback form. IEEE Trans Neural Netw. 2005; 16(1): 195-202.
- 38Liu YH. Adaptive dynamic surface asymptotic tracking for a class of uncertain nonlinear systems. Int J Robust Nonlinear Control. 2017; 1-13. https://doi.org/10.1002/rnc.3947
- 39Sun GF, Ren XM, Chen Q, Li D. A modified dynamic surface approach for control of nonlinear systems with unknown input dead zone. Int J Robust Nonlinear Control. 2015; 25(8): 1145-1167.
- 40Diao C, Xian B, Zhao B, Zhang X, Liu SB. An output feedback attitude tracking controller design for quadrotor unmanned aerial vehicles using quaternion. Paper presented at: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS); 2013; Tokyo, Japan.
- 41Wang X, Shirinzadeh B. Nonlinear augmented observer design and application to quadrotor aircraft. Nonlinear Dynamics. 2015; 80(3): 1463-1481.
- 42Khalil HK. High-gain observers in nonlinear feedback control. In: H Nijmeijer, TI Fossen, eds. New Directions in Nonlinear Observer Design. New York, NY: Springer-Verlag; 1999.
- 43Chen FY, Cai L, Jiang B, Tao G. Direct self-repairing control for a helicopter via quantum multi-model and disturbance observer. Int J Syst Sci. 2016; 47(3): 533-543.
- 44Chen FY, Jiang RQ, Wen C, Su R. Self-repairing control of a helicopter with input time delay via adaptive global sliding mode control and quantum logic. Inform Sci. 2015; 316: 123-131.