Control Theory and Technology

, Volume 16, Issue 2, pp 133–144 | Cite as

Nonlinear robust control of a quadrotor helicopter with finite time convergence

  • Guozhou Zheng
  • Bin Xian


In this paper, the control problem for a quadrotor helicopter which is subjected to modeling uncertainties and unknown external disturbance is investigated. A new nonlinear robust control strategy is proposed. First, a nonlinear complementary filter is developed to fuse the raw data from the onboard barometer and the accelerometer to decrease the negative effects from the noise associated with the low-cost onboard sensors Then the adaptive super-twisting methodology is combined with a backstepping method to formulate the nonlinear robust controller for the quadrotor’s attitude angles and the altitude position. Lyapunov based stability analysis shows that finite time convergence is ensured for the closed-loop operation of the quadrotor’s roll angle, pitch angle, row angle and the altitude position. Real-time flight experimental results, which are performed on a quadrotor flight testbed, are included to demonstrate the good control performance of the proposed control methodology.


Quadrotor nonlinear control finite time convergence real-time experiment 


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  1. [1]
    Y. Du, J. Fang, C. Miao. Frequency domain system identification of an unmanned helicopter based on adaptive genetic algorithm. IEEE Transactions on Industrial Electronics, 2014, 61(2): 870–881.CrossRefGoogle Scholar
  2. [2]
    M. D. Hua, T. Hamel, P. Morin, et al. Introduction to feedback control of underactuated VTOL vehicles: a review of basic control design ideas and principles. IEEE Control System Magzine, 2013, 33(1): 61–75.MathSciNetCrossRefGoogle Scholar
  3. [3]
    K. Alexis, G. Nikolakopoulos, A. Tzes. Model predictive quadrotor control: attitude, altitude and position experimental studies. IET Control Theory and Applications, 2012, 6(12): 1812–1827.MathSciNetCrossRefGoogle Scholar
  4. [4]
    B. Zhao, B. Xian, Y. Zhang, et al. Nonlinear robust adaptive tracking control of a quadrotor UAV via immersion and invariance methodology. IEEE Transactions on Industrial Electronics, 2015, 62(5): 2891–2902.CrossRefGoogle Scholar
  5. [5]
    B. Xian, X. Zhang, S. Yang. Nonlinear controller design for an unmanned aerical vehicle with a slung-load. Control Theory & Applications, 2016, 33(3): 273–279 (in Chinese).Google Scholar
  6. [6]
    W. Hao, B. Xian. Nonlinear fault tolerant control design for quadrotor unmanned aerial vehicle attitude system. Control Theory & Applications, 2015, 32(11): 1457–1463 (in Chinese).zbMATHGoogle Scholar
  7. [7]
    X. Zhang, B. Xian, B. Zhao, et al. Autonomous flight control of a nano quadrotor helicopter in a GPS-denied environment using on-board vision. IEEE Transactions on Industrial Electronics, 2015, 62(10): 6392–6403.CrossRefGoogle Scholar
  8. [8]
    J. Toledo, L. Acosta, D. Perea, et al. Stability and performance analysis of unmanned aerial vehicles: quadrotor against hexrotor. IET Control Theory and Applications, 2015, 9(8): 1190–1196.MathSciNetCrossRefGoogle Scholar
  9. [9]
    G. V. Raffo, M. G. Ortega, F. R. Rubio. An integral predictive/nonlinear H8 control structure for a quadrotor helicopter. Automatica, 2010, 46(1): 29–39.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    R. Zhang, Q. Quan, K. Y. Cai. Attitude control of a quadrotor aircraft subject to a class of time-varying disturbances. IET Control Theory and Applications, 2011, 5(1): 1140–1146.MathSciNetCrossRefGoogle Scholar
  11. [11]
    H. Ramirez-Rodriguez, V. Parra-Vega, A. Sanchez-Orta, et al. Robust backstepping control based on integral sliding modes for tracking of quadrotors. Journal of Intelligent and Robotic Systems, 2014, 73(1/4): 51–66.CrossRefGoogle Scholar
  12. [12]
    H. Liu, Y. Bai, G. Lu, et al. Robust motion control of uncertain quadrotors. Journal of the Franklin Institute, 2014, 351(12): 5494–5510.MathSciNetCrossRefGoogle Scholar
  13. [13]
    H. Liu, Y. Bai, G. Lu, et al. Robust tracking control of a quadrotor helicopter. Journal of Intelligent and Robotic Systems, 2014, 75(3/4): 595–608.CrossRefGoogle Scholar
  14. [14]
    B. J. Bialy, J. Klotz, K. Brink, et al. Lyapunov-based robust adaptive control of a quadrotor UAV in the presence of modeling uncertainties. Proceedings of the American Control Conference, Washington: IEEE, 2013: 13–18.Google Scholar
  15. [15]
    Y. Yu, X. Ding, J. Zhu. Attitude tracking control of a quadrotor UAV in the exponential coordinates. Journal of the Franklin Institute, 2013, 350(8): 2044–2068.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    L. Derafaa, A. Benallegueb, L. Fridman. Super twisting controlal gorithm for the attitude tracking of a four rotors UAV. Journal of the Franklin Institute, 2012, 349(2): 658–699.MathSciNetCrossRefGoogle Scholar
  17. [17]
    Y. Shtesse, M. Taleb, F. Plestan. A novel adaptive-gain supertwisting sliding mode controller: methodology and application. Automatica, 2012, 48(5): 759–769.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    F. Kendoul, Z. Yu, K. Nonami. Guidance and nonlinear control system for autonomous flight of minirotorcraft unmanned aerial vehicles. Journal of Field Robotics, 2010, 27(3): 311–334.Google Scholar
  19. [19]
    B. Xian, C. Diao, B. Zhao, et al. Nonlinear robust output feedback tracking control of a quadrotor UAV using quaternion representation. Nonlinear Dynamics, 2015, 79(4): 2735–2752.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    I. Gonzalez, S. Salazar, R. Lozano, et al. Real-time altitude robust controller for a quad-rotor aircraft using sliding-mode control technique. Proceeding of the International Conference on Unmanned Aircraft Systems, Atlanta: IEEE, 2013: 650–659.Google Scholar
  21. [21]
    J. Hu, H. Zhang. Immersion and invariance based commandfiltered adaptive backstepping control of VTOL vehicles. Automatica, 2013, 49(7): 2160–2167.MathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    R. Mahony, T. Hamel, J. M. Pflimlin. Nonlinear complementary filters on the special orthogonal group. IEEE Transactions on Automatic Control, 2008, 53(5): 1203–1218.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© South China University of Technology, Academy of Mathematics and Systems Science, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Electrical and Information EngineeringTianjin UniversityTianjinChina

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