Automation and Remote Control

, Volume 80, Issue 9, pp 1717–1733 | Cite as

Large Scale Systems Control

  • D. A. NikitinEmail author


In this paper we propose the quaternion-based control system for quadrotor. Adaptive scheme for thrust coefficients identification, based on speed-gradient method, is designed. Proofs of stability are provided, as well the results of numerical simulations. In existing theoretical works, Euler angles are often used as coordinates for describing quadrotor’s coordinates. Equations using those coordinates, however, have a singularity, which prevents their use near certain points. We use quaternions instead, which have no such restrictions. The process of discovering PID-regulator coefficients is known to be tedious, error-prone and specific for each quadcopter. We propose a control scheme in which most of the parameters are physical values, and the rest do not depend on the quadcopter and can be found once for the whole class of the flying machines. An identification algorithm for obtaining physical parameters is also described. MATLAB modelling is used to test and confirm the performance of the proposed scheme.


UAV quadrotor adaptive control speed-gradient method quaternions 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



This research was supported by the Russian Science Foundation, project no. 14-29-00142 in the Institute for Problems of Mechanical Engineering, of the Russian Academy of Sciences (IPME RAS).


  1. 1.
    Belyavskyi, A.O. and Tomashevich, S.I., Passivity-Based Method for Quadrotor Control, Upravlen. Bol’sh. Sist., 2016, no. 63, pp. 155–181.Google Scholar
  2. 2.
    Kanatnikov, A.N. and Akopyan, K.R., The Plane Motion Control of the Quadrocopter, Mat. Mat. Modelir., 2015, no. 2, pp. 23–36.CrossRefGoogle Scholar
  3. 3.
    Landau, L.D. and Lifshits, E.M., Teoreticheskaya fizika, tom 1: Mekhanika (Theoretical Physics, vol. 1: Mechanics), Moscow: Fizmatlit, 2013, 5th ed.zbMATHGoogle Scholar
  4. 4.
    Matveev, V.V. and Raspopov, V.Ya., Osnovy postroeniya besplatformennykh inertsial’nykh navigatsionnykh sistem (Fundamentals of Designing Strapdown Inertial Navigation Systems), St. Petersburg: TsNII “Elektropribor,” 2009.Google Scholar
  5. 5.
    Miroshnik, I.V., Nikiforov, V.O., and Fradkov, A.L., Nelineinoe i adaptivnoe upravlenie slozhnymi dinamicheskimi sistemami (Nonlinear and Adaptive Control for Complex Dynamical Systems), St. Petersburg: Nauka, 2000.zbMATHGoogle Scholar
  6. 6.
    Yakubovich, V.A., Frequency Theorem in the Control Theory, Sib. Mat. Zh., 1973, vol. 14, no. 2, pp. 384–419.MathSciNetCrossRefGoogle Scholar
  7. 7.
    Augugliaro, F., Schoellig, A.P., and D’Andrea, R., Generation of Collision-Free Trajectories for a Quadrocopter Fleet: A Sequential Convex Programming Approach, IEEE/RSJ Int. Conf. on Intelligent Robots and Systems (IROS), Vilamoura-Algarve, Portugal, October 7–11, 2012, pp. 1917–1922.Google Scholar
  8. 8.
    Chovancová, A., Fico, T., Chovanec, Ĺ., and Hubinsk, P., Mathematical Modelling and Parameter Identification of Quadrotor (A Survey), Procedia Eng., 2014, vol. 96, pp. 172–181.CrossRefGoogle Scholar
  9. 9.
    Fresk, E. and Nikolakopoulos, G., Full Quaternion Based Attitude Control for a Quadrotor, Eur. Control Conf. (ECC’2013), Zurich, Switzerland, July 17–19, 2013, pp. 3864–3869.Google Scholar
  10. 10.
    Hehn, M. and D’Andrea, R. A Frequency Domain Iterative Learning Algorithm for High-Performance, Periodic Quadrocopter Maneuvers, Mechatronics, 2014, vol. 24, no. 8, pp. 954–965.CrossRefGoogle Scholar
  11. 11.
    Hehn, M. and D’Andrea, R., Quadrocopter Trajectory Generation and Control, IFAC World Congress, Milano, Italy, August 28–September 2, 2011, vol. 18, no. 1, pp. 1485–1491.Google Scholar
  12. 12.
    Kalman, R.E., Lyapunov Functions for the Problem of Lur’e in Automatic Control, Proc. USA Natl. Acad. Sci., 1963, vol. 49(2), pp. 201–205.CrossRefGoogle Scholar
  13. 13.
    Khatoon, S., Shahid, M., and Chaudhary, H., Dynamic Modeling and Stabilization of Quadrotor Using PID Controller, IEEE Int. Conf. on Advances in Computing, Communications and Informatics (ICACCI), Delhi, India, September 24–27, 2014, pp. 746–750.Google Scholar
  14. 14.
    Lefferts, E.J., Markley, F.L., and Shuster, M.D., Kalman Filtering for Spacecraft Attitude Estimation, J. Guidance, Control, Dynam., 1982, vol. 5, no. 5, pp. 417–429.CrossRefGoogle Scholar
  15. 15.
    Leishman, J.G., Principles of Helicopter Aerodynamics, Cambridge: Cambridge Univ. Press, 2006, 2nd ed.Google Scholar
  16. 16.
    Lim, H., Park, J., Lee, D., and Kim, H.J., Build Your Own Quadrotor. Open-Source Projects on Unmanned Aerial Vehicles, IEEE Robot. Automat. Magaz., Septermer, 2012, pp. 33–45.Google Scholar
  17. 17.
    Madgwick, S.O.H., An Efficient Orientation Filter for Inertial and Inertial/Magnetic Sensor Arrays, Internal Report, 2010.Google Scholar
  18. 18.
    Mahony, R., Hamel, T., and Pflimlin, J.M., Nonlinear Complementary Filters on the Special Orthogonal Group, IEEE Trans. Automat. Control, 2008, vol. 53, no. 5, pp. 1203–1218.MathSciNetCrossRefGoogle Scholar
  19. 19.
    Mahony, R., Kumar, V., and Corke, P., Multirotor Aerial Vehicles. Modelling, Estimation, and Control of Quadrotor, IEEE Robot. Automat. Magaz., Septermer, 2012, pp. 20–32.Google Scholar
  20. 20.
    Perez, I.C., Flores-Araiza, D., Fortoul-Diaz, J.A., Maximo, R., and Gonzalez-Hernandez, H.G., Identification and PID Control for a Quadrocopter, IEEE Int. Conf. on Electronics, Communications and Computers (CONIELECOMP), Puebla, Mexico, Febuary 26–28, 2014, pp. 77–82.Google Scholar
  21. 21.
    Pounds, P., Mahony, R., and Corke, P., Modelling and Control of a Quad-Rotor Robot, Proc. Australasian Conf. on Robotics and Automation’2006, Auckland, New Zealand, December 6–8, 2006, pp. 1–10.Google Scholar
  22. 22.
    Rafflo, G.V., Ortega, M.G., and Rubio, F.R., MPC with Nonlinear H Control for Path Tracking of a Quad-Rotor Helicopter, Proc. 17th IFAC World Congress, Seoul, Korea, July 6–11, 2008, pp. 8564–8569.Google Scholar
  23. 23.
    Ritz, R., Muller, M.W., Hehn, M., and D’Andrea, R., Cooperative Quadrocopter Ball Throwing and Catching, IEEE/RSJ Int. Conf. on Intelligent Robots and Systems (IROS), Vilamoura-Algarve, Portugal, October 7–11, 2012, pp. 4972–4978.Google Scholar
  24. 24.
    Schoellig, A.P., Wiltsche, C., and D’Andrea R., Feed-Forward Parameter Identification for Precise Periodic Quadrocopter Motions, IEEE Am. Control Conf., Montreal, Canada, June 27–29, 2012, pp. 4313–4318.Google Scholar
  25. 25.
    Shen, S., Mulgaonkar, Y., Michael, N., and Kumar, V., Vision-Based State Estimation and Trajectory Control Towards High-Speed Flight with a Quadrotor, Robotics: Science and Systems, Berlin, Germany, June 24–28, 2013, vol. 1, p. 32.Google Scholar
  26. 26.
    Stegagno, P., Basile, M., Bulthoff, H.H., and Franchi, A., Vision-based Autonomous Control of a Quadrotor UAV using an Onboard RGB-D Camera and Its Application to Haptic Teleoperation, 2nd IFAC Work. on Research, Education and Development of Unmanned Aerial Systems, Compiegne, France, 2013, pp. 87–92.Google Scholar
  27. 27.
    Terekhov, A.N., Luchin, R.M., and Filippov, S.A., Educational Cybernetical Construction Set for schools and universities, Proc. 9th IFAC Symposium Advances in Control Education, Nizhny Novgorod, Russia, June 19–21, 2012, pp. 430–435.Google Scholar
  28. 28.
    Tournier, G.P., Valenti, M., and How, J.P., Estimation and Control of a Quadrotor Vehicle Using Monocular Vision and Moire Patterns, AIAA Guidance, Navigation and Control Conf. and Exhibit., 2006, pp. 21–24.Google Scholar
  29. 29.
    Zhu, J., Liu, E., Guo, S., and Xu, C., A Gradient Optimization Based PID Tuning Approach on Quadrotor, IEEE 27th Chinese Control and Decision Conference (CCDC), Qingdao, China, May 23–25, 2015, pp. 1588–1593.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

Personalised recommendations