Advertisement

Nonlinear Dynamics

, Volume 96, Issue 2, pp 1541–1557 | Cite as

Development and experimental investigation of a Quadrotor’s robust generalized dynamic inversion control system

  • Uzair Ansari
  • Abdulrahman H. BajodahEmail author
  • Belkacem Kada
Original Paper
  • 121 Downloads

Abstract

The development of a two-loops Quadrotor’s robust generalized dynamic inversion (RGDI)-based control system is presented. The outer (position) loop utilizes PD position control of the Quadrotor’s center of gravity (CG) in the three-dimensional inertial space, and it provides reference pitch and roll tilting angles commands to the inner loop, in addition to the thrust command that is required to track desired altitude trajectories. The inner (attitude) loop applies RGDI control of a prescribed asymptotically stable dynamics of tilting and attitude errors from reference-tilting and desired-attitude trajectories, and it provides the three required control torque values such that desired CG positions in instantaneous horizontal inertial planes and desired-attitude trajectories of the Quadrotor are tracked. The proposed closed loop system is shown to guarantee finite-time semi-global practically stable trajectory tracking. Numerical simulations of the proposed closed loop control system are performed on a six degrees of freedom Quadrotor’s mathematical model for nominal conditions and under parametric uncertainties and exogenous disturbances. Apart from numerical simulations, experimental tests are conducted on a three degrees of freedom Quadrotor test bench to assess performance of the RGDI control loop. Experimental results demonstrate improved tracking performance in comparison with classical Linear-Quadratic optimal control and conventional sliding mode control.

Keywords

Robust generalized dynamic inversion Sliding mode control Quadrotor control Hover experimental test bench Null control vector Trajectory tracking Finite-time stability Semi-global practical stability 

Notes

Compliance with ethical standards

Conflict of interest

The authors certify that they have NO affiliation with or involvement in any organization or entity with any financial interest, or non-financial interest in the subject matter or materials discussed in this manuscript.

References

  1. 1.
    Ghazbi, S.N., Aghli, Y., Alimohammadi, M., Akbari, A.A.: Quadrotors unmanned aerial vehicles: a review. Int. J. Smart Sens. Intell. Syst. 9(1), 309–333 (2016)Google Scholar
  2. 2.
    Mahony, R., Kumar, V., Corke, P.: Multirotor aerial vehicles: modeling, estimation, and control of quadrotor. IEEE Robot. Autom. Mag. 19(3), 20–32 (2012)CrossRefGoogle Scholar
  3. 3.
    Wang, S., Yang, Y.: Quadrotor aircraft attitude estimation and control based on Kalman filter. In: 31st Chinese Control Conference, Hefei, China, pp. 5634–5639 (2012)Google Scholar
  4. 4.
    Friedland, B.: Control System Design: An Introduction to State-Space Methods (Reprinted by Dover, 2005). McGrae-Hill Inc., New York (1986)Google Scholar
  5. 5.
    Ogata, K.: Modern Control Engineering, 4th edn. Pearson, London (2009)zbMATHGoogle Scholar
  6. 6.
    Nise, N.S.: Control Systems Engineering, 7th edn. Wiley, Hoboken (2015)zbMATHGoogle Scholar
  7. 7.
    Bouabdallah, S., Noth, A., Siegwart, R.: PID vs LQ control techniques applied to an indoor micro quadrotor. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, Sendai, Japan, pp. 2451–2456 (2004)Google Scholar
  8. 8.
    Erginer, B., Altug, E.: Modeling and PD control of a Quadrotor VTOL vehicle. In: IEEE Intelligent Vehicles Symposium, Istanbul, Turkey, pp. 894–899 (2007)Google Scholar
  9. 9.
    Pounds, P., Mahony, R., Corke, P.: Modelling and control of a large quadrotor robot. Control Eng. Pract. 18(7), 691–699 (2010)CrossRefGoogle Scholar
  10. 10.
    Li, J., Li, Y.: Dynamic analysis and PID control for a quadrotor. In: International Conference on Mechatronics and Applications, Beijing, China, pp. 573–578 (2011)Google Scholar
  11. 11.
    ElKholy, Ht.M.: Dynamic modeling and control of a quadrotor using linear and nonlinear approaches. In: Masters Thesis, School of Science and Engineering, American University in Cairo, Cairo (2014)Google Scholar
  12. 12.
    Kokotovic, P.V.: The joy of feedback: nonlinear and adaptive. IEEE Control Syst. Mag. 12(3), 7–17 (1992)CrossRefGoogle Scholar
  13. 13.
    Lozano, R., Brogliato, B.: Adaptive control of robot manipulators with flexible joints. IEEE Trans. Autom. Control 37(2), 174–181 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Zhou, J., Wen, C.: Adaptive Backstepping Control of Uncertain Systems: Nonsmooth Nonlinearities, Interactions or Time-Variations. Springer, New York (2008)zbMATHGoogle Scholar
  15. 15.
    Mian, A.A., Daobo, W.: Modeling and backstepping-based nonlinear control strategy for a 6 DOF quadrotor helicopter. Chin. J. Aeronaut. 21(3), 261–268 (2008)CrossRefGoogle Scholar
  16. 16.
    Khalil, H.K.: Nonlinear Control. Pearson Education, London (2015)zbMATHGoogle Scholar
  17. 17.
    Yang, Y., Yan, Y.: Attitude regulation for unmanned quadrotors using adaptive fuzzy gain-scheduling sliding mode control. Aerosp. Sci. Technol. 54, 208–217 (2016)CrossRefGoogle Scholar
  18. 18.
    Slotine, J.E., Li, W.: Applied Nonlinear Control. Pearson, London (1991)zbMATHGoogle Scholar
  19. 19.
    Utkin, V., Guldner, J., Shi, J.: Sliding Mode Control in Electro-Mechanical Systems, 2nd edn. CRC Press, Boca Raton (2009)CrossRefGoogle Scholar
  20. 20.
    Edwards, C., Spurgeon, S.: Sliding Mode Control: Theory and Applications. CRC Press, Boca Raton (1998)CrossRefzbMATHGoogle Scholar
  21. 21.
    Hamayun, M.T., Edwards, C., Alwi, H.: Fault Tolerant Control Schemes using Integral Sliding Modes. Springer, New York (2016)zbMATHGoogle Scholar
  22. 22.
    Xu, R., Ozguner, U.: Sliding mode control of a quadrotor helicopter. In: IEEE Conference on Decision and Control, San Diego, CA, USA, pp. 4957–4962 (2006)Google Scholar
  23. 23.
    Bouadi, H., Cunha, S.S., Drouin, A., Camino, F.M.: Adaptive sliding mode control for quadrotor attitude stabilization and altitude tracking. In: International Symposium on Computational Intelligence and Informatics, Budapest, Hungary, pp. 449–455 (2011)Google Scholar
  24. 24.
    Runcharoon, K., Srichatrapimuk, V.: Sliding mode control of quadrotor. In: International Conference on Technological Advances in Electrical, Electronics and Computer Engineering, Konya, Turkey, pp. 552–557 (2013)Google Scholar
  25. 25.
    Arellano-Muro, C.A., Castillo-Toledo, B., Loukianov, A.G., Luque-Vega, L.F., González-Jiménez, L.E.: Quaternion-based trajectory tracking robust control for a quadrotor. In: System of Systems Engineering Conference, San Antonio, TX, USA, pp. 386–391 (2015)Google Scholar
  26. 26.
    Xiong, J.J., Zheng, E.H.: Position and attitude tracking control for a quadrotor UAV. ISA Trans. 53(3), 725–731 (2014)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Zheng, E.H., Xiong, J.J., Luo, J.L.: Second order sliding mode control for a quadrotor UAV. ISA Trans. 53(4), 1350–1356 (2014)CrossRefGoogle Scholar
  28. 28.
    Xiong, J.J., Zhang, G.: Discrete-time sliding mode control for a quadrotor UAV. Opt. Int. J. Light Electron Opt. 127(8), 3718–3722 (2016)CrossRefGoogle Scholar
  29. 29.
    Xiong, J.J., Zhang, G.B.: Global fast dynamic terminal sliding mode control for a quadrotor UAV. ISA Trans. 66, 233–240 (2017)CrossRefGoogle Scholar
  30. 30.
    Ansari, U., Bajodah, A., Hamayun, M.T.: Quadrotor control via robust generalized dynamic inversion and adaptive non-singular terminal sliding mode. Asian J. Control  https://doi.org/10.1002/asjc.1800 (2018)
  31. 31.
    Das, A., Lewis, F.L., Subbarao, K.: Sliding Mode Approach to Control Quadrotor Using Dynamic Inversion. INTECH Open Access Publisher, Rijeka (2011)CrossRefGoogle Scholar
  32. 32.
    Voos, H.: Nonlinear control of a quadrotor micro-UAV using feedback-linearization. In: IEEE International Conference on Mechatronics, Malaga, Spain, pp. 1–6 (2009)Google Scholar
  33. 33.
    Tiwari, S.N., Padhi, R.: Simultaneous attitude control and trajectory tracking of a micro quadrotor: a SNAC aided nonlinear dynamic inversion. In: American Control Conference, Washington, DC, USA, pp. 194–199 (2013)Google Scholar
  34. 34.
    Bloch, A.: Nonholonomic Mechanics and Control. Springer, New York (2003)CrossRefGoogle Scholar
  35. 35.
    Bullo, F., Lewis, A.: Geometric Control of Mechanical Systems. Springer, New York (2005)CrossRefzbMATHGoogle Scholar
  36. 36.
    Lee, T., Leok, M., McClamroch, N.H.: Geometric tracking control of a quadrotor UAV on SE(3). In: Conference on Decision and Control, Atlanta, GA, USA, pp. 5420–5425 (2010)Google Scholar
  37. 37.
    Sreenath, K., Lee, T., Kumar, V.: Geometric control and differential flatness of a quadrotor UAV with a cable-suspended load. In: Conference on Decision and Control, Florence, Italy, pp. 2269–2274 (2013)Google Scholar
  38. 38.
    Lee, T.: Geometric control for a tethered quadrotor UAV. In: Conference on Decision and Control, Osaka, Japan, pp. 2749–2754 (2015)Google Scholar
  39. 39.
    Özbek, N.S., Önkol, M., Efe, M.O.: Feedback control strategies for quadrotor-type aerial robots: a survey. Trans. Inst. Meas. Control 38(5), 529–554 (2016)CrossRefGoogle Scholar
  40. 40.
    Bajodah, A.H., Hodges, D.H., Chen, Y.H.: Inverse dynamics of servo-constraints based on the generalized inverse. Nonlinear Dyn. 39(1), 179–196 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  41. 41.
    Bajodah, A.H.: Singularly perturbed feedback linearization with linear attitude deviation dynamics realization. Nonlinear Dyn. 53(4), 321–343 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  42. 42.
    Moore, E.H.: On the reciprocal of the general algebraic matrix. Bull. Am. Math. Soc. 26, 394–395 (1920)Google Scholar
  43. 43.
    Penrose, R.: A generalized inverse for matrices. Proc. Camb. Philos. Soc. 51, 406–413 (1955)CrossRefzbMATHGoogle Scholar
  44. 44.
    Greville, T.N.E.: The pseudoinverse of a rectangular or singular matrix and its applications to the solutions of systems of linear equations. SIAM Rev. 1(1), 3843 (1959)MathSciNetCrossRefGoogle Scholar
  45. 45.
    Ben-Israel, A., Greville, T.N.E.: Generalized Inverses: Theory and Applications, 2nd edn. Springer, New York (2003)zbMATHGoogle Scholar
  46. 46.
    Udwadia, F.E., Kalaba, R.E.: Analytical Dynamics, A New Approach. Cambridge University Press, Cambridge (1996)CrossRefzbMATHGoogle Scholar
  47. 47.
    Enns, D., Bugajski, D., Hendrick, R., Stein, G.: Dynamic inversion: an evolving methodology for flight control design. Int. J. Control 59(1), 71–91 (1994)CrossRefzbMATHGoogle Scholar
  48. 48.
    Pedro, J.O., Panday, A., Dala, L.: A nonlinear dynamic inversion-based neurocontroller for unmanned combat aerial vehicles during aerial refuelling. Int. J. Appl. Math. Comput. Sci. 23(1), 75–90 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  49. 49.
    Ireland, M.L., Vargas, A., Anderson, D.: A comparison of closed-loop performance of multirotor configurations using non-linear dynamic inversion control. Aerospace 2(2), 325–352 (2015)CrossRefGoogle Scholar
  50. 50.
    Bajodah, A.H.: Generalised dynamic inversion spacecraft control design methodologies. IET Control Theory Appl. 3(2), 239–251 (2009)MathSciNetCrossRefGoogle Scholar
  51. 51.
    Bajodah, A.H.: Asymptotic generalized dynamic inversion attitude control. IET Control Theory Appl. 4(5), 827–840 (2010)MathSciNetCrossRefGoogle Scholar
  52. 52.
    Hameduddin, I., Bajodah, A.H.: Nonlinear generalised dynamic inversion for aircraft manoeuvring control. Int. J. Control 85(4), 437–450 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  53. 53.
    Bajodah, A.H.: Asymptotic perturbed feedback linearization of under actuated Euler’s dynamics. Int. J. Control 82(10), 1856–1869 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  54. 54.
    Hall, J., Romano, M., Cristi, R.: Quaternion feedback regulator for large angle maneuvers of underactuated spacecraft. In: American Control Conference, Baltimore, MD, USA, pp. 2867–2872 (2010)Google Scholar
  55. 55.
    Gui, H., Jin, L., Xu, S.: Attitude control of a rigid spacecraft with one variable speed control moment gyro. Acta Mech. Sin. 29(5), 749–760 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  56. 56.
    Gui, H., Jin, L., Xu, S.: Attitude maneuver control of a two-wheeled spacecraft with bounded wheel speeds. Acta Astronaut. 88, 98–107 (2013)CrossRefGoogle Scholar
  57. 57.
    Leishman, J.G.: Principles of Helicopter Aerodynamics, 2nd edn. Cambridge University Press, Cambridge (2002)Google Scholar
  58. 58.
    Nelson, R.C.: Flight Stability and Automatic Control, 2nd edn. McGraw-Hill, New York (1998)Google Scholar
  59. 59.
    Kasdin, N.J., Paley, D.A.: Engineering Dynamics. Princeton University Press, Princeton (2011)CrossRefGoogle Scholar
  60. 60.
    Khalil, H.K.: Nonlinear Systems. Prentice-Hall, New Jersey (1996)Google Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Aeronautical Engineering DepartmentKing Abdulaziz UniversityJeddahSaudi Arabia

Personalised recommendations