Your browser does not support JavaScript!
http://iet.metastore.ingenta.com
1887

access icon free Online optimisation-based backstepping control design with application to quadrotor

  • Author(s): Hao Lu 1 ; Cunjia Liu 2 ; Matthew Coombes 2 ; Lei Guo 3 ; Wen-Hua Chen 2, 3
    • View affiliations
    • Affiliations: 1: School of Instrumentation Science and Opto-Electronics Engineering, Beihang University, Beijing 100191, People's Republic of China ;
      2: Department of Aeronautical and Automotive Engineering, Loughborough University, Loughborough, LE11 3TU, UK ;
      3: School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, People's Republic of China
  • Source: Volume 10, Issue 14, 19 September 2016, p. 1601 – 1611
    DOI:  10.1049/iet-cta.2015.0976 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Received 23/09/2015, Accepted 03/05/2016, Revised 04/04/2016, Published 09/06/2016

In backstepping implementation, the derivatives of virtual control signals are required at each step. This study provides a novel way to solve this problem by combining online optimisation with backstepping design in an outer and inner loop manner. The properties of differential flatness and the B-spline polynomial function are exploited to transform the optimal control problem into a computationally efficient form. The optimisation process generates not only the optimised states, but also their finite order derivatives which can be used to analytically calculate the derivatives of virtual control signal required in backstepping design. In addition, the online optimisation repeatedly performed in a receding horizon fashion can also realise local motion planning for obstacle avoidance. The stability of the receding horizon control scheme is analysed via Lyapunov method which is guaranteed by adding a parameterised terminal condition in the online optimisation. Numerical simulations and flight experiments of a quadrotor unmanned air vehicle are given to demonstrate the effectiveness of the proposed composite control method.

Inspec keywords: optimal control; optimisation; control system synthesis; polynomials; control nonlinearities; predictive control; autonomous aerial vehicles; Lyapunov methods; collision avoidance; splines (mathematics)

Other keywords: computationally efficient form; optimal control problem; local motion planning; finite order derivatives; Lyapunov method; composite control method; differential flatness properties; inner loop manner; B-spline polynomial function; quadrotor unmanned air vehicle; obstacle avoidance; virtual control signal derivatives; online optimisation-based backstepping control design; receding horizon fashion; receding horizon control scheme stability; outer loop manner; parameterised terminal condition

Subjects: Control system analysis and synthesis methods; Optimisation techniques; Telerobotics; Aerospace control; Nonlinear control systems; Stability in control theory; Spatial variables control; Mobile robots; Interpolation and function approximation (numerical analysis); Optimal control

References

    1. 1)
      • 24. Ferrin, J., Leishman, R., Beard, R., et al: ‘Differential flatness based control of a rotorcraft for aggressive maneuvers’, IEEE/RSJ Int. Conf. Intelligent and Robotic Systems, San Francisco, CA, September 2011, pp. 2688–2693.
    2. 2)
      • 18. Kendoul, F., Lara, D., Fantoni-Coichot, I., et al: ‘Real-time nonlinear embedded control for an autonomous quadrotor helicopter’, J. Guid. Control Dyn., 2007, 30, (4), pp. 1049–1061.
    3. 3)
      • 30. Gu, D., Hu, H.: ‘Receding horizon tracking control of wheeled mobile robots’, IEEE Trans. Control Syst. Technol., 2006, 14, (4), pp. 743–749.
    4. 4)
      • 5. Park, S.H., Han, S.I.: ‘Robust-tracking control for robot manipulator with deadzone and friction using backstepping and RFNN controller’, IET Control Theory Appl., 2011, 5, (12), pp. 1397–1417.
    5. 5)
      • 8. Farrell, J., Polycarpou, M., Sharma, M.: ‘Command filtered backstepping’, IEEE Trans. Autom. Control, 2009, 54, (6), pp. 1391–1395.
    6. 6)
      • 23. Hagenmeyer, V., Delaleau, E.: ‘Continuous-time non-linear flatness-based predictive control: an exact feedforward linearisation setting with an induction drive example’, Int. J. Control, 2008, 81, (10), pp. 1645–1663.
    7. 7)
      • 19. Hoffmann, G.M., Huang, H., Waslander, S.L., et al: ‘Quadrotor helicopter trajectory tracking control: theory and experiment’, AIAA Guidance, Navigation, and Control Conf. and Exhibit, Hilton Head, South Carolina, August 2007, pp. 1–20.
    8. 8)
      • 34. Coombes, M., Eaton, W., McAree, O., et al: ‘Development of a generic network enabled autonomous vehicle system’, 2014 UKACC Int. Conf. Control, Loughborough, UK, July 2014, pp. 621–627.
    9. 9)
      • 15. Suryawan, F., De Doná, J., Seron, M.: ‘Splines and polynomial tools for flatness-based constrained motion planning’, Int. J. Syst. Sci., 2013, 43, (8), pp. 1396–1411.
    10. 10)
      • 6. Lu, H., Liu, C., Guo, L.: et al. ‘Flight control design for small-scale helicopter using disturbance-observer-based backstepping’, J. Guid. Control Dyn., 2015, 38, (11), pp. 2235–2240.
    11. 11)
      • 12. Cowling, I.D., Yakimenko, O.A., Whidborne, J.F.: et al. ‘Direct method based control system for an autonomous quadrotor’, J. Intell. Robot. Syst., 2010, 60, (2), pp. 285–316.
    12. 12)
      • 21. Fliess, M., Lévine, J., Martin, P., et al: ‘Flatness and defect of non-linear systems: introductory theory and examples’, Int. J. Control, 1995, 61, (6), pp. 1327–1361.
    13. 13)
      • 7. Yip, P.P., Hedrick, J.K.: ‘Adaptive dynamic surface control: a simplified algorithm for adaptive backstepping control of nonlinear systems’, Int. J. Control, 1998, 71, (5), pp. 959–979.
    14. 14)
      • 25. Piegl, L., Tiller, W.: ‘The NURBS book’ (Springer Verlag, Berlin, 1997, 2nd edn.).
    15. 15)
      • 9. Berry, A.J., Howitt, J., Gu, D.-W.: et al. ‘A continuous local motion planning framework for unmanned vehicles in complex environments’, J. Intell. Robot. Syst., 2011, 66, (4), pp. 477–494.
    16. 16)
      • 32. Zuo, Z.: ‘Trajectory tracking control design with command-filtered compensation for a quadrotor’, IET Control Theory Appl., 2010, 4, (11), pp. 2343–2355.
    17. 17)
      • 35. (2016, March), AscTec Research Home, Available at: http://wiki.asctec.de/display/AR/AscTec+Research+Home.
    18. 18)
      • 27. Mayne, D.Q., Rawlings, J.B., Rao, C.V., et al: ‘Constrained model predictive control: stability and optimality’, Automatica, 2000, 36, (6), pp. 789–814.
    19. 19)
      • 22. Hagenmeyer, V., Delaleau, E.: ‘Exact feedforward linearization based on differential flatness’, Int. J. Control, 2003, 76, (6), pp. 537–556.
    20. 20)
      • 16. Prodan, I., Olaru, S., Bencatel, R., et al: ‘Receding horizon flight control for trajectory tracking of autonomous aerial vehicles’, Control Eng. Pract., 2013, 21, (10), pp. 1334–1349.
    21. 21)
      • 14. Liu, C., Chen, W.-H.: ‘A practical receding horizon control framework for path planning and control of autonomous VTOL vehicles’, 4th European Conf. for Aerospace Science Avionics, St. Petersburg, Russia, July 2011, pp. 1–11.
    22. 22)
      • 28. Chen, W.-H., Ballance, D.J., O'Reilly, J.: ‘Model predictive control of nonlinear systems: computational burden and stability’, IEE Proc. Control Theory Appl., 2000, 147, (4), pp. 387–394.
    23. 23)
      • 11. Flores, M., Milam, M.: ‘Trajectory generation for differentially flat systems via NURBS basis functions with obstacle avoidance’, Proc. American Control Conf., Minneapolis, MN, 2006, pp. 5769–5775.
    24. 24)
      • 1. Krstic, M., Kokotovic, P.V., Kanellakopoulos, I.: ‘Nonlinear and adaptive control design’ (John Wiley & Sons, Inc., New York, 1995).
    25. 25)
      • 4. Xia, Y., Zhu, Z., Fu, M.: ‘Back-stepping sliding mode control for missile systems based on an extended state observer’, IET Control Theory Appl., 2011, 5, (1), pp. 93–102.
    26. 26)
      • 26. Volpe, R., Khosla, P.: ‘Artificial potentials with elliptical isopotential contours for obstacle avoidance’, Proc. 26th Conf. Decision and Control, Los Angeles, CA, December 1987, pp. 180–185.
    27. 27)
      • 29. Chen, H., Allgöwer, F.: ‘A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability’, Automatica, 1998, 34, (10), pp. 1205–1217.
    28. 28)
      • 10. Mahadevan, R., Agrawal, S.K., Doyle, F.J.: ‘Differential flatness based nonlinear predictive control of fed-batch bioreactors’, Control Eng. Pract., 2001, 9, (8), pp. 889–899.
    29. 29)
      • 31. Chen, W.-H., Gawthrop, P.J.: ‘Constrained predictive pole-placement control with linear models’, Automatica, 2006, 42, (4), pp. 613–618.
    30. 30)
      • 17. Berry, A.J., Howitt, J., Gu, D.-W.: ‘Continuous local motion planning & control for Micro-Air-Vehicles in complex environments’, Guidance, Navigation, and Control Conf., Toronto, Canada, August 2010, pp. 1–16.
    31. 31)
      • 3. Farrell, J., Sharma, M., Polycarpou, M.: ‘Backstepping-based flight control with adaptive function approximation’, J. Guid. Control Dyn., 2005, 28, (6), pp. 1089–1102.
    32. 32)
      • 20. Mellinger, D., Michael, N., Kumar, V.: ‘Trajectory generation and control for precise aggressive maneuvers with quadrotors’, Int. J. Robot. Res., 2012, 31, (5), pp. 664–674.
    33. 33)
      • 2. Fierro, R., Lewis, F.L.: ‘Control of a nonholonomic mobile robot: backstepping kinematics into dynamics’, Proc. 34th Conf. Decision and Control, New Orleans, LA, December 1995, pp. 3805–3810.
    34. 34)
      • 13. Chamseddine, A., Zhang, Y., Rabbath, C.A.: et al. ‘Flatness-based trajectory planning/replanning for a quadrotor unmanned aerial vehicle’, IEEE Trans. Aerosp. Electron. Syst., 2012, 48, (4), pp. 2832–2848.
    35. 35)
      • 33. Liu, C., Chen, W.-H., Andrews, J.: ‘Tracking control of small-scale helicopters using explicit nonlinear MPC augmented with disturbance observers’, Control Eng. Pract., 2012, 20, (3), pp. 258–268.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2015.0976
Loading

Related content

content/journals/10.1049/iet-cta.2015.0976
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
Print this page
This is a required field
Please enter a valid email address