access icon free Distributed consensus protocols for coordinated control of multiple quadrotors under a directed topology

Two distributed consensus problems, including leadless consensus and tracking consensus, for multiple quadrotors with bounded disturbances under a directed topology are solved in this study. First, the model of a single quadrotor is divided into two subsystems. Some coupling terms between the two subsystems are regarded as external perturbations. For the case of leadless consensus, a distributed sliding-mode controller for the first subsystem and a state-feedback controller for the second subsystem are proposed to guarantee that the consensus is achieved with bounded errors that are only associated with disturbances. For the case of tracking consensus, by using the proposed sliding-mode consensus protocols combining with two sliding-mode observers, it is shown that all quadrotors can track the leader with bounded errors which can be manipulated suitably. Simulations show the effectiveness of the proposed control protocols.

Inspec keywords: distributed control; state feedback; variable structure systems; autonomous aerial vehicles; observers

Other keywords: distributed consensus protocol; directed topology; distributed sliding-mode controller; state-feedback controller; external perturbations; tracking consensus; sliding-mode observers; bounded disturbances; leadless consensus; multiple quadrotor coordinated control; single quadrotor model; sliding-mode consensus protocols

Subjects: Simulation, modelling and identification; Mobile robots; Multivariable control systems; Telerobotics; Aerospace control

References

    1. 1)
      • 15. Cortés, J.: ‘Distributed algorithms for reaching consensus on general functions’, Automatica, 2008, 44, (3), pp. 726737 (doi: 10.1016/j.automatica.2007.07.022).
    2. 2)
      • 3. Zhao, D., Li, S., Gao, F., Zhu, Q.: ‘Robust adaptive terminal sliding mode-based synchronised position control for multiple motion axes systems’, IET Control Theory Appl., 2009, 3, (1), pp. 136150 (doi: 10.1049/iet-cta:20070272).
    3. 3)
      • 16. Altug, E., Osreiwski, J.O., Mahony, R.: ‘Control of a quadrotor helicopter using visual feedback’. Proc. IEEE. Conf. Robotics and Automation, Washington, DC, 2002, pp. 7277.
    4. 4)
      • 26. Godsil, C., Royle, G.: ‘Algebraic graph theory’ (Springer-Verlag, New York, 2001).
    5. 5)
      • 23. Matthew, T., Nathan, M., Vijay, K.: ‘Decentralized formation control with variable shapes for aerial robots’. Proc. IEEE. Conf. Robotics and Automation, Saint Paul, May 2012, pp. 2330.
    6. 6)
      • 7. Ren, W.: ‘Distributed leadless consensus algorithms for networked Euler–Lagrange systems’, Int. J. Control, 2009, 82, (11), pp. 21372149 (doi: 10.1080/00207170902948027).
    7. 7)
      • 12. Ren, W.: ‘Multi-vehicle consensus with a time-varying reference state’, Syst. Control Lett., 2010, 56, (9–10), pp. 474483.
    8. 8)
      • 9. Mei, J., Ren, W., Ma, G.: ‘Distributed coordinated tracking with a dynamic leader for multiple Euler–Lagrange systems’, IEEE Trans. Autom. Control, 2011, 56, (6), pp. 14151421 (doi: 10.1109/TAC.2011.2109437).
    9. 9)
      • 6. Atkins, E.: ‘Distributed multi-vehicle coordinated control via local information exchange’, Int. J. Robust Nonlinear Control, 2007, 17, (10–11), pp. 10021033 (doi: 10.1002/rnc.1147).
    10. 10)
      • 18. Madahi, T., Benallegue, A.: ‘Control of a quadrotor mini-helicopter via full state backstepping technique’. Proc. IEEE. Conf. on Decision and Control, San Diego, December 2006, pp. 15151520.
    11. 11)
      • 20. Xü, R., Ümit, ö.: ‘Sliding mode control of a quadrotor helicopter’, Proc. IEEE. Conf. Decision and Control, San Diego, December 2006, pp. 49574962.
    12. 12)
      • 27. Ren, W., Beard, R.W.: ‘Distributed consensus in multi-vehicle cooperative control’ (Springer-Verlag, London, 2008).
    13. 13)
      • 13. Das, A., Lewis, F.L.: ‘Cooperative adaptive control for synchronization of second-order systems with unknown nonlinearities’, Int. J. Robust Nonlinear Control, 2011, 21, (13), pp. 15091524 (doi: 10.1002/rnc.1647).
    14. 14)
      • 8. Min, H., Sun, F., Wang, S., Li, H.: ‘Distributed adaptive consensus algorithm for networked Euler–Lagrange systems’, IET Control Theory Appl., 2011, 5, (1), pp. 145154 (doi: 10.1049/iet-cta.2009.0607).
    15. 15)
      • 4. Zhao, D., Zou, T., Li, S., Zhu, Q.: ‘Adaptive backstepping sliding mode control for leader–follower multi-agent systems’, IET Control Theory Appl., 2012, 6, (8), pp. 11091117 (doi: 10.1049/iet-cta.2011.0001).
    16. 16)
      • 28. Khali, K.: ‘Nonlinear Systems’, (Prentice-Hall, Upper Saddle River, NJ, 2002, 3rd edn.).
    17. 17)
      • 11. Cao, Y., Ren, W., Meng, Z.: ‘Decentralized finite-time sliding mode estimators and their applications in decentralized finite-time formation tracking’, Syst. Control Lett., 2010, 59, (9), pp. 522529 (doi: 10.1016/j.sysconle.2010.06.002).
    18. 18)
      • 19. Das, A., Subbarao, K., Lewis, F.: ‘Dynamic inversion with zero-dynamics stabilisation for quadrotor control’, IET Control Theory Appl., 2008, 3, (3), 303314 (doi: 10.1049/iet-cta:20080002).
    19. 19)
      • 5. Xie, G., Wang, L.: ‘Consensus control of a networks of dynamic agents’, Int. J. Robust Nonlinear Control, 2007, 17, (10–11), pp. 941959 (doi: 10.1002/rnc.1144).
    20. 20)
      • 14. Bauso, D., Giarré, L., Pesenti, R.: ‘Non-linear protocols for optimal distributed consensus in networks of dynamic agents’, Syst. Control Lett., 2006, 55, (11), pp. 918928 (doi: 10.1016/j.sysconle.2006.06.005).
    21. 21)
      • 1. Olfati-Saber, R., Murray, R.M.: ‘Consensus problems in networks of agents with switching topology and time-delays’, IEEE Trans. Autom. Control, 2004, 49, (9), pp. 15201533 (doi: 10.1109/TAC.2004.834113).
    22. 22)
      • 25. Horn, R., Johnson, C.: ‘Matrix analysis’ (Cambridge University Press, New York, 1985).
    23. 23)
      • 21. Juerreoro, J.A., Lozano, R., Castillo, P., Salazar, S.: ‘Mini rotorcraft flight formation control using bounded inputs’, J. Intell. Robot. Syst., 2012, 12, (6), pp. 175186.
    24. 24)
      • 24. Wang, Y., Wu, Q., Wang, Y.: ‘Containment control for multiple quadrotors with stationary leaders under directed graphs’. Proc. IEEE. Conf. Decision and Control, Hawaii, December 2012, pp. 27812786.
    25. 25)
      • 10. Mei, J., Ren, W., Ma, G.: ‘Distributed containment control for Lagrangian networks with parametric uncertainties under a directed graph’, Automatica, 2012, 48, (4), pp. 653659 (doi: 10.1016/j.automatica.2012.01.020).
    26. 26)
      • 22. Alon, D., Nadav, B., Shai, A.: ‘Formation flight using multiple integral backstepping controllers’, Proc. IEEE. Conf. Cybernetics and Intelligent Systems, Qingdao, September 2011, pp. 317322.
    27. 27)
      • 29. Das, A., Lewis, F.L.: ‘Distributed adaptive control for synchronization of unknown nonlinear networked systems’, Automatica, 2010, 46, (12), pp. 20142021 (doi: 10.1016/j.automatica.2010.08.008).
    28. 28)
      • 2. Hu, J., Lin, Y.S.: ‘Conesnsus control for multi-agent systems with double-integrator dynamics and time delays’, IET Control Theory Appl., 2010, 4, (1), pp. 109118 (doi: 10.1049/iet-cta.2008.0479).
    29. 29)
      • 17. Castillo, P., Lozano, R., Dzul, A.: ‘Stabilization of a mini rotorcraft having four rotors’, IEEE Control Syst. Mag., 2005, 25, (6), pp. 4555 (doi: 10.1109/MCS.2005.1550152).
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