Acta Mechanica Sinica

, Volume 25, Issue 1, pp 13–21 | Cite as

Stabilization control of a bumblebee in hovering and forward flight

  • Yan Xiong
  • Mao SunEmail author
Research Paper


Our previous study shows that the hovering and forward flight of a bumblebee do not have inherent stability (passive stability). But the bumblebees are observed to fly stably. Stabilization control must have been applied. In this study, we investigate the longitudinal stabilization control of the bumblebee. The method of computational fluid dynamics is used to compute the control derivatives and the techniques of eigenvalue and eigenvector analysis and modal decomposition are used for solving the equations of motion. Controllability analysis shows that at all flight speeds considered, although inherently unstable, the flight is controllable. By feedbacking the state variables, i.e. vertical and horizontal velocities, pitching rate and pitch angle (which can be measured by the sensory system of the insect), to produce changes in stroke angle and angle of attack of the wings, the flight can be stabilized, explaining why the bumblebees can fly stably even if they are passively unstable.


Insect Hovering and forward flight Stabilization control Navier–Stokes simulation Modal analysis 


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  1. 1.
    Taylor G.K., Thomas A.L.R.: Dynamic flight stability in the desert locust Schistocerca gregaria. J. Exp. Biol. 206, 2803–2829 (2003)CrossRefGoogle Scholar
  2. 2.
    Sun M., Xiong Y.: Dynamic flight stability of a hovering bumblebee. J. Exp. Biol. 208, 447–459 (2005)CrossRefGoogle Scholar
  3. 3.
    Xiong Y., Sun M.: Dynamic flight stability of a bumblebee in forward flight. Acta Mech. Sin. 24, 25–36 (2008)CrossRefGoogle Scholar
  4. 4.
    Dudley R.: The Biomechanics of Insect Flight: Form, Function, Evolution. Princeton University Press, Princeton (2000)Google Scholar
  5. 5.
    Sun M., Wang J.K.: Flight stabilization control of a hovering model insect. J. Exp. Biol. 210, 2714–2722 (2007)CrossRefGoogle Scholar
  6. 6.
    Sun M., Wang J.K., Xiong Y.: Dynamic flight stability of hovering insects. Acta Mech. Sin. 23, 231–246 (2007)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Dudley R., Ellington C.P.: Mechanics of forward flight in bumblebees. I. Kinematics and morphology. J. Exp. Biol. 148, 19–52 (1990)Google Scholar
  8. 8.
    Etkin B.: Dynamics of Atmospheric Flight. Wiley, New York (1972)Google Scholar
  9. 9.
    Bryson A.E.: Control of Spacecraft and Aircraft. Princeton University Press, Princeton (1994)Google Scholar
  10. 10.
    Wu J.H., Sun M.: Unsteady aerodynamic forces of a flapping wing. J. Exp. Biol. 207, 1137–1150 (2004)CrossRefGoogle Scholar
  11. 11.
    Usherwood J.R., Ellington C.P.: The aerodynamics of revolving wings. II. Propeller force coefficients from mayfly to quail. J. Exp. Biol. 205, 1565–1576 (2002)Google Scholar
  12. 12.
    Brogan W.L.: Modern Control Theory. Quantum Publishers Inc., New York (1974)Google Scholar
  13. 13.
    Ennos A.R.: The kinematics and aerodynamics of the free flight of some diptera. J. Exp. Biol. 142, 49–85 (1989)Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH 2008

Authors and Affiliations

  1. 1.Institute of Fluid MechanicsBeihang UniversityBeijingChina

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