Journal of Bionic Engineering

, Volume 15, Issue 3, pp 494–504 | Cite as

A Three-axis PD Control Model for Bumblebee Hovering Stabilization

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Abstract

Flight stabilization in insects is normally achieved through a closed-loop system integrating the internal dynamics and feedback control. Recent studies have reported that flight instability may exist in most flying insects but how insects achieve the flight stabilization still remains poorly understood. Here we propose a control model specified for bumblebee hovering stabilization by applying a three-axis PD (proportional-derivative)-controller to a free-flying bumblebee computational model with six Degrees of Freedom (DoFs). Morphological and kinematic models of a realistic bumblebee in hovering are built up based on measurements whereas a versatile bio-inspired dynamic flight simulator is employed in simulations. A simplified flight dynamic model is further developed as a fast model for control parameter tuning. Our results demonstrate that the stabilizing control model is capable of achieving the hovering stabilization with small perturbations in terms of 6-DoF, implying that the simplified linear algorithms can still work reasonably for bumblebee hovering. A further sensitivity analysis of the control parameters reveals that yaw control via manipulating pitch angle of the wing is mostly sensitive, implicating that bumblebee may utilize alternative yaw control strategies.

Keywords

flapping bumblebee flight stabilization PD controller multi-axis control 

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Notes

Acknowledgments

This paper was partly supported by the Grant-in-Aid for Scientific Research on Innovative Areas of No. 24120007, JSPS.

References

  1. [1]
    Liu H, Ravi S, Kolomenskiy D, Tanaka H. Biomechanics and biomimetics in insect-inspired flight systems. Philosophical Transactions of the Royal Society B, 2016, 371, 20150390.CrossRefGoogle Scholar
  2. [2]
    Taylor G K, Thomas A L R. Animal flight dynamics. II. Longitudinal stability in flapping flight. Journal of Theoretical Biology, 2002, 214, 351–370.Google Scholar
  3. [3]
    Sun M, Xiong Y. Dynamic flight stability of a hovering bumblebee. Journal of Experimental Biology, 2005, 208, 447–459.CrossRefGoogle Scholar
  4. [4]
    Gao N, Aono H, Liu H. Perturbation analysis of 6DoF flight dynamics and passive dynamic stability of hovering fruit fly Drosophila melanogaster. Journal of Theoretical Biology, 2011, 270, 98–111.CrossRefMATHGoogle Scholar
  5. [5]
    Liang B, Sun M. Nonlinear flight dynamics and stability of hovering insects. Journal of the Royal Society Interface, 2013, 10, 20130269.CrossRefGoogle Scholar
  6. [6]
    Zbikowski R, Ansari S A, Knowles K. On mathematical modelling of insect flight dynamics in the context of micro air vehicles. Bioinspiration & Biomimetics, 2006, 1, R26–R37.CrossRefGoogle Scholar
  7. [7]
    Zhang Y, Wu J H, Sun M. Lateral dynamic flight stability of hovering insects: Theory vs. numerical simulation. Acta Mechanica Sinica, 2012, 28, 221–231.MathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    Dickson W B, Polidoro P, Tanner M M, Dickinson M H. A linear systems analysis of the yaw dynamics of a dynamically scaled insect model. Journal of Experimental Biology, 2010, 213, 3047–3061.CrossRefGoogle Scholar
  9. [9]
    Cheng B, Deng X. Translational and rotational damping of flapping flight and its dynamics and stability at hovering. IEEE Transactions on Robotics, 2011, 27, 849–864.CrossRefGoogle Scholar
  10. [10]
    Meng X G, Liu Y P, Sun M. Aerodynamics of ascending flight in fruit flies. Journal of Bionic Engineering, 2017, 14, 75–87.CrossRefGoogle Scholar
  11. [11]
    Vogel S. Flight in Drosophila. II. Variations in stroke parameters and wing contour. Journal of Experimental Biology, 1967, 46, 383–392.Google Scholar
  12. [12]
    Alexander D E. Wind tunnel studies of turns by flying dragonflies. Journal of Experimental Biology, 1986, 122, 81–98.Google Scholar
  13. [13]
    Taylor G K. Mechanics and aerodynamics of insect flight control. Biological Reviews, 2001, 76, 449–471.CrossRefGoogle Scholar
  14. [14]
    Zanker J M. On the mechanism of speed and altitude control in Drosophila melanogaster. Physiological Entomology, 1988, 13, 351–361.CrossRefGoogle Scholar
  15. [15]
    Ma K Y, Chirarattananon P, Fuller S B, Wood R J. Controlled flight of a biologically inspired, insect-scale robot. Science, 2013, 340, 603–607.CrossRefGoogle Scholar
  16. [16]
    Bergou A J, Ristroph L, Guckenheimer J, Cohen I, Wang Z J. Fruit flies modulate passive wing pitching to generate in-flight turns. Physical Review Letters, 2010, 104, 148101.CrossRefGoogle Scholar
  17. [17]
    Muijres F T, Elzinga M J, Melis J M, Dickinson M H. Flies evade looming targets by executing rapid visually directed banked turns. Science, 2014, 344, 172–177.CrossRefGoogle Scholar
  18. [18]
    Tanaka K, Kawachi K. Response characteristics of visual altitude control system in Bombus terrestris. Journal of Experimental Biology, 2006, 209, 4533–4545.CrossRefGoogle Scholar
  19. [19]
    Dickinson M H. Haltere-mediated equilibrium reflexes of the fruit fly, Drosophila melanogaster. Philosophical Transactions of the Royal Society B, 1999, 354, 903–916.CrossRefGoogle Scholar
  20. [20]
    Faruque I, Humbert J S. Dipteran insect flight dynamics. Part 1: longitudinal motion about hover. Journal of Theoretical Biology, 2010, 264, 538–552.Google Scholar
  21. [21]
    Ristroph L, Bergou A J, Ristroph G, Coumes K, Berman G J, Guckenheimer J, Wang Z J, Cohen I. Discovering the flight auto-stabilizer of fruit flies by inducing aerial stumbles. Proceedings of the National Academy of Sciences, 2010, 107, 4820–4824.CrossRefGoogle Scholar
  22. [22]
    Ristroph L, Ristroph G, Morozova S, Bergou A J, Chang S, Guckenheimer J, Wang Z J, Cohen I. Active and passive stabilization of body pitch in insect flight. Journal of the Royal Society Interface, 2013, 10, 20130237.CrossRefGoogle Scholar
  23. [23]
    Beatus T, Guckenheimer J M, Cohen I. Controlling roll perturbations in fruit flies. Journal of the Royal Society Interface, 2015, 12, 20150075.CrossRefGoogle Scholar
  24. [24]
    Cheng B, Deng X, Hedrick T L. The mechanics and control of pitching manoeuvres in a freely flying hawkmoth (Manduca sexta). Journal of Experimental Biology, 2011, 214, 4092–4106.CrossRefGoogle Scholar
  25. [25]
    Liu H. Integrated modeling of insect flight: From morphology, kinematics to aerodynamics. Journal of Computational Physics, 2009, 228, 439–459.MathSciNetCrossRefMATHGoogle Scholar
  26. [26]
    Ravi S, Kolomenskiy D, Engles T, Schneider K, Wang C, Sesterhenn J, Liu H. Bumblebees minimize control challenges by combining active and passive modes in unsteady winds. Scientific Reports, 2016, 6, 35043.CrossRefGoogle Scholar
  27. [27]
    Liu H, Aono H. Size effects on insect hovering aerodynamics: An integrated computational study. Bioinspiration & Biomimetics, 2009, 4, 015002.CrossRefGoogle Scholar
  28. [28]
    Liu H, Nakata T, Gao N, Maeda M, Aono H, Shyy W. Micro air vehicle-motivated computational biomechanics in bio-flights: Aerodynamics, flight dynamics and maneuvering stability. Acta Mechanica Sinica, 2010, 26, 863–879.MathSciNetCrossRefMATHGoogle Scholar
  29. [29]
    Ueyama K, Kolomenskiy D, Ravi S, Nakata T, Liu H. Aerodynamic performance of bumblebees with flexible wing hinges. Proceedings of The 31st International Congress on High-speed Imaging and Photonics, Osaka, Japan, 2016.Google Scholar
  30. [30]
    Dickinson M H, Muijres F T. The aerodynamics and control of free flight manoeuvres in Drosophila. Philosophical Transactions of the Royal Society B, 2016, 371, 20150388.CrossRefGoogle Scholar
  31. [31]
    Hengstenberg R, Sandeman D, Hengstenberg B. Compensatory head roll in the blowfly Calliphora during flight. Proceedings of the Royal Society B, 1986, 227, 455–482.CrossRefGoogle Scholar
  32. [32]
    Gronenberg W. The fast mandible strike in the trap-jaw ant Odontomachus. 1. Temporal properties and morphological characteristics. Journal of Comparative Physiology A, 1995, 176, 391–398.Google Scholar
  33. [33]
    Camhi J M, Nolen T G. Properties of the escape system of cockroaches during walking. Journal of Comparative Physiology, 1981, 142, 339–346.CrossRefGoogle Scholar
  34. [34]
    Jindrich D L, Full R J. Dynamic stabilization of rapid hexapedal locomotion. Journal of Experimental Biology, 2002, 205, 2803–2823.Google Scholar
  35. [35]
    Fuller S B, Straw A D, Peek M Y, Murray R M, Dickinson M H. Flying Drosophila stabilize their vision-based velocity controller by sensing wind with their antennae. Proceedings of the National Academy of Sciences, 2014, 111, E1182–E1191.CrossRefGoogle Scholar
  36. [36]
    Liu P, Cheng B. Limitations of rotational manoeuvrability in insects and hummingbirds: Evaluating the effects of neuro- biomechanical delays and muscle mechanical power. Journal of the Royal Society Interface, 2017, 14, 20170068.CrossRefGoogle Scholar

Copyright information

© Jilin University 2018

Authors and Affiliations

  1. 1.Shanghai Jiao Tong University and Chiba University International Cooperative Research Centre (SJTU-CU ICRC)Shanghai Jiao Tong UniversityShanghaiChina
  2. 2.Graduate School of EngineeringChiba UniversityChibaJapan

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