Modeling and emergence of flapping flight of butterfly based on experimental measurements

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Senda, Kei ; Obara, Takuya ; Kitamura, Masahiko ; Nishikata, Tomomi ; Hirai, Norio ; Iima, Makoto ; Yokoyama, Naoto (2012)
  • Publisher: Elsevier B.V.
  • Journal: Robotics and Autonomous Systems, volume 60, issue 5, pages 670-678 (issn: 0921-8890)
  • Subject: Modeling | Experimental measurements | Butterfly | Flapping flight
    arxiv: Physics::Fluid Dynamics | Astrophysics::Solar and Stellar Astrophysics

The objective of this paper is to clarify the principle of stabilization in flapping-of-wing flight of a butterfly, which is a rhythmic and cyclic motion. For this purpose, a dynamics model of a butterfly is derived by Lagrange’s method, where the butterfly is considered as a rigid multi-body system. For the aerodynamic forces, a panel method is applied. Validity of the mathematical models is shown by an agreement of the numerical result with the measured data. Then, periodic orbits of flapping-of-wing flights are searched in order to fly the butterfly models. Almost periodic orbits are obtained, but the model in the searched flapping-of-wing flight is unstable. This research, then, studies how the wake-induced flow and the flexibly torsional wing’s effect on the flight stability. Numerical simulations demonstrate that both the wake-induced flow and the flexible torsion reduces the flight instability. Because the obtained periodic flapping-of-wing flight is unstable, a feedback control system is designed, and a stable flight is realized.
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