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A Modified Framework for Longitudinal Dynamic Stability Analysis on Vertical Takeoff of an Insect- Mimicking Flapping-Wing Micro Air Vehicle

Loan Thi Kim Au, Hoang Vu Phan, Kim Sang Tran, Hoon Cheol Park, Agus Budiyono


In the conventional frameworks for dynamic flight stability analysis, the linearized equations of motion are based on small disturbances from trim condition. This method may be not applicable for vertical takeoff analysis on an insect-mimicking flapping-wing micro air vehicle (FW-MAV) because of two reasons. First, the trim condition is unknown. Second, the initial flight condition, which was at rest on the ground, may be such a large disturbance from the equilibrium that the linearization is invalid. Here, we provide a framework for analyzing the vertical takeoff of an insect-mimicking FW-MAV without acquiring the trim condition. The reference flight condition for disturbances was chosen to be close to the initial flight condition, so that the linearization is applicable. To define the stability derivatives in the equations of motion, the computational fluid dynamics (CFD) software of ANSYS Fluent was used to compute the forces and pitching moments when the FW-MAV operated at various vertical flight speeds and inclined angles from the vertical line. By solving the equations of motion, the behavior of vertical takeoff of the FW-MAV could be analyzed and theoretically reproduced its actual vertical takeoff.

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M. Jansen, “Biology and physics of locust flight. III. The Aerodynamics

of locust flight,” Philos. Trans. Roy. Soc. Lond. Ser. B., vol. 239, pp. 511-551, July 1956.

J.M.V. Rayner, “A new approach to animal flight mechanics,” J. Exp. Biol., vol. 80, pp. 17-54, June 1979.

M.H. Dickinson, F.O. Lehman, and S.P. Sane, “Wing rotation and the

aerodynamics basis of insect flight,” Science, vol. 284, pp. 1954-1960, June 1999.

S.P. Sane, “The aerodynamics of insect flight,” J. Exp. Biol., vol. 206, pp. 4191-4208, December 2003.

T.T. Nguyen, and D. Byun, “Two-dimensional aerodynamic models of

insect flight for robotic flapping wing mechanisms of maximum

efficiency,” J. Bion. Eng., vol. 5, pp. 1-11, March 2008.

Q.V. Nguyen, Q.T. Truong, H.C. Park, N.S. Goo, and D. Byun, “Measurement of force produced by an insect-mimicking flapping-wing

system,” J. Bion. Eng., vol. 7, pp. S94-S102, September 2010.

Q.T. Truong, H.V. Phan, H.C. Park, and J.H. Koh, “Effect of wing twisting on aerodynamic performance of flapping wing system,” AIAA

J., vol. 51, pp. 1612-1620, July 2013.

G.K. Taylor, and A.L.R. Thomas, “Dynamic flight stability in the desert

locust Schistocerca Gregaria,” J. Exp. Biol., vol. 206, pp. 2803-2829,

August 2003.

M. Sun, and Y. Xiong, “Dynamic flight stability of a hovering bumblebee,” J. Exp. Biol., vol. 208, pp. 447-459, February 2004.

I. Faruque, and J.S. Humbert, “Dipteran insect flight dynamics. I. Longitudinal motion about hover,” J. Theor. Biol., vol. 264, pp. 538-552, May 2010.

I. Faruque, and J.S. Humbert, “Dipteran insect flight dynamics. II.

Lateral–directional motion about hover,” J. Theor. Biol., vol. 265, pp.

-313, August 2010.

B. Cheng, and X. Deng, “Translational and rotational damping of flapping flight and its dynamics and stability at hovering,” IEEE Trans. Robot., vol. 27, pp. 849-864, October 2011.

B. Etkin, and L.D. Reid, “Dynamics of flight: stability and control,” New York: John Wiley & Sons (1996).

H.V. Phan, Q.V. Nguyen, Q.T. Truong, V.T. Truong, H.C. Park, N.S.

Goo, D. Byun, and M.J. Kim, “Stable vertical takeoff of an insectmimicking

flapping-wing system without guide implementing inherent pitching stability,” J. Bion. Eng., vol. 9, pp. 391–401, December 2012.

Q.V. Nguyen, H.C. Park, N.S. Goo, and D. Byun, “Characteristics of a

beetle’s free flight and a flapping-wing system that mimics beetle flight,” J. Bion. Eng., vol. 7, pp. 77-86, March 2010.

H.V. Phan, “Measurement of forces produced by insect-mimicking flapping-wing systems and their vertical takeoff tests,” Master dissertation, Konkuk University, Dept. of Advanced Technology Fusion, South Korea, February 2012.

V.T. Truong, Q.T. Le, D. Byun, H.C. Park, and M. Kim, “Flexible wing

kinematics of a free-flying beetle (Rhinoceros Beetle Trypoxylus Dichotomus)”, J. Bion. Eng., vol. 9, pp. 177-184, June 2012.



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