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Saturation-based actuation for flapping MAVs in hovering and forward flight

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Abstract

Stringent weight and size constraints on flapping-wing microair-vehicles dictate minimal actuation. Unfortunately, hovering and forward flight require different wing motions and, as such, independent actuators. Therefore, either a hovering or a forward-flight requirement should be included in the mission and design statements of a flapping-wing microair-vehicle. This work proposes a design for an actuation mechanism that would provide the required kinematics in each flight condition using only one actuator. The idea is to exploit the nonlinear dynamics of the flapping wing to induce the saturation phenomenon. One physical spring in the plunging direction is needed along with a feedback of the plunging angle into the control torque of the actuator in the back and forth flapping direction. By detuning the feedback gains away from the saturation requirement, we obtain the flapping kinematics required for hovering. In contrast, tuning the feedback gains to induce the saturation phenomenon transfers the motion into the plunging direction. Moreover, the actuating torque (in the back and forth flapping direction) would then provide a direct control over the amplitude of the plunging motion, while the amplitude of the actuated flapping motion saturates and does not change as the amplitude of the actuating torque increases.

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Abbreviations

\(\bar{c}\) :

Mean chord length

g :

Gravitational acceleration

m v , m w :

Masses of the vehicle and wing respectively

r :

Radial coordinate along the wing

R :

Wing radius (length)

S :

Area of one wing

t :

Time variable

T, f :

Flapping period and frequency

x I , y I , and z I :

Inertial fixed frame

x w , y w , and z w :

Wing fixed frame

η :

Pitching angle

φ :

Back and forth flapping angle

ϑ :

Plunging angle

References

  1. Wood, R.J.: The first takeoff of a biologically inspired at-scale robotic insect. IEEE Trans. Robot. Autom. 24(2), 341–347 (2008)

    Article  Google Scholar 

  2. Doman, D.B., Oppenheimer, M.W., Sigthorsson, D.O.: Dynamics and control of a minimally actuated biomimetic vehicle. Part i: Aerodynamic model. 2009-6160. AIAA Guidance, Navigation, and Control Conference Chicago, Illinois

  3. Doman, D.B., Oppenheimer, M.W., Sigthorsson, D.O.: Wingbeat shape modulation for flapping-wing micro-air-vehicle control during hover. J. Guid. Control Dyn. 33(3), 724–739 (2010)

    Article  Google Scholar 

  4. Schenato, L., Campolo, D., Sastry, S.S.: Controllability issues in flapping flight for biomimetic mavs. ieee Conference on Decision and Control, Maui, HI (2003)

  5. Berman, G.J., Wang, Z.J.: Energy-minimizing kinematics in hovering insect flight. J. Fluid Mech. 582, 153,168 (2007)

    Article  MathSciNet  Google Scholar 

  6. Kurdi, M., Stanford, B., Beran, P.: Kinematic optimization of insect flight for minimum mechanical power. 2010-1420. 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, Fl (2010)

  7. Stanford, B.K., Beran, P.S.: Analytical sensitivity analysis of an unsteady vortex-lattice method for flapping-wing optimization. J. Aircr. 47(2), 647–662 (2010)

    Article  Google Scholar 

  8. Ghommem, M., Hajj, M.R., Mook, D.T., Stanford, B.K., Beran, P.S., Snyder, R.D., Watson, L.T.: Global optimization of actively morphing flapping wings. J. Fluids Struct. 33, 210–228 (2012)

    Article  Google Scholar 

  9. Taha, H.E., Hajj, M.R., Nayfeh, A.H.: Wing kinematics optimization for hovering micro air vehicles using calculus of variation. J. Aircr. (2013). doi:10.2514/1.C031969

    Google Scholar 

  10. Oppenheimer, M.W., Doman, D.B., Sigthorsson, D.O.: Dynamics and control of a biomimetic vehicle using biased wingbeat forcing functions. J. Guid. Control Dyn. 34(1), 204–217 (2011)

    Article  Google Scholar 

  11. Sigthorsson, D.O., Oppenheimer, M.W., Doman, D.B.: Flapping wing micro-air-vehicle control employing triangular wave strokes and cycle-averaging. 2010-7553. AIAA, Guidance, Navigation, and Control Conference, Toronto, Ontario, Canada (2010)

  12. Chung, S.J., Dorothy, M.: Neurobiologically inspired control of engineered flapping flight. J. Guid. Control Dyn. 33(2), 440–452 (2010)

    Article  Google Scholar 

  13. Stanford, B.K., Beran, P.S., Snyder, R., Patil, M.: Stability and power optimality in time-periodic flapping wing structures. AIAA 2012-1638. 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Honolulu, Hawaii (2012)

  14. Bhatia, M., Patil, M., Woolsey, C., Stanford, B., Beran, P.: Lqr controller for stabilization of flapping wing mavs in gust environments. AIAA, Atmospheric Flight Mechanics Conference, Minneapolis, Minnesota (2012)

  15. Weis-Fogh, T.: Quick estimates of flight fitness in hovering animals, including novel mechanisms for lift production. J. Exp. Biol. 59, 169–230 (1973)

    Google Scholar 

  16. Ellington, C.P.: The aerodynamics of hovering insect flight: iii. Kinematics. Philos. Trans. R. Soc. Lond. B 305, 41–78 (1984)

    Article  Google Scholar 

  17. Doman, D.B., Oppenheimer, M.W., Sigthorsson, D.O.: Dynamics and control of a biomimetic vehicle using biased wingbeat forcing functions. Part ii: Controller. AIAA 2010-1024

  18. Oppenheimer, M.W., Doman, D.B., Sigthorsson, D.O.: Dynamics and control of a minimally actuated biomimetic vehicle. Part ii: Controller. 2009-6161. AIAA Guidance, Navigation, and Control Conference, Chicago, Illinois

  19. Greenwood, D.T.: Advanced Dynamics. Cambridge University Press, Cambridge (2003)

    Book  Google Scholar 

  20. Taha, H.E., Hajj, M.R., Beran, P.S.: Unsteady nonlinear aerodynamics of hovering mavs/insects. AIAA 2013-0504. Aerospace Sciences Meeting, Dallas (2013)

  21. Nayfeh, A.H., Mook, D.T., Marshall, L.R.: Nonlinear coupling of pitch and roll modes in ship motion. J. Hydronaut. 7(4), 145–152 (1973)

    Article  Google Scholar 

  22. Haddow, A.G., Barr, A.D.S., Mook, D.T.: Theoretical and experimental study of modal interaction in a two-degree-of-freedom structure. J. Sound Vib. 97(3), 451–473 (1984)

    Article  MathSciNet  Google Scholar 

  23. Nayfeh, A.H., Balachandran, B.: Modal interactions in dynamical and structural systems. Appl. Mech. Rev. 42(11), 175–202 (1989)

    Article  MathSciNet  Google Scholar 

  24. Nayfeh, A.H.: Perturbation Methods. Wiley, New York (1973)

    MATH  Google Scholar 

  25. Nayfeh, A.H.: Introduction to Perturbation Techniques. Wiley, New York (1981)

    MATH  Google Scholar 

  26. Balachandran, B., Nayfeh, A.H.: Nonlinear motions of beam-mass structure. Nonlinear Dyn. 1, 39–61 (1990)

    Article  Google Scholar 

  27. Oueini, S.S., Nayfeh, A.H., Gonaraghi, M.A.: A theoretical and experimental implementation of a control method based on saturation. Nonlinear Dyn. 13, 189–202 (1997)

    Article  MATH  Google Scholar 

  28. Oueini, S.S., Nayfeh, A.H., Pratt, J.R.: A nonlinear vibration absorber for flexible structures. Nonlinear Dyn. 15(3), 259–282 (1998)

    Article  MATH  Google Scholar 

  29. Hall, B.D., Mook, D.T., Nayfeh, A.H., Preidikman, S.: Novel strategy for suppressing the flutter oscillations of aircraft wings. AIAA J. 39(10), 1843–1850 (2001). doi:10.2514/2.1190

    Article  Google Scholar 

  30. Nayfeh, A.H., Mook, D.T.: Nonlinear Oscillations. Wiley, New York (1979)

    MATH  Google Scholar 

  31. Nayfeh, A.H.: Nonlinear Interactions: Analytical, Computational, and Experimental Methods. Wiley, New York (2002)

    Google Scholar 

  32. Ellington, C.P.: The aerodynamics of hovering insect flight: ii. Morphological parameters. Philos. Trans. R. Soc. Lond. B 305, 17–40 (1984)

    Article  Google Scholar 

  33. Sun, M., Du, G.: Lift and power requirements of hovering insect flight. Acta Mech. Sin. 19(5), 458–469 (2003)

    Article  Google Scholar 

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Authors and Affiliations

  1. Virginia Tech, Blacksburg, VA, USA

    Haithem E. Taha, Ali H. Nayfeh & Muhammad R. Hajj

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  1. Haithem E. Taha
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  2. Ali H. Nayfeh
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  3. Muhammad R. Hajj
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Correspondence to Muhammad R. Hajj.

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Taha, H.E., Nayfeh, A.H. & Hajj, M.R. Saturation-based actuation for flapping MAVs in hovering and forward flight. Nonlinear Dyn 73, 1125–1138 (2013). https://doi.org/10.1007/s11071-013-0857-0

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  • DOI: https://doi.org/10.1007/s11071-013-0857-0

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