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Nonlinear Dynamics

, Volume 73, Issue 1–2, pp 1125–1138 | Cite as

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

  • Haithem E. Taha
  • Ali H. Nayfeh
  • Muhammad R. Hajj
Original Paper

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.

Keywords

Saturation phenomenon Micro-air vehicles Actuation Nonlinear dynamics 

Nomenclature

\(\bar{c}\)

Mean chord length

g

Gravitational acceleration

mv, mw

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

xI, yI, and zI

Inertial fixed frame

xw, yw, and zw

Wing fixed frame

η

Pitching angle

φ

Back and forth flapping angle

ϑ

Plunging angle

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Haithem E. Taha
    • 1
  • Ali H. Nayfeh
    • 1
  • Muhammad R. Hajj
    • 1
  1. 1.Virginia TechBlacksburgUSA

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