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Nonlinear Dynamics

, Volume 70, Issue 2, pp 907–939 | Cite as

Flight dynamics and control of flapping-wing MAVs: a review

  • Haithem E. Taha
  • Muhammad R. Hajj
  • Ali H. Nayfeh
Review

Abstract

This paper provides a thorough review of the significant work done so far in the area of flight dynamics and control of flapping-wing micro-air-vehicles (MAVs). It provides the background necessary to do research in that area. Furthermore, it raises questions that need to be addressed in the future. The three main blocks constituting the flight dynamic framework of flapping MAVs are reviewed. These blocks are the flapping kinematics, the aerodynamic modeling, and the body dynamics. The design and parametrization of the flapping kinematics necessary to produce high-control authority over the MAV, as well as design of kinematics suitable for different flight conditions, are reviewed. Aerodynamic models used for analysis of flapping flight are discussed. Particular attention is given to the physical aspects captured by these models. The issues and consequences of averaging the dynamics and neglecting the wing inertia are discussed. The dynamic stability analysis of flapping MAVs is usually performed by either averaging, linearization and subsequent analysis or using Floquet theory. Both approaches are discussed. The linear and nonlinear control design techniques for flapping MAVs are also reviewed and discussed.

Keywords

Flapping MAVs/insects Kinematic design Aerodynamic modeling Leading edge vortex Averaging Stability analysis Floquet theory High frequency periodic control and differential flatness 

Nomenclature

AR

Aspect ratio

c

Chord length

CL,CD

Lift and drag coefficient

CN,CT

Normal and tangential force coefficient

\(F_{x_{w}}, F_{y_{w}}\) and \(F_{z_{w}}\)

Aerodynamic forces in the wing frame

g

Gravitational acceleration

,d

Lift and drag forces

L,M, and N

Aerodynamic moments in the body frame

p,q, and r

Components of the body angular velocity vector in the body frame

R

Wing radius (length)

Rβ

Rotation matrix by an angle β about the corresponding axis

t

Time variable

T,f, and ω

Flapping period, frequency, and angular frequency

\(\hat{\mathbf{u}}\)

Control input vector

u,v, and w

Components of the body velocity vector in the body frame

Va

Air velocity seen by the airfoil section

Vb

Body velocity

\(V_{x_{w}}, V_{y_{w}}\) and \(V_{z_{w}}\)

Velocity of the airfoil in the wing frame

\(\hat{x}_{0}\)

Normalized position of the pitch axis

X,Y, and Z

Aerodynamic forces in the body frame

x,y, and z

Components of the position vector of the origin of body-frame in the inertial frame

xI,yI, and zI

Inertial fixed frame

xb,yb, and zb

Body fixed frame

xw,yw, and zw

Wing fixed frame

α

Angle of attack

η

Pitching angle

φ

Back and forth flapping angle

Γ

Circulation

ωIb

Angular velocity of the body with respect to the inertial frame

ωbw

Angular velocity of the wing with respect to the body

ψ,θ, and ϕ

Yaw–pitch–roll Euler angles defining the body frame with respect to the inertial frame

ρair

Air density

ϑ

Plunging angle

χ

State vector

(.)RW and (.)LW

Right and left wings, respectively

(.)R,LW

Right or the left wing

\(\overline{(.)}\)

Cycle average

QS

Quasi-steady

LEV

Leading-edge vortex

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

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

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