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Review of dynamic soaring: technical aspects, nonlinear modeling perspectives and future directions

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Abstract

In this paper, we present a comprehensive and detailed review of dynamic soaring process, and in particular, its application to unmanned aerial vehicles (UAVs). We start by explaining the biological inspiration that comes from soaring birds and how researchers have tried to utilize the dynamic soaring phenomenon/maneuver and apply it to UAVs. We present and discuss the fundamentals of wind shear models in both the linear and nonlinear cases. Moreover, a comprehensive parametric characterization of the key performance parameters for the dynamic soaring maneuver is given. Numerical methods for nonlinear trajectory optimization are summarized and methodologies capable of generating rapid solutions suitable for real-time implementation, are presented. Additionally, the paper introduces mathematical modeling and procedure to generate the optimized dynamic soaring trajectory. Through this paper, a consolidated platform is built, which not only covers technical aspects of advancements made over the passage of time, but also identifies and discusses the existing challenges. These challenges which are encountered by UAVs curtail the potential utility of dynamic soaring. Integrating dynamic soaring with morphology and inclusion of nonlinear control theory in the flight control system are introduced as a possible future research directions that may overcome the existing limitations.

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Abbreviations

UAV:

Unmanned aerial vehicle

sUAV:

Small unmanned aerial vehicle

V :

True air speed

\(\gamma \) :

Flight path angle

\(\psi \) :

Azimuth measured clockwise from the y-axis

x :

Position vector along east direction

y :

Position vector along north direction

h :

Altitude

\(\alpha _{L\,=\,0}\) :

Angle of attack at zero lift

b :

Wing span

\(\Lambda \) :

Sweep angle

\(C_\mathrm{L}\) :

Lift coefficient

\(\phi \) :

Bank angle

\(C_\mathrm{D}\) :

Drag coefficient

E :

Energy

M :

Mass of the vehicle

g :

Acceleration due to gravity

\(V_\mathrm{w}\) :

Wind velocity

n :

Load factor

\(n_{\max }\) :

Maximum load factor

\((.)_{\max }\) :

Maximum value of the variable

\((.)_{\min }\) :

Minimum value of the variable

\(t_\mathrm{o}\) :

Initial time

\(t_\mathrm{f}\) :

Final time

\((.)_{\mathrm{t}_{o}}\) :

Variable value at initial time

\((.)_{\mathrm{t}_{f}}\) :

Variable value at final time

\(\dot{(\cdot )}\) :

First-order time derivative

\(V_\mathrm{ref}\) :

Reference wind speed

\(h_\mathrm{ref}\) :

Reference altitude

\(h_{o}\) :

Surface correctness factor

\(c_{\mathrm{l}_{\alpha }}\) :

Lift curve slope of airfoil

\(C_{\mathrm{D}_{o}}\) :

Zero lift drag coefficient

\(\rho \) :

Density of the air

n :

Load factor

S :

Wing area

K :

Induced drag factor

AR :

Aspect ratio of the wing

L / D :

Lift-to-drag ratio

m:

meter

m/s:

meter per sec

s:

second

kg:

kilogram

\({}^{\circ }\) :

degree

NLP:

Non linear programming

IPOPT:

Interior point optimization

GPOPS:

General purpose optimal control software

\(f(\varvec{x})\) :

Drift vector

g :

Control input field

V1,V2:

Lie bracket between vector V1 and V2

LARC :

Lie algebraic rank condition

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Acknowledgements

Special thanks to Dr Haithem. E. Taha, Mechanical and Aerospace Engineering Department, UC Irvine for his continuous and sincere support throughout the phase of the research. The guidance and support extended by him contributed largely in making this research a success.

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Authors and Affiliations

  1. Research Center for Modeling and Simulation, National University of Sciences and Technology (NUST), Islamabad, Pakistan

    Imran Mir & Adnan Maqsood

  2. Mechanical and Aerospace Engineering Department, University of California, Irvine, USA

    Sameh A. Eisa

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  1. Imran Mir
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  2. Sameh A. Eisa
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  3. Adnan Maqsood
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Correspondence to Sameh A. Eisa.

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Mir, I., Eisa, S.A. & Maqsood, A. Review of dynamic soaring: technical aspects, nonlinear modeling perspectives and future directions. Nonlinear Dyn 94, 3117–3144 (2018). https://doi.org/10.1007/s11071-018-4540-3

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