Nonlinear Dynamics

, Volume 94, Issue 4, pp 3117–3144 | Cite as

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

  • Imran Mir
  • Sameh A. Eisa
  • Adnan Maqsood


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.


Dynamic soaring Nonlinear flight dynamics Nonlinear modeling Flight control system Morphing Optimal control Linear control Geometric nonlinear control 



Unmanned aerial vehicle


Small unmanned aerial vehicle


True air speed

\(\gamma \)

Flight path angle

\(\psi \)

Azimuth measured clockwise from the y-axis


Position vector along east direction


Position vector along north direction



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

Angle of attack at zero lift


Wing span

\(\Lambda \)

Sweep angle


Lift coefficient

\(\phi \)

Bank angle


Drag coefficient




Mass of the vehicle


Acceleration due to gravity


Wind velocity


Load factor

\(n_{\max }\)

Maximum load factor

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

Maximum value of the variable

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

Minimum value of the variable


Initial time


Final time


Variable value at initial time


Variable value at final time

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

First-order time derivative


Reference wind speed


Reference altitude


Surface correctness factor

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

Lift curve slope of airfoil


Zero lift drag coefficient

\(\rho \)

Density of the air


Load factor


Wing area


Induced drag factor


Aspect ratio of the wing

L / D

Lift-to-drag ratio




meter per sec





\({}^{\circ }\)



Non linear programming


Interior point optimization


General purpose optimal control software


Drift vector


Control input field


Lie bracket between vector V1 and V2


Lie algebraic rank condition



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.

Compliance with ethical standards

Conflict of Interest

The authors of this paper have no conflict of interest to declare.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Research Center for Modeling and SimulationNational University of Sciences and Technology (NUST)IslamabadPakistan
  2. 2.Mechanical and Aerospace Engineering DepartmentUniversity of CaliforniaIrvineUSA

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