Optimal patterns of dynamic soaring with a small unmanned aerial vehicle

Abstract

Like albatross, unmanned aerial vehicles can significantly make use of wind gradient to extract energy by the flight technique named dynamic soaring. The research aims to develop a general optimization method to compute all the possible patterns of dynamic soaring with a small unmanned aerial vehicle. A direct collocation approach based on the Runge-Kutta integrator is proposed to solve the trajectory optimization problem for dynamic soaring. The optimal dynamic soaring trajectories are classified into two patterns: closed trajectory pattern and travelling trajectory pattern by applying terminal constraints of zero horizontal displacement and a certain travelling direction, respectively. Using different terminal constrains for heading angle and initial guesses in the optimization process, the former pattern can be divided into two subtypes: O-shaped and 8-shaped trajectories, while the latter one is divided into C-shaped, α-shaped, S-shaped and Ω-shaped trajectories. The characteristics of these patterns and the correlation among patterns are analyzed and discussed.

Trajectory optimisation of six degree of freedom aircraft using differential flatness

“…Among the closed (loiter) trajectories, the "∞" shape requires a smaller wind strength than the "O" shape. Liu et al (23) have also arrived at the same conclusion and the optimal V R and t f calculated by them are very close to that obtained in the present work. The small discrepancy observed is due to the difference in the aircraft models considered.…”

“…So a steady wind whose strength varies exponentially with altitude is assumed to blow along the positive x-axis of the inertial frame as shown in (1). The exponential model provides a fairly good representation of the wind speed in the atmospheric boundary layer near the ground and it has been employed in several prior studies of dynamic soaring (7,23,24) . In (1), V R is the wind speed at a reference altitude H R and it denotes the strength of the wind field.…”

“…The trajectories associated with dynamic soaring necessitate all or most of the states to be periodic. It is then apt to consider a Fourier series-like representation for the flat outputs, y = [x y z ϕ θ ψ] T , given by (23), where M is the number of harmonics:…”

“…... (23) In (23), t f represents the time-period of the trajectory and the linear term d is incorporated to model travelling trajectories (7) . The elements corresponding to ϕ, θ and z in d are set to zero as these states are necessarily periodic for all kinds of energy-neutral trajectories.…”

“…A Fourier series representation of these is provided as an initial guess to the optimiser. A similar approach was followed in Liu et al (23) , although the optimisation was performed in time-domain. Cross-country or travelling trajectories can be obtained using the same initial guesses as that for the closed orbits but with constraints placed on the appropriate elements of d. Once the optimal solution for the flat outputs of the 3DoF implementation is obtained, the wind axes orientation angles can be computed by invoking the property of flatness.…”