Efficient Six Degree of Freedom Aircraft Trajectory Optimization with Application to Dynamic Soaring

Flanzer, Tristan C.; Bunge, Roberto; Kroo, Ilan

doi:10.2514/6.2012-5622

Cited by 4 publications

(13 citation statements)

References 21 publications

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“…For each variable, the exponent obtained by least-square fit is indicated in the legend. The asymptotic expansion of equations(11) and(12) predicts scalings that agree extremely well with the numerical trajectory optimization.IV.B. Validation against trajectory optimizations in logarithmic and power-law wind profiles[5, 6] simulate a glider of cruise speed V c = 15m/s (λ = 22 m) and (c 3/2…”

supporting

confidence: 63%

“…Overall, as noted in [6,12] the uncertainty is dominated by how close to the surface the glider can go and how well it is able to embed itself inside the slow boundary layer.…”

Section: −4mentioning

confidence: 93%

“…In [1], we solved the minimum wind problem numerically for various shear thicknesses δ by direct collocation, in a procedure adapted from [12,25]. It was observed that as δ is decreased, the trajectories become more and more 2D as the climb angle amplitude γ 0 decreases to 0.…”

Section: Step Wind Solutionmentioning

confidence: 99%

“…Finally the trajectory lowest and highest altitudes are the least well captured parameters, with errors up to 15% and 45% respectively. Comparison between the numerical trajectory optimization in [1], the asymptotic expansion in equations (9) and (11), numerical trajectory optimization in logarithmic fields from the literature 5,12 (red and blue), and albatross flight data 10 (green) as a function of the vertical travel during the lower turn. In the first plot, the horizontal green lines represent the individual turns of an albatross flying in a 7.8 m/s wind, reported in Figure 11 of [10] (the color intensity codes the length of the turns).…”

Section: Ivc Validation Against Recordings Of Flying Albatrossesmentioning

confidence: 99%

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Dynamic Soaring in Finite-Thickness Wind Shears: an Asymptotic Solution

Bousquet

Triantafyllou

Slotine

2017

AIAA Guidance, Navigation, and Control Conference

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Building upon our recent description of dynamic soaring as a succession of small amplitude arcs nearly crosswind, rather than a sequence of half-turns, we formulate an asymptotic expansion for the minimum-wind dynamic soaring cycle when the shear layer between the slow and fast regions has a thin but finite thickness. Our key assumption is that the trajectory remains approximately planar even in finite thickness shears. We obtain an analytical approximation for key flight parameters as a function of the shear layer thickness ∆. In particular we predict that the turn amplitude, maximum climb angle, and cycle altitude scale as ∆ 1/5 , ∆ 2/5 , and ∆ 3/5 , respectively. Our asymptotic expansion is validated against numerical trajectory optimizations and compared with recordings of albatross flights. While the model validity increases with wing loading, it appears to constitute an accurate description down to wing loadings as low as 4kg/m 2 for oceanic boundary layer soaring, a third that of the wandering albatross.

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supporting

confidence: 63%

“…Overall, as noted in [6,12] the uncertainty is dominated by how close to the surface the glider can go and how well it is able to embed itself inside the slow boundary layer.…”

Section: −4mentioning

confidence: 93%

Section: Step Wind Solutionmentioning

confidence: 99%

Section: Ivc Validation Against Recordings Of Flying Albatrossesmentioning

confidence: 99%

See 2 more Smart Citations

Dynamic Soaring in Finite-Thickness Wind Shears: an Asymptotic Solution

Bousquet

Triantafyllou

Slotine

2017

AIAA Guidance, Navigation, and Control Conference

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“…While the 3DoF dynamic soaring solution has been used to simulate the 6DoF aircraft's trajectory and attitude in several works (9)(10)(11) , not many have investigated the 6DoF trajectory optimisation. Flanzer et al (12) have used a compact vortex lattice method (CVLM) for computing the aerodynamic forces and moments, and have obtained travelling dynamic soaring trajectories using direct collocation. Liu et al (13) have demonstrated a piece-wise guidance and control strategy by means of a flight simulation platform for dynamic soaring.…”

Section: Introductionmentioning

confidence: 99%

Trajectory optimisation of six degree of freedom aircraft using differential flatness

Elango

Mohan

2018

Aeronaut. j.

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The flatness of a six-degree-of-freedom (6DoF) aircraft model with conventional control surfaces – aileron, flap, rudder and elevator, along with thrust vectoring ability is established in this work. Trajectory optimisation of an aircraft can be cast as an inverse problem where the solution for control inputs that yield desired trajectories for certain states is sought. The solution to the inverse problems for certain systems is made tractable when they exhibit differential flatness. Flatness-based trajectory optimisation has a significant advantage over an equivalent collocation-based method in terms of computational efficiency and viability for real-time implementation. An application for the flatness of 6DoF aircraft is shown in the trajectory optimisation for dynamic soaring, and its connection with an equivalent 3DoF flatness-based implementation is also brought out. The results are compared with that from a collocation-based approach.

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Optimal dynamic soaring consists of successive shallow arcs

Bousquet¹,

Triantafyllou²,

Slotine³

2017

J. R. Soc. Interface.

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Albatrosses can travel a thousand kilometres daily over the oceans. They extract their propulsive energy from horizontal wind shears with a flight strategy called dynamic soaring. While thermal soaring, exploited by birds of prey and sports gliders, consists of simply remaining in updrafts, extracting energy from horizontal winds necessitates redistributing momentum across the wind shear layer, by means of an intricate and dynamic flight manoeuvre. Dynamic soaring has been described as a sequence of half-turns connecting upwind climbs and downwind dives through the surface shear layer. Here, we investigate the optimal (minimum-wind) flight trajectory, with a combined numerical and analytic methodology. We show that contrary to current thinking, but consistent with GPS recordings of albatrosses, when the shear layer is thin the optimal trajectory is composed of small-angle, large-radius arcs. Essentially, the albatross is a flying sailboat, sequentially acting as sail and keel, and is most efficient when remaining crosswind at all times. Our analysis constitutes a general framework for dynamic soaring and more broadly energy extraction in complex winds. It is geared to improve the characterization of pelagic birds flight dynamics and habitat, and could enable the development of a robotic albatross that could travel with a virtually infinite range.

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Efficient Six Degree of Freedom Aircraft Trajectory Optimization with Application to Dynamic Soaring

Cited by 4 publications

References 21 publications

Dynamic Soaring in Finite-Thickness Wind Shears: an Asymptotic Solution

Dynamic Soaring in Finite-Thickness Wind Shears: an Asymptotic Solution

Trajectory optimisation of six degree of freedom aircraft using differential flatness

Optimal dynamic soaring consists of successive shallow arcs

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