Robust Trajectory Optimization for Dynamic Soaring

Flanzer, Tristan C.; Bower, Geoffrey C.; Kroo, Ilan

doi:10.2514/6.2012-4603

Cited by 32 publications

(19 citation statements)

References 17 publications

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“…(12)(13)(14)(15), which we accomplish using a conventional optimization technique such as the direct collocation method. We employ the pseudospectral method, a relatively new optimization technique that is categorized as a direct method [16][17][18].…”

Section: Solve Converted Problem By Direct Methodsmentioning

confidence: 99%

“…(12)(13)(14)(15) In the Legendre-Gauss pseudospectral method, the differential algebraic equations are collocated at N 0 Legendre-Gauss points τ 1 ; : : : ; τ N 0 that lie in the open interval (−1, 1). The initial time τ 0 −1 and terminal time τ N 0 1 1 are also added to the collocation points.…”

Section: Solve Converted Problem By Direct Methodsmentioning

confidence: 99%

“…Cottrill and Harmon [12] used both a pseudospectral method and the gPC technique to optimal control problems and examined the parameter sensitivity of the control output. Jia et al [13] used the gPC method to quantify the uncertainty propagation of systems, and Flanzer et al [14], who took the uncertainty of the five most sensitive parameters into account, employed it to obtain a robust trajectory for dynamic soaring. Although the gPC technique is an approximate method, it can deal with very small probabilities at a much lower computational cost than sampling methods.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimal Aircraft Control in Stochastic Severe Weather Conditions

Okamoto

Tsuchiya

2016

Journal of Guidance, Control, and Dynamics

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The purpose of this study is to apply a stochastic optimal control method to the guidance of an aircraft. The aircraft is given optimal control to make a final approach through a microburst, a hazardous weather phenomenon for lowflying aircraft that may cause accidents during landing. As the determination of the size and the strength of a microburst always involves uncertainty, its precise detection is difficult. To minimize the risk of accidents, we must account for system uncertainty, a difficult task using conventional optimization techniques, which cannot handle random variables. This paper aims to solve this problem by employing a stochastic optimization algorithm that incorporates the generalized polynomial chaos method into a conventional direct method. The generalized polynomial chaos method is a numerical technique for solving stochastic differential equations. To demonstrate the effectiveness of the proposed algorithm, we conduct a numerical simulation in which an aircraft flies through a microburst and attempts to land. The results of the simulation successfully verify its effectiveness. Nomenclature a = vector of static variables that are independent of timeacceleration, 9.81 m∕s i = index of random variables p j = index of set of collocation points and weight functions L = lift, N l = index of root of the Nth-degree Legendre orthogonal polynomial M = aircraft mass, kg m, n = indices indicating degree of orthogonal polynomials N = number of random variables N 0 = number of Legendre-Gauss collocation points P = maximum degree of N-variate orthogonal polynomial p = vector of random variables that are independent of time Q = total number of sets of collocation points and weight functions q i = number of sets of collocation points and weight functions of each random variable r p = microburst radius parameter, m S = wing surface, m 2 T = thrust, N t = time, s u = control variable u d = deterministic optimal control u m = microburst intensity parameter, m∕s u s = stochastic optimal control u = approximating function of control u = optimal control Var = variance v a = airspeed, m∕s w x = wind speed in x direction, m∕s w y = wind speed in y direction, m∕s w z = wind speed in z direction, m∕s x = horizontal position, m x c = microburst center parameter, m x = state variablẽ x = approximated state variable by generalized polynomial chaos methodx = approximatedx by Legendre-Gauss pseudospectral method z = altitude, m z m = microburst height parameter, where horizontal wind speed is strongest, m α = angle of attack, rad Γ = N-dimensional probability space γ = flight-path angle relative to air, rad γ g = flight-path angle relative to ground, rad ρ = probability density functions ρ air = density of air from standard atmosphere model, kg∕m 3 σ = standard deviation τ = normalized time τ T = time constant of thrust, s τ α = time constant of angle of attack, s Ψ = multidimensional orthogonal polynomials ψ = one-dimensional orthogonal polynomials Subscripts com = commanded value f = final nom = necessary value with no d...

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Section: Solve Converted Problem By Direct Methodsmentioning

confidence: 99%

Section: Solve Converted Problem By Direct Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal Aircraft Control in Stochastic Severe Weather Conditions

Okamoto

Tsuchiya

2016

Journal of Guidance, Control, and Dynamics

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“…Then, an optimal control problem is formulated in order to search for the control sequence that minimizes a probabilistic functional that aggregates the cost among all of the trajectories (see Figure 1.b). Some examples of aerospace applications employing this technique are robust trajectory optimization for an aircraft based on dynamic soaring [17,Chapters 2,3], trajectory optimization for a supersonic aircraft with uncertainties in the aerodynamic data [18] and optimization of a spacecraft reorientation maneuver [16].…”

Section: Uncertainty Durationmentioning

confidence: 99%

Robust Aircraft Trajectory Planning Under Wind Uncertainty Using Optimal Control

González-Arribas

Soler

Sanjurjo-Rivo

2018

Journal of Guidance, Control, and Dynamics

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Uncertainty in aircraft trajectory planning and prediction generates major challenges for the future Air Traffic Management system. Therefore, understanding and managing uncertainty will be necessary to realize improvements in air traffic capacity, safety, efficiency and environmental impact. Meteorology (and, in particular, winds) represents one of the most relevant sources of uncertainty. In the present work, a framework based on optimal control is introduced to address the problem of robust and efficient trajectory planning under wind forecast uncertainty, which is modeled with probabilistic forecasts generated by Ensemble Prediction Systems. The proposed methodology is applied to a flight p l anning s c enario u n der a f r ee-routing operational paradigm and employed to compute trajectories for different sets of user preferences, exploring the trade-off between average flight cost and p r edictability. Results show how the impact of wind forecast uncertainty in trajectory predictability at a pre-tactical planning horizon can be not only quantified, b u t a l so r e duced t h rough t h e application of the proposed approach.

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“…In another example, the performance index being minimized is the accumulated heat in the Apollo capsule during descent [7]. The ability of optimal control solvers to take into 40 account wind velocity has been demonstrated in [8] where a collocation technique was used to increase the energy of the vehicle using wind gradients. Direct collocation, solves the optimal control problem by approximating the solution with polynomials and minimizing the differential errors.…”

mentioning

confidence: 99%

Optimal control for the trajectory planning of micro airships

Blouin

Lanteigne

Gueaieb

2017

2017 International Conference on Unmanned Aircraft Systems (ICUAS)

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Abstract-The objective of this paper is to demonstrate the application of optimal control for generating dynamically constrained minimal time trajectories in micro unmanned airships. By design, airships are generally underactuated and underpowered limiting their maneuvering capabilities. Using a simplified dynamic model derived with experimentally derived coefficients, two trajectory planning simulations are solved using optimal control. The generated trajectories are then evaluated experimentally on a micro airship to demonstrate that optimal control can be used in open loop over short distances.

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Robust Trajectory Optimization for Dynamic Soaring

Cited by 32 publications

References 17 publications

Optimal Aircraft Control in Stochastic Severe Weather Conditions

Optimal Aircraft Control in Stochastic Severe Weather Conditions

Robust Aircraft Trajectory Planning Under Wind Uncertainty Using Optimal Control

Optimal control for the trajectory planning of micro airships

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