Direct Multiple Shooting Optimization with Variable Problem Parameters

Whitley, Ryan J.; Ocampo, Cesar A.

doi:10.2514/6.2009-803

Cited by 7 publications

(5 citation statements)

References 7 publications

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“…Provided a tentative solution is given, the equations of motion and adjoint differential equations are integrated to determine the errors on the boundary conditions. The initial values of the unknown constants that rule the state equations (Δ t 1 , Δ t 2 , Δ v r 1 , Δ v θ 1 ) are easily estimated from their physical meaning; one only needs to ensure that they are within reasonable ranges (Section 6), which can be determined according to the existing literature . Therefore, in this paper, attention is focused on estimating only the initial adjoints, as finding appropriate values is a quite difficult task.…”

Section: Indirect Optimization Methodsmentioning

confidence: 99%

“…The optimal trajectory with minimal Δ v is depicted in Figure . By referring to the results of and , the ranges for the unknown constants to estimate the initial adjoints are assumed as

0.25 h \leq Δ {italict}_{1} \leq 0.75 h, 2.5 day \leq Δ {italict}_{2} \leq 4.5 day, Δ {italicv}_{r 1} = 0, 0.8 km / s \leq Δ {italicv}_{θ 1} \leq 1 km / s

and the procedures usually provide a suitable initial guess for any set of values within these ranges. In the following example, Δ t 1 = 0.5 h, Δ t 2 = 4 day, Δ v r 1 = 0, and Δ v θ 1 = 0.85 km/s are used.…”

Section: Validationmentioning

confidence: 99%

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Adjoints estimation methods for impulsive Moon-to-Earth trajectories in the restricted three-body problem

Shen

Casalino

2014

Optim. Control Appl. Meth.

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SUMMARYA study of optimal impulsive Moon-to-Earth trajectories is presented in a planar circular restricted threebody framework. Two-dimensional return trajectories from circular lunar orbits are considered, and the optimization criterion is the total velocity change. The optimal conditions are provided by the optimal control theory. The boundary value problem that arises from the application of the theory of optimal control is solved using a procedure based on Newton's method. Motivated by the difficulty of obtaining convergence, the search for the initial adjoints is carried out by means of two different techniques: homotopic approach and adjoint control transformation. Numerical results demonstrate that both initial adjoints estimation methods are effective and efficient to find the optimal solution and allow exploring the fundamental tradeoff between the time of flight and required ΔV.

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Section: Indirect Optimization Methodsmentioning

confidence: 99%

“…The optimal trajectory with minimal Δ v is depicted in Figure . By referring to the results of and , the ranges for the unknown constants to estimate the initial adjoints are assumed as

0.25 h \leq Δ {italict}_{1} \leq 0.75 h, 2.5 day \leq Δ {italict}_{2} \leq 4.5 day, Δ {italicv}_{r 1} = 0, 0.8 km / s \leq Δ {italicv}_{θ 1} \leq 1 km / s

Section: Validationmentioning

confidence: 99%

Adjoints estimation methods for impulsive Moon-to-Earth trajectories in the restricted three-body problem

Shen

Casalino

2014

Optim. Control Appl. Meth.

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“…( 17) with respect to x k , τ k , and τ k+1 (superscripts are dropped to ease notation). An analytical result is used to link the derivative of the flow with its STM [14,31]:…”

Section: Accurate Computation Of Jacobian Of Defect Constraintsmentioning

confidence: 99%

High-Fidelity Trajectory Optimization with Application to Saddle-Point Transfers

Tos

Topputo

2019

Journal of Guidance, Control, and Dynamics

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A method to optimize space trajectories subject to impulsive controls is presented. The method employs a high-fidelity model and a multiple shooting technique. The model accounts for an arbitrary number of gravitational attractions, their corrections due to celestial bodies oblateness, and solar radiation pressure. The peculiarity of this paradigm is that the equations of motion are written in a roto-pulsating frame, where two primaries are at rest despite the fact that their motion and the one of the perturbers is given by a real ephemeris model. Direct transcription of the dynamics coupled with a multiple shooting technique, and an efficient computation of the Jacobian of the defects are used to optimize trajectories subject to a finite number of impulsive controls. The method has been applied to find a multitude of solutions to the problem of transferring a spacecraft from the Sun-Earth collinear Lagrange points to the Sun-Earth gravitational saddle point, where a theoretical zero background acceleration allows testing possible deviations from General Relativity. The problem of targeting the Sun-Earth saddle point with high accuracy represents a major flight dynamics challenge. The applicative scenario encompasses the possible mission extension option for LISA Pathfinder as special case.

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“…The use of STM for gradient calculation is well established 5 . The STM method uses linear approximations of state perturbations.…”

Section: B State Transition Matrix (Stm) Based Derivativesmentioning

confidence: 99%

Implementation of an Autonomous Multi-Maneuver Targeting Sequence for Lunar Trans-Earth Injection

Whitley

Ocampo

Williams

2010

AIAA Guidance, Navigation, and Control Conference

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Direct Multiple Shooting Optimization with Variable Problem Parameters

Cited by 7 publications

References 7 publications

Adjoints estimation methods for impulsive Moon-to-Earth trajectories in the restricted three-body problem

Adjoints estimation methods for impulsive Moon-to-Earth trajectories in the restricted three-body problem

High-Fidelity Trajectory Optimization with Application to Saddle-Point Transfers

Implementation of an Autonomous Multi-Maneuver Targeting Sequence for Lunar Trans-Earth Injection

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