Finite thrust orbital transfers

Mazzini, Leonardo

doi:10.1016/j.actaastro.2014.04.004

Cited by 13 publications

(5 citation statements)

References 10 publications

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“…Because appears in Eqs. (30) and (31), their explicit form is problem-dependent, unlike what occurs for the adjoint equations (33). Moreover, Eqs.…”

Section: Necessary Conditions For Optimalitymentioning

confidence: 98%

“…They proposed an effective methodology for circumventing the theoretical difficulties inherent to the state-dependent control. Most recently, Mazzini [33] utilized a smooth eclipse function, to restore the regularity conditions, for the purpose of applying the Pontryagin minimum principle, whereas Taheri and Junkins [50] proposed the hyperbolic tangent as a smoothing function. Similarly, Aziz et al [1] smoothed the eclipse transition with a logistic function and computed the optimal paths through differential dynamic programming, a second-order gradient-based method.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Space Trajectories with Multiple Coast Arcs Using Modified Equinoctial Elements

Pontani

2021

J Optim Theory Appl

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The detection of optimal trajectories with multiple coast arcs represents a significant and challenging problem of practical relevance in space mission analysis. Two such types of optimal paths are analyzed in this study: (a) minimum-time low-thrust trajectories with eclipse intervals and (b) minimum-fuel finite-thrust paths. Modified equinoctial elements are used to describe the orbit dynamics. Problem (a) is formulated as a multiple-arc optimization problem, and additional, specific multipoint necessary conditions for optimality are derived. These yield the jump conditions for the costate variables at the transitions from light to shadow (and vice versa). A sequential solution methodology capable of enforcing all the multipoint conditions is proposed and successfully applied in an illustrative numerical example. Unlike several preceding researches, no regularization or averaging is required to make tractable and solve the problem. Moreover, this work revisits problem (b), formulated as a single-arc optimization problem, while emphasizing the substantial analytical differences between minimum-fuel paths and problem (a). This study also proves the existence and provides the derivation of the closed-form expressions for the costate variables (associated with equinoctial elements) along optimal coast arcs.

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“…Because appears in Eqs. (30) and (31), their explicit form is problem-dependent, unlike what occurs for the adjoint equations (33). Moreover, Eqs.…”

Section: Necessary Conditions For Optimalitymentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Optimal Space Trajectories with Multiple Coast Arcs Using Modified Equinoctial Elements

Pontani

2021

J Optim Theory Appl

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“…In the indirect method, the optimal transfer trajectories are obtained using a calculus of variations approach and a shooting method. However, a fairly accurate initial guess for the starting costate vector ( ) 0 t λ is required, which can be challenging because the costate vector are variables without intuitive physical meaning [3,4] . In the direct method, the control vector at discrete time nodes are parameterized, and the resulted constrained parameter optimization problem is handled as nonlinear programming (NLP) problem.…”

Section: Introductionmentioning

confidence: 99%

Optimal strategy for low-thrust spiral trajectories using Lyapunov-based guidance

Yang

Gao

2015

Advances in Space Research

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“…«Неполная» краевая задача «возникла» при попытке учесть влияние обнуления малой тяги (МТ) в области тени на траекторию перелета на геостационарную орбиту (ГСО) космического аппарата (КА) с питанием от солнечных батарей. Влияние тени рассматривалось в различных работах, использовавших как прямые, так и непрямые методы оптимизации, методы осреднения уравнений движения, синтез управления с обратной связью [1][2][3][4][5][6][7].…”

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Some examples of “non-completed” boundary value problem solutions for multi-orbital transfers to geostationary orbit with zero thrust in the shadow

Akhmetshin

2019

KIAM Prepr.

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О р д е н а Л е н и н а ИНСТИТУТ ПРИКЛАДНОЙ МАТЕМАТИКИ имени М.В.Келдыша Р о с с и й с к о й а к а д е м и и н а у к Р.З. Ахметшин Примеры решения «неполной» краевой задачи для многовитковых перелетов на геостационарную орбиту с нулевой тягой в области тени Москва-2019 Ахметшин Р.З. Примеры решения «неполной» краевой задачи для многовитковых перелетов на геостационарную орбиту с нулевой тягой в области тени Рассматриваются перелеты космического аппарата в центральном ньютоновом поле Земли с высокоэллиптических орбит на геостационарную орбиту с малой тягой, которая обнуляется при попадании в тень Земли. Для получения таких перелетов решается двухточечная краевая задача, названная "неполной", поскольку в ней не учитываются условия оптимального пересечения границ тени. Показано, что если долгота восходящего узла начальной орбиты  0 = 180 0 , то таким образом можно получать траектории, близкие по затратам рабочего вещества к траекториям "номинальным" (без обнуления тяги). А для траекторий продолжительностью полгода или меньше за счет выбора наилучших  0 затраты получаются меньше номинальных. Ключевые слова: многовитковые траектории, космический аппарат, малая тяга, геостационарная орбита, тень Земли, двухточечная краевая задача Rauf Zulfarovich Akhmetshin Some examples of "non-completed" boundary value problem solutions for multi-orbital transfers to geostationary orbit with zero thrust in the shadow Transfers in the central Newtonian field from high-elliptical orbits to geostationary one of a spacecraft with low thrust, which becomes zero in the Earth shadow, are considered. To find such trajectories so called "non-completed" twopoint boundary value problem that do not include a condition of optimal crossing the shadow boundary is solved. It's shown that when a longitude of ascending node  0 is equal to 180 0 expenditures of working substance are not much more than for a basic transfer (without switching the low thrust off). If  0 is chosen the best and the duration of flight is half-year or smaller then expenditures are less than for a basic transfer.

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Finite thrust orbital transfers

Cited by 13 publications

References 10 publications

Optimal Space Trajectories with Multiple Coast Arcs Using Modified Equinoctial Elements

Optimal Space Trajectories with Multiple Coast Arcs Using Modified Equinoctial Elements

Optimal strategy for low-thrust spiral trajectories using Lyapunov-based guidance

Some examples of “non-completed” boundary value problem solutions for multi-orbital transfers to geostationary orbit with zero thrust in the shadow

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