Reformulation of Edelbaum's Low-Thrust Transfer Problem Using Optimal Control Theory

Kechichian, Jean Albert

doi:10.2514/2.4145

Cited by 85 publications

(40 citation statements)

References 4 publications

(4 reference statements)

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“…The average orbital semimajor axis can be used to replace the osculating one in Eq. (10). For the phasing mission, the average orbital semi-major axis of the anti-tangential thrust duration should be same as that of the tangential thrust duration, which can be estimated as…”

Section: Circular Orbit Phasingmentioning

confidence: 99%

“…Edelbaum suggested that changing station using tangential thrust is the most effective approach [4]. On the basis of Edelbaum's approach, the trajectory from one circular orbit to another is optimized under the assumption of quasi-circular orbits [2,10,13]. In addition, the phasing mission between different orbits has been investigated by many researchers.…”

Section: Introductionmentioning

confidence: 99%

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Design and optimization of low-thrust orbital phasing maneuver

Shang

Shuai

2015

Aerospace Science and Technology

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Section: Circular Orbit Phasingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Design and optimization of low-thrust orbital phasing maneuver

Shang

Shuai

2015

Aerospace Science and Technology

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“…All of these analyses assume that the orbit remains circular after each cycle or revolution. In reference [9], the original Edelbum theory is revisited by extending, completing, and deriving the yaw steering expressions without ambiguity and recasting the theory within the framework of optimal control for minimum time. In reference [10], the authors reexamine Edelbum's approach and some improvements are introduced, while maintaining the assumption of quasi-circular orbits.…”

Section: Shafieenejad and A B Novinzadehmentioning

confidence: 99%

“…In other words, system equation (24) is autonomous and the Hamiltonian is a constant. Finally, this constant must be zero because final time is unspecified [9,11] …”

Section: Minimum-time Low-thrust Orbital Transfermentioning

confidence: 99%

Closed form optimal continuous guidance scheme for new dynamic of electrical propulsion plane change transfers

Shafieenejad

Novinzadeh

2010

Proceedings of the Institution of Mechanical Engineers, Part K:

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New guidance policies for the problem of low-thrust transfer between inclined orbits are developed within the framework of optimal control theory. The objectives of this guidance schemes are to provide appropriate thrust steering programmes that will transfer the vehicle from inclined low earth orbits to high earth orbits. The presented guidance schemes are determined by using optimal control theory such that two optimal performance measures are minimized. In this work, the independent variable is changed from time to thrust angle and some properties of autonomous system equations are considered to obtain the exact closed form solutions. Three states are considered, orbital inclination, velocity, and ascending node, to establish this dynamic system. Finally, two performances are investigated for new class of electrical propulsion plane change manoeuvres.

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“…A systematic mathematical representation of these problems is considered. T HE optimization problem of continuous-thrust spacecraft trajectories has been studied extensively [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The optimization methods for the trajectories have been mainly of two types: indirect and direct techniques or their combinations.…”

mentioning

confidence: 99%

Spacecraft Trajectory Optimization Based on Discrete Sets of Pseudoimpulses

Ulybyshev

2009

Journal of Guidance, Control, and Dynamics

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A brief review of new methods for continuous-thrust trajectory optimization is presented. The methods use discretization of the spacecraft trajectory on segments and sets of pseudoimpulses for each segment. Boundary conditions are presented as a linear matrix equation. A matrix inequality on the sum of the characteristic velocities for the pseudoimpulses is used to transform the problem into a large-scale linear programming form. Present-day linear programming methods use interior-point algorithms to solve such problems. In the general case, the continuous burns include a number of adjacent segments and a postprocessing of the linear programming solutions is needed to form a sequence of the burns. An optimal number of the burns is automatically determined in the postprocessing. The methods provide flexible opportunities for the trajectory computation in complex missions with various requirements and constraints. A systematic mathematical representation of these problems is considered. A summary of examples for orbit transfer, rendezvous, and moon ascent trajectories is presented. Application examples of lunar landing trajectories are examined. The examples represent a set of optimal unconstrained trajectories for different thrust-to-weight ratios and trajectories with safety descent profile, thrust level, and attitude constraints. Nomenclature A = matrix of inequality constraints A e = matrix of partial derivatives a = thrust acceleration a o = initial thrust acceleration b = vector of inequality constraints e = thrust-direction unit vector F = boundary-condition function f T = dimensionless thrust level g = vector of gravitational acceleration g M = gravitational acceleration on the moon surface h = altitude I sp = specific impulse i = segment number J = performance index j = pseudoimpulse number k = quantity of pseudoimpulses at each segment L = horizontal range M = spacecraft dimensionless mass (for initial time M 1) _ M = dimensionless mass rate for maximum thrust level m = number of boundary conditions n = quantity of segments P f = vector of boundary conditions P f = vector of boundary parameters along the trajectory without any maneuvers r = radius vector Q = function of interior-point inequality constraints q = weight coefficient vector of the fuel usage for the segments t = time V = spacecraft velocity vector X = vector of decision variables Y = state vector P f = target vector t i = duration of the ith segment V iopt = optimal characteristic velocity vector at the ith segment V j i = dimensionless characteristic velocity of the jth pseudoimpulse at the ith segment V X = characteristic velocity # = thrust angle ' = pitch angle

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Reformulation of Edelbaum's Low-Thrust Transfer Problem Using Optimal Control Theory

Cited by 85 publications

References 4 publications

Design and optimization of low-thrust orbital phasing maneuver

Design and optimization of low-thrust orbital phasing maneuver

Closed form optimal continuous guidance scheme for new dynamic of electrical propulsion plane change transfers

Spacecraft Trajectory Optimization Based on Discrete Sets of Pseudoimpulses

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