The implementation of the cluster II constellation

Dow, J. M.; Matussi, Sandro; Dow, Roberta Mugellesi; Schmidt, Michaël; Warhaut, M.

doi:10.1016/j.actaastro.2003.06.006

Cited by 12 publications

(8 citation statements)

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“…Dow et al [2004] used a modified Hohmann transfer maneuver to transfer four satellites from a circular orbit to a final elliptical orbit. In their paper, a small consumption of fuel was obtained because the tetrahedron constellation was deployed using intermediate elliptical orbits.…”

Section: Transfer From a Circular Orbit To The Elliptical Orbit (Stagmentioning

confidence: 99%

“…This transfer maneuver represents the most fuel efficient procedure to obtain the desired elliptical orbit for the four satellites. The Hohmann transfer orbit has been used to deploy a different tetrahedron constellation as shown in [Dow et al 2004]. Also, Bainum et al [2005] have showed that, by using a modified Hohmann transfer, an along-track constellation can be launched from a circular orbit to an elliptical orbit.…”

Section: Introductionmentioning

confidence: 99%

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Deployment procedure for the Tetrahedron Constellation

Capó-Lugo

Bainum

2009

JOMMS

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The NASA Benchmark Tetrahedron Constellation is a four-satellite formation that requires a nominal separation distance at every apogee point. The deployment procedure of a tetrahedron constellation is complex and depends on the separation distance between any pair of satellites within the constellation. In this paper, the deployment procedure of the tetrahedron constellation will be divided into two stages: the deployment from a circular parking orbit to an elliptical orbit, and the correction of the separation distance between pairs of satellites within the constellation. The solution of this problem will be implemented with a combination of Hohmann transfer maneuvers and the digital linear quadratic regulator control scheme showing a minimum consumption of fuel. In summary, the combination of these two techniques will provide a different approach to the deployment procedure of the NASA benchmark tetrahedron constellation.

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Section: Transfer From a Circular Orbit To The Elliptical Orbit (Stagmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Deployment procedure for the Tetrahedron Constellation

Capó-Lugo

Bainum

2009

JOMMS

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“…(9)(10)(11)(12)(13). However, there are several issues that make this difficult, if not impossible, to solve exactly.…”

Section: General Problem Statementmentioning

confidence: 99%

“…Many researchers have developed methods that simultaneously solve the guidance and control problem. Hocken and Schoenmaekers [11] presented an optimization approach to minimize V while simultaneously satisfying guidance constraints for the Cluster constellation [12,13]. Huntington et al [14,15] used the Gauss pseudospectral method to solve the optimal control problem while satisfying guidance constraints.…”

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confidence: 99%

General Method for Optimal Guidance of Spacecraft Formations

Hughes

2008

Journal of Guidance, Control, and Dynamics

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One of the most interesting and challenging aspects of formation guidance algorithm design is the coupling of the orbit design and the science return. The effectiveness of the formation as a science instrument is intimately coupled with the relative geometry and evolution of the collection of spacecraft. Therefore, the science return can be maximized by optimizing the orbit design according to a performance metric relevant to the science mission goals. In this work, we present a general method for optimal formation guidance that is applicable to missions whose performance metric, requirements, and constraints can be cast as functions that are explicitly dependent upon the orbit states and spacecraft relative positions and velocities. The approach is fully nonlinear, accommodates orbital perturbations, and is applicable to multiple flight regimes including highly eccentric, hyperbolic, interplanetary, or libration point orbits. Furthermore, the method is applicable to small formations, as well as large formations and constellations. We present a general form for the cost and constraint functions, and derive their semi-analytic gradients with respect to the formation initial conditions. The gradients are broken down into two types. The first type are gradients of the mission-specific performance metric with respect to formation geometry. The second type are derivatives of the formation geometry with respect to the orbit initial conditions. The fact that these two types of derivatives appear separately allows us to derive and implement a general framework that requires minimal modification to be applied to different missions or mission phases. To illustrate the applicability of the approach, we conclude with applications to two missions: the Magnetospheric Multiscale Mission, and the Laser Interferometer Space Antenna. Nomenclature A = upper left 3 3 partition of B = upper right 3 3 partition of C = lower left 3 3 partition of c k = quadrature constant at point k D = lower right 3 3 partition of m = no. of unique sides in the formation N = no. of path constraints n = no. of spacecraft n k = no. of quadrature points r = position vector s ik = vector defining side i at quadrature point k _ s ik = rate vector of side i at quadrature point k s ik = length of side i at quadrature point k _ s ik = rate of change in length of side i at quadrature point k v = velocity vector = orbit state transition matrix Subscripts C = indicates association with constraints i = side index J = indicates association with cost function j = spacecraft index k = quadrature point index ' = spacecraft index p = dummy index

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“…First, for the case of a circular reference orbit, formation flying can be applicable to Earth observation, including space interferometry, and synthetic apertures. The second main category is for the case of an eccentric reference orbit, which has several advantages in scientific missions, such as the magnetospheric multiscale (MMS) mission (Curtis 2000, Curtis et al 2003) and the cluster II mission (Dow et al 2004). To meet the scientific mission goals, four-spacecraft formations are commonly used to take measurements in three dimensions at intersatellite distances on the order of several kilometers.…”

Section: Introductionmentioning

confidence: 99%

Determination of Initial Conditions for Tetrahedral Satellite Formation

Yoo

Park²

2011

Journal of Astronomy and Space Sciences

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This paper presents an algorithm that can provide initial conditions for formation flying at the beginning of a region of interest to maximize scientific mission goals in the case of a tetrahedral satellite formation. The performance measure is to maximize the quality factor that affects scientific measurement performance. Several path constraints and periodicity conditions at the beginning of the region of interest are identified. The optimization problem is solved numerically using a direct transcription method. Our numerical results indicate that there exist an optimal configuration and states of a tetrahedral satellite formation. Furthermore, the initial states and algorithm presented here may be used for reconfiguration maneuvers and fuel balancing problems.

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The implementation of the cluster II constellation

Cited by 12 publications

References 0 publications

Deployment procedure for the Tetrahedron Constellation

Deployment procedure for the Tetrahedron Constellation

General Method for Optimal Guidance of Spacecraft Formations

Determination of Initial Conditions for Tetrahedral Satellite Formation

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