Optimal Formation Design for Magnetospheric Multiscale Mission Using Differential Orbital Elements

Roscoe, Christopher W. T.; Vadali, Srinivas R.; Alfriend, Kyle T.; Desai, Uri

doi:10.2514/1.52484

Cited by 20 publications

(5 citation statements)

References 10 publications

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“…The first track originates from an STM derived by Gim and Alfriend that includes first-order secular and osculating J 2 effects in arbitrarily eccentric orbits [20]. This STM was used in the design process for NASA's MMS mission [21] and is employed in the maneuver-planning algorithm of NASA's CubeSat proximity operations demonstration mission [22]. A similar STM was later derived for a fully nonsingular ROE state [23] and more recent works have expanded this approach to include higher-order zonal geopotential harmonics [24].…”

Section: Introductionmentioning

confidence: 99%

New State Transition Matrices for Spacecraft Relative Motion in Perturbed Orbits

Koenig

Guffanti

D’Amico

2017

Journal of Guidance, Control, and Dynamics

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This paper presents new state transition matrices that model the relative motion of two spacecraft in arbitrarily eccentric orbits perturbed by J 2 and differential drag for three state definitions based on relative orbital elements. Both density-model-specific and density-model-free formulations of the effects of differential drag are included. The state transition matrices are derived by first performing a Taylor expansion on the equations of relative motion and subsequently computing an exact closed-form solution of the resulting linear differential equations. The resulting state transition matrices are used to generalize the geometric interpretation of the effects of J 2 and differential drag on relative motion in near-circular orbits provided in previous works to arbitrarily eccentric orbits. Additionally, this paper harmonizes current literature by demonstrating that a number of state transition matrices derived by previous authors using various techniques can be found by subjecting the models presented in this paper to more restrictive assumptions. Finally, the presented state transition matrices are validated through comparison with a high-fidelity numerical orbit propagator. It is found that these models are able to match or exceed the accuracy of comparable models in the literature over a broad range of orbit scenarios.

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Section: Introductionmentioning

confidence: 99%

New State Transition Matrices for Spacecraft Relative Motion in Perturbed Orbits

Koenig

Guffanti

D’Amico

2017

Journal of Guidance, Control, and Dynamics

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“…Studies on design [6][7][8][9][10], guidance [11][12][13], navigation [14][15][16][17], and control [18][19][20][21][22] of spacecraft formations are widely available in the literature. More comprehensive reviews of these studies can be found in recent survey papers [23][24][25][26].…”

Section: B State Of the Artmentioning

confidence: 99%

Formation Design of Distributed Telescopes in Earth Orbit for Astrophysics Applications

Koenig

Macintosh

D’Amico

2019

Journal of Spacecraft and Rockets

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“…One of these missions, the MMS, will operate in an orbit with a semi-major axis of a ¼ 42,905 km and eccentricities varying between e ¼ 0.81818 and e ¼ 0.9084. 12 Closed aperture formations operating in Molniya orbits with a ¼ 46,000 km and e ¼ 0.67 have been proposed for distributed Earth imaging applications. 13 Although, at these high orbits, the specific magnitude of the J 2 gravity perturbation is on the order of 1 Â 10 À6 N/kg, differences in the mean orbital element drift rates of the chief and deputy spacecraft can cause formation drift on the order of 1-100 m/orbit, depending on the formation.…”

Section: J2 Drift For Formations In Eccentric Orbitsmentioning

confidence: 99%

Stability of an impulsive control scheme for spacecraft formations in eccentric orbits

Sobiesiak

Damaren

2012

Proceedings of the Institution of Mechanical Engineers, Part G:

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An N-impulse control scheme for spacecraft formations in elliptical orbits is developed to regulate the differential elements of the deputy spacecraft in the presence of the J 2 perturbation. The presented control scheme is an extension of an existing circular-orbit formation control scheme and is shown to perform well at large eccentricities where the circular control scheme fails. For the case of two impulses being applied at arbitrary firing times, a discrete-time approach for ascertaining the stability of the controlled spacecraft formation, under the assumption of small impulsive thrusts, is presented. It is found that stability is guaranteed for the majority of firing time pairs; however, the requisite ÁV can be prohibitive for some firing time pairs. The control scheme and stability predictions for formations in high eccentricity orbits are validated in numerical simulation.

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Optimal Formation Design for Magnetospheric Multiscale Mission Using Differential Orbital Elements

Cited by 20 publications

References 10 publications

New State Transition Matrices for Spacecraft Relative Motion in Perturbed Orbits

New State Transition Matrices for Spacecraft Relative Motion in Perturbed Orbits

Formation Design of Distributed Telescopes in Earth Orbit for Astrophysics Applications

Stability of an impulsive control scheme for spacecraft formations in eccentric orbits

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