Formation Establishment and Reconfiguration Using Differential Elements in<i>J</i>2-Perturbed Orbits

Roscoe, Christopher W. T.; Westphal, Jason J.; Griesbach, J.D.; Schaub, Hanspeter

doi:10.2514/1.g000999

Cited by 51 publications

(36 citation statements)

References 29 publications

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“…The averaging theory [13] can be used to derive the variation of the mean ROE due to the Earth's oblateness J 2 [7,14]. Moreover, as discussed by the authors in [7], the well-known GVE [5] can be exploited to determine the change of the mean ROE due to the continuous control acceleration ft ∈ R 3 . Hence, the set of nonlinear differential equations describing the mean relative motion under the effects of J 2 perturbing acceleration and the continuous control acceleration acting on the deputy can be written as follows [7]:…”

Section: A Relative Dynamics Modelmentioning

confidence: 99%

“…They demonstrated that the derived analytical solution is also fuel-optimal when only magnitudes of the relative eccentricity and inclination vectors are varied and the initial relative semimajor axis is null, comparing it with the result obtained using NPOPT, a numerical nonlinear optimization tool. Roscoe et al [5] proposed an iterative method based on Lawden's primer vector theory to determine the n-impulse fuel-optimal maneuvers for the establishment and reconfiguration of spacecraft formations. The proposed method is valid in circular and elliptic orbits and includes first-order secular J 2 effects, whereas the dynamics is expressed in terms of differential mean orbital elements.…”

Section: Introductionmentioning

confidence: 99%

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Minimum-Fuel Control Strategy for Spacecraft Formation Reconfiguration via Finite-Time Maneuvers

Mauro

Spiller

Carnà

et al. 2019

Journal of Guidance, Control, and Dynamics

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This paper addresses the minimum-fuel spacecraft formation reconfiguration maneuver in J 2 perturbed nearcircular orbits. In this study, only the deputy is assumed to be maneuverable and capable of providing a piecewise constant control thrust. The optimal control problem is formulated as a mixed-integer linear programming problem. To make the proposed strategy compliant with the requirements deriving from a realistic flight scenario, the collision avoidance and the maneuvering time constraints dictated by mission operations are included in the mathematical formulation. A linear dynamics model based on relative orbit elements parameterization and its associated closedform solution are used to impose the boundary conditions, avoiding the dynamics integration within the optimization process. Several examples are shown to demonstrate the effectiveness of the proposed approach.

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Section: A Relative Dynamics Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Minimum-Fuel Control Strategy for Spacecraft Formation Reconfiguration via Finite-Time Maneuvers

Mauro

Spiller

Carnà

et al. 2019

Journal of Guidance, Control, and Dynamics

View full text Add to dashboard Cite

show abstract

“…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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“…For the most part, preliminary mission design methods rely on lowfidelity dynamical models, which in turn, frequently leads to analytical propagation of the state dynamics through Keplerian orbit models [20] or by utilizing the solution of Lambert's problem [21][22][23][24][25]. Impulsive maneuvers are also used extensively for formation flight optimal control problems [26][27][28][29][30][31][32][33][34][35][36] and orbit reachability analyses problems [37][38][39][40][41][42][43].…”

mentioning

confidence: 99%

How Many Impulses Redux

Taheri

Junkins

2019

J Astronaut Sci

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A central problem in orbit transfer optimization is to determine the number, time, direction and magnitude of velocity impulses that minimize the total impulse. This problem was posed in 1967 by T. N. Edelbaum, and while notable advances have been made, a rigorous means to answer Edelbaum's question for multiple-revolution maneuvers has remained elusive for over five decades. We revisit Edelbaum's question by taking a bottom-up approach to generate a minimum-fuel switching surface. Sweeping through time profiles of the minimum-fuel switching function for increasing admissible thrust magnitude, and in the high-thrust limit, we find that the continuous thrust switching surface reveals the N -impulse solution. It is also shown that a fundamental minimum-thrust solution plays a pivotal role in our process to determine the optimal minimum-fuel maneuver for all thrust levels. Remarkably, we find the answer to Edelbaum's question is not generally unique, but is frequently a set of equal-∆v extremals. We further find, when Edelbaum's question is refined to seek the number of finite-duration thrust arcs for a specific rocket engine, that a unique extremal is usually found. Numerical results demonstrate the ideas and their utility for several interplanetary and Earth-bound optimal transfers that consist of up to eleven impulses or, for finite thrust, short thrust arcs. Another significant contribution of the paper can be viewed as a unification in astrodynamics where the connection between impulsive and continuous-thrust trajectories are demonstrated through the notion of optimal switching surfaces. NOMENCLATURE f = vector function of unforced dynamics B = control influence matrix c = exhaust velocity, m/s g 0 = Earth gravitational acceleration, m/s 2 h = specific angular momentum vector, km 2 /s H = Hamiltonian I sp = specific impulse, s J = cost functional

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Formation Establishment and Reconfiguration Using Differential Elements inJ2-Perturbed Orbits

Cited by 51 publications

References 29 publications

Minimum-Fuel Control Strategy for Spacecraft Formation Reconfiguration via Finite-Time Maneuvers

Minimum-Fuel Control Strategy for Spacecraft Formation Reconfiguration via Finite-Time Maneuvers

Formation Design of Distributed Telescopes in Earth Orbit for Astrophysics Applications

How Many Impulses Redux

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