Comprehensive Survey and Assessment of Spacecraft Relative Motion Dynamics Models

Sullivan, Josephine; Grimberg, Sebastian; D’Amico, Simone

doi:10.2514/1.g002309

Cited by 130 publications

(67 citation statements)

References 62 publications

(116 reference statements)

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“…10. 7 14 Fig. 6 The contours of (solid lines), the contours of (dashed lines), the line of , and the forbidden regions according to the safety corridors.…”

Section: Case Studymentioning

confidence: 99%

See 1 more Smart Citation

Covariance-Based Multiple-Impulse Rendezvous Design

Shakouri¹,

Kiani²,

Pourtakdoust³

2019

IEEE Trans. Aerosp. Electron. Syst.

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A novel trajectory design methodology is proposed in the current work to minimize the state uncertainty in the crucial mission of spacecraft rendezvous. The trajectory is shaped under constraints utilizing a multiple-impulse approach. State uncertainty is characterized in terms of covariance, and the impulse time as the only affective parameter in uncertainty propagation is selected to minimize the trace of the covariance matrix. Further, the impulse location is also adopted as the other design parameter to satisfy various translational constraints of the space mission. Efficiency and viability of the proposed idea have been investigated through some scenarios that include constraints on final time, control effort, and maximum thruster limit addition to considering safe corridors. The obtained results show that proper selection of the impulse time and impulse position fulfils a successful feasible rendezvous mission with minimum uncertainty.

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“…10. 7 14 Fig. 6 The contours of (solid lines), the contours of (dashed lines), the line of , and the forbidden regions according to the safety corridors.…”

Section: Case Studymentioning

confidence: 99%

“…Maryam Kiani one can consider for perturbations and/or orbital characteristics [7]. The Clohessy-Wiltshire (CW) model [8] develops a LTI system of equations for rendezvous between close spacecraft in near circular orbits.…”

Section: Introductionmentioning

confidence: 99%

Covariance-Based Multiple-Impulse Rendezvous Design

Shakouri¹,

Kiani²,

Pourtakdoust³

2019

IEEE Trans. Aerosp. Electron. Syst.

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show abstract

“…(B14) in Ref. [30]. Suppose the error covariances are given by Because the mean of the error in each of the four sources was zero, the mean of the error in the final achieved ROE is also zero.…”

Section: Fig 13 Evolution Of the Roe In Test 1 With Full-force Dynammentioning

confidence: 99%

New Closed-Form Solutions for Optimal Impulsive Control of Spacecraft Relative Motion

Chernick

D’Amico

2018

Journal of Guidance, Control, and Dynamics

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This paper addresses the spacecraft relative orbit reconfiguration problem of minimizing the delta-v cost of impulsive control actions while achieving a desired state in fixed time. The problem is posed in relative orbit element (ROE) space, which yields insight into relative motion geometry and allows for the straightforward inclusion of perturbations in linear timevariant form. Reachable set theory is used to translate the cost-minimization problem into a geometric path-planning problem and formulate the reachable delta-v minimum, a new metric to assess optimality and quantify reachability of a maneuver scheme. Next, this paper presents a methodology to compute maneuver schemes that meet this new optimality criteria and achieve a prescribed reconfiguration. Though the methodology is applicable to any linear time-variant system, this paper leverages a state representation in ROE to derive new globally optimal maneuver schemes in orbits of arbitrary eccentricity. The methodology is also used to generate quantifiably sub-optimal solutions when the optimal solutions are unreachable. Further, this paper determines the mathematical impact of uncertainties on achieving the desired end state and provides a geometric visualization of those effects on the reachable set. The proposed algorithms are tested in realistic reconfiguration scenarios and validated in a high-fidelity simulation environment.

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“…For the interested reader, the paper of Sullivan et al [1] is recommended. According to the survey here, we can conclude that the Cartesian coordinate-based solution (i.e., TH solution) for relative motion is applicable for all kinds of Keplerian orbits (circular, elliptic, parabolic and hyperbolic).…”

Section: Introductionmentioning

confidence: 99%

“…The most widely used method in modeling the relative motion of vehicles in nearby eccentric orbits is to solve a set of differential equations about the Cartesian coordinates in the rotating frame [1]. The Hill-ClohessyWiltshire (HCW) equations had been used extensively since the 1960s for circular or near circular reference orbits.…”

Section: Introductionmentioning

confidence: 99%

Linearized relative motion equations through orbital element differences for general Keplerian orbits

Dang

Zhang

2018

Astrodyn

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A new formulation of the orbital element-based relative motion equations is developed for general Keplerian orbits. This new solution is derived by performing a Taylor expansion on the Cartesian coordinates in the rotating frame with respect to the orbital elements. The resulted solution is expressed in terms of two different sets of orbital elements. The first one is the classical orbital elements and the second one is the nonsingular orbital elements. Among of them, however, the semi-latus rectum and true anomaly are used due to their generality, rather than the semi-major axis and mean anomaly that are used in most references. This specific selection for orbital elements yields a new solution that is universally applicable to elliptic, parabolic and hyperbolic orbits. It is shown that the new orbital element-based relative motion equations are equivalent to the Tschauner-Hempel equations. A linear map between the initial orbital element differences and the integration constants associated with the solution of the Tschauner-Hempel equations is constructed. Finally, the presented solution is validated through comparison with a high-fidelity numerical orbit propagator.The numerical results demonstrate that the new solution is computationally effective; and the result is able to match the accuracy that is required for linear propagation of spacecraft relative motion over a broad range of Keplerian orbits.

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Comprehensive Survey and Assessment of Spacecraft Relative Motion Dynamics Models

Cited by 130 publications

References 62 publications

Covariance-Based Multiple-Impulse Rendezvous Design

Covariance-Based Multiple-Impulse Rendezvous Design

New Closed-Form Solutions for Optimal Impulsive Control of Spacecraft Relative Motion

Linearized relative motion equations through orbital element differences for general Keplerian orbits

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