Relative Motion and the Geometry of Formations in Keplerian Elliptic Orbits with Arbitrary Eccentricity

Sengupta, Prasenjit; Vadali, Srinivas R.

doi:10.2514/1.25941

Cited by 77 publications

(57 citation statements)

References 27 publications

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“…A similar approach to Dang [10] for evaluating the fundamental integral in terms of true anomaly and transition time for the case of elliptic orbit can also be found in Ref. [11]. It is also intuitive to describe the relative motion in terms of orbital element differences, i.e., via a geometrical approach.…”

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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Section: Introductionmentioning

confidence: 99%

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

Dang

Zhang

2018

Astrodyn

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“…In a previous study, Sengupta & Vadali (2007) found the necessary conditions on the initial states that produce periodic solutions at an arbitrary true anomaly as follows. …”

Section: Constraintsmentioning

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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“…In particular, rewriting the measurement Eq. (10) in the standard form of the Kalman filter vector notation leads to (12) Now, the measurements for partial matrix is computed to be (10a) 10 …”

Section: Measurement Modelmentioning

confidence: 99%

“…They found complete solutions for elliptical orbits, in terms of the eccentric anomaly. This advancement was followed by additional papers that presented the complete analytical solution explicit in time, expanding the state transition matrix in terms of eccentricity [5][6][7][8][9][10][11]. These solutions are used to analyze the relative motion between the chaser and the target vehicles in the relative frame of motion more efficiently and rapidly than solving the exact nonlinear differential equations in the inertial coordinate system.…”

Section: Introductionmentioning

confidence: 99%

Modeling, Dynamics and Control of Spacecraft Relative Motion in a Perturbed Keplerian Orbit

Okasha¹,

Newman²

2015

International Journal of Aeronautical and Space Sciences

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The dynamics of relative motion in a perturbed orbital environment are exploited based on Gauss' and Cowell's variational equations. The inertial coordinate frame and relative coordinate frame (Hill frame) are used, and a linear high fidelity model is developed to describe the relative motion. This model takes into account the primary gravitational and atmospheric drag perturbations. Then, this model is used in the design of a navigation, guidance, and control system of a chaser vehicle to approach towards and to depart from a target vehicle in proximity operations. Relative navigation uses an extended Kalman filter based on this relative model to estimate the relative position/velocity of the chaser vehicle with respect to the target vehicle. This filter uses the range and angle measurements of the target relative to the chaser from a simulated LIDAR system. The corresponding measurement models, process noise matrix, and other filter parameters are provided. Numerical simulations are performed to assess the precision of this model with respect to the full nonlinear model. The analyses include the navigation errors and trajectory dispersions.

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Relative Motion and the Geometry of Formations in Keplerian Elliptic Orbits with Arbitrary Eccentricity

Cited by 77 publications

References 27 publications

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

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

Determination of Initial Conditions for Tetrahedral Satellite Formation

Modeling, Dynamics and Control of Spacecraft Relative Motion in a Perturbed Keplerian Orbit

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