Second-order state transition for relative motion near perturbed, elliptic orbits

Sengupta, Prasenjit; Vadali, Srinivas R.; Alfriend, Kyle T.

doi:10.1007/s10569-006-9054-5

Cited by 54 publications

(41 citation statements)

References 31 publications

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“…The reason is obvious since TH equations are second order dynamics, more accurate than CW equations. Anyway, there are still more accurate dynamics [28,29] than TH equations, but relevant state transition matrices need to be obtained before these improved dynamics can be used. IROD performance would be absolutely improved when highorder dynamics is used.…”

Section: Irod Performance Analysismentioning

confidence: 99%

Angles-only initial relative orbit determination algorithm for non-cooperative spacecraft proximity operations

Gong

et al. 2018

Astrodyn

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This research furthers the development of a closed-form solution to the angles-only initial relative orbit determination problem for non-cooperative target close-in proximity operations when the camera offset from the vehicle center-of-mass allows for range observability. In previous work, the solution to this problem had been shown to be non-global optimal in the sense of least square and had only been discussed in the context of Clohessy-Wiltshire. In this paper, the emphasis is placed on developing a more compact and improved solution to the problem by using state augmentation least square method in the context of the

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Section: Irod Performance Analysismentioning

confidence: 99%

Angles-only initial relative orbit determination algorithm for non-cooperative spacecraft proximity operations

Gong

et al. 2018

Astrodyn

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“…Possible improvements in the relative dynamics' description can be obtained by removing the hypothesis of circular reference orbit (Sengupta et al 2007), or the hypothesis of unperturbed keplerian field (Halsall and Palmer 2007). However, simplicity has been the main driver in the evaluation of behavioral actions.…”

Section: Collective Behaviourmentioning

confidence: 99%

Collective control of spacecraft swarms for space exploration

Sabatini

Palmerini

2009

Celest Mech Dyn Astr

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Swarms are characterized in nature by a dynamic behaviour which is quite appealing for researchers involved in numerous fields of study, like robotics, computer science, pure mathematics and space sciences. Global group organization acquired in absence of centralized control is the feature of natural swarms which is most interesting to reproduce. This study proposes to make use of some evolutionary robotics findings in order to obtain the autonomous group organization in the framework of a deeper knowledge of the astrodynamics. The main task which will be accomplished is the implementation of the control laws for the single satellite. A careful tuning of the parameters at member level is necessary in order to gain an autonomously evolving global behaviour in a number of space missions of immediate interest. In remote sensing missions, for example, trains of a small number of satellites are already orbiting and integrating their collected data: in near future entire swarms of agents could accomplish this task, and should be controlled in order to acquire and maintain the desired leader-follower configuration. Another example can be seen in deep space exploration of unknown celestial bodies, where the migration of the entire swarm from a reference orbit to a (previously unknown) targeted one is an issue; the same group migration is of interest in Earth orbit, when transferring from parking to operational orbit. Finally, self-assembly of rigid-like virtual structures is also simulated. This paper shows that all these cases are autonomously performed by the swarm by correctly implementing four simple rules at individual level, which assess the primal needs for any satellite: avoid collision, remain grouped, align to the neighbor, reach a goal

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“…For example, the STMs for relative motion derived by Carter (1998); Yamanaka and Ankersen (2002); Sengupta et al (2007) are formulated using the true anomaly, and for application purposes, require a conversion from time (mean anomaly) to true anomaly, using numerical techniques. A series representation of the functions of true anomaly, in terms of mean anomaly, would result in and infinite number of terms with coefficients based on Bessel functions.…”

Section: Keplerian Anomalies and Kepler's Equationmentioning

confidence: 99%

The Lambert W function and solutions to Kepler’s equation

Sengupta

2007

Celestial Mech Dyn Astr

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This paper presents a method for the truncation of infinite Fourier-Bessel representations for functions requiring a solution to Kepler's equation. Use is made of the Lambert W function to solve for the desired index that bounds the remainder terms of the series, within the prescribed tolerance. The enforcement of a maximum on the number of Bessel functions is also useful in truncating the Bessel functions themselves, resulting in an analytical representation of the solution to a desired tolerance, without the use of infinite series.

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Second-order state transition for relative motion near perturbed, elliptic orbits

Cited by 54 publications

References 31 publications

Angles-only initial relative orbit determination algorithm for non-cooperative spacecraft proximity operations

Angles-only initial relative orbit determination algorithm for non-cooperative spacecraft proximity operations

Collective control of spacecraft swarms for space exploration

The Lambert W function and solutions to Kepler’s equation

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