• Journal of Astronomy and Space Sciences
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• v.36 no.4
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• pp.235-248
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• 2019

This paper suggests a relative orbit control strategy for the CubeSat Astronomy by NASA and Yonsei using Virtual Telescope Alignment eXperiment (CANYVAL-X) mission whose main goal is to demonstrate an essential technique, which is an arrangement among two satellites and a specific celestial object, referred to as inertial alignment, for a next-generation virtual space telescope. The inertial alignment system is a relative orbit control system and has requirements for the relative state. Through the proposed orbit control strategy, consisting of separation, proximity keeping, and reconfiguration, the requirements will be satisfied. The separation direction of the two CubeSats with respect to the orbital plane is decided to provide advantageous initial condition to the orbit controller. Proximity keeping is accomplished by differential atmospheric drag control (DADC), which generates acceleration by changing the spacecraft's effective cross section via attitude control rather than consuming propellant. Reconfiguration is performed to meet the requirements after proximity keeping. Numerical simulations show that the requirements can be satisfied by the relative orbit control strategy. Furthermore, through numerical simulations, it is demonstrated that the inertial alignment can be achieved. A beacon signal had been received for several months after the launch; however, we have lost the signal at present.

• Journal of Institute of Control, Robotics and Systems
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• v.13 no.10
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• pp.962-969
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• 2007

In this paper, an approach is developed for relative state estimation of satellite formation flying. To estimate relative states of two satellites, the Extended Kalman Filter Algorithm is adopted with the relative distance and speed between two satellites and attitude of satellite for measurements. Numerical simulations are conducted under two circumstances. The first one presents both chief and deputy satellites are orbiting a circular reference orbit around a perfectly spherical Earth model with no disturbing acceleration, in which the elementary relative orbital motion is taken into account. In reality, however, the Earth is not a perfect sphere, but rather an oblate spheroid, and both satellites are under the effect of $J_2$ geopotential disturbance, which causes the relative distance between two satellites to be on the gradual increase. A near-Earth orbit decays as a result of atmospheric drag. In order to remove the modeling error, the second scenario incorporates the effect of the $J_2$ geopotential force, and the atmospheric drag, and the eccentricity in satellite orbit are also considered.

• International Journal of Aeronautical and Space Sciences
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• v.16 no.1
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• pp.77-88
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• 2015

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.

• Journal of Astronomy and Space Sciences
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• v.26 no.4
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• pp.499-510
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• 2009

In this paper, relative orbit of Low Earth Orbit satellites is determined using only GPS measurements and the effects of Equatorial Spread-F (ESF), that is one of biggest ionospheric irregularities, are investigated. First, relative orbit determiation process is constructed based on doubly differenced GPS observations. In order to see orbit determination performance, relative orbit of two GRACE satellites is estimated for one month in 2004 when no ESF is observed. The root mean square of the achieved baselines compared with that from K-Band Ranger sensor is about 2~3 mm and average of 95% of ambiguities are resolved. Based on this performance, the relative orbit is estimated for two weeks of two difference years, 2003 when there are lots of ESF occurred, and 2004 when only few ESF occurred. For 2003, the averaged baseline error over two weeks is about 15 mm. That is about 4 times larger than the case of 2004 (3.6 mm). Ionospheric status achieved from K-Band Ranging sensor also shows that more Equatorial Spread-F occurred at 2003 than 2004. Investigation on raw observations and screening process revealed that the ionospheric irregualarities caused by Equatorial Spread-F gave significant effects on GPS signal like signal loss or enhancement ionospheric error, From this study, relative orbit determination using GPS observations should consider the effect of Equatorial Spread-F and adjust orbit determination strategy, especially at the time of solar maximum.

• Bulletin of the Korean Space Science Society
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• 2008.04a
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• pp.25.5-26
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• 2008

• International Journal of Aeronautical and Space Sciences
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• v.14 no.2
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• pp.183-192
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• 2013

This paper presents formation reconfiguration using impulsive control input for spacecraft formation flying. Spacecraft in a formation should change the formation size and/or geometry according to the mission requirements and space environment. To modify the formation radius and geometry with respect to the leader spacecraft, the follower spacecraft generates additional control inputs; the two impulsive control inputs are general control type of the spacecraft system. For the impulsive control input, Lambert's problem is modified to construct the transfer orbit in relative motion, given two position vectors at the initial and final time. Moreover, the numerical simulation results show the transfer trajectories to resize the formation radius in the radial/along-track plane formation and in the along-track/cross-track plane formation. In addition, the maneuver characteristics are described by comparing the differential orbital elements between the reference orbit and transfer orbit in the radial/along-track plane formation and along-track/cross-track plane formation.

• Journal of Astronomy and Space Sciences
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• v.29 no.4
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• pp.351-362
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• 2012

We made a study on real-time determination method for relative position using the laser-measured distance data between satellites. We numerically performed the determination of relative position in accordance with extended Kalman filter algorithm using the vectors obtained through nonlinear equation of relative motion, laser simulator for distance measurement, and attitude determination of chief satellite. Because the spherical parameters of relative distance and direction are used, there occur some changes in precision depending on changes in relative distance when determining the relative position. As a result of simulation, it was possible to determine the relative position with several millimeter-level errors at a distance of 10 km, and sub-millimeter level errors at a distance of 1 km. In addition, we performed the determination of relative position assuming the case that global positioning system data was not received for long hours to see the impact of determination of chief satellite orbit on the determination of relative position. The determination of precise relative position at a long distance carried out in this study can be used for scientific mission using the satellite formation flying.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.33 no.10
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• pp.51-59
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• 2005

In this paper, results of a multiple spacecraft formation-keeping control using the orbital relative motion and optimization technique are presented. To analyze and predict the relative motion between the formation-flying satellites, a closed-form orbit propagator obtained using the method of ephemeris compression is used. This closed-form orbit propagator is combined with optimization technique to plan a series of impulsive maneuvers, which maintain the formation configuration within the specified limit. As an example, this method is applied to the problem of maintaining the projected circular formation geometry and results from nonlinear simulation are presented.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.34 no.5
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• pp.56-64
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• 2006

Station collocation of closely placed multiple GEO spacecraft is required to avoid the problem of collision risk, attitude sensor interference and/or occultation. This paper presents the method of obtaining the orbit correction scheme for collocating two GEO spacecraft within a small station-keeping box. The relative motion of each spacecraft with respect to the virtual geostationary satellite is precisely expressed in terms of power and trigonometry functions. This closed-form orbit propagator is used to define the constraint conditions which meet the requirements for the station collocation. Finally, the technique of constrained optimization is used to find the orbit maneuver sequence. Nonlinear simulations are performed and their results are compared with those of the classical method.

• Journal of Astronomy and Space Sciences
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• v.25 no.3
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• pp.255-266
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• 2008

The current paper presents application of a new analytic solution in general relative motion to spacecraft formation flying in an elliptic orbit. The calculus of variations is used to analytically find optimal trajectories and controls for the given problem. The inverse of the fundamental matrix associated with the dynamic equations is not required for the solution in the current study. It is verified that the optimal thrust vector is a function of the fundamental matrix of the given state equations. The cost function and the state vector during the reconfiguration can be analytically obtained as well. The results predict the form of optimal solutions in advance without having to solve the problem. Numerical simulation shows the brevity and the accuracy of the general analytic solutions developed in the current paper.