• 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.

• International Journal of Aeronautical and Space Sciences
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• v.10 no.1
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• pp.58-66
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• 2009

Formation controller for multiple spacecrafts is designed based on a decentralized approach. The objective of the proposed controller is to make each spacecraft fly to the desired waypoints, while keeping the formation shape of multiple spacecrafts. To design the decentralized formation controller, the output feedback linearization technique using error functions for goal convergence and formation keeping is utilized for spacecraft dynamics. The primary contribution of this paper is to proposed optimal controller for formation flying based on the decentralized approach. To design the optimal controller, eigenvalue assignment technique is used. To verify the effectiveness of the proposed controller, numerical simulations are performed for three-dimensional waypoint-passing missions of multiple spacecrafts.

• Journal of Astronomy and Space Sciences
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• v.35 no.3
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• pp.163-173
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• 2018

This paper presents relative navigation using intermittent laser-based measurement data for spacecraft flying formation that consist of two spacecrafts; namely, chief and deputy spacecrafts. The measurement data consists of the relative distance measured by a femtosecond laser, and the relative angles between the two spacecrafts. The filtering algorithms used for the relative navigation are the extended Kalman filter (EKF), unscented Kalman filter (UKF), and least squares recursive filter (LSRF). Numerical simulations reveal that the relative navigation performances of the EKF- and UKF-based relative navigation algorithms decrease in accuracy as the measurement outage period increases. However, the relative navigation performance of the UKF-based algorithm is 95 % more accurate than that of the EKF-based algorithm when the measurement outage period is 80 sec. Although the relative navigation performance of the LSRF-based relative navigation algorithm is 94 % and 370 % less accurate than those of the EKF- and UKF-based navigation algorithms, respectively, when the measurement outage period is 5 sec; the navigation error varies within a range of 4 %, even though the measurement outage period is increased. The results of this study can be applied to the design of a relative navigation strategy using the developed algorithms with laser-based measurements for spacecraft formation flying.

• 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.

• Bulletin of the Korean Space Science Society
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• 2008.10a
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• pp.26.3-26.3
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• 2008

This research develops a GPS-based formation-flying testbed (FFTB) for formation navigation and control. The FFTB is a simulator in which spacecraft simulation and modeling software and loop test capabilities are integrated for test and evaluation of spacecraft navigation and formation control technologies. The FFTB is composed of a GPS measurement simulation computer, flight computer, environmental computer for providing true environment data and 3D visualization computer. The testbed can be simulated with one to two spacecraft, thus enabling a variety of navigation and control algorithms to be evaluated. In a formation flying simulation, GPS measurement are generated by a GPS measurement simulator to produce pseudorange, carrier phase measurements, which are collected and exchanged by the flight processors and subsequently processed in a navigation filter to generate relative and/or absolute state estimates. These state estimates are the fed into control algorithm, which are used to generate maneuvers required to maintain the formation. In this manner, the flight processor also serves as a test platform for candidate formation control algorithm. Such maneuvers are fed back through the controller and applied to the modeled truth trajectories to close simulation loop. Currently, The FFTB has a closed-loop capability of simulating a satellite navigation solution using software based GPS measurement, we move forward to improve using SPIRENT GPS RF signal simulator and space-based GPS receiver

• International Journal of Aeronautical and Space Sciences
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• v.6 no.2
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• pp.56-63
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• 2005

Some methods have been presented to avoid collisions among satellites for satellite formation flying mission. The potential function method based on Lyapunov's theory is known as a powerful tool for collision avoidance in the robotic system because of its robustness and flexibility. During the last decade, a potential function has also been applied to UAV's and spacecraft operations, which consists of repulsive and attractive potential. In this study, the controller is designed using a potential function via sliding mode technique for the configuration of satellite formation flying. The strategy is based on enforcing the satellite to move along the gradient of a given potential function. The new scalar velocity function is introduced such that all satellites reach the goal points simultaneously. Simulation results show that the controller drives the satellite toward the desired point along the gradient of the potential function and is robust against external disturbances.

• Journal of Astronomy and Space Sciences
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• v.32 no.4
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• pp.387-393
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• 2015

This study presents a precise relative navigation algorithm using both laser and Global Positioning System (GPS) measurements in real time. The measurement model of the navigation algorithm between two spacecraft is comprised of relative distances measured by laser instruments and single differences of GPS pseudo-range measurements in spherical coordinates. Based on the measurement model, the Extended Kalman Filter (EKF) is applied to smooth the pseudo-range measurements and to obtain the relative navigation solution. While the navigation algorithm using only laser measurements might become inaccurate because of the limited accuracy of spacecraft attitude estimation when the distance between spacecraft is rather large, the proposed approach is able to provide an accurate solution even in such cases by employing the smoothed GPS pseudo-range measurements. Numerical simulations demonstrate that the errors of the proposed algorithm are reduced by more than about 12% compared to those of an algorithm using only laser measurements, as the accuracy of angular measurements is greater than $0.001^{\circ}$ at relative distances greater than 30 km.

• Journal of Astronomy and Space Sciences
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• v.25 no.4
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• pp.361-374
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• 2008

Recently, satellite formation flying has been a topic of significant research interest in aerospace society because it provides potential benefits compared to a large spacecraft. Some techniques have been proposed to design optimal formation trajectories minimizing fuel consumption in the process of formation configuration or reconfiguration. In this study, a method is introduced to build fuel-optimal trajectories minimizing a cost function that combines the total fuel consumption of all satellites and assignment of fuel consumption rate for each satellite. This approach is based on collocation and nonlinear programming to solve constraints for collision avoidance and the final configuration. New constraints of nonlinear equality or inequality are derived for final configuration, and nonlinear inequality constraints are established for collision avoidance. The final configuration constraints are that three or more satellites should form a projected circular orbit and make an equilateral polygon in the horizontal plane. Example scenarios, including these constraints and the cost function, are simulated by the method to generate optimal trajectories for the formation configuration and reconfiguration of multiple satellites.

• 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 Astronomy and Space Sciences
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• v.28 no.1
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• pp.63-70
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• 2011

The needs for satellite formation flying are gradually increasing to perform the advanced space missions in remote sensing and observation of the space or Earth. Formation flying in low Earth orbit can perform the scientific missions that cannot be realized with a single spacecraft. One of the various techniques of satellite formation flying is the determination of the precise baselines between the satellites within the formation, which has to be in company with the precision validation. In this paper, the baseline of Gravity Recovery and Climate Experiment (GRACE) A and B was determined with the real global positioning system (GPS) measurements of GRACE satellites. And baseline precision was validated with the batch and sequential processing methods using K/Ka-band ranging system (KBR) biased range measurements. Because the proposed sequential method validate the baseline precision, removing the KBR bias with the epoch difference instead of its estimation, the validating data (KBR biased range) are independent of the data validated (GPS-baseline) and this method can be applied to the real-time precision validation. The result of sequential precision validation was 1.5~3.0 mm which is similar to the batch precision validation.