Gauss's Variational Equation-Based Dynamics and Control for Formation Flying Spacecraft

Breger, Louis; How, Jonathan P.

doi:10.2514/1.22649

Cited by 79 publications

(39 citation statements)

References 9 publications

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“…One of the main challenges of FF spacecraft is the guidance, navigation, and control (GN&C) of the formation. As a result, a substantial amount of research has been done on the GN&C of FF spacecraft [3][4][5][6][7][8][9][10][11][12] in the last decade.…”

Section: Introductionmentioning

confidence: 99%

Swarm-Keeping Strategies for Spacecraft Under J2 and Atmospheric Drag Perturbations

Morgan

Chung²,

Blackmore

et al. 2012

Journal of Guidance, Control, and Dynamics

102

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This paper presents several new open-loop guidance methods for spacecraft swarms composed of hundreds to thousands of agents with each spacecraft having modest capabilities. These methods have three main goals: preventing relative drift of the swarm, preventing collisions within the swarm, and minimizing the propellant used throughout the mission. The development of these methods progresses by eliminating drift using the Hill-Clohessy-Wiltshire equations, removing drift due to nonlinearity, and minimizing the J2 drift. In order to verify these guidance methods, a new dynamic model for the relative motion of spacecraft is developed. These dynamics include the two main disturbances for spacecraft in Low Earth Orbit (LEO), J2 and atmospheric drag. Using this dynamic model, numerical simulations are provided at each step to show the effectiveness of each method and to see where improvements can be made. The main result is a set of initial conditions for each spacecraft in the swarm which provides the trajectories for hundreds of collision-free orbits in the presence of J2. Finally, a multi-burn strategy is developed in order to provide hundreds of collision-free orbits under the influence of atmospheric drag. This last method works by enforcing the initial conditions multiple times throughout the mission thereby providing collision-free trajectories for the duration of the mission.

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Section: Introductionmentioning

confidence: 99%

Swarm-Keeping Strategies for Spacecraft Under J2 and Atmospheric Drag Perturbations

Morgan

Chung²,

Blackmore

et al. 2012

Journal of Guidance, Control, and Dynamics

102

View full text Add to dashboard Cite

show abstract

“…Ref. 26 presents a Hamiltonian approach to modelling relative spacecraft motion based on a derivation of canonical coordinates for the relative state-space dynamics, while another paper 27 introduces a new linear time-varying form of the equations of relative motions developed from Gauss's variational equations.…”

Section: Robustness Issuesmentioning

confidence: 99%

Attitude and Phase Synchronization of Formation Flying Spacecraft: Lagrangian Approach

Chung

Ahsun

Slotine

2008

AIAA Guidance, Navigation and Control Conference and Exhibit

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This article presents a unified synchronization framework with application to precision formation flying spacecraft. Central to the proposed innovation, in applying synchronization to both translational and rotational dynamics in the Lagrangian form, is the use of the distributed stability and performance analysis tool, called contraction analysis that yields exact nonlinear stability proofs. The proposed decentralized tracking control law synchronizes the attitude of an arbitrary number of spacecraft into a common time-varying trajectory with global exponential convergence. Moreover, a decentralized translational tracking control law based on phase synchronization is presented, thus enabling coupled translational and rotational maneuvers. While the translational dynamics can be adequately controlled by linear control laws, the proposed method permits highly nonlinear systems with nonlinearly coupled inertia matrices such as the attitude dynamics of spacecraft whose large and rapid slew maneuvers justify the nonlinear control approach. The proposed method integrates both the trajectory tracking and synchronization problems in a single control framework.

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“…where K c is a diagonal matrix of positive gains [36]. If the gain matrix is large enough to compensate for differential disturbances (A(ē) − A(ê)), and perfect information (ê = e) is assumed, this control law guarantees asymptotic tracking of the reference orbital elements (see [34,37] for a thorough…”

Section: Orbital Station-keepingmentioning

confidence: 99%

Autonomous Low-Earth-Orbit Station-Keeping with Electric Propulsion

Garulli

Giannitrapani

Leomanni³

et al. 2011

Journal of Guidance, Control, and Dynamics

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This paper studies the application of an electric propulsion system for autonomous station-keeping of a remote sensing spacecraft flying at low altitude. The considered propulsion system exploits a Xenon propellant bus, which operates both a low power Hall effect thruster and a resistojet. The former is used for continuous in-track control, while the latter provides the impulsive thrusts necessary for cross-track maneuvers. The adopted navigation solution is based on an extended Kalman filter, employing gyro, star-tracker and GPS measurements. Lyapunov-based and proportionalderivative feedback laws are used for orbit and attitude control, respectively. The performance of the proposed electric propulsion system and guidance, navigation and control solution is evaluated on a low Earth orbit mission.

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Gauss's Variational Equation-Based Dynamics and Control for Formation Flying Spacecraft

Cited by 79 publications

References 9 publications

Swarm-Keeping Strategies for Spacecraft Under J2 and Atmospheric Drag Perturbations

Swarm-Keeping Strategies for Spacecraft Under J2 and Atmospheric Drag Perturbations

Attitude and Phase Synchronization of Formation Flying Spacecraft: Lagrangian Approach

Autonomous Low-Earth-Orbit Station-Keeping with Electric Propulsion

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