Formation dynamics in geostationary ring

Spiridonova, Sofya

doi:10.1007/s10569-016-9693-0

Cited by 12 publications

(15 citation statements)

References 19 publications

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“…where ≈ 4.56 × 10 −6 Nm −2 is the constant of the SRP, accounts for the mean reflectivity of the surface, A is the spacecraft cross-sectional area assumed constant, m is the mass of the spacecraft, AU is the Astronomical Unit, and the norm of ⊙ /‖ ⊙ ‖ 3 ⋅ AU 2 approximates 1. SRP model in (10) has been widely used in analyzing the effect of SRP on spacecraft absolute orbit and relative motion between two spacecraft [12,39,40]. It is noted that model of differential SRP perturbation in (10) is derived with assumption that the normal vector of spacecraft's surface points in the direction of the Sun [41].…”

Section: Differential 2 Perturbation the Most Important Nonsphericalmentioning

confidence: 99%

“…The modeled is used in numerical simulations to evaluate the performance of the analytical solutions and the robustness of the designed control law, which is discussed in detail later. Given the large distance to the Sun as compared with the distance between the spacecraft, it suffices to assume that the distance to the Sun and the unit direction-to-the-Sun vector are the same for both spacecraft [12]. In this way, the differential SRP perturbation can be represented as…”

Section: Differential 2 Perturbation the Most Important Nonsphericalmentioning

confidence: 99%

“…An extension to elliptic Keplerian orbits is the Lawden or TH equations, yet still assuming no orbital perturbations [9,10]. Other mentionable approaches for modeling relative motion are orbit element differences [11,12].…”

Section: Introductionmentioning

confidence: 99%

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Automated Orbital Transfer and Hovering Control Using Artificial Potential

Wang

Zhang

2019

Mathematical Problems in Engineering

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On-orbit servicing for GEO targets has attracted great attention due to particular significance. In this study, the GEO nearby flying is considered, which denotes that the servicing spacecraft approaches GEO targets within tens of meters. Based on the analysis of differential spherical Earth gravity, J2 perturbation, third-body perturbation, and solar radiation pressure (SRP) between two spacecraft, a relative dynamics of GEO nearby flying is built, in which the differential SRP has great influence on relative motion. Therein, considering the differential SRP, an analytical solution to relative dynamics is obtained, which is an extension to CW equation’s solution. Based on the derived relative dynamics, a novel control method utilizing feedback compensation and artificial potential is developed for spacecraft orbital transfer and hovering at the desired position. During orbital transfer, a bounded space is constrained with maximum and minimum relative distance between two spacecraft. An improved repulsive potential based on Gauss function is designed to drive the servicer off the bound and guarantee the potential value converge to zero at the desired position. Meanwhile, a novel attractive potential about relative distance that drives the servicer to the desired position and to hover with high accuracy against perturbations is designed. Besides, a velocity potential with variable gain is designed to ensure that the servicer achieve the desired position without overshoot. The stability of the system is proved with Lyapunov theory, and the feasibility of the proposed control law is verified through numerical simulations with obvious advantages.

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Section: Differential 2 Perturbation the Most Important Nonsphericalmentioning

confidence: 99%

Section: Differential 2 Perturbation the Most Important Nonsphericalmentioning

confidence: 99%

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Automated Orbital Transfer and Hovering Control Using Artificial Potential

Wang

Zhang

2019

Mathematical Problems in Engineering

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“…An application of averaging theory, in conjunction with the Gauss variational equations (GVE) and Lagrange planetary equations (LPE), provides an analytical framework for describing the secular and long-period effects caused by conservative and nonconservative perturbations on the ROE. Several authors have leveraged this advantage to solve the variational equations in closed form, providing relative motion dynamics models that are valid in the presence of higher-order geopotential, third-body gravity, atmospheric drag, and solar radiation pressure effects [21][22][23]. Furthermore, D'Amico and Montenbruck [12] and D'Amico [24] extensively formulated a powerful connection relating the mean ROE state of Eq.…”

Section: Development Of the Dynamical System Representationmentioning

confidence: 99%

Nonlinear Kalman Filtering for Improved Angles-Only Navigation Using Relative Orbital Elements

Sullivan

D’Amico

2017

Journal of Guidance, Control, and Dynamics

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This paper addresses the design and validation of an accurate estimation architecture for autonomous angles-only navigation in orbits of arbitrary eccentricity. The proposed filtering strategy overcomes the major deficiencies of existing approaches in the literature, which mainly focus on applications in near-circular orbits and generally suffer from poor dynamical observability due to linearizing the filter dynamics and measurement models. Consequently, traditional angles-only navigation solutions require conducting known orbital maneuvers to reconcile the ambiguous range. In contrast, the algorithms developed in this work enable accurate maneuver-free reconstruction of the relative orbital motion. This is done through the full exploitation of nonlinearities in the measurement model using the unscented Kalman filter to improve dynamical observability and filter performance. The filter estimates mean relative orbit elements, adopting a state transition matrix subject to secular and long-period J 2 perturbation effects to decouple observable from unobservable parameters. The complete state is then reconciled with the angle measurements in the measurement model through a nonlinear transformation that includes the conversion from mean to osculating orbital elements. The resulting linear dynamics model is supplemented by either first-order Gauss-Markov processes (that is, differential empirical accelerations) or by a covariance-matching approach to online adaptive process noise tuning to increase performance at minimal computational complexity. Finally, the estimation architecture is completed by a novel deterministic algorithm for batch initial relative orbit determination to accurately initialize the sequential filter.

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“…Assumption 3 As per Assumption 2, the differential effects of atmospheric drag, solar radiation pressure, and third-body gravity are negligible compared to the forces caused by the primary body [13,87];…”

Section: Assumptionmentioning

confidence: 99%

Adaptive Extended Kalman Filtering Strategies for Autonomous Relative Navigation of Formation Flying Spacecraft

Fraser¹

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This research addresses the relative navigation problem for spacecraft formation Ćying missions in near-Earth orbit. Technological and economic inĆuences have expedited the miniaturization of spacecraft systems, popularizing the notion of satellite teamwork due to the potential reductions in overall costs and complexity. It is now feasible to use a coordinated group of close-proximity satellites, known as a formation, to autonomously perform rendezvous, on-orbit servicing and science-based missions for a fraction of the resources a large-scale satellite would require. Despite the growing interest in formation Ćying spacecraft however, only a limited number of applications have been Ćight validated as a result of the difficulties associated with accurately determining the relative motion of the spacecraft within a formation. To enhance the capabilities of onboard autonomous guidance, navigation and control systems, this thesis presents the development of two adaptive extended Kalman Ąlter navigation algorithms for spacecraft formation Ćying. The proposed adaptive Ąlters are capable of updating the internal noise characteristics of the Kalman Ąlter in real time, and are viable in all orbit scenarios, including highly elliptical orbits in the presence of perturbations. The Ąrst Kalman Ąlter approach uses maximum likelihood estimation techniques to derive analytical adaptations laws for the Ąlter, which are then improved through the novel inclusion of an intrinsic smoothing routine. The second approach uses an embedded fuzzy logic system based on a covariancematching analysis of the Ąlter residuals, where the fuzzy system has been speciĄcally designed for the spacecraft navigation problem at hand. Numerical simulations of three spacecraft formations are used to demonstrate that the proposed adaptive navigation algorithms are appreciably more robust to Ąlter initialization errors, dynamics modelling deĄciencies, and measurement noise than the standard Kalman Ąlter. iii To Dr. Steve Ulrich, formally my supervisor, but more importantly my mentor, my professor, and my friend; your steadfast support and leadership have made my studies in Ottawa immensely fulĄlling. Thank you for providing this opportunity to continually learn from your expertise, and for instilling conĄdence and direction throughout the span of our collaboration. The dedication you have shown to me, and all of the members of our research group, is remarkable. It has been an honor to work with you, and a whole lot of fun too. To the professors who have guided me along this journey, including Bruce Burlton, Tarik Kaya, Alex Ellery, Victor Aitken, Howard Schwartz, and many others from Carleton University. The knowledge and wisdom you have shared has been invaluable to my growth as an engineer. And from the days at Dalhousie University, my thanks in particular to Professors Darrel Doman, Jeff Dahn, Timothy Little, and Guy Kember. You managed to imbue a fascination with space elevators, the laws of nature, the rules of mathematics, and the process of learning,...

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Formation dynamics in geostationary ring

Cited by 12 publications

References 19 publications

Automated Orbital Transfer and Hovering Control Using Artificial Potential

Automated Orbital Transfer and Hovering Control Using Artificial Potential

Nonlinear Kalman Filtering for Improved Angles-Only Navigation Using Relative Orbital Elements

Adaptive Extended Kalman Filtering Strategies for Autonomous Relative Navigation of Formation Flying Spacecraft

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