Stationary Configurations of a Tetrahedral Tethered Satellite Formation

Guerman, Anna D.; Smirnov, Georgi; Paglione, Pedro; Seabra, Ana

doi:10.2514/1.31979

Cited by 25 publications

(11 citation statements)

References 15 publications

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“…The kinetic and the potential energies are unchanged compared to (15) and (16). Inserting the energies including the out-of-plane motion into Lagrange's equation, the system can be written as…”

Section: Appendix B Equations Of Motion In Three Dimensionsmentioning

confidence: 99%

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Modeling of tethered satellite formations using graph theory

2011

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a b s t r a c tTethered satellite formations have recently gained increasing attention due to future mission proposals. Several different formations have been investigated for their dynamic properties and control schemes have been suggested. Formulating the equations of motion and investigation which geometries could form stable formations in space are cumbersome when done at a case to case basis, and a common framework providing a basic model of the dynamics of tethered satellite formations can therefore be advantageous. This paper suggests the use of graph theoretical quantities to describe a tethered satellite formation and proposes a method to deduce the equations of motion for the attitude dynamics of the formation in a compact form. The use of graph theory and Lagrange mechanics together allows a broad class of formations to be described using the same framework. A method is stated for finding stationary configurations and an upper limit of their number is determined. The method is shown to be valid for general tethered satellite formations that form a tree structure.

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Section: Appendix B Equations Of Motion In Three Dimensionsmentioning

confidence: 99%

“…Chain topologies with a small number of satellites, three or four, were studied in [14,15], and [8,9] extended the analysis to general N-body chains. The simplest case of a chain topology is the one with two tethered satellites.…”

Section: Introductionmentioning

confidence: 99%

Modeling of tethered satellite formations using graph theory

2011

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“…Corrêa and Gómez [97] numerically determined the equilibrium configurations of a four-body TSS in the plane of a circular orbit through the use of a continuation method, with the solutions of the four-body system obtained by using a parameterization to trace the solutions of the three-body tethered configuration. Recently, Guerman et al [98] studied two classes of tetrahedral equilibrium configurations of a chain consisting of four satellites connected by three rigid weightless rods, and found that all tetrahedral equilibrium configurations should contain one unloaded link and at least one compressed rod that cannot be replaced with tethers.…”

Section: Dynamics and Control Of Tethered Satellite Formationsmentioning

confidence: 99%

Advances in dynamics and control of tethered satellite systems

2008

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The concept of tethered satellite system (TSS) promises to revolutionize many aspects of space exploration and exploitation. It provides not only numerous possible and valuable applications, but also challenging and interesting problems related to their dynamics, control, and physical implementation. Over the past decades, this exciting topic has attracted significant attention from many researchers and gained a vast number of analytical, numerical and experimental achievements with a focus on the two essential aspects of both dynamics and control. This review article presents the historic background and recent hot topics for the space tethers, and introduces the dynamics and control of TSSs in a progressive manner, from basic operating principles to the state-of-the-art achievements.

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“…S ATELLITE formations show such promise for enhanced performance of missions in space that researchers are arduously researching relative control using conventional thrusting [1], tethers [2][3][4], Lorentz forces [5], coulomb forces from charged satellites [6][7][8], and the linear impulse from lasers [9][10][11]. Theoretically, all of these stationkeeping approaches except for thrusting can provide some formation control without expenditure of fuel.…”

Section: Introductionmentioning

confidence: 99%

Static Formations Using Momentum Exchange Between Satellites

Tragesser

2009

Journal of Guidance, Control, and Dynamics

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Feasible operations of satellite formations are dependent upon an efficient way to affect the relative motion. One possible means of formation stationkeeping is for satellites to exchange momentum in the form of radiation or mass. This approach could potentially provide a mutually repulsive force between satellites without the expenditure of propellant. This paper characterizes equilibria positions in the rotating orbital frame for an arbitrary number of satellites subjected to equal and opposite repulsive force between specifiable satellite pairs. Equilibrium configurations are found that allow arbitrary dispersion in the plane perpendicular to nadir. Stability analysis of these equilibria show stable out-of-plane motion and unstable in-plane motion. A strategy is developed to stabilize the system and to reconfigure the formation geometry. Finally, a simulation including Earth oblateness demonstrates the dynamic feasibility of this method of orbit control. Nomenclature d = nominal distance between satellites K D = derivative gain for out-of-plane damping K p = proportional gain for in-plane control m i = mass of ith satellite n = mean motion of the reference orbit R i = position of the ith satellite in an Earth-centered inertial frame r i = position of the ith satellite relative to a circular reference orbit r ij = position of the ith satellite relative to the jth satellite ( r ij r i r j ) u ij = repulsive force between ith and jth satellite ( u ji ) u ix = x component of control acceleration on the ith satellite u iy = y component of control acceleration on the ith satellite x i = radial coordinate for ith satellite x i = equilibrium (nominal) value of radial coordinate for ith satellite y i = along-track coordinate for ith satellite y i = equilibrium (nominal) value of along-track coordinate for ith satellite z i = out-of-plane coordinate for ith satellite z i = equilibrium (nominal) value of out-of-plane coordinate for ith satellite ij = magnitude of the repulsive force between the ith and jth satellite z i = nominal separation distance between the ith and (i 1) th satellites (z i z i z i1 ) x i = radial displacement from equilibrium for ith satellite y i = along-track displacement from equilibrium for ith satellite z i = out-of-plane displacement from equilibrium for ith satellite

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Stationary Configurations of a Tetrahedral Tethered Satellite Formation

Cited by 25 publications

References 15 publications

Modeling of tethered satellite formations using graph theory

Modeling of tethered satellite formations using graph theory

Advances in dynamics and control of tethered satellite systems

Static Formations Using Momentum Exchange Between Satellites

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