Collinear invariant shapes for three-spacecraft Coulomb formations

Hogan, Erik A.; Schaub, Hanspeter

doi:10.1016/j.actaastro.2011.10.020

Cited by 23 publications

(3 citation statements)

References 12 publications

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“…Hogan and Schaub in Ref. [14] investigated invariant shape conditions for a three-craft collinear formation in deep space. They proved that there always exists an infinite set of open-loop charges, which yield an equilibrium shape for any three-craft collinear invariant shape formations.…”

Section: Introductionmentioning

confidence: 99%

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Coulomb control of a triangular three-body satellite formation using nonlinear model predictive method

Huang

et al. 2014

Proceedings of the 33rd Chinese Control Conference

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In this paper, a nonlinear model predictive controller for a three-body Coulomb satellite formation is designed. For a formation of three satellites flying freely in deep space, actively controlled Coulomb forces are used to stabilize the formation shape to a desired triangular configuration. The control problem is challenging because the system is nonlinear and nonaffine, and the system constraints need to be taken into account. The proposed solution to the control problem is a nonlinear model predictive controller ensuring stability and optimal control performance while satisfying system constraints. Perfect convergence to desired triangular shape is not physically achievable with Coulomb forces alone because the triangle is not a natural equilibrium solution. Numerical simulations illustrate the effectiveness of the proposed control strategy.

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Section: Introductionmentioning

confidence: 99%

“…Refs. [10][11][12][13][14][15][16] are more closely related to the Coulomb formation reconfiguration problem considered in this paper. Ref.…”

Section: Introductionmentioning

confidence: 99%

Coulomb control of a triangular three-body satellite formation using nonlinear model predictive method

Huang

et al. 2014

Proceedings of the 33rd Chinese Control Conference

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“…Asymptotic stability was achieved if the system's angular momentum was equivalent to the estimated/ nominal angular momentum, which was used to calculate the nominal charges [8]. Hogan and Schaub [9] investigated invariant shape conditions for a three-craft collinear formation and proved that, for any collinear formations, there always exists an infinite set of real open-loop charges for equilibrium. Hogan and Schaub [10] also explored the solution families for collinear three-craft CFF, and distinct regions where invariant shape solutions exist were analyzed to determine what range of trajectories were possible.…”

Section: Introductionmentioning

confidence: 99%

Reconfiguration of Three-Craft Coulomb Formation Based on Patched-Conic-Section Trajectories

Wang

2016

Journal of Guidance, Control, and Dynamics

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This paper investigates the nonequilibrium fixed-shape three-craft Coulomb formation reconfiguration problem. Being aware that using the feedback-control approach might result in the chattering of the charges due to the nonequilibrium nature of the system dynamics, this paper proposes a trajectory planning approach to accomplish the reconfiguration. Entire maneuver trajectories are divided into multiple phases. During each phase, only two of the three craft are charged. In this way, the relative trajectory of the charged spacecraft during a certain phase is a conic section. Entire trajectories are composed of patched conics and/or straight lines. The procedures determining the three-phase maneuver strategy are developed, including a preadjusting phase and two transition phases. Numerical simulations demonstrate the effectiveness of the algorithm and the elegance of the charge histories.

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Exact solutions and adiabatic invariants for equations of satellite attitude motion under Coulomb torque

Aslanov

2017

Nonlinear Dyn

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Collinear invariant shapes for three-spacecraft Coulomb formations

Cited by 23 publications

References 12 publications

Coulomb control of a triangular three-body satellite formation using nonlinear model predictive method

Coulomb control of a triangular three-body satellite formation using nonlinear model predictive method

Reconfiguration of Three-Craft Coulomb Formation Based on Patched-Conic-Section Trajectories

Exact solutions and adiabatic invariants for equations of satellite attitude motion under Coulomb torque

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