The Journal of the Astronautical Sciences

, Volume 58, Issue 2, pp 221–240 | Cite as

Closed-Loop Control of Satellite Formations Using a Quasi-Rigid Body Formulation

  • Christopher Blake
  • Arun K. Misra
Article
First Online:

Abstract

Satellites in formation work together to fulfill the role of a larger satellite. The purpose of this article is to develop a quasi-rigid body formulation for modeling and controlling such a formation as a single entity. In this article, a definition of a quasi-rigid body coordinate frame is presented, which, when attached to a formation, conveniently describes its orientation in space. Using this formulation, the equations of motion for a satellite formation are recast, and natural circular formations are expressed more succinctly. When the J 2 perturbation is considered, a correction factor on the formation’s spin rate is introduced. The control of a satellite formation can effectively be separated into (1) a control torque to maintain the attitude and (2) control forces that maintain the rigidity of the formation. With this in mind, a nonlinear Lyapunov controller is derived using the formulation, which acts on the formation as a whole. Simulations validate this controller and illustrate its utility for maintaining circular formations, in particular, in the presence of gravitational perturbations.

Keywords

Orientation Error Circular Formation Gravitational Perturbation Relative Orbit Satellite Formation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© American Astronautical Society, Inc. 2011

Authors and Affiliations

  • Christopher Blake
    • 1
  • Arun K. Misra
    • 2
  1. 1.Department of Mechanical EngineeringMcGill UniversityMontrealCanada
  2. 2.Department of Mechanical EngineeringMcGill UniversityMontrealCanada

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