### Abstract

This paper presents a new methodology yielding high-order, nonlinear approximations to the relative orbital dynamics of spacecraft flying in formation. A nonlinear formationkeeping control law is then developed. Nonlinear models of relative spacecraft dynamics are parameterized as time-series. Instead of using the Cartesian initial conditions as constants of motion, classical orbital elements are utilized. Variation of these elements enables the incorporation of perturbations and control forces in a straightforward manner. The method presented in the paper does not require solution of the differential equations, thus offering a simple derivation of models for relative motion. The known inertial configuration space is utilized and projected onto a classical rotating Hill frame. Based on the nonlinear modeling, a globally asymptotically stabilizing low-thrust Lyapunov-based formationkeeping controller is developed. The merits of the proposed modeling and control are validated by a few illustrative examples.

Original language | English (US) |
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Pages (from-to) | 153-169 |

Number of pages | 17 |

Journal | Advances in the Astronautical Sciences |

Volume | 114 I |

State | Published - 2003 |

Event | Spaceflight Mechanics 2003: Proceedings of the AAS/AIAA Space Flight Mechanics Meeting - Ponce, Puerto Rico Duration: Feb 9 2003 → Feb 13 2003 |

### All Science Journal Classification (ASJC) codes

- Aerospace Engineering
- Space and Planetary Science

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## Cite this

*Advances in the Astronautical Sciences*,

*114 I*, 153-169.