### Abstract

A spacecraft hovering scheme over a uniformly rotating asteroid in the asteroid body-fixed frame using geometric mechanics is presented. The configuration space for the spacecraft is the Lie group SE(3), which is the set of positions and orientations of the rigid spacecraft in three-dimensional Euclidean space. The asteroid trajectory, in the form of natural attitude and translational (orbital) motion of a satellite, is assumed to be available through a spacecraft on-board navigation. The spacecraft tracks a desired relative configuration with respect to the asteroid in an autonomous manner. The relative configuration between the spacecraft and the asteroid is described in terms of exponential coordinates on the Lie group of rigid body motions. A continuous-time feedback tracking control using these exponential coordinates and the relative velocities is employed. A Lyapunov analysis guarantees that the spacecraft asymptotically converges to the desired trajectory. Numerical simulation results demonstrate the successful spacecraft hovering control in the asteroid body-fixed frame for a selected uniformly rotating asteroid.

Original language | English (US) |
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Title of host publication | Advances in the Astronautical Sciences |

Publisher | Univelt Inc. |

Pages | 1757-1773 |

Number of pages | 17 |

Volume | 150 |

ISBN (Print) | 9780877036050 |

State | Published - 2014 |

Externally published | Yes |

Event | 2013 AAS/AIAA Astrodynamics Specialist Conference, Astrodynamics 2013 - Hilton Head Island, SC, United States Duration: Aug 11 2013 → Aug 15 2013 |

### Other

Other | 2013 AAS/AIAA Astrodynamics Specialist Conference, Astrodynamics 2013 |
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Country | United States |

City | Hilton Head Island, SC |

Period | 8/11/13 → 8/15/13 |

### Fingerprint

### ASJC Scopus subject areas

- Aerospace Engineering
- Space and Planetary Science

### Cite this

*Advances in the Astronautical Sciences*(Vol. 150, pp. 1757-1773). Univelt Inc..

**Spacecraft hovering control for body-fixed hovering over a uniformly rotating asteroid using geometric mechanics.** / Lee, Daero; Sanyal, Amit K.; Butcher, Eric; Scheeres, Daniel J.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Advances in the Astronautical Sciences.*vol. 150, Univelt Inc., pp. 1757-1773, 2013 AAS/AIAA Astrodynamics Specialist Conference, Astrodynamics 2013, Hilton Head Island, SC, United States, 8/11/13.

}

TY - GEN

T1 - Spacecraft hovering control for body-fixed hovering over a uniformly rotating asteroid using geometric mechanics

AU - Lee, Daero

AU - Sanyal, Amit K.

AU - Butcher, Eric

AU - Scheeres, Daniel J.

PY - 2014

Y1 - 2014

N2 - A spacecraft hovering scheme over a uniformly rotating asteroid in the asteroid body-fixed frame using geometric mechanics is presented. The configuration space for the spacecraft is the Lie group SE(3), which is the set of positions and orientations of the rigid spacecraft in three-dimensional Euclidean space. The asteroid trajectory, in the form of natural attitude and translational (orbital) motion of a satellite, is assumed to be available through a spacecraft on-board navigation. The spacecraft tracks a desired relative configuration with respect to the asteroid in an autonomous manner. The relative configuration between the spacecraft and the asteroid is described in terms of exponential coordinates on the Lie group of rigid body motions. A continuous-time feedback tracking control using these exponential coordinates and the relative velocities is employed. A Lyapunov analysis guarantees that the spacecraft asymptotically converges to the desired trajectory. Numerical simulation results demonstrate the successful spacecraft hovering control in the asteroid body-fixed frame for a selected uniformly rotating asteroid.

AB - A spacecraft hovering scheme over a uniformly rotating asteroid in the asteroid body-fixed frame using geometric mechanics is presented. The configuration space for the spacecraft is the Lie group SE(3), which is the set of positions and orientations of the rigid spacecraft in three-dimensional Euclidean space. The asteroid trajectory, in the form of natural attitude and translational (orbital) motion of a satellite, is assumed to be available through a spacecraft on-board navigation. The spacecraft tracks a desired relative configuration with respect to the asteroid in an autonomous manner. The relative configuration between the spacecraft and the asteroid is described in terms of exponential coordinates on the Lie group of rigid body motions. A continuous-time feedback tracking control using these exponential coordinates and the relative velocities is employed. A Lyapunov analysis guarantees that the spacecraft asymptotically converges to the desired trajectory. Numerical simulation results demonstrate the successful spacecraft hovering control in the asteroid body-fixed frame for a selected uniformly rotating asteroid.

UR - http://www.scopus.com/inward/record.url?scp=84898975118&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84898975118&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84898975118

SN - 9780877036050

VL - 150

SP - 1757

EP - 1773

BT - Advances in the Astronautical Sciences

PB - Univelt Inc.

ER -