### Abstract

This paper looks at the robust trajectory control of spatial mechanical systems using sliding mode techniques. Two distinctions of the proposed method from reported methods are: (1) The measure of attitudinal error used is intrinsically defined, Euclidean-geometric, and intuitive. From Euler's theorem it follows that given a desired and actual attitude of a rigid body there exists an axis and angle of rotation relating the two attitudes. This defines a relative rotation vector, which is used as an intrinsically defined, intuitive measure of error. Reported methods use algebraic differences of entities such as generalized coordinates representing attitude. While functionally correlated to attitudinal error, these measures are not intrinsically defined. (2) A novel, dynamically nonlinear sliding function is used that results in a simple control law. The parameters of this function are dynamically and geometrically intuitive. Simulation results are given for a spacecraft tracking a complex desired trajectory.

Original language | English |
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Title of host publication | Proceedings of the ASME Dynamic Systems and Control Division |

Subtitle of host publication | presented at the 1997 ASME International Mechanical Engineering Congress and Exposition, November 16-21, 1997, Dallas, Texas |

Editors | Giorgio Rizzoni |

Place of Publication | New York, N.Y. |

Publisher | American Society of Mechanical Engineers (ASME) |

Pages | 545-554 |

Number of pages | 10 |

ISBN (Print) | 9780791818244 |

Publication status | Published - 16 Nov 1997 |

Event | ASME International Mechanical Engineering Congress & Exposition, IMECE 1997 - Dallas, United States Duration: 16 Nov 1997 → 21 Nov 1997 |

### Publication series

Name | ASME Dynamic Systems and Control Division |
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Publisher | American Society of Mechanical Engineers |

Volume | 61 |

### Conference

Conference | ASME International Mechanical Engineering Congress & Exposition, IMECE 1997 |
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Abbreviated title | IMECE |

Country | United States |

City | Dallas |

Period | 16/11/97 → 21/11/97 |

### Keywords

- METIS-113490
- IR-99985

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## Cite this

Goeree, B. B., Fasse, E. D., Tiernego, M. J. L., & Broenink, J. F. (1997). Sliding mode control of spatial mechanical systems decoupling translation and rotation. In G. Rizzoni (Ed.),

*Proceedings of the ASME Dynamic Systems and Control Division: presented at the 1997 ASME International Mechanical Engineering Congress and Exposition, November 16-21, 1997, Dallas, Texas*(pp. 545-554). (ASME Dynamic Systems and Control Division; Vol. 61). New York, N.Y.: American Society of Mechanical Engineers (ASME).