### Abstract

In this paper we study a discrete variational optimal control problem for the rigid body. The cost to be minimized is the external torque applied to move the rigid body from an initial condition to a pre-specified terminal condition. Instead of discretizing the equations of motion, we use the discrete equations obtained from the discrete Lagrange-d'Alembert principle, a process that better approximates the equations of motion. Within the discrete-time setting, these two approaches are not equivalent in general. The kinematics are discretized using a natural Lie-algebraic formulation that guarantees that the flow remains on the Lie group SO(3) and its algebra so (3). We uše Lagrange's method for constrained problems in the calculus of variations to derive the discrete-time necessary conditions. We give a numerical example for a three-dimensional rigid body maneuver.

Original language | English (US) |
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Title of host publication | Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 6636-6641 |

Number of pages | 6 |

ISBN (Print) | 1424401712, 9781424401710 |

DOIs | |

State | Published - 2006 |

Event | 45th IEEE Conference on Decision and Control 2006, CDC - San Diego, CA, United States Duration: Dec 13 2006 → Dec 15 2006 |

### Publication series

Name | Proceedings of the IEEE Conference on Decision and Control |
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ISSN (Print) | 0191-2216 |

### Other

Other | 45th IEEE Conference on Decision and Control 2006, CDC |
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Country | United States |

City | San Diego, CA |

Period | 12/13/06 → 12/15/06 |

### ASJC Scopus subject areas

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization

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## Cite this

*Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC*(pp. 6636-6641). [4177888] (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/cdc.2006.377818