### Abstract

Consider a formation control problem in which agents in Euclidean space are tasked with stabilizing their positions at prescribed target distances from each other, and for which these distances are described by a rigid graph. There is a mismatch in target distances if there is a pair of neighboring agents i and j such that agent i aims to stabilize from agent j at a distance d_{ij}, but agent j from agent i at a slightly different distance d′_{ij}. A mismatch in target distances results in a mismatch in the associated interaction laws. It was shown in a recent paper [1] that when there is a small mismatch in the interaction laws, the entire formation undergoes a constant rigid motion. In this work, we build on this observation to establish a controllability result. Specifically, given that there is a selected subset of agents that can control the mismatches in interactions among them, we show that if these agents are fully connected and form a nondegenerate triangle (or more generally, a nondegenerate k-simplex in the k-dimensional case), then it is possible to control an arbitrary rigid motion of the entire formation.

Original language | English (US) |
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Title of host publication | 2016 IEEE 55th Conference on Decision and Control, CDC 2016 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 57-62 |

Number of pages | 6 |

ISBN (Electronic) | 9781509018376 |

DOIs | |

State | Published - Dec 27 2016 |

Event | 55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States Duration: Dec 12 2016 → Dec 14 2016 |

### Publication series

Name | 2016 IEEE 55th Conference on Decision and Control, CDC 2016 |
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### Other

Other | 55th IEEE Conference on Decision and Control, CDC 2016 |
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Country | United States |

City | Las Vegas |

Period | 12/12/16 → 12/14/16 |

### ASJC Scopus subject areas

- Artificial Intelligence
- Decision Sciences (miscellaneous)
- Control and Optimization

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## Cite this

*2016 IEEE 55th Conference on Decision and Control, CDC 2016*(pp. 57-62). [7798246] (2016 IEEE 55th Conference on Decision and Control, CDC 2016). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2016.7798246