### Abstract

A common algorithm for deployment of a mobile sensor network in a bounded domain moves each sensor toward the centroid of its Voronoi cell. This algorithm is optimal for a particular cost function that is expressed as a sum over Voronoi cells, where the placement of a sensor in its own cell has no effect on cost in other cells. We provide a probabilistic interpretation of this "partitioned" cost function in the context of a target detection task, where each sensor has a chance of seeing the target that decreases monotonically with distance and where the goal is to minimize the total probability of missed detection. We show that the partitioned cost function is exactly the probability of missed detection given that a sensor can only see a target in its own Voronoi cell. We derive the probability of missed detection in the general case - where each sensor might see the target anywhere - and show that optimal sensor placement changes. Finally, we derive the probability of missed detection given the possibility of sensor failure, producing a robust measure of cost with respect to which optimal sensor placement is different yet again. Our results are illustrated by several examples in simulation.

Original language | English (US) |
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Title of host publication | 2012 IEEE International Conference on Robotics and Automation, ICRA 2012 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 671-676 |

Number of pages | 6 |

ISBN (Print) | 9781467314039 |

DOIs | |

State | Published - Jan 1 2012 |

Event | 2012 IEEE International Conference on Robotics and Automation, ICRA 2012 - Saint Paul, MN, United States Duration: May 14 2012 → May 18 2012 |

### Publication series

Name | Proceedings - IEEE International Conference on Robotics and Automation |
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ISSN (Print) | 1050-4729 |

### Other

Other | 2012 IEEE International Conference on Robotics and Automation, ICRA 2012 |
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Country | United States |

City | Saint Paul, MN |

Period | 5/14/12 → 5/18/12 |

### ASJC Scopus subject areas

- Software
- Control and Systems Engineering
- Artificial Intelligence
- Electrical and Electronic Engineering

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## Cite this

*2012 IEEE International Conference on Robotics and Automation, ICRA 2012*(pp. 671-676). [6225200] (Proceedings - IEEE International Conference on Robotics and Automation). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICRA.2012.6225200