### Abstract

We present an approach to position k servers (e.g. mobile robots) to provide a service to n independently moving clients; for example, in mobile ad-hoc networking applications where inter-agent distances need to be minimized, connectivity constraints exist between servers, and no a priori knowledge of the clients' motion can be assumed. Our primary contribution is an algorithm to compute and maintain a small representative set, called a kinematic coreset, of the n moving clients.We prove that, in any given moment, the maximum distance between the clients and any set of k servers is approximated by the coreset up to a factor of (1 ± ε), where ε > 0 is an arbitrarily small constant. We prove that both the size of our coreset and its update time is polynomial in k log(n)/ε. Although our optimization problem is NP-hard (i.e., takes time exponential in the number of servers to solve), solving it on the small coreset instead of the original clients results in a tractable controller. The approach is validated in a small scale hardware experiment using robot servers and human clients, and in a large scale numerical simulation using thousands of clients.

Original language | English (US) |
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Title of host publication | 2013 IEEE International Conference on Robotics and Automation, ICRA 2013 |

Pages | 881-888 |

Number of pages | 8 |

DOIs | |

State | Published - Nov 14 2013 |

Externally published | Yes |

Event | 2013 IEEE International Conference on Robotics and Automation, ICRA 2013 - Karlsruhe, Germany Duration: May 6 2013 → May 10 2013 |

### Other

Other | 2013 IEEE International Conference on Robotics and Automation, ICRA 2013 |
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Country | Germany |

City | Karlsruhe |

Period | 5/6/13 → 5/10/13 |

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### ASJC Scopus subject areas

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

### Cite this

*2013 IEEE International Conference on Robotics and Automation, ICRA 2013*(pp. 881-888). [6630677] https://doi.org/10.1109/ICRA.2013.6630677