### Abstract

We present an O(n log^{1+ε}n)-time algorithm for computing the optimal robot motion that maintains line-of-sight visibility between a target moving inside a polygon with n vertices which may contain holes. The motion is optimal for the tracking robot (the observer) in the sense that the target either remains visible for the longest possible time, or it is captured by the observer in the minimum time when feasible. Thus, the algorithm maximizes the minimum time-to-escape. Our algorithm assumes that the target moves along a known path. Thus, it is an off-line algorithm. Our theoretical results for the algorithm's runtime assume that the target is moving along a shortest path from its source to its destination. This assumption, however is not required to prove the optimality of the computed solution, hence the algorithm remains correct for the general case.

Original language | English (US) |
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Title of host publication | Proceedings - IEEE International Conference on Robotics and Automation |

Pages | 3789-3796 |

Number of pages | 8 |

Volume | 3 |

State | Published - 2003 |

Event | 2003 IEEE International Conference on Robotics and Automation - Taipei, Taiwan, Province of China Duration: Sep 14 2003 → Sep 19 2003 |

### Other

Other | 2003 IEEE International Conference on Robotics and Automation |
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Country | Taiwan, Province of China |

City | Taipei |

Period | 9/14/03 → 9/19/03 |

### Fingerprint

### ASJC Scopus subject areas

- Software
- Control and Systems Engineering

### Cite this

*Proceedings - IEEE International Conference on Robotics and Automation*(Vol. 3, pp. 3789-3796)

**Optimal strategies to track and capture a predictable target.** / Efrat, Alon; González-Baños, Hector H.; Kobourov, Stephen G; Palaniappan, Lingeshwaran.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings - IEEE International Conference on Robotics and Automation.*vol. 3, pp. 3789-3796, 2003 IEEE International Conference on Robotics and Automation, Taipei, Taiwan, Province of China, 9/14/03.

}

TY - GEN

T1 - Optimal strategies to track and capture a predictable target

AU - Efrat, Alon

AU - González-Baños, Hector H.

AU - Kobourov, Stephen G

AU - Palaniappan, Lingeshwaran

PY - 2003

Y1 - 2003

N2 - We present an O(n log1+εn)-time algorithm for computing the optimal robot motion that maintains line-of-sight visibility between a target moving inside a polygon with n vertices which may contain holes. The motion is optimal for the tracking robot (the observer) in the sense that the target either remains visible for the longest possible time, or it is captured by the observer in the minimum time when feasible. Thus, the algorithm maximizes the minimum time-to-escape. Our algorithm assumes that the target moves along a known path. Thus, it is an off-line algorithm. Our theoretical results for the algorithm's runtime assume that the target is moving along a shortest path from its source to its destination. This assumption, however is not required to prove the optimality of the computed solution, hence the algorithm remains correct for the general case.

AB - We present an O(n log1+εn)-time algorithm for computing the optimal robot motion that maintains line-of-sight visibility between a target moving inside a polygon with n vertices which may contain holes. The motion is optimal for the tracking robot (the observer) in the sense that the target either remains visible for the longest possible time, or it is captured by the observer in the minimum time when feasible. Thus, the algorithm maximizes the minimum time-to-escape. Our algorithm assumes that the target moves along a known path. Thus, it is an off-line algorithm. Our theoretical results for the algorithm's runtime assume that the target is moving along a shortest path from its source to its destination. This assumption, however is not required to prove the optimality of the computed solution, hence the algorithm remains correct for the general case.

UR - http://www.scopus.com/inward/record.url?scp=0344464817&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0344464817&partnerID=8YFLogxK

M3 - Conference contribution

VL - 3

SP - 3789

EP - 3796

BT - Proceedings - IEEE International Conference on Robotics and Automation

ER -