# Visibility-Based Pursuit-Evasion in a Polygonal Environment

@inproceedings{Guibas1997VisibilityBasedPI, title={Visibility-Based Pursuit-Evasion in a Polygonal Environment}, author={Leonidas J. Guibas and Jean-Claude Latombe and Steven M. LaValle and David C. Lin and Rajeev Motwani}, booktitle={Workshop on Algorithms and Data Structures}, year={1997} }

This paper addresses the problem of planning the motion of one or more pursuers in a polygonal environment to eventually “see” an evader that is unpredictable, has unknown initial position, and is capable of moving arbitrarily fast. This problem was first introduced by Suzuki and Yamashita. Our study of this problem is motivated in part by robotics applications, such as surveillance with a mobile robot equipped with a camera that must find a moving target in a cluttered workspace. A few bounds…

## 228 Citations

### Planning for robust visibility-based pursuit-evasion

- Mathematics2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
- 2020

This paper considers the case in which a pursuer with an omnidirectional sensor searches a known environment to locate an evader that may move arbitrarily quickly, and introduces the notion of an ε-robust solution strategy, in which ε is an upper bound on the positioning error that the pursuer may experience.

### A Visibility Roadmap Sampling Approach for a Multi-Robot Visibility-Based Pursuit-Evasion Problem

- Computer Science2021 IEEE International Conference on Robotics and Automation (ICRA)
- 2021

This paper proposes a new algorithm that takes an environment as its input and returns a joint motion strategy which ensures that the evader is captured by one of the pursuers, and describes an implementation of this algorithm and presents quantitative results that show significant improvement in comparison to the existing algorithm.

### Visibility-Based Pursuit-Evasion in an Unknown Planar Environment

- BusinessInt. J. Robotics Res.
- 2004

A complete algorithm is presented that enables the limited pursuer to clear the same environments that a pursuer with a complete map, perfect localization, and perfect control can clear (under certain general position assumptions).

### Complete and optimal visibility-based pursuit-evasion

- Computer ScienceInt. J. Robotics Res.
- 2017

This paper presents a complete algorithm that computes a minimum-cost pursuer trajectory that ensures that the evader is captured, or reports in finite time that no such trajectory exists, and describes an implementation of the algorithm, along with experiments that measure its performance in several environments with a variety of pruning operations.

### Pursuit-evasion in an unknown environment using gap navigation trees

- Computer Science2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE Cat. No.04CH37566)
- 2004

It is proved that a pursuer with k + 1 sentries can clear any environment that could be cleared by k pursuers using the algorithm in L.J. Guibas et al. (1999), which required a complete map and perfect sensing.

### Maintaining strong mutual visibility of an evader moving over the reduced visibility graph

- Computer ScienceAuton. Robots
- 2016

This paper provides a constructive method to solve the decision problem of determining whether or not the pursuer is able to maintain strong mutual visibility of the evader, and proves decidability of this problem, and provides a complexity measure to this evader surveillance game.

### Maintaining strong mutual visibility of an evader moving over the reduced visibility graph

- Computer ScienceAutonomous Robots
- 2015

This paper provides a constructive method to solve the decision problem of determining whether or not the pursuer is able to maintain strong mutual visibility of the evader, and proves decidability of this problem, and provides a complexity measure to this evader surveillance game.

### A complete algorithm for visibility-based pursuit-evasion with multiple pursuers

- Computer Science2014 IEEE International Conference on Robotics and Automation (ICRA)
- 2014

This work introduces a centralized algorithm for a visibility-based pursuit-evasion problem in a two-dimensional environment for the case of multiple pursuers and constructs a Pursuit Evasion Graph induced by the adjacency graph.

### Rapid Recovery from Robot Failures in Multi-Robot Visibility-Based Pursuit-Evasion

- Computer Science2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
- 2021

This paper proposes an algorithm that can rapidly recover from catastrophic failures of a team of pursuer robots operating in a two-dimensional polygonal space and describes an implementation and provides quantitative results that show that the proposed method is able to recover from robot failures more rapidly than a baseline approach that plans from scratch.

### Evasion with Bounded Speed − − Visibility-based Pursuit

- Computer Science
- 2008

A characterization of the set of possible evader positions as a function of time (the reachable sets) is developed, more complex than the unbounded-speed case, because it no longer depends only on the combinatorial changes in the visibility region of the pursuer.

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