In

2016

**Abstract**
We introduce a complete algorithm for solving a pursuit-evasion problem in
a simply-connected two-dimensional environment, for the case of a single
pursuer equipped with fixed beam sensors. The input for our algorithm is
an environment and a collection of sensor directions, in which each is
capable of line-of-sight detection in a fixed direction. The output is a
pursuer motion strategy that ensures the detection of an evader that moves
with unbounded speed, or a statement that no such such strategy exists.
The intuition of the algorithm is to decompose the environment into a
collection of convex conservative regions, within which the evader cannot
sneak between any pair of adjacent sensors. This decomposition induces a
graph we call the *pursuit-evasion graph (PEG)*, such that any correct
solution strategy can be expressed as a path through the PEG. We have
implemented the algorithm and present some computed examples illustrating
the algorithm's correctness.

@inproceedings{StiOKa16, author = {Nicholas M. Stiffler and Jason M. O'Kane}, booktitle = {Proc. IEEE International Conference on Robotics and Automation}, title = {Pursuit-evasion with fixed beams}, year = {2016} }