- Published 2009

In this paper, we will incrementally build a complete pursuit algorithm to deal with a 2-players PEG in presence of a single unknown convex obstacle. We will first provide a sufficient condition to achieve capture without disappearance. Then, we will solve the circular obstacle problem, a particular problem highlighting a necessary trade-off between surveillance and capture. Next, the pole problem, as a generalization, of the convex obstacle problem will be tackled. The solution and the corresponding strategies will be detailed. A quasi-optimal pursuit strategy as regards the time to capture will be provided for the pole problem, and then transposed for the more general convex obstacle problem. For the cases leading to the evader victory in the pole problem, a last strategy allowing a maximal deviation of the line of disappearance will be added to complete to our pursuit algorithm. Finally, our complete pursuit algorithm will be adapted to use a heuristic minimization method instead of the strategy suggested by the resolution of the pole problem for the cases leading to the pursuer victory. Different heuristics, one being an approximation of the solution of the pole problem, will be compared with respect to the size of the capture basin and will highlight thez interest of our pursuit algorithm.

@inproceedings{Giovannangeli2009PursuitEvasionGI,
title={Pursuit-Evasion Games in Presence of Obstacles in Unknown Environments: Towards an Optimal Pursuit Strategy},
author={Christophe Giovannangeli and Murray Heymann and Ehud Rivlin},
year={2009}
}