Pursuit-evasion in an unknown environment using gap navigation trees

In this paper we present an online algorithm for pursuit-evasion in a unknown simply connected environment, for one pursuer that has minimal sensing and carries a set of stationary sentries that it can drop off and pick up during the pursuit. In our sensing model, the pursuer is only able to detect discontinuities in depth information (gaps), and it is able to find all of the evaders without any explicit localization or geometric information, by using a gap navigation tree. The strategy is based on growing an evader-free region, by reading "exploration" schedules from the gap navigation tree, that is constructed online. We prove 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.