Abstract

With the advent of autonomous robots with two- and three-dimensional scanning capabilities, classical visibility-based exploration methods from computational geometry have gained in practical importance. However, real-life laser scanning of useful accuracy does not allow the robot to scan continuously while in motion; instead, it has to stop each time it surveys its environment. This requirement was studied by Fekete, Klein and N"uchter for the subproblem of looking around a corner, but until now has not been considered for whole polygonal regions. We give the first comprehensive algorithmic study for this important algorithmic problem that combines stationary art gallery-type aspects with watchman-type issues in an online scenario. We show that there is a lower bound of $Omega(sqrt{n})$ on the competitive ratio in an orthogonal polygon with holes; we also demonstrate that even for orthoconvex polygons, a competitive strategy can only be achieved for limited aspect ratio $A$, i.e., for a given lower bound on the size of an edge. Our main result is an $O(log A)$-competitive strategy for simple rectilinear polygons, which is best possible up to constants.

@InProceedings{fekete_et_al:DSP:2007:871,
  author =	{S{\'a}ndor Fekete and Christiane Schmidt},
  title =	{Polygon Exploration with Discrete Vision},
  booktitle =	{Robot Navigation},
  year =	{2007},
  editor =	{S{\'a}ndor Fekete and Rudolf Fleischer and Rolf Klein and Alejandro Lopez-Ortiz},
  number =	{06421},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2007/871},
  annote =	{Keywords: Searching, scan cost, visibility problems, watchman problems, online searching, competitive strategies, autonomous mobile robots.}
}