Polygon exploration with time-discrete vision

  • Authors:

  • Sándor P. Fekete;Christiane Schmidt

  • Affiliations:

  • Department of Computer Science, Technische Universität Braunschweig, D-38106 Braunschweig, Germany;Department of Computer Science, Technische Universität Braunschweig, D-38106 Braunschweig, Germany

  • Venue:
  • Computational Geometry: Theory and Applications
  • Year:
  • 2010

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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 Nuchter for the subproblem of looking around a corner, but until now has not been considered in an online setting for whole polygonal regions. We give the first algorithmic results for this important optimization problem that combines stationary art gallery-type aspects with watchman-type issues in an online scenario: We demonstrate that even for orthoconvex polygons, a competitive strategy can be achieved only for limited aspect ratio A (the ratio of the maximum and minimum edge length of the polygon), i.e., for a given lower bound on the size of an edge; we give a matching upper bound by providing an O(logA)-competitive strategy for simple rectilinear polygons, using the assumption that each edge of the polygon has to be fully visible from some scan point.