Polygon Exploration with Time-Discrete Vision

TL;DR

This paper introduces algorithms for polygon exploration by autonomous robots with discrete vision, addressing the challenge of limited scanning capabilities and providing competitive strategies for specific polygon classes.

Contribution

It presents the first algorithmic solutions for online polygon exploration with stationary scanning, including bounds for orthoconvex and rectilinear polygons based on aspect ratio.

Findings

Achieves O(log A)-competitive strategy for rectilinear polygons

Demonstrates limitations for orthoconvex polygons with high aspect ratio

Provides bounds linking polygon edge lengths to exploration competitiveness

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 Nuechter 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 algorithmic 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(log A)-competitive strategy for simple rectilinear polygons, using the assumption that each edge of the polygon has to be fully visible from some scan point.