Exploring Grid Polygons Online

TL;DR

This paper studies efficient exploration strategies for a mobile robot in unknown grid environments, providing bounds on the tour length based on environment complexity and obstacles.

Contribution

It introduces new exploration strategies with provable bounds for both obstacle-free and obstacle-rich environments.

Findings

Strategy for obstacle-free environments with tour length <= C + 0.5 E - 3.

Strategy for environments with obstacles with tour length <= C + 0.5 E + 3H + WCW - 2.

Provides theoretical bounds relating environment features to exploration efficiency.

Abstract

We investigate the exploration problem of a short-sighted mobile robot moving in an unknown cellular room. To explore a cell, the robot must enter it. Once inside, the robot knows which of the 4 adjacent cells exist and which are boundary edges. The robot starts from a specified cell adjacent to the room's outer wall; it visits each cell, and returns to the start. Our interest is in a short exploration tour; that is, in keeping the number of multiple cell visits small. For abitrary environments containing no obstacles we provide a strategy producing tours of length S <= C + 1/2 E - 3, and for environments containing obstacles we provide a strategy, that is bound by S <= C + 1/2 E + 3H + WCW - 2, where C denotes the number of cells-the area-, E denotes the number of boundary edges-the perimeter-, and H is the number of obstacles, and WCW is a measure for the sinuosity of the given environment.