Exploring Grid Polygons Online
Christian Icking, Tom Kamphans, Rolf Klein, Elmar Langetepe

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…
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Taxonomy
TopicsOptimization and Search Problems · Computational Geometry and Mesh Generation · Robotic Path Planning Algorithms
