DIMACS TR: 95-40

Localizing a Robot with Minimum Travel

Authors: Gregory Dudek, Kathleen Romanik, Sue Whitesides


We consider the problem of localizing a robot in a known environment modeled by a simple polygon P. We assume that the robot has a map of P but is placed at an unknown location inside P. From its initial location, the robot sees a set of points called the visibility polygon V of its location. In general, sensing at a single point will not suffice to uniquely localize the robot, since the set H of points in P with visibility polygon V may have more than one element. Hence, the robot must move around and use range sensing and a compass to determine its position (i.e. localize itself). We seek a strategy that minimizes the distance the robot travels to determine its exact location.

We show that the problem of localizing a robot with minimum travel is NP-hard. We then give a polynomial time approximation scheme that causes the robot to travel a distance of at most (k-1)d, where k = |H| and d is the length of a minumum length tour that would allow the robot to verify its true initial location by sensing. We also show that this bound is the best possible.

Paper available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1995/95-40.ps.gz

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