LOCALIZING A ROBOT WITH MINIMUM TRAVEL. Kathleen A. Romanik, Gregory
Dudek, Sue Whitesides, McGill University, MontrÈal, QuÈbec,
Canada (NIST address: Building 220, Room B124, NIST, Gaithersburg, MD 20899,
301-975-5068, email: email@example.com)
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|, which is no greater than the number of reflex vertices of P, and d is the length of a minimum 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.