No. 318 on SWAT 88: 1st Scandinavian workshop on algorithm theory
The robot localization problem in two dimensions
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Information and Computation
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Map learning and high-speed navigation in RHINO
Artificial intelligence and mobile robots
Localizing a robot with minimum travel
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Exploring unknown environments with real-time search or reinforcement learning
Proceedings of the 1998 conference on Advances in neural information processing systems II
Optimal robot localization in trees
Information and Computation
Interleaving Planning and Execution for Autonomous Robots
Interleaving Planning and Execution for Autonomous Robots
Gridworlds as Testbeds for Planning with Incomplete Information
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Efficient Robot Self-Localization in Simple Polygons
Intelligent Robots: Sensing, Modeling and Planning [Dagstuhl Workshop, September 1-6, 1996]
Efficient visibility queries in simple polygons
Computational Geometry: Theory and Applications
Active Appearance-Based Robot Localization Using Stereo Vision
Autonomous Robots
Randomized Algorithms for Minimum Distance Localization
International Journal of Robotics Research
Query point visibility computation in polygons with holes
Computational Geometry: Theory and Applications
The localization problem for mobile robots
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
A Near-Tight Approximation Algorithm for the Robot Localization Problem
SIAM Journal on Computing
LICA: robust localization using cluster analysis to improve GPS coordinates
Proceedings of the first ACM international symposium on Design and analysis of intelligent vehicular networks and applications
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Localization, which is the determination of one's location in a known terrain, is a fundamental task for autonomous robots. This paper presents several new basic theoretical results about localization.We show that, even under the idealized assumptions of accurate sensing and perfect actuation, it is intrinsically difficult to localize a robot with a travel distance that is close to minimal. Our result helps to theoretically justify the common use of fast localization heuristics, such as greedy localization, which always moves the robot to a closest informative location (where the robot makes an observation that decreases the number of its possible locations). We show that the travel distance of greedy localization is much larger thanminimal in some terrains because the closest informative location can distract greedy localization from a slightly farther, but much more informative, location. However, we also show that the travel distance of greedy localization can be larger, but not much larger, than the terrain size n. Thus, the travel distance of greedy localization scales well with the terrain size and is much larger than minimal in some terrains, not because it is large with respect to the terrain size, but because the minimal travel distance is exceptionally small in these terrains. As a corollary to our analysis, we show that the travel distance of greedy mapping (which always moves the robot to a closest location, where it makes an observation that increases its knowledge of the terrain) cannot be much larger than the terrain size. In theoretical terms, we prove the NP-hardness of minimization of travel distance for localization to within a logarithmic factor of the terrain size. We prove that the travel distance of greedy localization is at least order n/ log2 n larger than minimal in some terrains and that it is at least order n log n/ log log n in the worst case. Finally, we prove that the travel distance of both greedy localization and greedy mapping is at most order n log n. Previously, it was only known that it is NP-hard to localize with minimal travel distance and that the travel distances of greedy localization and greedy mapping are at most order n3/2.