Data structures and algorithms 3: multi-dimensional searching and computational geometry
Data structures and algorithms 3: multi-dimensional searching and computational geometry
Optimal point location in a monotone subdivision
SIAM Journal on Computing
Journal of Algorithms
Visibility and intersection problems in plane geometry
Discrete & Computational Geometry
Location estimation and uncertainty analysis for mobile robots
Autonomous robot vehicles
An optical rangefinder for autonomous robot cart navigation
Autonomous robot vehicles
Ray shooting in polygons using Geodesic triangulations
Proceedings of the 18th international colloquium on Automata, languages and programming
Triangulation and shape-complexity
ACM Transactions on Graphics (TOG)
Triangulating Simple Polygons and Equivalent Problems
ACM Transactions on Graphics (TOG)
Geometric probing
Planning the Motions of a Mobile Robot in a Sensory Uncertainty Field
IEEE Transactions on Pattern Analysis and Machine Intelligence
Optimal robot localization in trees
Proceedings of the twelfth annual symposium on Computational geometry
Localizing a robot with minimum travel
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Optimal robot localization in trees
Information and Computation
Visibility Queries in Simple Polygons and Applications
ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
A near-tight approximation lower bound and algorithm for the kidnapped robot problem
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Localization: approximation and performance bounds to minimize travel distance
IEEE Transactions on Robotics
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We consider the following problem: given a simple polygon P and a star-shaped polygon V, find a point (or the set of points) in P from which the portion of P that is visible is congruent to V. The problem arises in the localization of robots using a range-finder—P is a map of a known environment, V is the portion visible from the robot's position, and the robot must use this information to determine its position in the map. We give a scheme that preprocesses P so that any subsequent query V is answered in optimal time O(m + log n + A), where m and n are the number of vertices in V and P, and A is the number of points in P that are valid answers (the output size). Our technique allows us to trade off smoothly between the query time and the preprocessing time or space. We also devise a data structure for output-sensitive determination of the visibility polygon of a query point inside a polygon P. We then consider a variant of the localization problem in which there is a maximum distance to which the robot can “see”—this is motivated by practical considerations, and we outline a similar solution for this case. We also show that a single localization query V can be answered in time O(mn) with no preprocessing.