Topologically sweeping an arrangement
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Optimal point location in a monotone subdivision
SIAM Journal on Computing
Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
A new algebraic method for robot motion planning and real geometry
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Localizing a robot with minimum travel
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Robot Localization without Depth Perception
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
International Journal of Robotics Research
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We consider the problem posed by Sugihara of locating a robot in a planar environment containing n indistinguishable mark points. The robot takes k angular measurements between an unknown subset of mark points. When the robot has a compass, we show that all valid placements of the robot consistent with the measurements may be determined in O(kn^2) time and O(kn) space. When the robot does not have a compass, we show how to determine all valid placements in O(kn^3) time and O(kn) space. We show that with polynomial-time preprocessing both types of location queries can be answered in O(log n) time. For both cases we give bounds on the maximum number of valid placements. We also consider the case where there are image processing errors involved in the angle measurements.