Mapping a polygon with holes using a compass

Yann Disser, Matús Mihalák, Subir Kumar Ghosh, Peter Widmayer

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review


We consider a simple robot inside a polygon \mathcal{p}\mathcal{p} with holes. The robot can move between vertices of \mathcal{p}\mathcal{p} along lines of sight. When sitting at a vertex, the robot observes the vertices visible from its current location, and it can use a compass to measure the angle of the boundary of \mathcal{p}\mathcal{p} towards north. The robot initially only knows an upper bound \bar{n}\bar{n} on the total number of vertices of \mathcal{p}\mathcal{p}. We study the mapping problem in which the robot needs to infer the visibility graph g vis of \mathcal{p}\mathcal{p} and needs to localize itself within g vis. We show that the robot can always solve this mapping problem. To do this, we show that the minimum base graph of g vis is identical to g vis itself. This proves that the robot can solve the mapping problem, since knowing an upper bound on the number of vertices was previously shown to suffice for computing g vis.
Original languageEnglish
Title of host publicationProceedings of the 8th International Symposium on Algorithms for Sensor Systems, Wireless Ad Hoc Networks and Autonomous Mobile Entities (Algosensors)
PublisherSpringer Verlag
Number of pages12
Publication statusPublished - 2012
Externally publishedYes

Publication series

SeriesLecture Notes in Computer Science


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