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

Abstract

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
Pages78-89
Number of pages12
DOIs
Publication statusPublished - 2012

Publication series

SeriesLecture Notes in Computer Science
Volume7718

Cite this

Disser, Y., Mihalák, M., Ghosh, S. K., & Widmayer, P. (2012). Mapping a polygon with holes using a compass. In Proceedings of the 8th International Symposium on Algorithms for Sensor Systems, Wireless Ad Hoc Networks and Autonomous Mobile Entities (Algosensors) (pp. 78-89). Springer Verlag. Lecture Notes in Computer Science, Vol.. 7718 https://doi.org/10.1007/978-3-642-36092-3_9