Low-discrepancy curves and efficient coverage of space

Subramanian Ramamoorthy, Ram Rajagopal, Qing Ruan, Lothar Wenzel

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We introduce the notion of low-discrepancy curves and use it to solve the problem of optimally covering space. In doing so, we extend the notion of low-discrepancy sequences in such a way that sufficiently smooth curves with low discrepancy properties can be defined and generated. Based on a class of curves that cover the unit square in an efficient way, we define induced low discrepancy curves in Riemannian spaces. This allows us to efficiently cover an arbitrarily chosen abstract surface that admits a diffeomorphism to the unit square. We demonstrate the application of these ideas by presenting concrete examples of low-discrepancy curves on some surfaces that are of interest in robotics.
Original languageEnglish
Title of host publicationAlgorithmic Foundation of Robotics VII
Subtitle of host publicationSelected Contributions of the Seventh International Workshop on the Algorithmic Foundations of Robotics
PublisherSpringer Berlin Heidelberg
Pages203-218
Number of pages16
ISBN (Electronic)978-3-540-68405-3
ISBN (Print)978-3-540-68404-6
DOIs
Publication statusPublished - 2008

Publication series

NameSpringer Tracts in Advanced Robotics
PublisherSpringer Berlin Heidelberg
Volume47
ISSN (Print)1610-7438

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