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Efficient, incremental coverage of space with a continuous curve

Published online by Cambridge University Press:  01 July 2008

Subramanian Ramamoorthy ,
Ram Rajagopal  and
Lothar Wenzel
Subramanian Ramamoorthy*
Affiliation:
School of Informatics, The University of Edinburgh, Scotland, UK.
Ram Rajagopal
Affiliation:
Department of Electrical Engineering and Computer Sciences, The University of California at Berkeley, Berkeley, CA, USA.
Lothar Wenzel
Affiliation:
Mathematics and Signal Processing Group, National Instruments Corp., Austin, TX, USA.
*
*Corresponding author. E-mail: [email protected]
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Summary

This paper is concerned with algorithmic techniques for the incremental generation of continuous curves that can efficiently cover an abstract surface. We introduce the notion of low-discrepancy curves as an extension of the notion of low-discrepancy sequences—such that sufficiently smooth curves with low-discrepancy properties can be defined and generated. We then devise a procedure for lifting these curves, that efficiently cover the unit cube, to abstract surfaces, such as nonlinear manifolds. We present algorithms that yield suitable fair mappings between the unit cube and the abstract surface. We demonstrate the application of these ideas using some concrete examples of interest in robotics.

Keywords

space coveragelow-discrepancy curvenonlinear manifold
Type
Article
Information
Robotica , Volume 26 , Special Issue 4: Geometry in Robotics: Sensing , July 2008 , pp. 503 - 512
Copyright
Copyright © Cambridge University Press 2008

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