PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Low-discrepancy curves and efficient coverage of space
Subramanian Ramamoorthy, R. Rajagopal, Q. Ruan and L. Wenzel
In: Algorithmic Foundations of Robotics VII, Springer Tracts in Advanced Robotics, 2006, New York, USA.

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.

EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:4830
Deposited By:Subramanian Ramamoorthy
Deposited On:24 March 2009