Nonsmooth Analysis, Convex Analysis, and their Applications to Motion Planning
Journal Article, International Journal of Computational Geometry and Applications: Special Issue on Selected Papers from the 1st CGC Workshop on Computational Geometry, Vol. 9, No. 4, pp. 447 - 469, August, 1997
Abstract
Nonsmooth analysis of a broad class of functions taking the form $F(x) = min_i f_i(x)$, where each $f_i$ is a convex function. One element of this class of functions is the distance function, which measures the distance between a point and the nearest point on the nearest obstacle. Many motion planning algorithms are based on the distance function, and thus rigorous analysis of the distance function can provide a better understanding of how to implement traditional motion planning algorithms. Finally, this paper enumerates some useful results in convex analysis.
BibTeX
@article{Choset-1997-16477,author = {Howie Choset},
title = {Nonsmooth Analysis, Convex Analysis, and their Applications to Motion Planning},
journal = {International Journal of Computational Geometry and Applications: Special Issue on Selected Papers from the 1st CGC Workshop on Computational Geometry},
year = {1997},
month = {August},
volume = {9},
number = {4},
pages = {447 - 469},
}
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