Nonsmooth Analysis, Convex Analysis, and their Applications to Motion Planning

Howie Choset
Special Issue of the International Journal of Computational Geometry and Applications, , 1997


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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.

Notes
Associated Lab(s) / Group(s): Biorobotics

Text Reference
Howie Choset, "Nonsmooth Analysis, Convex Analysis, and their Applications to Motion Planning," Special Issue of the International Journal of Computational Geometry and Applications, , 1997

BibTeX Reference
@article{Choset_1997_2864,
   author = "Howie Choset",
   title = "Nonsmooth Analysis, Convex Analysis, and their Applications to Motion Planning",
   journal = "Special Issue of the International Journal of Computational Geometry and Applications",
   year = "1997",
}