Programming Research Group
Research Report RR-01-13
Sensor-based motion planning in SE(2) and SE(3) via nonsmooth analysis
Shawn Rusaw
August 2001, 21pp.
Abstract
We study the sensor-based motion planning problem using the concepts of
weak slope and generalised gradient from nonsmooth
analysis. We give a nonsmooth analysis of the pointwise minima
function Fmin(x) = mini {fi(x)} where each
of the fi(x) are nonsmooth and non-convex, and in particular present
a method to determine critical points of Fmin(x). We present a
detailed nonsmooth analysis of the distance function of a free-floating body
in SE(3) and SE(3) and use this to develop a novel algorithm for navigating in
unknown environments for SE(2).
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