=ADD=
=author=
Van Geem; Carl
=title=
Enclosing Robot Links by Superellipses and Superellipsoids
=number=
96-01
=year=
1996
=url=
ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1996/96-01.ps.gz
=abstract=
As a part of an approach for solving the robot
motion planning problem for robot arms, we want to
decide whether or not a link collides with an
obstacle for a given range of values for (some of)
the joint parameters. We want to use the so called
Roider Method for fast collision checking, and want
to  model the link by enclosing it by superellipses
(in 2 dimensional space) of by a superellipsoid (in
3 dimensional space).

\xpar
We show in this paper that it is possible to model
these swept areas using some elementary geometrical
and trigonometrical tools. We describe for all swept
volumes occuring for some robot arm topologies the
extreme points needed for the enclosure of solids by
a superellipse or by a superellipsoid. We also
compute the volume of the swept areas and of the
enclosing superellipse or superellipsoid. The rate
between these volumes is a measure for the accuracy
of the enclosure.
=location=
2
=owner=
2
=source=
3
=reftype=
14