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Abstract
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We study the topology of configuration spaces
of two thick particles
(robots) of radius moving
on a metric graph .
As the size of the robots increases, the topology of
varies.
Given
and ,
we provide an algorithm for computing the number of path components of
. Using our
main tool of PL Morse–Bott theory, we show that there are finitely many critical values of
where the
homotopy type of
changes. We study the transition across a critical value
by computing the ranks of the relative homology groups of
.
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Keywords
topology of configuration spaces, metric graph, PL
topology, topological robotics
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Mathematical Subject Classification 2010
Primary: 55R80, 57Q05
Secondary: 57M15
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Publication
Received: 23 October 2010
Revised: 15 March 2011
Accepted: 26 April 2011
Published: 14 June 2011
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