Counting the number of connected components of a set and its application to robotics

Authors:
Nicolas Delanoue;Luc Jaulin;Bertrand Cottenceau
Affiliations:
Laboratoire d'Ingénierie des Systèmes Automatisés, LISA FRE 2656 CNRS, Université d'Angers, Angers;Laboratoire E–3I–2, ENSIETA, Brest;Laboratoire d'Ingénierie des Systèmes Automatisés, LISA FRE 2656 CNRS, Université d'Angers, Angers
Venue:
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
Year:
2004

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Abstract

This paper gives a numerical algorithm able to compute the number of path-connected components of a set $\mathbb{S}$ defined by nonlinear inequalities. This algorithm uses interval analysis to create a graph which has the same number of connected components as $\mathbb{S}$. An example coming from robotics is presented to illustrate the interest of this algorithm for path-planning.