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The Zermelo-Voronoi Diagram: a dynamic partition problem

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2 Author(s)
Efstathios Bakolas ; School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, 30332-0150, USA ; Panagiotis Tsiotras

We consider a Dirichlet-Voronoi like partition problem for a small airplane operating in the horizontal plane in the presence of winds that vary uniformly with time. It is shown that the problem can be interpreted as a Dynamic Voronoi Diagram problem, where the generators are not fixed, but rather they are moving targets to be reached in minimum time. The problem is solved by reducing it to a standard Voronoi Diagram by means of a time-varying coordinate transformation.

Published in:

Proceedings of the 2010 American Control Conference

Date of Conference:

June 30 2010-July 2 2010