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Dynamic voronoi diagrams in motion planning

  • Thomas Roos
  • Hartmut Noltemeier
II Mathematical Programming II.1 Computational Geometry
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 180)

Abstract

Given a set of n points in the Euclidean plane each of which is continuously moving along a given trajectory. At each instant of time, these points define a Voronoi diagram which also changes continuously, except for certain critical instances — so-called topological events.

In [Ro 90], an efficient method is presented of maintaining the Voronoi diagram over time. Recently Guibas, Mitchell and Roos [GuMiRo 91] improved the trivial quartic upper bound on the number of topological events by almost a linear factor to the nearly cubic upper bound of O(n 2 λs,(n)) topological events, where λs(n)) is the maximum length of an (n, s)-Davenport-Schinzel sequence and s is a constant depending on the motion of the sites. Each topological event uses only O(log n) time (which is worst-case optimal).

Now in this work, we present a new algorithm for planning the motion of a disc in a dynamic scene of moving sites which is based on the corresponding sequence of Voronoi diagrams. Thereby we make use of the well-known fact, that locally the Voronoi edges are the safest paths in the dynamic scene. We present a quite simple approach combining local and global strategies for planning a feasible path through the dynamic scene.

One basic advantage of our algorithm is that only the topological structure of the dynamic Voronoi diagram is required for the computation. Additionally, our goal oriented approach provides that we can maintain an existing feasible path over time. This guarantees that we reach the goal if there is a feasible path in the dynamic scene at all. Finally our approach can easily be extended to general convex objects.

Keywords

Span Tree Topological Structure Voronoi Diagram Computational Geometry Euclidean Plane 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© International Federation for Information Processing 1992

Authors and Affiliations

  • Thomas Roos
    • 1
  • Hartmut Noltemeier
    • 1
  1. 1.University of WürzburgGermany

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