Abstract
A multiplicatively weighted crystal growth Voronoi diagram is a type of planar segmentation diagram that can result when crystals grow at different speeds from several points. In this paper, we first define a multiplicatively weighted crystal growth Voronoi diagram, discuss its properties, and find the analytic solution for the simple case. The approximate solution method for the complex case is constructed by using a difference method for partial differential equations called the fast marching method. Then the multiplicatively weighted crystal growth Voronoi diagram is used to construct a technique for optimum path planning of competing mobile robots.
| Original language | English |
|---|---|
| Pages (from-to) | 21-31 |
| Number of pages | 11 |
| Journal | Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi) |
| Volume | 85 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 2002 Jun 1 |
| Externally published | Yes |
Keywords
- Competing robots
- Crystal growth model
- Fast marching method
- Multiplicatively weighted Voronoi diagram
- Robot path planning
ASJC Scopus subject areas
- Electrical and Electronic Engineering
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Cite this
Kobayashi, K., & Sugihara, K. (2002). Approximation of multiplicatively weighted crystal growth voronoi diagram and its application. Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi), 85(6), 21-31. https://doi.org/10.1002/ecjc.1098