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 |
| Externally published | Yes |
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Keywords
- Competing robots
- Crystal growth model
- Fast marching method
- Multiplicatively weighted Voronoi diagram
- Robot path planning
ASJC Scopus subject areas
- Electrical and Electronic Engineering
Cite this
Approximation of multiplicatively weighted crystal growth voronoi diagram and its application. / Kobayashi, Kei; Sugihara, Kokichi.
In: Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi), Vol. 85, No. 6, 06.2002, p. 21-31.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Approximation of multiplicatively weighted crystal growth voronoi diagram and its application
AU - Kobayashi, Kei
AU - Sugihara, Kokichi
PY - 2002/6
Y1 - 2002/6
N2 - 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.
AB - 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.
KW - Competing robots
KW - Crystal growth model
KW - Fast marching method
KW - Multiplicatively weighted Voronoi diagram
KW - Robot path planning
UR - http://www.scopus.com/inward/record.url?scp=0036604844&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0036604844&partnerID=8YFLogxK
U2 - 10.1002/ecjc.1098
DO - 10.1002/ecjc.1098
M3 - Article
AN - SCOPUS:0036604844
VL - 85
SP - 21
EP - 31
JO - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)
JF - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)
SN - 1042-0967
IS - 6
ER -