2014 Fiscal Year Final Research Report
Research on the topological complexity of robot motion planning
| Project/Area Number |
22540091
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | University of the Ryukyus |
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Principal Investigator |
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| Project Period (FY) |
2010-04-01 – 2015-03-31
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| Keywords | ロボット運動 / 配置空間 / 位相的複雑さ / 多角形のモジュライ空間 / クモの巣装置 / モーメント角複体 / ボット・モース関数 / パーフェクト関数 |
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| Outline of Final Research Achievements |
As a topological invariant which describes motion planning of a robot effectively, we study the topological complexity. The moduli space of polygons and arachnoid mechanism are typical examples of robots. We constructed a robot which unifies these robots. Then we defined a function on it. Our main theorems assert that the function is a Bott-Morse function. Using the Bott-Morse theory, we obtained results from which the known results follow immediately, for example, the Euler characteristic formula. Since there are close connections between the critical points of a Morse function and the topological complexity, we can deduce fruitful information on the topological complexity of the new robot.
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| Free Research Field |
数物系科学
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