Research on the topological complexity of robot motion planning
Project/Area Number |
22540091
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Geometry
|
Research Institution | University of the Ryukyus |
Principal Investigator |
|
Project Period (FY) |
2010-04-01 – 2015-03-31
|
Project Status |
Completed (Fiscal Year 2014)
|
Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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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 / ボット・モース / 臨界多様体 / 指数 / 黄金比 / 内接球 / コホモロジー環 / イデアル / 高さ / 微分同相写像 / 正二面体群 / 表現空間 / レフシェッツの不動点公式 / ユークリッド体積 / 正多面体 / 商空間 / ホモロジー / ガウス・ボンネの定理 / 多角形 / モース関数 / パーフェクト |
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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Report
(6 results)
Research Products
(17 results)