| 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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| 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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