2013 Fiscal Year Final Research Report
The construction of infinite dimensional singularity theory of completely non-integrable systems and its applications to the singular motion-planning problem
| Project/Area Number |
23654058
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Global analysis
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| Research Institution | Hokkaido University |
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Principal Investigator |
ISHIKAWA Goo 北海道大学, 理学(系)研究科(研究院), 教授 (50176161)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 特異トラジェクトリ / 制御系 / 終点写像 |
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| Research Abstract |
For generic polynomial control-affine systems, we have several results on the general properties that singular paths possess. We have the characterization of singular paths for the G2 Cartan systems, which are important also in classical differential geometry.
We have studied the approximation problem of arbitrary path by a singular path and several ideas on the applications to singular motion-planning problem. We have analyzed the singularity theory of mappings on infinite dimensional manifolds associated to completely non-integrable systems and applied to concrete singular motion-planning problems. From the viewpoint of infinite dimensional sub-Riemannian geometry, we have tried to formulate the basic theory on singular points of mapping spaces with constraints. Moreover we have the new insights on the dependence of systems of vector fields, which will defy known results.
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