The construction of infinite dimensional singularity theory of completely non-integrable systems and its applications to the singular motion-planning problem

完全不可积系统无限维奇点理论的构建及其在奇异运动规划问题中的应用

• 批准号: 23654058
• 负责人: ISHIKAWA Goo
• 金额: $ 2.25万
• 依托单位: Hokkaido University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Challenging Exploratory Research
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23654058/
• 关键词: 特異トラジェクトリ; 制御系; 終点写像; 特異パス

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.

对于通用多项式控制膜系统，我们在单数路径所具有的一般特性上有几个结果。我们对G2 cartan系统的奇异路径的表征也很重要，在经典的差异几何学中也很重要。我们研究了通过单数路径的任意路径的近似问题，以及关于奇异运动规划问题的应用的几个想法。我们已经分析了与完全不可融合系统相关的无限维歧管上映射的奇异性理论，并应用于具体的奇异运动规划问题。从无限尺寸次摩曼尼亚几何形状的角度来看，我们试图在绘制空间的奇异点上制定基本理论。此外，我们对向量场系统的依赖性有了新的见解，这将无视已知结果。

项目成果

Generic bifurcations of framed curves in a space form and their envelopes

• DOI: 10.1016/j.topol.2011.09.024
• 发表时间: 2010-02
• 期刊: arXiv: Differential Geometry
• 作者: G. Ishikawa

Duality of singular paths for (2,3,5)-distributions

(2,3,5)-分布的奇异路径的对偶性

• DOI: 10.1007/s10883-014-9216-9
• 发表时间: 2014
• 期刊: Journal of Dynamical and Control Systems
• 影响因子: 0.9
• 作者: G. Ishikawa;Y. Kitagawa;W. Yukuno
• 通讯作者: W. Yukuno

Sigularities of tangent varieties to curves and surfaces

曲线和曲面的切线品种的奇异性

• DOI: 10.5427/jsing.2012.6f
• 发表时间: 2012
• 期刊: Journal of Singularities
• 影响因子: 0.4
• 作者: T. Adachi;Y. Giga;T. Hishida;Y. Kagei;K. Kozono;T. Ogawa;Shinya Nishibata;Makoto Nakamura;Yusuke Yamauchi;Goo Ishikawa
• 通讯作者: Goo Ishikawa

幾何学的制御理論から観たCartan 分布の特異パス双対性

几何控制理论视角下嘉当分布的奇异路径对偶性

• 发表时间: 2013
• 作者: G.Ishikawa;Y.Machida;M.Takahashi;Sumio Yamada;石川剛郎
• 通讯作者: 石川剛郎

Singularities of tangent surfaces in Cartan's split G2-geometry

嘉当分裂 G2 几何中切面的奇点

• DOI: 10.4310/ajm.2016.v20.n2.a6
• 发表时间: 2016
• 期刊: Asian Journal of Mathematics
• 影响因子: 0.6
• 作者: Goo Ishikawa;Yoshinori Machida;Masatomo Takahashi
• 通讯作者: Masatomo Takahashi