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

对于一般多项式控制仿射系统，我们有几个结果的一般性质，奇异路径拥有。我们给出了G_2 Cartan系统的奇异路径的特征，这在经典微分几何中也是很重要的，我们研究了任意路径的奇异路径逼近问题，以及在奇异运动规划问题中应用的一些想法。我们分析了与完全不可积系统相关的无穷维流形上映射的奇异性理论，并将其应用于具体的奇异运动规划问题。本文从无穷维次黎曼几何的观点出发，试图建立关于约束映射空间奇点的基本理论。此外，我们有新的见解的依赖系统的向量场，这将违背已知的结果。

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.