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首页> 外文期刊>IEEE Transactions on Automatic Control >Nonhomogeneous nilpotent approximations for nonholonomic systems with singularities
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Nonhomogeneous nilpotent approximations for nonholonomic systems with singularities

机译：具有奇异性的非完整系统的非齐次幂等逼近

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摘要

Nilpotent approximations are a useful tool for analyzing and controlling systems whose tangent linearization does not preserve controllability, such as nonholonomic mechanisms. However, conventional homogeneous approximations exhibit a drawback: in the neighborhood of singular points (where the system growth vector is not constant) the vector fields of the approximate dynamics do not vary continuously with the approximation point. The geometric counterpart of this situation is that the sub-Riemannian distance estimate provided by the classical Ball-Box Theorem is not uniform at singular points. With reference to a specific family of driftless systems, we show how to build a nonhomogeneous nilpotent approximation whose vector fields vary continuously around singular points. It is also proven that the privileged coordinates associated to such an approximation provide a uniform estimate of the distance.
机译：幂函数逼近是用于分析和控制切线线性化不能保持可控制性的系统（例如非完整机制）的有用工具。但是，常规的均质逼近具有一个缺点：在奇异点（系统增长矢量不是恒定的）附近，逼近动力学的矢量场不会随逼近点连续变化。这种情况的几何对应关系是，经典Ball-Box定理提供的次黎曼距离估计在奇异点处不一致。参考特定的无漂移系统族，我们展示了如何建立一个矢量场围绕奇异点连续变化的非齐次幂等逼近。还证明了与这种近似相关联的特权坐标提供了距离的统一估计。

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