Flatness of heavy chain systems
Flatness of heavy chain systems
复制标题
重链系统的平坦度
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
P. Rouchon
中科院分区：
文献类型：
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作者：
N. Petit;P. Rouchon
本文综述了Petit和Rouchon(2001)的结果。此外，它还包含一些以前未发表的关于承载载荷的均质链的材料。本文在偏导数方程的框架下讨论了重链系统的平坦度问题，即小车承载固定长度的可承载重链的问题。利用系统自由端的运动轨迹对系统的运动轨迹进行参数化，解决了运动规划问题，即从一个状态转向另一个状态。当考虑为有限个小摆的集合时，这些系统在Murray(1996)中被证明是平坦的。我们的研究是无限维情形的推广。在小角度近似下，这些重链系统可用一维偏微分波方程来描述。在处理这种无限维描述时，我们展示了如何利用链轨迹自由端的(分布的和准时的)推进和延迟来获得链轨迹的显式参数化。
This paper gives an overview of the results of Petit and Rouchon (2001). Furthermore it contains some previously unpublished material concerning the homogeneous chain carrying a load. In the above paper the flatness of heavy chain systems, i.e. trolleys carrying a fixed length heavy chain that may carry a load, is addressed in the partial derivatives equations framework. We parameterize the system trajectories by the trajectories of its free end and solve the motion planning problem, namely steering from one state to another state. When considered as a finite set of small pendulums these systems were shown to be flat in Murray (1996). Our study is an extension to the infinite dimensional case. Under small angle approximations, these heavy chain systems are described by a 1D partial differential wave equation. Dealing with this infinite dimensional description, we show how to get the explicit parameterization of the chain trajectory using (distributed and punctual) advances and delays of its free end.