具有脉冲效应的系统稳定性分析:在双足机器人中的应用

Limei Liu, Yantao Tian, Peijie Zhang, Zhenze Liu
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引用次数: 0

摘要

给出了具有脉冲效应的非线性系统在不动点处庞加莱返回映射的近似雅可比矩阵。利用扰动理论和线性化方法,给出了该近似雅可比矩阵存在的充分条件。由于该近似表达式仅依赖于具有脉冲效应的系统的结构,因此可以保证该近似表达式的唯一性,并可以精确地得到该近似表达式。此外,该近似雅可比矩阵还可以作为研究脉冲作用下系统渐近稳定性的工具。由于双足机器人的步态可以用具有脉冲效应的非线性系统来描述,因此利用该工具可以研究双足机器人行走周期的稳定性。为了研究其稳定性,将该近似雅可比矩阵应用于类罗经被动双足机器人步态。结果表明,本文提出的近似雅可比矩阵与数值方法中提出的近似雅可比矩阵一样有用。最后通过仿真验证了这一结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An Analysis of Stability of Systems with Impulse Effects: Application to Biped Robots
The approximate Jacobian matrix of the Poincare return map at the fixed point is presented for the nonlinear system with impulse effects. And the sufficient condition to the existence of this approximate Jacobian matrix is given with the disturbance theory and linearization method. Since this approximate expression depends only on the configuration of the system with impulse effects, then the uniqueness of this approximate expression can be guaranteed and this approximate expression can be obtained precisely. In addition, this approximate Jacobian matrix can be used as a tool to study the asymptotical stability of the system with impulse effects. Since the biped robot gaits can be described by the nonlinear system with impulse effects, then the stability of the biped robot walking cycle can be studied with this tool. In order to study the stability, this approximate Jacobian matrix is applied to the compass-like passive biped robot gaits. It is shown that the approximate Jacobian matrix proposed in this paper is as useful as the ones proposed in the numerical methods. In the end this result is confirmed by simulations.
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