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首页> 外文期刊>Applied Mathematical Modelling >A new Poincare map for investigating the complex walking behavior of the compass-gait biped robot
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A new Poincare map for investigating the complex walking behavior of the compass-gait biped robot

机译：用于调查罗盘 - 步态的复杂行走机器人的新庞纳罗地图

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摘要

The planar compass-gait biped robot is recognized by its simple passive morphological structure and by a complex dynamic walking system modeled by an impulsive hybrid nonlinear dynamics. Such complexity inhibits investigating the biped locomotive mechanism by means of the Poincare map. Nevertheless, it is very difficult (and even impossible) to establish the exact closed form of the Poincare mapping. This paper is concerned with the development of an improved closed-form analytical expression of the impact-to-impact Poincare map for analyzing the complex walking behavior of the passive-dynamics biped walker and its stability. Our methodology consists in linearizing and then approximating the hybrid dynamics of the compass-gait biped robot around a predefined hybrid limit cycle. Based on the second-order Taylor series expansion, we design first an enhanced closed-form expression of the Poincare map as well as an analytical expression for the computation of the step period of the bipedal locomotion. Furthermore, a simplification of these developed expressions is presented by decreasing the dimension. We provide also an expression of the Jacobian matrix for investigating the stability of the period-1 fixed point of the designed simplified Poincare map. At the end of this work, we illustrate some simulation results in order to evaluate the validity of the new developed expression of the impact-to-impact Poincare map in analyzing the stability and the complex walking behavior of passive-dynamics compass biped robot.
机译：平面罗盘 - 步态双方机器人被其简单的被动形态结构和由脉冲混合非线性动力学建模的复杂动态行走系统识别。这种复杂性通过Poincare地图抑制了研究了搭配机车机制。尽管如此，它非常困难（甚至不可能）建立庞加雷映射的确切封闭形式。本文涉及开发改进的封闭式庞内华地图的分析表达，用于分析被动动力学伴侣的复杂行走行为及其稳定性。我们的方法包括线性化，然后近似于围绕预定义的混合限制循环映射罗盘步态的混合动力学。基于二阶泰勒系列扩展，我们设计了庞加雷地图的增强封闭式表达，以及分析表达式，用于计算双面运动的步进阶段。此外，通过降低尺寸来提出这些发育表达式的简化。我们还提供了雅可比矩阵的表达，用于调查设计的简化庞纳罗地图的时期-1定点的稳定性。在这项工作结束时，我们说明了一些仿真结果，以评估冲击庞的庞然保罗地图的新发达表达的有效性分析了被动动力学罗盘双方机器人的稳定性和复杂的走路行为。

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  • 来源
    《Applied Mathematical Modelling》 |2021年第6期|534-557|共24页
  • 作者

    Wafa Znegui; Hassene Gritli; Safya Belghith;

  • 作者单位

    Laboratory of Robotics Informatics and Complex Systems (RISC Lab - LR16ES07) National Engineering School of Tunis Universite de Tunis El Manar BP. 37 Le Belvedere 1002 Tunis Tunisia;

    Laboratory of Robotics Informatics and Complex Systems (RISC Lab - LR16ES07) National Engineering School of Tunis Universite de Tunis El Manar BP. 37 Le Belvedere 1002 Tunis Tunisia Higher Institute of Information and Communication Technologies Universite de Carthage Tunis 1764 Borj Cedria Tunisia;

    Laboratory of Robotics Informatics and Complex Systems (RISC Lab - LR16ES07) National Engineering School of Tunis Universite de Tunis El Manar BP. 37 Le Belvedere 1002 Tunis Tunisia;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Compass-gait biped robot; Impulsive hybrid nonlinear system; Quadratic Taylor polynomial; Closed-form Poincaremap; Chaos and bifurcation; Stability;

    机译：指南针 - 步态Biped机器人;脉冲混合非线性系统;二次泰勒多项式;封闭式poincaremap;混乱和分叉;稳定;

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