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A Method to Estimate the Basin of Attraction of the System with Impulse Effects: Application to the Biped Robots

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Intelligent Robotics and Applications (ICIRA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5314))

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Abstract

A new method is presented for the estimation of the basin of attraction of the system with impulse effects. This method is called Poincaré-like-alter-cell-to-cell mapping method. This method synthesizes and generalizes the theories of the simple cell mapping and the Poincaré mapping. Since the robustness of the system can be estimated by the size of the basin of attraction, then the optimal configurable parameter can be estimated by using this method. In the end, the basin of attraction of the simplest walking model is obtained with this method, when the mass proportion of upper legs and lower legs is increased. Simulation tests verify the validity of this method. The simulations show that the size of basin of attraction of the simplest walking model diminishes with increasing the configurable parameter that is mass proportion of upper legs and lower legs. In addition, the size of basin of attraction of the system with impulse effects is not directly related to the convergence rate of recovering from a small disturbance.

This work is supported by National High Technology Research and Development Program of China (863 Program), grant No. 2006AA04Z251, and Science and Technology Development Program of Ji lin Province, grant No. 20070524.

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Authors and Affiliations

  1. College of Communication Engineering, Ji lin University, Chang chun, 130025, China

    Limei Liu, Yantao Tian & Xiaoliang Huang

  2. Department of Mathematics of Chang chun Taxation College, Chang chun, 130117, China

    Limei Liu

Authors
  1. Limei Liu
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  2. Yantao Tian
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  3. Xiaoliang Huang
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Editor information

Editors and Affiliations

  1. School of Mechanical Science and Engineering, Huazhong University of Science and Technology, 430074, Wuhan, China

    Caihua Xiong , Yongan Huang  & Youlun Xiong ,  & 

  2. Institute of Industrial Research, University of Portsmouth, Burnaby Building, PO1 3QL, Portsmouth, UK

    Honghai Liu

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© 2008 Springer-Verlag Berlin Heidelberg

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Liu, L., Tian, Y., Huang, X. (2008). A Method to Estimate the Basin of Attraction of the System with Impulse Effects: Application to the Biped Robots. In: Xiong, C., Huang, Y., Xiong, Y., Liu, H. (eds) Intelligent Robotics and Applications. ICIRA 2008. Lecture Notes in Computer Science(), vol 5314. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88513-9_102

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  • DOI: https://doi.org/10.1007/978-3-540-88513-9_102

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88512-2

  • Online ISBN: 978-3-540-88513-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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