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Intelligent analysis of chaos roughness in regularity of walk for a two legged robot

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  • Kaygisiz, Burak H.
  • Erkmen, Ismet
  • Erkmen, Aydan M.

Abstract

We describe in this paper a new approach to the identification of the chaotic boundaries of regular (periodic and quasiperiodic) regions in nonlinear systems, using cell mapping equipped with measures of fractal dimension and rough sets. The proposed fractal-rough set approach considers a state space divided into cells where cell trajectories are determined using cell to cell mapping technique. All image cells in the state space, equipped with their individual fractal dimension are then classified as being members of lower approximation, upper approximation or boundary region of regular regions with the help of rough set theory. The rough set with fractal dimension as its attribute is used to model the uncertainty of the regular regions, treated as sets of cells in this paper. This uncertainty is then smoothed by a reinforcement learning algorithm in order to enrich regular regions that are used for control. Our approach is applied to the walking control of a two legged robot, which fails very frequently due to chaotic behavior.

Suggested Citation

  • Kaygisiz, Burak H. & Erkmen, Ismet & Erkmen, Aydan M., 2006. "Intelligent analysis of chaos roughness in regularity of walk for a two legged robot," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 148-161.
    • Handle: RePEc:eee:chsofr:v:29:y:2006:i:1:p:148-161
    DOI: 10.1016/j.chaos.2005.08.047
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    References listed on IDEAS

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    1. Pawlak, Zdzislaw, 1997. "Rough set approach to knowledge-based decision support," European Journal of Operational Research, Elsevier, vol. 99(1), pages 48-57, May.
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    1. Gritli, Hassène & Belghith, Safya, 2018. "Walking dynamics of the passive compass-gait model under OGY-based state-feedback control: Rise of the Neimark–Sacker bifurcation," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 158-168.
    2. Gritli, Hassène & Belghith, Safya, 2017. "Walking dynamics of the passive compass-gait model under OGY-based state-feedback control: Analysis of local bifurcations via the hybrid Poincaré map," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 72-87.

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