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Emergence of Complexity and Chaos via Symmetry Breaking in Coupled Engineering Systems.

Research Project

Project/Area Number 13650251
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Dynamics/Control
Research InstitutionKoBe University

Principal Investigator

MUREITHI Njuki  Kobe University, Faculty of engineering Associate Professor, 工学部, 助教授 (60294196)

Project Period (FY) 2001 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 2002: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2001: ¥2,400,000 (Direct Cost: ¥2,400,000)
KeywordsZ2-symmetry / Markov Decision Process MDP / Optimal Value Function / state symmetry / action symmetry / symmetrical MDP / Transition function / passive network / Oitimal Value Function / 学習ロボット / 対称性 / 励振系ネットワーク / ロボットのタスク / 対称的MDP
Research Abstract

A passive coupled network having D3-Symmetry was previously studied. Changes in initial conditions showed that dynamics with the full D3 symmetry as well as symmetry breaking to Z2 and O (no symmetry) also occurred. For D3-symmetric solutions all oscillators behave identically. For Z2-symmetry, two oscillators behave identically which the 3^<rd> oscillator behaves differently from the other two. In the last case, each oscillator behaved differently from the other two. The important finding was that the complex dynamics are determined by the symmetry of the original system. Recently an active network of cooperating robots is studied. Robot behavior may be described by a Markov Decision Process (MDP). In the presence symmetry, the Optimal Value Function is also Symmetrical. All states related by symmetry are mapped to the same single state. Similarly, symmetrical actions are related to the same action. Thus, the effective MDP can be drastically reduced. In the case of Z2-symmetrical states, the MDP is reduced half its original size. Exploiting such symmetry, learning speeds can be increased. Multiple identical (symmetrical) robots increase learning speed by exchanging information. A 2-robot system has been studied. This system has Z2-symmetry. Identifying symmetry in a problem is quite complex. In our analysis, a robot is designed to 'inherently' identify symmetry in the environment. Identical robots also indicate inter-robot symmetry. Our results confirm that symmetrical robots in a symmetrical environment lead to a symmetrical MDP. More importantly it is shown that considering symmetry, Robot learning (in the navigation of a symmetrical environment) is much faster when symmetry is considered.

Report

(3 results)
  • 2002 Annual Research Report   Final Research Report Summary
  • 2001 Annual Research Report
  • Research Products

    (6 results)

All Other

All Publications (6 results)

  • [Publications] Mureithi N: "Symmetry breaking and mode-interaction in vortex-structure interaction"Proc. ASME-IMECE 2002. 1-11 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Mureithi N: "Symmeliy breaking and mode-interaction in vortex-strcture interaction"Proc.ASME-IMECE. 1-11 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Mureithi N.: "Symmetry breaking and mode-interaction in vortex-structure interaction"Proc. ASME-IMECE 2002. (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Mureithi N.W.: "Multi-Agent Exploration via Reduced Symmetrical MDP"Autonomous Robots. (準備中). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] Mureithi N.: "Multi-Agent Exploration and Cooperation Exploiting MDP Symmetry"Motion and Vibration Control, MOVIC 2002. (発表予定). (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] Mureithi N.: "Symmetry Breaking Bifurcations in 2 and 3-Oscillator Networks"Nonlinear Dynamics. (準備中). (2002)

    • Related Report
      2001 Annual Research Report

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Published: 2001-04-01   Modified: 2021-04-07  

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