Emergence of Complexity and Chaos via Symmetry Breaking in Coupled Engineering Systems.
Project/Area Number  13650251 
Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Dynamics/Control

Research Institution  KoBe 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)

Keywords  Z2symmetry / 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 D3Symmetry 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 D3symmetric solutions all oscillators behave identically. For Z2symmetry, 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 Z2symmetrical 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 2robot system has been studied. This system has Z2symmetry. 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 interrobot 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
(3results)
Research Products
(6results)