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

耦合工程系统中对称性破缺导致复杂性和混沌的出现。

基本信息

批准号：
13650251
负责人：
MUREITHI Njuki
金额：
$ 2.11万
依托单位：
KoBe University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2002
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13650251/
关键词：
Z2-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

项目摘要

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.

具有D3对称性的无源耦合网络是以前研究过的。初始条件的变化表明，动力学与完整的D3对称性以及对称性破缺Z2和O（无对称性）也发生。对于D3-对称解，所有振子的行为相同。对于Z2对称性，两个振子的行为相同，而3^<rd>振子的行为与其他两个不同。在最后一种情况下，每个振荡器的行为与其他两个不同。重要的发现是，复杂的动力学是由原系统的对称性决定的。最近，一个主动网络的合作机器人进行了研究。机器人行为可以通过马尔可夫决策过程（MDP）来描述。在对称性存在的情况下，最优值函数也是对称的。所有由对称性相关的状态都映射到同一个状态。类似地，对称动作与同一动作相关。因此，有效的MDP可以显著降低。在Z2对称状态的情况下，MDP减小了其原始大小的一半。利用这种对称性，可以提高学习速度。多个相同的（对称的）机器人通过交换信息来提高学习速度。研究了一个两机器人系统。该系统具有Z2对称性。识别问题中的对称性是相当复杂的。在我们的分析中，机器人被设计为“固有地”识别环境中的对称性。相同的机器人也表明机器人之间的对称性。我们的研究结果证实，对称的机器人在对称的环境中导致对称的MDP。更重要的是，它表明，考虑对称性，机器人学习（在对称环境中的导航）是更快的对称性时，被认为是。