Engineering entrainment and adaptation in limit cycle systems - From biological inspiration to applications in robotics
Engineering entrainment and adaptation in limit cycle systems - From biological inspiration to applications in robotics
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DOI：
10.1007/s00422-006-0128-y
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发表时间：
2006-12-01
影响因子：
1.9
通讯作者：
Ijspeert, Auke Jan
中科院分区：
文献类型：
--
作者：
Buchli, Jonas;Righetti, Ludovic;Ijspeert, Auke Jan
周期性行为是生命的关键，在我们的新陈代谢、自然环境和工程环境中的多个实例和多个时间尺度上都可以观察到。建模或生成周期性行为的自然方式是通过使用振荡器来完成的，即，表现出极限环行为的动力系统。虽然有大量的文献的方法来分析这样的动力系统，少得多的工作已经做的方法来合成一个振荡器，表现出一些特定的期望的特性。本文的目标是双重的：（1）提供一个表征和设计振荡器的框架和（2）审查如何类知名的振荡器可以理解和相关的框架。该框架的基础是根据振荡器的基本时间和空间行为以及这两种行为可以被设计为表现出的属性来表征振荡器。这种对基本性质的关注是很重要的，因为它使我们能够系统地比较大量的振荡器，这些振荡器乍一看可能彼此非常不同。我们确定了几个对设计有用的规格，例如频率锁定行为，相位锁定行为和特定的输出信号形状。我们还确定了两类设计方法，这些规格可以满足，即离线方法和在线方法。通过将这些规范与我们的框架相关联，并通过介绍文献中如何设计振荡器的几个例子，本文为设计各种用途的振荡器提供了有用的方法和工具箱。特别是，集中在极限环动力系统的合成应该是有用的工程和计算建模的物理或生物现象。
\Periodic behavior is key to life and is observed in multiple instances and at multiple time scales in our metabolism, our natural environment, and our engineered environment. A natural way of modeling or generating periodic behavior is done by using oscillators, i.e., dynamical systems that exhibit limit cycle behavior. While there is extensive literature on methods to analyze such dynamical systems, much less work has been done on methods to synthesize an oscillator to exhibit some specific desired characteristics. The goal of this article is twofold: (1) to provide a framework for characterizing and designing oscillators and (2) to review how classes of well-known oscillators can be understood and related to this framework. The basis of the framework is to characterize oscillators in terms of their fundamental temporal and spatial behavior and in terms of properties that these two behaviors can be designed to exhibit. This focus on fundamental properties is important because it allows us to systematically compare a large variety of oscillators that might at first sight appear very different from each other. We identify several specifications that are useful for design, such as frequency-locking behavior, phase-locking behavior, and specific output signal shape. We also identify two classes of design methods by which these specifications can be met, namely offline methods and online methods. By relating these specifications to our framework and by presenting several examples of how oscillators have been designed in the literature, this article provides a useful methodology and toolbox for designing oscillators for a wide range of purposes. In particular, the focus on synthesis of limit cycle dynamical systems should be useful both for engineering and for computational modeling of physical or biological phenomena.