Dynamic Hebbian learning in adaptive frequency oscillators

Righetti, Ludovic; Buchli, Jonas; Ijspeert, Auke Jan

doi:10.1016/j.physd.2006.02.009

Cited by 294 publications

(253 citation statements)

References 20 publications

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“…(2) DynamicallyHere the relevant parameters are turned into state variables and a dynamic law in form of ODEs has to be found that will tune the system into the required dynamics. This is very recent research with oscillators (early work (Ermentrout, 1991;Nishii, 1998Nishii, , 1999, more recent (Buchli & Ijspeert, 2004b;Righetti et al, 2006)). We only call such systems adaptive, since they combine the to be exploited dynamics and the adaptation process into a single dynamical system.…”

Section: On-line Adaptationmentioning

confidence: 90%

“…There are some investigations on adaptation of parameters (frequency, others), e.g. in (Nishii, 1999;Large, 1994;Buchli & Ijspeert, 2004b;Righetti et al, 2006). …”

Section: Adaptation: Lasting Changes To the Dynamicsmentioning

confidence: 99%

“…An example is introduced in (Buchli & Ijspeert, 2004b) and analyzed in detail in (Righetti et al, 2006) where a Hopf oscillator (Eqs. 30-31) is enhanced with a evolution law for the frequency ω in the following waẏ…”

Section: Adaptation: Lasting Changes To the Dynamicsmentioning

confidence: 99%

“…It would of course be interesting to exploit such substrates for engineering applications. algorithmic dynamic algorithmic dynamic (Ermentrout & Kopell, 1994) R 1a (Williamson, 1998) R 1a R 1a (Matsuoka, 1985(Matsuoka, , 1987 R 1a (Schöner, Jiang, & Kelso, 1990) R 1a (Schöner & Kelso, 1988) R 1a (Endo et al, 2005) R 1a (Morimoto et al, 2006) R 1a (Righetti & Ijspeert, 2006a) R 1b (Taga, 1994(Taga, , 1995b(Taga, , 1995a R 1a (Buchli & Ijspeert, 2004a) R 1a (22, 2003 R 1a (Schöner & Santos, 2001;Santos, 2003Santos, , 2004 R 1a (Collins & Richmond, 1994) R 1a (Ijspeert, 2001) R 1a/2 (Zegers & Sundareshan, 2003) R 2b (Okada, Tatani, & Nakamura, 2002;Okada, Nakamura, & Nakamura, 2003) R 2a (Ijspeert, Nakanishi, & Schaal, 2002) R 2b (Ruiz, Owens, & Townley, 1998) R 2 (Galicki, Leistritz, & Witte, 1999;Leistritz, Galicki, Witte, & Kochs, 2002) R 2 (Righetti & Ijspeert, 2006b) R 1a/2b (Marbach & Ijspeert, 2005) A 1a (Nishii, 1999) A 1c/1a (Ermentrout, 1991) A 1c (Large, 1994(Large, , 1996 A 1a 1c (Buchli & Ijspeert, 2004b;Righetti, Buchli, & Ijspeert, 2006;Buchli, Righetti, & Ijspeert, 2005;Buchli et al, 2006) A 1c Table 3 Table classifying …”

Section: Adaptation: Lasting Changes To the Dynamicsmentioning

confidence: 99%

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Engineering entrainment and adaptation in limit cycle systems

2006

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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 modelling 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 two-fold: (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 which might at first sight appear very different from each other. We identify several specifications that are useful for design, such as frequency-locking behavior, phaselocking behavior, and specific output signal shape. We also identify two classes of design methods by which these specifications can be met, namely off-line methods and on-line 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 modelling of physical or biological phenomena.

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Section: On-line Adaptationmentioning

confidence: 90%

“…There are some investigations on adaptation of parameters (frequency, others), e.g. in (Nishii, 1999;Large, 1994;Buchli & Ijspeert, 2004b;Righetti et al, 2006). …”

Section: Adaptation: Lasting Changes To the Dynamicsmentioning

confidence: 99%

Section: Adaptation: Lasting Changes To the Dynamicsmentioning

confidence: 99%

Section: Adaptation: Lasting Changes To the Dynamicsmentioning

confidence: 99%

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Engineering entrainment and adaptation in limit cycle systems

2006

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“…In this work we combined a learning rule [4] With the Matsuoka oscillator, and we have made an adaptive oscillator that can learn arbitrary periodic signals in a supervised learning framework very fast and it is completely embedded into the dynamical system, and does not require any external regression or optimization algorithms, or any preprocessing of the teaching signal. Then, we used a CPG with this adaptive oscillator for learning to walk a humanoid robot.…”

Section: Introductionmentioning

confidence: 99%

A System for Learning to Locomotion Using Adaptive Oscillators in the Humanoid Robot

Saif¹

2011

IJCTE

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Abstract-This paper proposes a central pattern generators based control architecture using a frequency adaptive oscillator for learning to locomotion of humanoid robot. Central pattern generators are biological neural networks that can produce coordinated multidimensional rhythmic signals, under the control of simple input signals. They are found both in vertebrate and invertebrate animals for the control of locomotion. In this article, we present a novel system composed of adaptive nonlinear oscillators that can learn arbitrary rhythmic signals in a supervised learning framework, and apply it to control a simulated humanoid robot with up to 22 degrees of freedom. A key feature of the proposed architecture is that the learning is completely embedded in to the dynamical control, and does not require external optimization algorithms. As a test bed, we chose Robocup 3D soccer simulation environment (spark). Experimental results show that learn to walk of the robot could be successfully performed, thus allowing the biped robot to walk fast, stable and straightly.

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A Dynamical Systems Approach to Learning: A Frequency-Adaptive Hopper Robot

Buchli

Righetti

Ijspeert

2005

Advances in Artificial Life

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Abstract. We present an example of the dynamical systems approach to learning and adaptation. Our goal is to explore how both control and learning can be embedded into a single dynamical system, rather than having a separation between controller and learning algorithm. First, we present our adaptive frequency Hopf oscillator, and illustrate how it can learn the frequencies of complex rhythmic input signals. Then, we present a controller based on these adaptive oscillators applied to the control of a simulated 4-degrees-of-freedom spring-mass hopper. By the appropriate design of the couplings between the adaptive oscillators and the mechanical system, the controller adapts to the mechanical properties of the hopper, in particular its resonant frequency. As a result, hopping is initiated and locomotion similar to the bound emerges. Interestingly, efficient locomotion is achieved without explicit inter-limb coupling, i.e. the only effective inter-limb coupling is established via the mechanical system and the environment. Furthermore, the self-organization process leads to forward locomotion which is optimal with respect to the velocity/power ratio.

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Dynamic Hebbian learning in adaptive frequency oscillators

Cited by 294 publications

References 20 publications

Engineering entrainment and adaptation in limit cycle systems

Engineering entrainment and adaptation in limit cycle systems

A System for Learning to Locomotion Using Adaptive Oscillators in the Humanoid Robot

A Dynamical Systems Approach to Learning: A Frequency-Adaptive Hopper Robot

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