A synergetic theory of quadrupedal gaits and gait transitions

Schöner, Gregor; Jiang, Wei; Kelso, J. A. Scott

doi:10.1016/s0022-5193(05)80558-2

Cited by 344 publications

(194 citation statements)

References 21 publications

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“…In this category we can count all the exploitation of synchronization, phase resetting etc. (such as in (Ermentrout & Kopell, 1994;Williamson, 1998;Ijspeert et al, 2005;Matsuoka, 1985Matsuoka, , 1987Schöner et al, 1990;Schöner & Kelso, 1988;Taga, 1994Taga, , 1995bTaga, , 1995aBuchli & Ijspeert, 2004a;22, 2003;Schöner & Santos, 2001;Santos, 2003Santos, , 2004Collins & Richmond, 1994;Endo et al, 2005)). As an example, in case of phase locking the oscillator is matching its frequency to the frequency of the input.…”

Section: Reactive: Temporary Entrainment and Shape Changesmentioning

confidence: 99%

“…Another way of designing phase relationship in networks of coupled oscillators is by help of the theory of symmetry, where the phase pattern can be achieved without the single oscillator satisfying necessarily the correct properties in the PRC/PS (Golubitsky & Stewart, 2006;Schöner et al, 1990;Righetti & Ijspeert, 2006a). However, even along with this method the consideration of the properties of the single oscillator helps to design non-frustrated systems, i.e.…”

Section: Reactive: Temporary Entrainment and Shape Changesmentioning

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: Reactive: Temporary Entrainment and Shape Changesmentioning

confidence: 99%

Section: Reactive: Temporary Entrainment and Shape Changesmentioning

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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“…This “exchangeability” property, conservation of the macroscopic coordination ensuring the function despite components changes, is also termed sometimes termed degeneracy. Edelman and Gally (2001) proposed that degeneracy is ubiquitous at all levels of organization of biological systems: “unlike redundancy, which occurs when the same function is performed by identical elements, degeneracy, which involves structurally different elements, may yield the same or different functions depending on the context in which it is expressed.” Using group symmetry arguments, Golubitsky et al (1999) (see Schöner et al, 1990) have shown that a whole class of specific neurophysiological systems can produce the same set of locomotion behaviors in various species, as long as they satisfy symmetric requirements. This means that the same behaviors can be achieved adaptively by a family of systems of interacting components.…”

Section: The Case For Topological Equivalencementioning

confidence: 99%

Challenges for the understanding of the dynamics of social coordination

Lagarde

2013

Front. Neurorobot.

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The way people interact can be examined by looking at the way they move relative to each other. Seeking the principles behind those interactions have consequences potentially related to any type of interpersonal function, far beyond the so-called “motor” processes typically associated with the study of movements, be it perceptive, cognitive, affective, pragmatic, or epistemic. Here, we present the way the framework of coordination dynamics define and addresses the interactive actions in a dyad. We first introduce the basics of pattern formation as the roots of the theoretical approach of coordination dynamics, and then the way this framework may contribute to establish a solution to classify behaviors. Thereafter we review promising empirical results on the dynamics of interpersonal coordination, and finally discuss were to go next to decipher the way the coordination between two people and the way each individual contribute may be disentangled.

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“…Thus, in the case of CPGs the importance of oscillatory behavior is clear and without doubt. Various models based on coupled oscillators have been suggested for quadruped locomotion ( [6,56,14]). Undulatory swimming in the leech [4], the lamprey [13], and other animals is controlled by a series of segmental oscillators [12].…”

Section: Introductionmentioning

confidence: 99%

An Introduction to Neural Oscillators

Ermentrout

1994

Neural Modeling and Neural Networks

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A synergetic theory of quadrupedal gaits and gait transitions

Cited by 344 publications

References 21 publications

Engineering entrainment and adaptation in limit cycle systems

Engineering entrainment and adaptation in limit cycle systems

Challenges for the understanding of the dynamics of social coordination

An Introduction to Neural Oscillators

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