Repeated impacts on a sinusoidally vibrating table reappraised

Bapat, C.N.; Sankar, S.; Popplewell, N.

doi:10.1016/s0022-460x(86)80314-5

Cited by 35 publications

(33 citation statements)

References 6 publications

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“…The input considered in this paper is a sinusoidal vibration on both edges, directly inspired by the extensively studied bouncing ball system (Holmes, 1982;Guckenheimer and Holmes, 1986;Bapat et al, 1986). A ball bouncing on a sinusoidally vibrating The square wedge billiard (α = 1) is a very special case of the general wedge billiard.…”

Section: A Bouncing Ball Approximation Of the Vibrating Square Wedge mentioning

confidence: 99%

“…This inequality holds if a "small amplitude" assumption is made. (Bapat et al, 1986) studied and quantified this assumption. Significant differences between the exact and the approximated model are more likely if e is below about 0.8, but the approximated model provides a good description of the qualitative dynamical behavior.…”

Section: A Bouncing Ball Approximation Of the Vibrating Square Wedge mentioning

confidence: 99%

“…(Sternad, 1999) proposed a comparison between human juggling and a 1D impact dynamical process amenable to mathematical analysis, i.e. the celebrated bouncing ball model, extensively studied in the literature (Holmes, 1982;Guckenheimer and Holmes, 1986;Bapat et al, 1986). Her team explored deeply the human abilities to exploit the open-loop stable solutions inherent to the bouncing ball dynamics with a sinusoidal vibration as control input (Schaal et al, 1996;Sternad et al, 2001a;Sternad et al, 2001b).…”

Section: Introductionmentioning

confidence: 99%

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Open-Loop stabilization of 2d impact juggling

Ronsse

Lefèvre

Sepulchre

2004

IFAC Proceedings Volumes

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The paper studies the properties of a sinusoidally vibrating wedge billiard as a model for 2D impact juggling. It is shown that some periodic orbits that are unstable in the elastic fixed wedge become exponentially stable in the (non-)elastic vibrating wedge. These orbits are linked with some classical juggling patterns, providing an interesting benchmark for the study of the frequency-locking properties in human rhythmic tasks.

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Section: A Bouncing Ball Approximation Of the Vibrating Square Wedge mentioning

confidence: 99%

Section: A Bouncing Ball Approximation Of the Vibrating Square Wedge mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Open-Loop stabilization of 2d impact juggling

Ronsse

Lefèvre

Sepulchre

2004

IFAC Proceedings Volumes

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“…Sensorless open-loop control is efficient for the simplest juggling pattern, revealing a 2D analogy with the stable bouncing ball under sinusoidal actuation (Bapat et al, 1986;Guckenheimer & Holmes, 1986;Holmes, 1982). However, when considering more complex periodic patterns, the predicted basin of attraction of the stabilized orbit is small and the experimental implementation is not robust, due to large uncertainties of the real setup not accounted for in the model.…”

Section: Resultsmentioning

confidence: 99%

“…A further simplification of Wiper's dynamics is of interest to connect the model with the popular 1D bouncing ball model (Bapat, Sankar, & Popplewell, 1986;Guckenheimer & Holmes, 1986;Holmes, 1982). Assuming an orthogonal wedge angle and parallel actuations of the edges (that is, the two edges are assumed to remain aligned with the two orthogonal axes of Fig.…”

Section: Wiper: An Experimental Setup Amenable To Mathematical Modelingmentioning

confidence: 99%

Robotics and neuroscience: A rhythmic interaction

2008

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a b s t r a c tAt the crossing between motor control neuroscience and robotics system theory, the paper presents a rhythmic experiment that is amenable both to handy laboratory implementation and simple mathematical modeling. The experiment is based on an impact juggling task, requiring the coordination of two upper-limb effectors and some phase-locking with the trajectories of one or several juggled objects. We describe the experiment, its implementation and the mathematical model used for the analysis. Our underlying research focuses on the role of sensory feedback in rhythmic tasks. In a robotic implementation of our experiment, we study the minimum feedback that is required to achieve robust control. A limited source of feedback, measuring only the impact times, is shown to give promising results. A second field of investigation concerns the human behavior in the same impact juggling task. We study how a variation of the tempo induces a transition between two distinct control strategies with different sensory feedback requirements. Analogies and differences between the robotic and human behaviors are obviously of high relevance in such a flexible setup.

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1992

Chaotic and Fractal Dynamics

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Repeated impacts on a sinusoidally vibrating table reappraised

Cited by 35 publications

References 6 publications

Open-Loop stabilization of 2d impact juggling

Open-Loop stabilization of 2d impact juggling

Robotics and neuroscience: A rhythmic interaction

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