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From stable to chaotic juggling: theory, simulation, and experiments

International Conference on Robotics and Automation, May 1990

Martin Buehler and D. E. Koditschek
Electrical Engineering, Yale University

Full PDF | Scholarly Commons

Abstract
      Robotic tasks involving intermittent robot-environment interactions give rise to return maps defining discrete dynamicalsystems that are, in general, strongly nonlinear. In our work on robotic juggling, we encounter return maps for which a global stability analysis has heretofore proven intractable. At the same time, local linear analysis has proven inadequate for any practical purposes.
      In this paper we appeal to recent results of dynamical systems theory to derive strong predictions concerning the global properties of a simplified model of our planar juggling robot. In particular, we find that the local (linearized) stability properties determine the essential global (nonlinear) stability properties, and that successive increments in the controller gain settings give rise to a cascade of stable period doubling bifurcations that comprise a “universal route to chaos”. The theoretical predictions are first verified via simulation and subsequently corroborated by experimental data from the juggling robot.
BibTeX entry
@inproceedings{buehler_ICRA_1990,
  author       = {Martin Buehler and Dan E. Koditschek},
  title        = {From stable to chaotic juggling: theory, simulation, and experiments},
  booktitle    = {IEEE International Conference on Robotics and Automation},
  year         = {1990},
  volume       = {3},
  pages        = {1976--1981},
  month        = {May}
}

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