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# Stability of Coupled Hybrid Oscillators

#### *Proceedings of the IEEE International Conference on Robotics and Automation, Seoul, Korea*, January 2001

E. Klavins and D. E. Koditschek

Department of Electrical Engineering and Computer Science

University of Michigan

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Abstract |

We describe a method for the decentralized phase regulation of two coupled hybrid oscillators. In particular, we prove that the application of this synchronization method to two hopping robots, each of which individually achieves only asymptotically stable hopping, results in an asymptotically stable limit cycle for the coupled system exhibiting the desired phase difference. This extends our previous work wherein the application of the method to two individually deadbeat-stabilized oscillators (paddle juggling mechanisms) was shown to yield the desired result. Central to this method is the idea that cyclic systems may be composed into a larger, aggregate, cyclic system. Its application entails moving from physical coordinates (for example, the position and velocity of each constituent mechanism) to the coordinates of phase and phase velocity. Within this canonical coordinate system we construct a model dynamical system, called a reference field, which encodes the desired behavior of each cyclic system as well as the phase relationships between them. We then force the actual composite system to behave like the model. |

BibTeX entry |

@inproceedings{klavins-ICRA-2001,
author = "E. Klavins and D.E. Koditschek",
title = "Stability of Coupled Hybrid Oscillators",
booktitle = "Proceedings of the IEEE International Conference on Robotics and Automation, Seoul, Korea",
year = "2001"
} |