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Characterization of Monoped Equilibrium Gaits

Proceedings of the IEEE International Conference on Robotics and Automation, April 1997

William J. Schwind and Daniel E. Koditschek
Department of Electrical Engineering and Computer Science, University of Michigan
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       We characterize equilibrium gaits of a small knee monoped in terms of manifest parameters by recourse to approximate closed form expressions. We first eliminate gravity during stance and choose a very special model of potential energy storage in the knee. Next, we introduce simple closed form approximations, motivated by the mean value theorem, to the elliptic integrals arising in the more general case. In so doing, we derive a conjectured generalization applicable to small knee monopeds with an arbitrary knee potential. Finally, we introduce a new closed form perturbation intended to adjust the approximate coordinate transformations to the presence of gravity. Simulation data is offered as evidence for the efficacy (to within roughly 5–10% accuracy) of both the proposed generalization across knee potentials and the proposed perturbation for the presence of gravity during stance.
BibTeX entry
  author       = "William J. Schwind and Daniel E. Koditschek",
  title        = "Characterization of Monoped Equilibrium Gaits",
  booktitle    = "Proceedings of the IEEE International Conference on Robotics and Automation",
  year         = "1997",
Copyright 1997 IEEE. Reprinted from Proceedings of the IEEE International Conference on Robotics and Automation, Volume 3, 1997, pages 1986–1992.
This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania’s products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
NOTE: At the time of publication, author Daniel Koditschek was affiliated with the University of Michigan. Currently, he is a faculty member in the Department of Electrical and Systems Engineering at the University of Pennsylvania.

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