Departmental Papers (ESE)

Document Type

Conference Paper

Date of this Version

April 1997


Copyright 1997 IEEE. Reprinted from Proceedings of the IEEE International Conference on Robotics and Automation, Volume 3, 1997, pages 1986-1992.

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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.


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.



Date Posted: 03 June 2008

This document has been peer reviewed.