Departmental Papers (ESE)


The zero dynamics of a hybrid model of bipedal walking are introduced and studied for a class of N-link, planar robots with one degree of underactuation and outputs that depend only on the configuration variables. Asymptotically stable solutions of the zero dynamics correspond to asymptotically stabilizable orbits of the full hybrid model of the walker. The Poincaré map of the zero dynamics is computed and proven to be diffeomorphic to a scalar, linear, time-invariant system, thereby rendering transparent the existence and stability properties of periodic orbits.

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Document Type

Conference Paper

Subject Area

GRASP, Kodlab

Date of this Version



BibTeX entry

@inproceedings{IFAC-2002, author = {E. Westervelt and J. Grizzle et al}, title = {Zero Dynamics of Planar Biped Walkers with One Degree of Under Actuation}, booktitle = {IFAC 2002, Barcelona, Spain}, year = {2002}, city = {Barcelona, Spain}, month = {July}, }

The work of J.W. Grizzle and E. Westervelt was supported in part by NSF grants
INT-9980227 and IIS-9988695, and in part by the University of Michigan Center
for Biomedical Engineering Research (CBER). The work of D.E. Koditschek was
supported in part by DARPA/ONR N00014–98–1−0747.



Date Posted: 19 February 2014

This document has been peer reviewed.