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Rank deficiency and superstability of hybrid systems with application to bipedal robots

Wendel, Eric and Ames, Aaron D. (2011) Rank deficiency and superstability of hybrid systems with application to bipedal robots. In: 2011 50th IEEE Conference on Decision and Control and European Control Conference. IEEE , Piscataway, NJ, pp. 7422-7427. ISBN 978-1-61284-801-3. https://resolver.caltech.edu/CaltechAUTHORS:20190220-110834216

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Abstract

The objectives of this paper are to study the rank properties of flows of hybrid systems, show that they are fundamentally different from those of smooth dynamical systems, and consider applications that emphasize the importance of these differences. In contrast with smooth dynamical systems, the rank of a solution to a hybrid system, a hybrid execution, is always less than the dimension of the space on which it evolves and falls within easily-computed and possibly distinct upper and lower bounds. Our main contribution is the derivation of conditions for when an execution fails to have maximal rank, i.e., when it is rank deficient. Given the importance of periodic behavior in many hybrid systems applications, for example in bipedal robots, these rank deficiency conditions are applied to the special case of periodic hybrid executions. Our secondary contribution is the derivation of superstability conditions for when a periodic execution has rank equal to 0 and is therefore completely insensitive to perturbations in initial conditions. The results are illustrated in application to a planar kneed biped.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/CDC.2011.6160972DOIArticle
ORCID:
AuthorORCID
Ames, Aaron D.0000-0003-0848-3177
Additional Information:© 2011 IEEE. This research is supported in part by NSF award CNS-0953823 and NHARP Award 000512-0184-2009.
Funders:
Funding AgencyGrant Number
NSFCNS-0953823
Norman Hackerman Advanced Research Program (NHARP)000512-0184-2009
Record Number:CaltechAUTHORS:20190220-110834216
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190220-110834216
Official Citation:E. Wendel and A. D. Ames, "Rank deficiency and superstability of hybrid systems with application to bipedal robots," 2011 50th IEEE Conference on Decision and Control and European Control Conference, Orlando, FL, 2011, pp. 7422-7427. doi: 10.1109/CDC.2011.6160972
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:93007
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:20 Feb 2019 19:18
Last Modified:03 Oct 2019 20:50

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