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2014 | OriginalPaper | Chapter

How to Run a Centipede: a Topological Perspective

Authors : Yuliy Baryshnikov, Boris Shapiro

Published in: Geometric Control Theory and Sub-Riemannian Geometry

Publisher: Springer International Publishing

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Abstract

In this paper we study the topology of the configuration space of a device with d legs (“centipede”) under some constraints, such as the impossibility to have more than k legs off the ground. We construct feedback controls stabilizing the system on a periodic gait and defined on a ‘maximal’ subset of the configuration space.
A centipede was happy quite!
Until a toad in fun
Said, “Pray, which leg moves after
which?”
This raised her doubts to such a pitch,
She fell exhausted in the ditch
Not knowing how to run.
Katherine Craster

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previous chapter Geometry of Maslov cycles
next chapter Geometric and numerical techniques to compute conjugate and cut loci on Riemannian surfaces
Appendix
Available only for authorised users
Literature
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Altendorfer, R., Moore, N., Komsuoglu, H., Brown Jr., H.B., McMordie, D., Saranli, U., Full, R., Koditschek, D.E.: RHex: A Biologically Inspired Hexapod Runner. Autonomous Robots (2001)
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Mumford, D.: Algebraic geometry I: Complex projective varieties. Reprint of the 1976 edition. Classics in Mathematics. Springer-Verlag, Berlin Heidelberg New York (1995)
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Sontag, E.: Stability and stabilization: discontinuities and the effect of disturbances. In: Nonlinear analysis, differential equations and control (Montreal, QC, 1998), 551-598 (1999)
Metadata
Title
How to Run a Centipede: a Topological Perspective
Authors
Yuliy Baryshnikov
Boris Shapiro
Copyright Year
2014
Publisher
Springer International Publishing
Book
Geometric Control Theory and Sub-Riemannian Geometry

Print ISBN: 978-3-319-02131-7

Electronic ISBN: 978-3-319-02132-4

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-319-02132-4_3

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