Transactions of the Institute of Systems, Control and Information Engineers
Online ISSN : 2185-811X
Print ISSN : 1342-5668
ISSN-L : 1342-5668
Stability of a Wheel with Various Radius Rim
Tetsuya KinugasaKoji Yoshida
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2009 Volume 22 Issue 3 Pages 116-122


This paper describes the dynamics and impact model of a wheel with various radius rim. The dynamics is expressed by a rst order linear ordinary dierential equation with respect to the absolute orientation of the wheel, and an analytic solution is derived. Poincaré map is also derived analytically. Stability and basin of attraction (BoA) of the Poincaré map are discussed. Finally, the analysis is validated through some numerical simulations. As a result, the rim radius aects the stability and broadens its BoA. The analysis helps understanding of not only a geometric tracking control but also many underactuated control methods for bipeds.

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© 2009 The Institute of Systems, Control and Information Engineers
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