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Journal Articles IEEE Transactions on Automatic Control Year : 2004

Nonhomogeneous nilpotent approximations for systems with singularities

Marilena Vendittelli
  • Function : Author
Giuseppe Oriolo
  • Function : Author
Frédéric Jean
Jean-Paul Laumond
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  • PersonId : 841546


Nilpotent approximations are a useful tool for analyzing and controlling systems whose tangent linearization does not preserve controllability, such as nonholonomic mechanisms. However, conventional homogeneous approximations exhibit a drawback: in the neighborhood of singular points (where the system growth vector is not constant) the vector fields of the approximate dynamics do not vary continuously with the approximation point. The geometric counterpart of this situation is that the sub-Riemannian distance estimate provided by the classical Ball-Box Theorem is not uniform at singular points. With reference to a specific family of driftless systems, we show how to build a nonhomogeneous nilpotent approximation whose vector fields vary continuously around singular points. It is also proven that the privileged coordinates associated to such an approximation provide a uniform estimate of the distance.
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Dates and versions

hal-00988934 , version 1 (09-05-2014)



Marilena Vendittelli, Giuseppe Oriolo, Frédéric Jean, Jean-Paul Laumond. Nonhomogeneous nilpotent approximations for systems with singularities. IEEE Transactions on Automatic Control, 2004, 49 (2), pp.261-266. ⟨10.1109/TAC.2003.822872⟩. ⟨hal-00988934⟩


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