Nonhomogeneous nilpotent approximations for nonholonomic systems with singularities

@article{Vendittelli2004NonhomogeneousNA,
  title={Nonhomogeneous nilpotent approximations for nonholonomic systems with singularities},
  author={Marilena Vendittelli and Giuseppe Oriolo and Fr{\'e}d{\'e}ric Jean and Jean-Paul Laumond},
  journal={IEEE Transactions on Automatic Control},
  year={2004},
  volume={49},
  pages={261-266}
}
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… CONTINUE READING
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