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\title{Complexity of control-affine motion planning}
\author{Fr\'{e}d\'{e}ric Jean}
\institute{ENSTA ParisTech}
\email{frederic.jean@ensta-paristech.fr}
\coauthor{Dario Prandi, LSIS Universit\'{e} de Toulon} % comment out if not needed

\mymaketitle

\section{Abstract}
In this talk we study the complexity of the motion planning problem for control-affine
systems. Such complexities are already defined and rather well-understood in the particular case
of nonholonomic systems. Our aim is to generalize these notions and results
to systems with a drift. Accordingly, we present various definitions of complexity as functions of
the curve that is approximated and of the precision of the approximation. These functions appear as value functions of some optimal control problems with state constraints. Note that due to the lack of time-rescaling
invariance of the control-affine systems, we consider geometric and parameterized curves separately.
Then, we give some asymptotic estimates for these quantities.

\paragraph{Acknowledgments}
This work was supported by the Commission of the European Communities
under the 7th Framework Programme Marie Curie Initial Training
Network (FP7-PEOPLE-2010-ITN), project SADCO, contract number
264735, and by the European Research Council, ERC StG 2009 GeCoMethods,
contract number 239748.


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