01202nas a2200133   4500008004100000245004900041210004800090300001200138490000700150520084200157100001300999700001801012856003801030       2015                        eng d00aComplexity of Control-Affine Motion Planning0 aComplexity of ControlAffine Motion Planning  a816-8440 v533 a<p>In this paper 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 (or sub-Riemannian) 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. Due to the lack of time-rescaling invariance of these systems, we consider geometric and parametrized curves separately. Then, we give some asymptotic estimates for these quantities. As a byproduct, we are able to treat the long time local controllability problem, giving quantitative estimates on the cost of stabilizing the system near a nonequilibrium point of the drift.</p>1 aJean, F.1 aPrandi, Dario  uhttps://doi.org/10.1137/130950793