%0 Journal Article %J SIAM Journal on Control and Optimization %D 2015 %T Complexity of Control-Affine Motion Planning %A Jean, F. %A Dario Prandi %X

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.

%B SIAM Journal on Control and Optimization %V 53 %P 816-844 %G eng %U https://doi.org/10.1137/130950793 %R 10.1137/130950793