@article {doi:10.1137/130950793,
	title = {Complexity of Control-Affine Motion Planning},
	journal = {SIAM Journal on Control and Optimization},
	volume = {53},
	number = {2},
	year = {2015},
	pages = {816-844},
	abstract = {<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>},
	doi = {10.1137/130950793},
	url = {https://doi.org/10.1137/130950793},
	author = {Jean, F. and Dario Prandi}
}
