{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:00:30Z","timestamp":1787320830611,"version":"build-2736575974"},"reference-count":28,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2015,1]]},"abstract":"<jats: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.<\/jats:p>","DOI":"10.1137\/130950793","type":"journal-article","created":{"date-parts":[[2015,3,31]],"date-time":"2015-03-31T16:12:34Z","timestamp":1427818354000},"page":"816-844","source":"Crossref","is-referenced-by-count":5,"title":["Complexity of Control-Affine Motion Planning"],"prefix":"10.1137","volume":"53","author":[{"given":"F.","family":"Jean","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"D.","family":"Prandi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,3,31]]},"reference":[{"key":"atypb1","unstructured":"A. Agrachev, D. Barilari, and U. Boscain,\n                      Introduction to Riemannian and Sub-Riemannian Geometry\n                      , lecture notes, \\burlhttp:\/\/webusers.imj-prg.fr\/ davide.barilari\/Notes.php, 2012."},{"key":"atypb2","doi-asserted-by":"crossref","unstructured":"A. A. Agrachev and Y. L. Sachkov,\n                      Control Theory from the Geometric Viewpoint\n                      , Control Theory and Optimization II, Encyclopaedia Math. 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