https://confremo.hal.science/hal-00700932v2Jean, FrédéricFrédéricJeanOC - Optimisation et commande - UMA - Unité de Mathématiques Appliquées - ENSTA Paris - École Nationale Supérieure de Techniques AvancéesControl of Nonholonomic Systems and Sub-Riemannian GeometryHAL CCSD2012[MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG]Fardoun, AliSensitivity Analysis for Deterministic Controller Design - SADCO - - EC:FP7:PEOPLE2011-01-01 - 2014-12-31 - 264735 - VALID - 2012-09-20 16:15:402022-05-11 12:06:052012-09-20 16:46:10enConference papershttps://confremo.hal.science/hal-00700932v1application/pdf2Nonholonomic systems are control systems which depend linearly on the control. Their underlying geometry is the sub-Riemannian geometry, which plays for these systems the same role as Euclidean geometry does for linear systems. In particular the usual notions of approximations at the first order, that are essential for control purposes, have to be defined in terms of this geometry. The aim of these notes is to present these notions of approximation and their link with the metric tangent structure in sub-Riemannian geometry.