Characteristic numbers and normal form for a class of driftlesssystems in a one-dimension sub-manifold neighborhood

摘要

From the works of Murray and Sastry (1993) sufficient conditionsto transform a driftless system into a so-called one chained form arewell known. Some of these conditions are the involutivity of specificdistributions, which may be too restrictive. Thus in this paper, inorder to relax theses conditions, we use the higher-order techniqueintroduced by Krener (1984). A quadratic normal form is found fordriftless system. Moreover, we give conditions in order to transform,due to homogeneous feedback and diffeomorphism, the system into achained form at least up to the third order in an approximated state andinputs meaning