In this paper, we present an iterative steering algorithm for nonholonomic systems (also called driftless control-affine systems) and we prove its global convergence under the sole assumption that the Lie Algebraic Rank Condition (LARC) holds true everywhere. That algorithm is an extension of the one introduced in Jean et al. (2005) [21] for regular systems. The first novelty here consists in the explicit algebraic construction, starting from the original control system, of a lifted control system which is regular. The second contribution of the paper is an exact motion planning method for nilpotent systems, which makes use of sinusoidal control laws and which is a generalization of the algorithm described in Murray and Sastry (1993) [29] for chained-form systems.
This work was supported by grants from Digiteo and Région Ile-de-France, by the ANR project GCM, program “Blanche”, project number NT09_504490, and by the Commission of the European Communities under the 7th Framework Program Marie Curie Initial Training Network (FP7-PEOPLE-2010-ITN), project SADCO, contract number 264735.