Flat outputs of two-input driftless control systems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 3, pp. 774-798.

We study the problem of flatness of two-input driftless control systems. Although a characterization of flat systems of that class is known, the problems of describing all flat outputs and of calculating them is open and we solve it in the paper. We show that all x-flat outputs are parameterized by an arbitrary function of three canonically defined variables. We also construct a system of 1st order PDE's whose solutions give all x-flat outputs of two-input driftless systems. We illustrate our results by describing all x-flat outputs of models of a nonholonomic car and the n-trailer system.

DOI : 10.1051/cocv/2011181
Classification : 93B27, 93C10, 93C95
Mots-clés : control system, flatness, flat output, feedback equivalence, characteristic distribution, n-trailer system 
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Li, Shun-Jie; Respondek, Witold. Flat outputs of two-input driftless control systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 3, pp. 774-798. doi : 10.1051/cocv/2011181. http://www.numdam.org/articles/10.1051/cocv/2011181/

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