Control of a class of 1-generator nonholonomic system with drift through input-dependent coordinate transformation.

In this paper, a new control strategy for a class of 1-generator nonholonomic systems with drift is proposed: 1$$ \begin{gathered} y_1^{(k_1 )} = u_1 \hfill \\ y_2^{(k_2 )} = u_2 \hfill \\ y_3^{(k_3 )} = \ell _{31} (y_3 ,...,y_3^{(k_3 )} ) \hfill \\ + \ell _{32} (y_2 ,...,y_2^{(k_2 - 1)} ) \times \ell _g (u_1 ,y_1 ,...,y_1^{(k_1 - 1)} ) \hfill \\ \vdots \hfill \\ y_n^{(k_n )} = \ell _{n1} (y_n ,...,y_n^{(k_n )} ) \hfill \\ + \ell _{n2} (y_{n - 1} ,...,y_{n - 1}^{(k_{n - 1} - 1)} ) \times \ell _g (u_1 ,y_1 ,...,y_1^{(k_1 - 1)} ), \hfill \\ \end{gathered} $$ where each ℓ*(·) represents a homogeneous linear term. This system is an asymmetric affine nonholonomic system of the form x=f(x)+g(x)u with 1-generator controllability structure. including such as high-order chained form [5], underactuated surface vessel [4] and so on. [ABSTRACT FROM AUTHOR]