Exponential stabilization of second-order nonholonomic chained systems

Abstract

In this paper, an underactuated control method is considered for an X4-AUV with four thrusters and 6-DOFs. A second-order chained form transformation is introduced to the dynamical model by separating a system into three parts of controller model. Then, the Astolfi's discontinuous control method is applied to realize an underactuated control method to stabilize the system. This approach is motivated by the fact that the discontinuous dynamic model without using a chained form transformation assures only a local stability (or controllability) of the dynamic based control system, instead of guaranteeing a global stability of the system. A computer simulation is presented to demonstrate the effectiveness of our approach. © 2013 Springer-Verlag Berlin Heidelberg.