Stabilization of an Underactuated X4-AUV Using a Discontinuous Control Law

Abstract

In this paper, stabilization of a class of second-order nonholonomic systems in canonical chained form is investigated. We first derive the dynamic model of an underactuated X4-AUV with six degrees-of-freedom (DOF) and four thrusters using Lagrange approach. Then the system is written in control-affine form by applying a partial linearization technique and a dynamic controller based on Astolfi’s discontinuous control is derived by using transformations of coordinate and input to obtain locally asymtotically stable response. A simulation is conducted to demonstrate the effectiveness of the present approach to controlling the origin of the system.