A Discontinuous Exponential Stabilization of Chained form System for an X4-AUV

In this paper, stabilization of a class of second-order nonholonomic systems for an underactuated X4-AUV is investigated. We present a model of the underactuated X4-AUV with six degrees of freedom (DOF) and four control inputs. Then, the system is written in a control-affine form by applying a partial linearization technique, and a dynamic controller based on Astolfi’s discontinuous control is derived to stabilize all states of the system to the desired equilibrium point exponentially. The present approach does not necessitate the conversion of the system model into a “chained form”, and thus does not rely on any special transformation techniques to obtain a canonical form. A simulation is conducted to demonstrate the effectiveness of the proposed controlle