Transverse function approach to practical stabilisation of underactuated surface vessels with modelling uncertainties and unknown disturbances

This study addresses the problem of stabilising a desired trajectory (also referred to as the trajectory tracking problem) for underactuated surface vessels. The desired trajectory does not need to be a particular type (e.g. feasible trajectory) and can be any sufficiently smooth curve parameterised by time. To overcome difficulties caused by underactuation, the authors apply the transverse function approach to introduce an additional control input in backstepping design procedure. They give the calculation of transverse functions accordingly. To compensate for the effects of the external disturbances, they employ disturbance observer to estimate the unknown time-varying disturbances. Subsequently, disturbance-observer-based tracking control is designed that achieves practical stabilisation of any smooth reference trajectory (i.e. the vessel position and orientation tracking errors converge to a small neighbourhood of zero). A noticeable feature of the design technique is that the desired reference trajectory allows to be feasible or non-feasible. Besides the nominal case where exact knowledge of the vessel model is available, they also deal with scenarios wherein modelling uncertainties are present. The proposed control is robust not only to modelling uncertainties but also to external disturbances. Simulation studies are performed to demonstrate the effectiveness of the proposed design technique.