According to the model uncertainties problem of an underactuated autonomous underwater vehicle(AUV) and
the enviromental current disturbances problem, in order to achieve the three-dimensional path tracking control of the
underactuated AUV, the space movement error model is established based on virtual guidance method. The discrete-time
sliding mode predictive controller is designed based on recursive sliding mode designing theory. Feedback correction and
receding horizon optimization approaches are employed to compensate the influence of uncertainties for the sliding mode
predictive model. Finally, space curve tracking simulation experiment is carried out by an underactuated AUV. The simulation
results show that the designed controller can overcome the influence of time-varying nonlinear hydrodynamic damping to the
control system, even the proposed control scheme has better effect on attenuating the external current disturbances. Thus the
robustness of three-dimensional path following system is guaranteed and the tracking control with high tracking precision
can be achieved.