## 1 Introduction
In order to precisely estimate completely external disturbances and unknown dynamics, a finite-time tracking controller was presented for trajectory tracking in [19]. In addition, it improves the robustness and tracking accuracy of the control system. A finite-time sliding mode controller for an USV with model parametric uncertainties and external disturbances was presented in [20]. A path following controller based on a finite-time observer was proposed in [21], which only considers the large sideslip angle and external disturbances. However, the influence of position error constraints on vessel path following control are not considered. In [22], a fuzzy finite-time controller was proposed for the underactuated MSV, subject to external disturbances, parametric uncertainties, sideslip angle and actuator saturation in finite-time, but the position error constraint was not considered in the controller design. Therefore, considering the influence of position error constraint on path following controller, an FT-LOS guidance law was designed by introducing time-varying BLF into the design process of LOS guidance law. Based on the above observations, this paper presents a finite-time path following control scheme for the underactuated MSV under the conditions of position constraint, external disturbances, model parameter uncertainties, and actuator saturation. The main contributions and superiority of this paper are summarized as follows:  
1. A finite-time line-of-sight (FT-LOS) guidance law is designed by integrating a time-varying BLF into the classical LOS guidance law design process. The proposed FT-LOS guidance law can ensure that the position errors will not exceed the error constraints, and converge into a small neighborhood around zero in finite time. 2. The finite-time attitude constraint controller and the finite-time velocity constraint controller are designed to achieve tracking control in finite time. A command filter is designed to eliminate the complex calculation of the virtual control law. 3. The finite-time disturbance observers are proposed to reduce the compound disturbance. In addition the finite-time input saturation compensators are designed to avoid the actuator saturation and satisfy the finite-time convergence requirement. 4. The stability analysis shows that the proposed finite-time path following control algorithm can strictly guarantee the constraint requirement of the position, and all error signals of the whole closed-loop control system can converge into a small neighborhood around zero in finite time. Comparative simulation results illustrate the effectiveness and superiority of the proposed finite-time control scheme. The rest of this paper is arranged as follows. Section 2 presents the preliminaries and problem formulation. The finite-time path following control algorithm is proposed in Section 3, consisting of the FT-LOS guidance law design, the finite-time attitude constraint controller design, and the finite-time velocity constraint controller design. Section 4 analyses the stability of the whole closed-loop control system. Comparative simulation results are shown and analyzed in Section 5 to demonstrate the effectiveness and superiority of the proposed finite-time path following control algorithm. Finally, the conclusions are shown in Section 6.