# An Automatic Navigation System for Unmanned Surface Vehicles in Realistic Sea Environments
## 1 Introduction
[PERSON] used a robust neural control algorithm to follow the path generated by the DVS [19]. [PERSON] adopted a double-loop indirect track-keeping control structure with the Proportional-Integral-Derivative (PID) control algorithm [22]. Nevertheless, these studies focused solely on path-following or trajectory-tracking algorithms, and these algorithms assume the impossibility of collisions during the tracking process [5]. The failure or delay of the guidance system will cause the USV to lose the collision avoidance ability. In consequence, it is important for USVs to adopt the collision avoidance control algorithm in the CAS. To date, the collision avoidance control algorithm has been developed in mobile robots [23], unmanned vehicles [24; 25], and unmanned aerial vehicles (UAVs) [26], but there are few studies on USVs. A CAS for USVs emerged in relevant literature [8], in which the fuzzy estimator method was developed for collision avoidance control. The method is able to avoid collision with a change of course. However, collision avoidance not only needs to change the course, but also the speed needs to be adjusted. Model predictive control (MPC), which combines path planning with on-line stability and convergence guarantees, is increasingly being applied to collision avoidance problem [27]. One significant study can be found in the work undertaken by [PERSON] [28], who applied MPC in the CAS of ship with a simple external environment. However in contrast to ordinary ships, considering that USVs have the characteristics of high speed and smaller volume, the CAS needs shorter computation times and stronger robustness. Finite control set model predictive control (FCS-MPC) is used as the collision avoidance control algorithm, and has advantages such as fast dynamic response, optimal control of multiple objectives, inherent decoupling, and easy inclusion of nonlinear constraints [29]. To improve the autonomy of USVs, an ANS with a PPS (dynamic domain tunable fast marching square, DTFMS) and CAS (FCS-MPC) is proposed in this paper. The main contributions of this paper can be summarized in five main points. Firstly, the proposed DTFMS method is able to construct a potential map from a real electronic chart, where both static and dynamic obstacles are well represented. To represent the dynamic obstacles, the algorithm adds the dynamic domain models of own and target vessels into the planning space, and the domain models can be changed according to vessel motion states and updated environment times. Secondly, the proportion of the safe area in potential maps can be adjusted by \(Saturation\) to assess security and path length. Thirdly, using the potential map from the DTFMS method, a collision-free smooth path can be generated which can be used as dynamic target points of the CAS. Fourthly, a fast and safe CAS is proposed based on FCS-MPC, and it has the ability for trajectory tracking and local collision avoidance for underactuating USVs. Meanwhile, to fully evaluate the safety of the predicted trajectories, its security evaluation comes from the potential map of the DTFMS method. Finally, the simulations are undertaken in a realistic sea environment with three types of encounter situations, and the target vessels have the possibility of changing their course, which is similar to the practical context. The rest of the paper is organized as follows. Section 2 introduces the structure of the USV system. Section 3 describes the static environment modeling and path planning method. Section 4 establishes the mathematical model of the USV and designs the CAS based on FCS-MPC. In Section 5, the DTFMS method is proposed for path re-planning in a dynamic environment. In Section 6, the ANS is verified in the simulation and real environments, and their results are compared in the dynamic and static cases. Finally, Section 7 gives the conclusions on the system and identifies future works on the ANSs of USVs.