# Collision Avoidance Using Finite Control Set Model Predictive Control for Unmanned Surface Vehicle
## 1 Introduction  
As a device for monitoring the marine environment, protecting marine rights and modern military weapons, the unmanned surface vehicle (USV) has a wide range of application prospects and has become a hot research topic for intelligent ships [1]. In the complex marine environment conditions, dynamically autonomous collision avoidance is the premise and foundation for the USV to navigate safely and successfully accomplish the assigned tasks [2]. It is also one of the key research contents of the automatic decision-making in USV intelligent control technology. In recent years, some scholars's research interest in the development of USV has increased. Collision avoidance is one of the major areas in this field. With the development of research, more and more papers rely on the real environment. [PERSON] et al. used the finite angle A-Star algorithm (FAA*) to solve the path planning problem of USV in real satellite thermal images [3]. [PERSON] et al. suggested a grid map-based on the Theta* algorithm to create paths in real-time, considering both the yaw rate and course angle of USV [4]. Combining global path planning with local path planning, the shortcut Dijkstra algorithm and modified artificial potential field (APF) algorithm were used for the vessel's navigation in [5]. After, [6] improved the global path planning, that is the artificial potential field-ant colony optimization (APF-ACO) obstacle-avoidance algorithm. Based on the Voronoi diagram and Fermat's spiral, [7] produced the path in real time, which steered the vessel course by an indirect adaptive line-of-sight (LOS) guidance algorithm. [PERSON] integrated obstacle detection, risk assessment and path planning (avoidance) tasks. The detection system is based on a vision-LiDAR (light detection and ranging) system, and the Rule-based Repairing A-Star (R-RA*) algorithm is adopted in pathplanning [8]. [PERSON] et al. [9] completed the task of safe maritime autonomous navigation by using the velocity obstacles (VO) method. The environmental information of the works in [3; 4; 5; 6] was obtained from satellite images, and that of [8; 9] from cameras or sonar. As previously mentioned, although many papers choose satellite images, some invisible information, such as reefs, ocean depth, and so on, does not exist. The observing ability of cameras and sonar will also be affected by light and shocks, resulting in their small observation range and low accuracy. Therefore, the paper is based on the environmental information from the electronic chart. Generally, the collision avoidance system (CAS) requires the vessel to finish the task safely, stably and rapidly, i.e., attainability, safety, stability and rapidity [2]. For high speed USV, [10] proposed a local reaction avoidance method. However, we find that the realization of CAS is divided into path planning and the control system. If the control and planning are combined into an algorithm, the real-time performance of the algorithm will be greatly improved to meet the needs of collision avoidance for USV. Therefore, we need an approach that employs ideas from optimization-based control and that can take into account the motion characteristics of the vessel. Model predictive control (MPC) is increasingly being applied to vehicle navigation problems [11; 12]. It has been combined with path planning to achieve online stability and robustness [13; 14]. This was accomplished by the constant re-planning path process at each time, then applying the initial control related to the chosen trajectory to the vehicle [15]. In the literature on robust MPC, the concept of optimization of a finite control set is well known, e.g., [15; 16]. The finite control set model predictive control (FCS-MPC) algorithm has the advantages of direct control and easy handling of system constraints [17; 18; 19]. In [18], the collision avoidance of a ship was realized with MPC. Compared with ordinary ships, USV have a smaller volume and faster speed, so their CAS should have better responsiveness and stability.