## 1 Introduction  
An unmanned surface vehicle (USV) is an autonomous surface vehicle capable of conducting port patrols and performing special maritime tasks, and has been intensively researched by various countries in recent years [1, 2]. A USV is required to perform autonomous avoidance of obstacles on the sea during its maritime tasks, so autonomous collision avoidance control technology has been one of the key technologies for USV research [3]. Recently, some researchers have performed more research on the technology of USV collision avoidance. A motion collision avoidance algorithm for a USV in a dynamic and complex environment has been proposed, which is realized based on the velocity obstacle method and combined with the rules of collision avoidance at sea, so as to complete the autonomous collision avoidance of the USV [4]. In [5], the angular velocity and linear velocity of a USV in the collision avoidance process are calculated, and the angular velocity buffer model is introduced, so as to ensure stable output and realize the avoidance of local static obstacles. A layered collision avoidance method is designed in [6]. The velocity obstacle method and the improved artificial potential field method are used to solve the collision avoidance problem for a USV under normal and emergency conditions, respectively. [PERSON] et al. [7] present elite group-based evolutionary algorithms based on the simulated annealing algorithm and particle swarm optimization for path planning using multiple USVs. [PERSON] et al. [8] use the fast marching method combined with a model predictive control algorithm to design an autonomous navigation control system. [PERSON]. [9] proposes a fast collision avoidance method based on velocity resolution to realize a fast response for a USV in an unknown complex marine environment. For the path navigation method of a USV, a chaotic and sharing-learning particle swarm optimization algorithm is developed to solve the extended traveling salesman problem and the nonlinear multi-objective model in [10]. These collision avoidance algorithms for USVs include the velocity obstacle method [11], field theory [12; 13; 14; 15], the finite state machine [16], A star [17; 18], the LROABRA (local reactive obstacle avoidance based on region analysis) method [15], the VFH+ method [15], the fast marching method [19], and so on. Most of the above literature focuses on the generation of a collision avoidance strategy, but there is not much research on the combination of a collision avoidance strategy and a controller. In the research for USV collision avoidance strategies, the optimization algorithm is often used to obtain the optimal collision avoidance strategy [20; 21]. [PERSON] et al. introduced a two-level collision avoidance algorithm and improved the calculation efficiency and accuracy through the particle swarm optimization (PSO) algorithm [6]. For this solution space of the collision avoidance strategy, the objective function is solved by the PSO algorithm in [22]. [PERSON] et al. designed an extended chaos and shared learning PSO (CSPSO) algorithm to solve the traveling salesman problem (TSP) and nonlinear multi-objective model in a collision avoidance algorithm [10]. [PERSON] et al. proposed a modified quantum PSO (MQPSO) method to obtain the optimal velocity variation of a USV to avoid collision and reduce energy consumption [23]. [PERSON] proposed a path-planning method in a dynamic environment based on ant colony optimization (ACO) [24]. Subsequently, the method was applied in a ship control system [25]. [PERSON] et al. proposed an improved ACO algorithm to solve the problem of insufficient search ability in a collision avoidance planning algorithm for a USV [26]. The improved pseudo-random proportion rule was used to select the ant state transition, and the wolf colony allocation principle and the maximum minimum ant system were used to update the global pheromone to avoid the search falling into the local optimum.