# Fuzzy Risk Evaluation and Collision Avoidance Control of Unmanned Surface Vessels
## 1 Introduction  
Merchant shipping is the lifeblood of the world economy, and 90% of world trade is seaborne. Eleven billion tons cargo, of which the value is approximately US$14 trillion, was shipped internationally in 2019 [1]. Shipping traffic has increased dramatically in recent years. The shortage of seafarers, rising wage costs, and rising insurance fees continue to be painful areas for shipping companies. In 2020, there were 1.6 million seafarers around the world, and they were trapped working on 50 thousand merchant ships with limited space to keep the physical distance needed to help stop the spread of the COVID-19 pandemic [2]. The move to unmanned surface vessels (USVs) from human manipulation has accelerated because of the pandemic, reducing human power, and keeping costs down. In addition, major types of maritime accidents are ship collisions, and about 75% to 96% of these were caused by human-made errors [3], such as lack of experience or due to negligence. However, over few past centuries, ship collision avoidance totally depended on seafarers' experiences. Fortunately, the explosion of artificial intelligence and sensing technologies have revealed the potential of using USVs to eliminate human-made errors. The farsighted international marine technology group, Kongsberg, and the Norwegian chemical company, Yara International, cooperated to design the world's first fully electric and autonomous container ship, Yara Birkeland, in 2017. This vessel was launched in 2020 and will gradually move from manned operation to fully autonomous operation by 2022 [4]. After this successful outcome, Kongsberg and the global maritime industry group Wilhelmsen founded a joint venture, Massterly, which is the world's first autonomousshipping company, in 2018. Massterly offers the entire value chain for autonomous ships for customers, including vessel design, control systems, logistic services, vessel operations, and so on [5; 6]. This new and cost-effective commercial shipping operation model is expected to increase the investment of research resources into USVs. Additionally, military activities at sea are also increasing. Militaries have displayed a growing interest in deploying USVs for patrols, mine warfare sweep missions, anti-submarine missions, and other dangerous missions. A military unmanned surface vessel that is equipped for fire-fighting and environmental protection has been developed [7]. Defense organizations expect that with the rising accessibility of USVs for military activities, and that many dangerous activities that need to be completed by humans can be replaced. Due to the growing commercial and military interest, designs of control algorithms have become the hot topic in the field of developing smart USVs, as they are the most important part to achieve a well-developed USV. Control algorithms for smart USVs essentially include a navigation system, a control law, and a collision avoidance methodology, which needs to perfectly comply with maritime rules and regulations. Over the past few decades, numerous researchers have proposed static optimized collision avoidance trajectory algorithms through geometric analyses between ships or by integrating collision avoidance trajectory algorithms with linear controllers [8; 9], such as PI or PID controllers. These types of algorithms basically do not model dynamic information between ships into their designs. These designs are only capable of avoiding collisions under certain operating conditions and cannot be used in practical applications. However, these types of collision avoidance algorithm designs are still the main methods in the field of USV collision-avoidance research. To the best knowledge of the authors, there are limited studies that consider nonlinear dynamic information of ships or that integrate collision avoidance algorithms with a nonlinear controller.