# Fuzzy Risk Evaluation and Collision Avoidance Control of Unmanned Surface Vessels
## 1 Introduction
Korean researchers, in June 2020, proposed a method that integrates a collision avoidance methodology with a simplified nonlinear ship model--the Noorbin mathematic model: \(Tr+r+\overset{\alpha}{\bar{\alpha}}r^{3}=K\delta\), where \(\delta\) is the rudder angle, \(r\) is the angular deflection rate, and \(T\), \(K\), and \(\alpha\) are parameters of ship dynamics [10]. Although the simplified nonlinear ship model was used, this paper is still a rare example to be applied in the collision avoidance design of ships. This achievement brought collision avoidance research of USVs into the next chapter; however, this result is only a small step forward for the collision avoidance design of USVs, since the model that was proposed in this paper did not include hull resistance, the hydro-elasticity effect, ocean environmental disturbance (wind, waves, and ocean current), and COLREGs rules into the design. This developed methodology can be predicted to unacceptably work in the global ocean environment. Based on these depicted reasons, this paper aims to propose a smart collision avoidance control system for USVs that is able to work well in the challenging global ocean environment. For solving the above-mentioned technical issues and to deliver a satisfactory collision avoidance performance for USVs, a smart collision avoidance system that integrates a collision risk index, a collision avoidance act timing indicator, a collision avoidance trajectory generator, and an optimal nonlinear control for complying with COLREGs rules [11] is developed in this paper. The collision avoidance problem of USVs contains two sub-problems: conflict detection and conflict resolution. Solving the problem of conflict detection is to determine if a risk of collision exists and the timing needed to perform the right evasion act. The actions that must be taken to solve the conflict resolution problem have been proposed in [12]. The collision risk index mainly depends on two key parameters, which are distance to closest point of approach (DCPA) and time to closest point of approach (TCPA) [13; 14]. By using this developed collision risk indicator, the risk of collision will be visualized as a collision circle zone around the ship itself, and a collision alarm will be triggered when a target ship enters the collision circle zone. The collision avoidance act timing indicator mainly depends on three key parameters, which are the velocity of USV, the heading angle of the target ship and the modified relative distance. By using this developed collision avoidance act timing indicator, the speed of the controlled USV will be decreased to the level of no collision. After the collision alarm is been triggered, an instantaneous collision avoidance trajectory will be generated using the cubic spline interpolation method [15]. Based on this collision avoidance trajectory, an optimal nonlinear control system [16] is then adopted to guide the USV to precisely follow the desired course under the effects of environmental disturbances. This paper is organized as follows: in Section 2, the actions for collision avoidance of USVs are discussed; in Section 3, the proposed smart collision avoidance control design for USVs is derived; in Section 4, the simulation results of two scenarios: a crossing situation and multiple fixed obstacles, are shown and discussed; in the last section, the major conclusions of this design are stated.