# Pursuit-Evasion Problem of Unmanned Surface Vehicles in a Complex Marine Environment
## 1 Introduction  
In recent years, with the continuous development of intelligent control theory and with continuous improvements to actual demand, unmanned surface vehicles (USVs) have been considered for a wide range of potential applications in ocean exploration, coastal defense, and intelligent cruises [1, 2]. Under an efficient communication network technology [3], there has been a lot of work and focus on the path tracking control of USVs, such as environmental monitoring, hydrological measurement, and path tracking [4, 5]. Since the pursuit-evasion problem involves many hot issues in control fields, this issue has always been the focus of intelligent systems [6, 7]. Nevertheless, the pursuit-evasion of USVs is still an open problem that needs to be overcome. In the implementation of target interception, Ref. [8] intercepted an escaping target based on the initial position and relative orientation of the tracker and the escaping target. The authors of [9] achieved the capture of an escaping target, but the motion model assumed in that article only allows the evader and the hunter to move in the horizontal or vertical directions, which is obviously inconsistent with actual motion. In addition, a method based on Reinforcement Learning [10] was gradually applied to solve the pursuit-evasion problem and allowed multiple robots to track a single target. Ref. [11] encircled escaping targets with multiple hunters in an environment of obstacles. By establishing multiple enriclement points around the target, multiple pursuers blocked the escape route of the evader in all directions [12]. Additionally, the encircled strategy is often used to encircle static targets [13]. However, once the trajectory of the dynamic target becomes complex, the applicability of this algorithm becomes questionable. Although more pursuers can ensure a higher success rate of hunting, the strategy of multiple pursuers is based on tracking and interception by a single pursuer. An accurate target location is of great significance for intercepting the escaping target. In article [14], a target position estimator was proposed, and a corresponding control law was designed. However, it cannot be ignored that the escaping target has high mobility. Moreover, the interception direction of the pursuer should be time-varying; that is, itshould be changed according to the movement of the target. The Kalman filter is widely used because it can predict the motion and position of the target simply and conveniently. To intercept the escaping target more accurately, the Kalman filter algorithm is adopted in this paper to track and predict an escaping target's trajectory. For target tracking, the algorithm based on line of sight (LOS) is generally used in the marine field [15]. However, the LOS cannot predict the target trajectory in advance for interception. As a simple and effective interception algorithm, the missile guidance law is widely used in the aviation field. Therefore, the missile guidance law is adopted to intercept escaping vessels in the marine field. When performing tasks in an actual environment, an USV will be affected by environmental interference by the wind, waves, and currents in a marine environment [16] and by threats from moving obstacles such as sailing ships [17]. A small USV will be more sensitive to external disturbances due to its small main scale and displacement [18]. Although Ref. [19] carried out sea trials of an USV and avoided obstacles and rescued people from drowning, it did not consider interference from the external environment. How to deal with uncertain nonlinearity and interference is an important problem in target tracking and interception [20]. However, the above article does not consider the uncertainty of the environment, which brings challenges to the interception of dynamic escaping targets. Previous studies on the pursuit-evasion problem had several shortcomings. First, many studies set the escaping target as static, which is not consistent with pursuit-evasion movement in an actual scenario.