# Fast Path Planning for Autonomous Ships in Restricted Waters
## 1 Introduction
[16] assigns a potential function for each individual obstacle based on image processing and integrates them into a scalar potential surface (SPS). By computing a trade-off potential value between two objectives, i.e., fast approaching to the goal and collision-free obstacles, this method can find the optimal direction for the mobile robot to navigate and ultimately obtain the shortest path. [PERSON] et al. [10] proposed a path-guided APF-SR (stochastic reachable) method. By taking a known collision-free path in the presence of many static obstacles as an attractive intermediate goal bias, an APF planning method is used to safely navigate through the moving obstacles. Tests with 300 stochastic moving obstacles show that this method can avoid local minima and has a high success rate (over 90%) in highly dynamic environments. Additionally, the above methods have problems in environment modeling. Most obstacles are considered points or convex polygons in a grid map, and obstacles with arbitrary shapes are usually represented by an image map. This oversimplification makes the navigable area or obstacle position information distorted to use, and their respective attributes cannot be retained, which may result in danger for the actual navigation of autonomous ships. Table 1 shows a comparison of some typical APF approaches mentioned above in chronological order. These methods were evaluated according to the fulfillment of 11 requirements/features: COLREGS compliance (the degree of fulfillment is specified as N/A, no, low, medium, or high); map type; consideration of static and dynamic obstacles (quantities and shapes); consideration of dynamic properties and emergency CA actions for the own ship or mobile robots; computational time, as well as the local minima; the GNRON problem; and the principle of potential and/or gradient-following used in the method. Some requirements are evaluated straightforwardly based on fulfillment (yes in the table) or failure of fulfillment (no in the table) of a defined criterion. The computational time has  
its own scale of evaluation, where the time can be very low (milliseconds), low (seconds), medium (several or tens of seconds) or high (hundreds of seconds). In the last column, this paper's method is evaluated for comparison with existing approaches. In this paper, we propose a path-guided hybrid artificial potential field (PGHAPF) method that has low computational time, works flexibly with any offline path planning method, and shows the ability to cope with CA problems in restricted waters with consideration of COLREGS. We focus on the problem of safe navigation for power-driven vessels in dynamic and complex environments, where narrow channels, arbitrary shape obstacles and moving TSs that are not obeying COLREGS may exist. The highlight contributions of this work are:  
* Fast path planning in restricted waters where both static obstacles with arbitrary shapes and dynamic TSs exist. * The potential to acquire safe and optimal trajectories by compositing with other offline path planning methods so long as suitable waypoints are chosen in static environments. * Constructing a simple and exact APF environment model for static obstacles with arbitrary shapes through implicit functions. The corresponding clearance to these obstacles can be easily configured by adjusting a parameter of this method according to the risk level. This achievement is an important step forward for the application of the CA algorithm in ECDIS (electronic chart display information systems). * The PGHAPF method shows the potential to overcome the main limitations of APF methods: local minima and GNRON problem. * The trajectory is calculated based on a three-degree-of-freedom Mariner class ship, which provides a more practical solution. The remaining parts of this paper are organized as follows. Section 2 introduces the environment modeling of static obstacles, TSs and COLREGS requirements, as well as the PGHAPF method.