# Fast Path Planning for Autonomous Ships in Restricted Waters
## 4 Discussion  
When an autonomous ship is navigating according to the planned path, she will inevitably encounter dynamic TSs. Once the collision risk is detected, she should take actions under applicable regulations such as COLREGS, and she may deviate from the planned path temporarily due to her give-way obligations in some encounter situations. This may lead to collision risk with surrounding static obstacles, especially in restricted waters. Therefore, she needs to consider all static and dynamic obstacles at the same time and then make a fast, feasible and comprehensive decision. However, many studies are based on the following test environments or assumptions:  
Figure 18: Real-time maneuvering data obtained by a PD controller. (**a**) Own ship yaw angle, i.e., the heading at every second. This data curve is consistent with the heading data of the algorithm at each step. (**b**) This diagram reflects the change of the own ship speed (m/s) during the path planning. There is a small decrease in the velocity at each turn, which is consistent with the actual situation. (**c**) This diagram shows that the yaw rate is limited to \(\pm 0.5^{\circ}/\)s. (**d**) The rudder angle of each turn does not exceed the starboard or port rudder of \(15^{\circ}\). * They do not take static obstacles into account [9; 27; 28] or simplifies them into point obstacles [13] or convex polygons [3] when making CA decisions. * The own ship is deemed as a mass point without considering the dynamic properties of a ship [27; 29], for example, the speed loss in a turning maneuver and practicability of steering angles (path smoothness). * All TSs keep course and speed [3], or their actions are strictly predictable according to COLREGS [2]. This assumption leads to a reassessment of the path planning results and a non real-time CA decision should any TS fail to maneuver according to COLREGS or another agreed-upon framework. * Based on a starting point and a goal to generate a collision-free path with short length [6; 30] without taking into consideration the long-distance path planning that is necessary for autonomous ships. Therefore, a fast path planning algorithm is designed and tested as above that is constrained by a ship's dynamic properties, COLREGS and planned route and can consider many irregular static obstacles, multiple dynamic TSs and their uncoordinated CA operations at the same time. First, the PGHAPF method can avoid static obstacles with arbitrary shapes (including points, lines, and planes) in addition to the ability to avoid dynamic TSs under COLREGS. There are three key steps for this method:  
* the potential-based method to model the environment for any irregular static obstacles. Very simple parameters such as \(\beta\) or \(\gamma\) can be adjusted to change the range of the potential field of obstacles with different attributes, which is convenient for environmental modeling with ENC data in the future. * the gradient-based method to produce the COLREGS-constrained repulsive forces for dynamic TSs and the attractive force for the goal, which is achieved in [13] and improved in this paper for the emergency CA module. * the PGHAPF method, which is a fusion of the potential field and gradient methods (the above two) based on a prior path, is proposed first in this paper. Under the static potential field, a decision-making time in advance is selected according to the surroundings and speed of the own ship to determine whether there is danger at the predetermined position. If there is, the own ship turns right or left with _maxturn_ angle at the current time step, which is dependent on the direction of the minimum potential location referring to the predetermined position. Otherwise, the own ship takes the actions based on the second step. This method can effectively reduce the local minima problem of the traditional APF method caused by the vector sum of attractive and repulsive forces.