# Fast Path Planning for Autonomous Ships in Restricted Waters
## 5 Conclusions  
The PGHAPF method proposed in this paper can quickly plan a deterministic collision-free path in the presence of a variety of static obstacles with arbitrary shapes and multiple dynamic ships with variable headings. This method takes into account the constraints of COLREGS, the dynamics of a Mariner class vessel, and the results of offline path planning and can adjust the path immediately according to a change in the dynamic environment, including the uncoordinated CA actions of other ships and the collision risk with nearby static obstacles caused by path adjustment. Additionally, a simple waypoint selection scheme is implemented together with the PGHAPF method to obtain a more optimized path and avoid danger. The results show the potential to perform path planning on ECDIS and to overcome the inherent defects of APF methods, such as the local minima, GNRON and oscillations in narrow passages. Furthermore, the PGHAPF method may be used in the fields of USVs, AUVs (autonomous underwater vehicles) and robots.  
There are some directions in which to expand our work. First, the CA actions taken by ships should not be limited to course change only. Multiship encounter situations may be further quantified and judged to acquire COLREGS-compliant behaviors accurately for autonomous ships. Furthermore, the potential field model for static obstacles is planned to be integrated into ECDIS so that the PGHAPF method can be validated in a more real-life experiment.  
The following is available online at [[http://www.mdpi.com/2076-3417/8/12/2592/s1](http://www.mdpi.com/2076-3417/8/12/2592/s1)]([http://www.mdpi.com/2076-3417/8/12/2592/s1](http://www.mdpi.com/2076-3417/8/12/2592/s1)): Video S1: COLREGS-constrained PGHAPF method navigating an autonomous ship in a complex environment with 5 arbitrary static obstacles and 4 other dynamic ships.  
Conceptualization, H.L. and Y.Y.; Methodology, H.L.; Software, H.L.; Validation, H.L. and Y.Y.; Writing-Original Draft Preparation, H.L.; Writing-Review and Editing, H.L. and Y.Y.; Visualization, H.L.; Funding Acquisition, H.L. and Y.Y.  
This research was funded by Traffic Youth Science and Technology Talent Project grant number 36260401, Natural Science Foundation of Liaoning Province of China grant number 201602081 and Fundamental Research Funds for the Central Universities grant number 3132018306.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**No.** & \begin{tabular}{c} **Static** \\ **Obstacles** \\ \end{tabular} & \begin{tabular}{c} **Dynamic** \\ **TSs** \\ \end{tabular} & \begin{tabular}{c} **Distance** \\ **[nm]** \\ \end{tabular} & \begin{tabular}{c} **Time** \\ **Steps** \\ \end{tabular} & \
\begin{tabular}{c} **Total Run** \\ **Time [s]** \\ \end{tabular} &
\begin{tabular}{c} **Time of Each** \\ **Time [ms]** \\ \end{tabular} \\ \hline
1 & 1 & 0 & 18.22 & 293 & 0.490 & 1.7 \\
2 & 1 & 0 & 13.49 & 219 & 0.387 & 1.8 \\
3 & 5 & 0 & 22.17 & 358 & 0.611 & 1.7 \\
4 & 5 & 0 & 17.57 & 284 & 0.527 & 1.9 \\
5 & 0 & 1 & 15.5 & 311 & 0.11–0.12 & 0.4 \\
6 & 0 & 1 & 15.1 & 302 & 0.10–0.12 & 0.4 \\
7 & 5 & 4 & 19.38 & 315 & 0.804–0.833 & 2.6 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Initial inputs and simulation results for U-shaped obstacles.