## 3 Improved A-Star Algorithm
### A-Star Algorithm Considering Risk Models
#### 3.2.3 Combined Path Generation of Vessels
Please note that the traffic separation rule is not applied by the navigation rule in this waterway. Sailing vessels in this scenarios are not recognized as the obstacles because only moored or anchored vessels are considered as obstacles for the global path planning in this article. The other parameters are set the same as Case 1. The paths planned with the proposed A-Star algorithm, which consists of the normal path and the berthing path, and the traditional A-Star algorithm are shown in Figure 11, respectively. From Figure 11, it can be seen that the traditional A-Star has high risk to collide with the bridge and cannot guarantee the safety of berthing. To verify that a heuristic algorithm, e.g., A-Star algorithm, has a higher efficiency than a non-heuristic algorithm. The computation time records for A-Star algorithm with the improved A-Star algorithm and the search algorithm without heuristic guide for this case are 935 ms and 1127 ms, respectively. It means that the algorithm without heuristic guide actually has a higher efficiency. The path smoothed with the uniform B-spline curve of order 3 for the improved

Figure 10: Combined path generated by an improved A-Star algorithm considering or not considering smoothing (The definition of the graphic symbols in this figure is the same as the definition in Figure 7). A-Star algorithm is shown Figure 12. The path in Figure 12 can be set as a safety path that can be followed by a vessel. ## 5 Conclusions and Future Research

According to the defects of the traditional A-Star algorithm when it is used for vessel path planning, an improved A-Star algorithm has been proposed in this article. Firstly, the risk models of obstacles (bridge pier, moored or anchored ship, port, shore, etc.) with currents, traffic separation,

Figure 11: The path planned by the proposed A-Star algorithm in Wuhan waterway of Yangtze river. Figure 8:0 The smoothed path planned by the proposed A-Star algorithm in Wuhan waterway of Yangtze river. berthing, manoeuvrability restriction have been built. Then, the procedure of the normal path generation and the berthing path generation with the proposed A-Star algorithm have been depicted, respectively. Moreover, the problem of combining the normal path and the berthing path has been also solved. Four cases have been studied to verify the effectiveness of the proposed A-Star algorithm. The simulation and real experiment results show that the proposed A-Star path planning methods can avoid the high risk of obstacle collision, obey the separation rule and meet the requirements of berthing for vessels. In a word, the proposed algorithms can realize the trade-off between the path length and the navigation safety. In future work, wind and water depth can be also considered during vessel path following, because wind will affect the ship navigation safety and economical efficiency, and shallow water will increase the vessel stranding risk. Conceptualization, C.L. and Q.M. ; Methodology, C.L. ; Software, C.L. ; Validation, C.L and S.X. ; Writing-Original Draft Preparation, C.L. ; Writing-Review and Editing, C.L., Q.M. and X.C. ; Visualization, X.C. and S.X. ; Funding Acquisition, C.L, Q.M. and X.C. This research is supported by the China Postdoctoral Science Foundation (2018M632923), the Wuhan Science and Technology Project (2017010201010132), and the Fundamental Research Funds for the Central Universities (2042017 KF0235). The authors declare no conflict of interest. ## References

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