## 5 Conclusions  
In numerical research carried out based on a high-dimensional map expressing the port environment, the effectiveness of the modified A* method was compared with its basic version. The simulation results confirm the proposed method's effectiveness, which reduces the calculation time by over 500 times with a slight increase in the route length compared to the basic version of the A* algorithm. Additionally, as a result of the analysis, it can be concluded that the map image processing used in the proposed approach increases the path's safety by treating narrow and risky areas as prohibited for vehicle movement. Based on the above results, it can be concluded that the proposed method is suitable for use in AUVs and ASVs. In the case of AUVs, this study assumes that the path is planned only in the horizontal plane and that the vehicle has the ability to maintain constant depth. However, due to the easy implementation, the method is also promising in 3D map processing. For this reason, further work is planned to test the algorithm's operation based on an artificially generated three-dimensional map of the underwater environment. In this article, the planned paths are presented in their raw form to compare the effectiveness of the proposed modification of the A* method and its basic version. The use of the above method in a real mission planner requires knowledge of the physical parameters and manoeuvring limitations of the vehicle intended to be used in the mission. Based on this knowledge, the path can be smoothed to avoid sharp turns and reduce energy consumption. Additionally, in relation to vehicles with a trajectory tracking control system, specific arrival times should be added to the smoothed path depending on the dynamic parameters of the vehicle in order to obtain a feasible trajectory. For AUVs, depth changing is usually ensured by adding specific depth values that the vehicle should achieve at a given waypoint. However, for large changes in depth, it is also necessary to consider the manoeuvring limitations to calculate arrival times for each waypoint in a set trajectory. Additional aspects to be taken into account when planning a mission include information on weather conditions, sea currents, and other vessels operating in the mission area, as well as specific areas related to maritime traffic (e.g., anchorages, traffic separation zones, etc.). While the proposed method demonstrates significant improvements in computation time for global path planning, its application in real-time local collision avoidance scenarios requires additional modifications and the tuning of image processing parameters such as the scaling factor and detection threshold, as well as the shape and size of structural elements of mathematical morphology depending on the resolution of data from the environmental sensor. Further improvements may include planning a path to a virtual point located in the direction of the destination point in an artificial map window around the vehicle, which, in combination with the proposed image processing, should provide close to real-time decision-making for standard computers currently used in ASVs and AUVs. Since the method was primarily designed for global path planning where the environment is known and static, strong surface waves and sea currents will reduce the algorithm's efficiency in local collision avoidance systems. However, the applied image processing methods allow for compensating this issue by closing narrow passages where the vehicle's path may be risky and adding a buffer zone as a result of the artificial enlargement of obstacles. Additionally, in a complex and rapidly changing environment, it is necessary to use replanning to ensure vehicle safety. The following supporting information can be downloaded at: [[https://doi.org/10.6084/m9.figshare.26827198](https://doi.org/10.6084/m9.figshare.26827198)]([https://doi.org/10.6084/m9.figshare.26827198](https://doi.org/10.6084/m9.figshare.26827198)). Conceptualisation: R.K. and P.S. ; methodology: R.K., P.S. and K.N.