**5. Conclusions**

In this paper, hydrodynamic numerical simulation of a new marine surveying and mapping USV platform developed by the author's research group is performed to evaluate its navigation status in irregular waves. It is found that the heave and pitch of the USV decrease with the increase of velocity and increase with the increase of significant wave height. The heave and pitch navigation status of the unmanned surface vehicle is evaluated through the analysis of 9 working conditions to ascertain minimum safe depth for navigation.

A grid environment modeling method considering water depth is carried out, in which the spline function interpolation algorithm with obstacles is employed to acquire the gridding prediction depth according to the discrete sparse depth points of ENC. The grid modeling method considering water depth can make the utmost of the water depth information provided by ENC to evaluate the depth risk level of path of unmanned surface vehicles.

The quantitative evaluation method of the depth risk level of the path is proposed, and the simulation of path planning is carried out based on A\* algorithm using depth hazard degree as an index, named the water depth risk level A\* algorithm (WDRLA\*). The results show that WDRLA\* can hit a safer and shorter path taking into account of the mean draft, the hydrodynamic property, including the maximum heave value and the maximum pitch angle of a USV sailing in an irregular wave, position errors, including ENC positioning errors, positioning system errors and chart depth errors. WDRLA\* algorithm can reduce the risk of planned paths in shallow offshore waters to ensure the navigation safety of a USV. The method of path depth risk assessment is not only appropriate to USV path planning, but also can provide guidance for manned ship path planning.

The works are still not completed for the limitations existing. For example, we neglected the influence of tide to water depth, which determines dynamic depth, since the depth on ENC is defined as the vertical distance between the theoretically lowest tide level and seabed. In the future, dynamic water depth will be involved in to acquire bathymetric in better accuracy. The search efficiency of the safe path planning algorithm is expected to be improved in the future.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/2076-3417/9/16/3228/s1, Figure S1: Heave versus time, Figure S2: Pitch versus time.

**Author Contributions:** The manuscript was written S.L. and C.W. All authors discussed the original idea. conceptualization, S.L.; methodology, S.L. and C.W.; software, S.L.; validation, S.L.; formal analysis, C.W.; investigation, S.L.; resources, A.Z.; data curation, A.Z.; writing—original draft preparation, S.L. and C.W.; writing—review and editing, A.Z. and C.W.; visualization, S.L. and C.W.; project administration, A.Z.; funding acquisition, A.Z. and C.W.

**Funding:** This research was funded by National key research and development program of China, grant number 2018YFC1407400.

**Conflicts of Interest:** The authors declare no conflict of interest.
