## 4 Conclusions  
In summary, we proposed a path planning method for AUV navigations based on the MDP algorithm. Using Daya Bay as a trial area, the algorithm's performance is examined. The grid size of 2000 m turns out to be a computation-efficient and feature-resolved resolution suitable for Daya Bay. In this study, the ocean current is predicted using a regional ocean model (FVCOM) and is inputted into the MDP algorithm as a priori. Since ocean currents always vary with time and their magnitude is in the same order as the AUV's cruising speed, including the ocean currents in the MDP algorithm, they can apparently change the predicted optimal path and arrival time, especially for the cases in that the AUV must make several detours to avoid obstacles, such as islands or coastline. The MDP algorithm is validated through comparison with the A* algorithms, demonstrating its advantages in underwater navigation. The optimal paths obtained by the MDP algorithm are shorter than the A* algorithm with the same spatial resolution. It is especially suitable for the underwater navigation of AUVs, which have a slow speed and limited basic actions. The MDP method also avoids high complexity in the algorithm design. Information on ocean currents can be easily included in the algorithm so that it is more adaptive for the real operational environment in the ocean. The MDP algorithm with consideration of ocean currents can guarantee that the grids with extra-large counter-currents will not appear in the predicted optimal path. Using the value iteration method, the optimal paths to the target from all points in the navigation area can be updated in one step, which makes the algorithm robust and convenient to be used in the ocean, where varying oceanic currents and other uncertainties exist. This method is especially suitable for underwater navigation in ocean observations. Collaboration and networking of autonomous vehicles, such as AUVs, gliders, etc., is becoming a trend in ocean explorations. To quickly move and arrive at the target locations requires robust and efficient path searching under the limit of the maximum speed for underwater or surface vehicles. Background circulation, eddies, and tides, which may have comparable velocities as the vehicles, can dramatically affect the optimal path. The MDP method proposed in this paper, with an input of predicted ocean currents, provides a feasible solution for finding the optimal path. The operation of the ocean forecast model can be deployed on computers on land or embedded inside the vehicles. In turn, measured ocean currents during the time of the underwater vehicle traveling can be transmitted back to the forecast model to update the ocean current prediction using some optimized methods, such as data assimilation, thus producing more accurate background ocean currents to feed back to the MDP method and guide the optimal path of underwater vehicles. The performance of the MDP algorithm is numerically verified. Field experiments in Daya Bay will be conducted to verify the algorithm in the near future. The computing time \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Longitude (\({}^{\circ}\)E)** & **Latitude (\({}^{\circ}\)N)** & **Depth (m)** \\ \hline Start & 114.9512 & 22.4315 & 15 \\ \hline Target & 114.6203 & 22.7375 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The coordinates and depths of starting point and target point in the 3D-MDP algorithm simulation. increases dramatically when the grids increase. Even though some more efficient methods are available for a large grid number [31], the computing efficiency and spatial resolution must be balanced for the AUV to acquire an optimal path in practical applications. Resources, Q.L. ; Methodology, F.L. ; Software, M.S., X.Z., F.L. and K.W. ; Writing--original draft, M.S., X.Z. and F.L. ; Writing--review & editing, Q.L. All authors have read and agreed to the published version of the manuscript.