**1. Introduction**

As a sort of autonomous ocean vehicles, USV (unmanned surface vehicles) can autonomously perform tasks in various environments without human intervention [1]. USV with non-linear dynamic characteristics have better endurance ability and payload ability than other unmanned vehicles, which makes them to be essential tools in the area of marine scientific research, marine resources development, marine environment monitoring and national marine security [2–4]. Autonomy and intellectualization are the crucial manifestations of the development of USV. Research on intelligent planning and controlling can improve the working performance of USV [5].

In the area of intelligent planning and control, path planning of single objectives, such as shortest distance, time optimality, energy consumption optimality, smoothness optimality and minimal risk, has gradually been studied furtherly [6]. Multi-objective motion planning and intelligent decision-making [7,8] considering dynamic constraints of mobile robots is the difficulty of current research, where it is necessary to obtain more comprehensive and accurate environmental information by using environmental comprehensive perception methods, such as maps to optimize the path planning results. In this context, it is of great significance to study the path planning algorithm based on ENC (electronic navigation chart) considering the hydrodynamic characteristics of USVs for improving the USV's autonomous environmental awareness, optimizing the path planning results and improving the autonomy and intelligence level of USVs.

A star algorithm, (A\* algorithm) is a deterministic algorithm with outstanding consistency and completeness which is widely applied in the research of path planning. It was firstly proposed by Hart P. et al. [9] and usually combined with grid method [10]. The minimum cost function is used to search the minimum cost path from the starting node to the end node. The grid-based A\* path search methods are mainly based on the center point of the grid [11–16] and grid vertexes [7,10,17–19]. Grid method can be divided into a uniform grid and non-uniform grid with diverse shapes and sizes of the grid. Aiming at the deficiencies of the grid-based A\* algorithm, such as huge memory expenditure, large path turning angle and unsmooth path, studies have been done to improve it.

Larson et al. [20] found the optimal path with the least nodes in limited time by using A\*. Svec et al. [21] combined the A\* and locally bounded plan, Naeem et al. [22] proved A\* by direction priority sequential selection (DPSS), Improving path quality and computational capacity. Svec et al. [23] introduced a model prediction algorithm and combined it with A\* algorithm. The above work concentrates on improving the computational performance and path quality of traditional A\* algorithm.

Daniel, K [16] and Soulignac, M [24] carried out the Theta\* which released the limited that the center points of the grid can only moves along the center points within A\*. Kim et al. [13] solved the problem of unlimited direction with the theory of limit-cycle circle set. Nash, A et al. [15] carried out Lazy Theta\*, it was found that vertexes visibility check decreases by using this method. Improved dynamic search D\* was put forward by Yang, J.M. et al. [17] based on A\*, it was demonstrated that this algorithm fits the dynamic map very well.

Wu, P.P et al. [7] carried out a multi-objective A\*, it improves the real-time performance of A\*. Naus et al. [25] applied A\* to search the shortest and safest trajectory in electronic chart. Kim et al. [26] carried out a curvature path planning algorithm which considering the turning ability of USV through perfecting A\*. Liu, C.G. et al. [18] established the surface obstacles risk model considering current, traffic separation and maneuverability and improved the practicability of A\* algorithm, but ignored the effect of water depth on navigation safety. In the above work, the A\* algorithm is applied to the area of path planning for USVs.

Previous researches perfected the calculating quality of A\* and expanded the range where A\* could be involved in, and they focused on the estimation of the criticality of surface obstacles in the research concerning safest path planning of USVs, rarely discussed the hazard, due to the shallow depth. Depth is a crucial factor affecting navigation safety and performance for unmanned surface vehicles operation in shallow waters, which is more vulnerable to ocean disturbances, such as wind, waves and currents, [27]. On the other hand, the hydrodynamic characteristics can well reveal the navigation stability of small USVs in shallow waters [28,29], and then evaluate the safe depth of navigation.

In this paper, a method of safe path planning is carried out to improve the depth safety of the shortest path of USV, which guarantees navigation safety in different conditions. In this paper, the navigation stability of USVs in various situations is studied, and the minimum safe water depth is calculated according to the results of hydrodynamics simulation. On this basis, the safer path of USVs is calculated by considering the risk of water depth. The depth safety of USV, which followed the shortest path, could be improved by using the information of depth in ENC, the water depth risk level (WDRL) of shortest path could be reduced as well.
