## 1 Introduction
[18] also summarized AUV path planning methods based on the geometric model search algorithms, probabilistic sampling algorithms, artificial potential field algorithms, and intelligent algorithms. The graph search algorithm is a classic path planning method in the robotic field. The graph search algorithm uses the D or A* algorithm and their various variants to search for the optimal path between the start point and the goal point by representing the environment as a raster map or a topological map with a smaller amount of data. [PERSON] et al. [19] applied the D algorithm to the global path planning problem of AUVs in the underwater environment, and the algorithm generated a path without collision. [PERSON] et al. [20] represented the marine environment as a quadtree map and used the A* algorithm to search for the optimal path in the map. [PERSON] et al. [21] applied the 3D Field D* algorithm to solve the three-dimensional space path planning problems. The sampling-based method mainly includes the probabilistic roadmap algorithm (PRM) and random trees algorithm (RRT) [22] and its various variants, which are used to quickly obtain feasible solutions for complex path planning problems. The PRM algorithm first generates a network graph by a series of random position points, and then uses the A* algorithm to search for the path from the start point to the goal point. [PERSON] et al. [23] successfully applied the PRM algorithm to the path planning problem under the complex constraints of AUVs in a 3D underwater environment and carried out experimental verification. RRT uses a special incremental sampling search method, which is more efficient than PRM in single-request planning and has a good performance in high-dimensional space planning problems. [PERSON] et al. (2019) used the RRT* algorithm in the path planning problem of AUV in a real-time two-dimensional environment. The simulation results showed that the method had excellent adaptability in the real marine environment. The artificial potential field method mainly includes APF and BUG algorithms, and this kind of algorithm is suitable for real-time obstacle avoidance. [PERSON] et al. (2019) modeled the AUV path planning problem as an optimization problem under multiple constraints and solved the model by APF algorithm. [PERSON] et al. (2019) used the BUG algorithm for AUVs local emergency obstacle avoidance and performed the simulation verification. AI-based algorithms (or biological heuristic algorithms) mainly include particle swarm optimization (PSO) ([PERSON] et al., 2019; [PERSON] et al., 2020), ant colony algorithms (ACO) ([PERSON] et al., 2020), genetic algorithms (GA), tabu search (TS) algorithms, or bioinspired self-organizing maps ([PERSON] et al., 2020). In recent years, such algorithms have drawn increasing attention to the solution of AUVs path planning problems ([PERSON] et al., 2020). [PERSON] et al. (2020) applied the PSO algorithm to the AUV path planning problem. The simulation results showed that the algorithm was simple and easy to implement, with high robustness and fast convergence. [PERSON] et al. (2020) proposed an adaptive ACO algorithm to solve the AUV path planning problem, which solved the shortcomings of slow convergence and easy to fall into the local optimal solution. [PERSON] et al. (2020) applied a genetic algorithm (GA) to the AUV path planning problem to minimize the energy consumption of the path considering ocean current information. Differing from these omnidirectional ground robots and quadrotors, most of the AUVs are typical underactuated systems, which only rely on the propeller of the tail to generate power. The search method for discrete paths by rasterizing environmental maps is difficult to apply in underactuated AUVs. The AUV path planning method puts forward the higher requirements on the smoothness of planned paths. The path not only needs to be smooth, but also cannot exceed its maximum turning radius of the kinematic constraints and controllability of AUVs.