**1. Introduction**

With the rapid development of science and technology, the USV is an indispensable means to accomplish tasks at sea. In addition, it is the outstanding advantage of USV that it is intelligent [1]. Individual USVs can perform intelligence acquisition, surface search and rescue, and marine resource exploration, while cluster of USVs can perform cooperative sensing and formation, intelligent escorting, and other operational tasks [2,3]. USV path planning is one of the most significant aspects of its safe navigation in the working environment, which directly affects the safety and economy of USVs during navigation [4]. Path planning is also one of the prominent technologies for the automation and intelligence of USVs and for performing complex tasks [5]. The evaluation criteria for USV path planning are to seek a safe and feasible optimal path from a defined starting point to an endpoint in an obstacle-ridden working environment. The aim of the path planning algorithm is the optimal selection of routes to maximize efficiency. An optimal path is predicted by analyzing the path length, smoothness, safety, and other indicators to save time and energy consumption.

**Citation:** Xing, B.; Yu, M.; Liu, Z.; Tan, Y.; Sun, Y.; Li, B. A Review of Path Planning for Unmanned Surface Vehicles. *J. Mar. Sci. Eng.* **2023**, *11*, 1556. https://doi.org/10.3390/ jmse11081556

Academic Editors: Rafael Morales and Tieshan Li

Received: 23 May 2023 Revised: 13 July 2023 Accepted: 3 August 2023 Published: 6 August 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

The research method for this paper is the literature research method. New findings are obtained through extensive reading of the latest current literature to gain a comprehensive and correct understanding of the problems associated with USV path planning. In the past five years, several review papers [2–4,6–12] have been published summarizing the advancement of research on path planning. The following is a list of the most relevant review papers:

Ref. [2] describes the progress of USV path planning research based on multi-modality constraints in three stages: route planning, trajectory planning, and motion planning. Ref. [3] provides a comprehensive review of the development of USV from target tracking, trajectory tracking, path tracking, and cooperative formation control. This study focuses on intelligent motion control with less description of path planning. Ref. [4] addresses the USV local path planning problem and describes the characteristics of various algorithms at two levels of path search and trajectory optimization. Ref. [6] reviews recent advances and new breakthroughs in AUV path planning and obstacle avoidance methods, and compares constraints and marine environmental impacts of AUV from global and local path planning algorithms. Ref. [7] explores a path planning algorithm for autonomous maritime vehicles and its collision regulation correlation. This study focuses on USVs and COLREGs from the perspective of the safety of navigation.

Next, we will present the purpose and contribution of our review paper and emphasize the necessity of this work in comparison to current review papers. We present an up-to-date review of USV path planning. Not only are traditional graph-based search and sampling methods covered, but recent developments in reinforcement learning, neural networks, and swarm-intelligence-based optimization algorithms are also included. The innovation of this paper is to point out the limitations of current path planning methods, namely, most of them ignore the effects of winds, waves, and currents at sea on the ship. However, this paper systematically and comprehensively introduces new developments in current research into path planning algorithms in the face of unknown complex maritime situations. Secondly, in the face of multiple moving obstacles, this paper introduces the relevant algorithms to accomplish multi-objective task assignment planning and cooperation using USV clusters to achieve autonomous obstacle avoidance of vehicles. The rest of the paper is structured as follows: Section 2 presents and compares conventional as well as evolutionary algorithms under global path planning; Section 3 presents algorithms related to local path planning; Section 4 presents types of and methods for hazard avoidance in proximity response; Section 5 presents path planning algorithms under clustering; Section 6 gives conclusions and analyzes valuable future research directions in this area.

#### **2. Global Path Planning**

Global path planning is a large-scale offline path planning method based on provided information about the marine environment (electronic charts) to obtain information about static obstacles in the area that USV passes through. The global path planning algorithm acquires information about the entire environment, modeling the environment based on the obtained information pairs and performing the preliminary planning for a given path [13]. Global path planning is a viable path from the starting point to the ending point of the USV in a known operating environment. Once in sophisticated maritime environments, or when obstacles suddenly appear in the route, it can easily lead to a local optimization situation. Currently, the main global path planning methods are traditional algorithms such as the Dijkstra algorithm and A start (\*) heuristic search algorithm, and evolutionary algorithms such as the genetic algorithm and neural network algorithm, as shown in Figure 1.

**Figure 1.** Global path planning algorithm.

#### *2.1. Dijkstra Algorithm*

The Dijkstra algorithm, a classical shortest-path search algorithm, was formulated by E.W. Dijkstra in 1959 [14]. By searching the graph and choosing any starting point among the schema, it is possible to calculate the closest path to all vertices. Due to the Dijkstra algorithm computing all vertices during the search process, it is less efficient to run. To address the problem of low operational efficiency, ref. [15] proposed an improved Dijkstra algorithm to add key nodes and divide regions, which can effectively reduce the computation time and improve the operational effectiveness of the algorithm. In [16], another improved Dijkstra algorithm was proposed, which needs to select the nearest node. As a result, the computation of non-critical nodes decreased, which saves time and speeds up the path-planning operation. Nevertheless, the method does not select an optimal route for the appearance of multiple paths with the same shortest distance. In [17], a running time calculation function was introduced to calculate the optimal route by running time when several paths of the same length occur. Once the data are heavy, the method consumes a lot of time. To address the inefficiency caused by a large amount of data, ref. [18] proposed a hierarchical Dijkstra improvement algorithm. It saves the location information that has been searched to be synchronized to avoid repeated searches for the same location. The algorithm can quickly find a more suitable path when there are large amounts of data. In a way, it saves time and improves efficiency, even if it is not the best path. For considering the effect of under static obstacles, ref. [19] raised a distance-seeking Dijkstra algorithm based on electronic nautical charts to solve the global path planning problem for USVs. By finding the node with the shortest path, the algorithm speeds up planning, optimizes the global route, and makes the planned path smoother. In [20], a three-dimensional Dijkstra optimization algorithm was proposed to generate globally optimal routes. Compared with the two-dimensional Dijkstra algorithm, this algorithm has a high global search capability, finds the globally optimal path more precisely, and saves time and fuel costs. Considering the effect of dynamic obstacles on global paths, ref. [21] presented a D\*Lite algorithm. The prediction of dynamic path planning using dynamic information from the first computed path enables a bi-directional variable search in an unknown environment. If the map changes too much, it will calculate duplicate nodes and result in a slow planning efficiency. Moreover, the results are not convergent and the algorithm becomes stuck in a dead loop. In [22], a path planning algorithm was raised, based on the improved D\*Lite algorithm was by enhancing the path cost function and reducing the expansion range of nodes. As a result, it avoids double-node computation and raises computational efficiency.

#### *2.2. A\* Algorithm*

The A\* algorithm, proposed by Cove in 1967 [23], was a heuristic search algorithm for discovering the shortest route between two nodes. The A\* algorithm is simple in principle, and quicker than Dijkstra's algorithm. Using an optimal search approach ensures that the path has the lowest cost and enhances the efficiency of the operation. However, it relies more on heuristic functions. Once the heuristic functions are complex or invalid, it produces poor smoothness and continuity of the paths, which are not detrimental to the navigation of the vessel [24]. At present, the main improvements of the A\* algorithm in academia include: firstly, expanding the number of neighboring points to be searched to improve the smoothness; secondly, optimizing the heuristic function to reduce the computation time; and thirdly, reducing the computation of the raster to hence efficiency. In [25], a finite angle FFA\* algorithm was proposed by introducing a safety distance parameter. This algorithm expands the search range and increases the number of adjacent points, thus improving the smoothness of the generated route and increasing the safety of ship navigation. However, adding branches leads to more computing time and less efficiency. In [26], a limited destructive A\* (LDA\*) was raised, based on the problem of the slow running of the FFA\* algorithm. By optimizing the heuristic function, the shortest path from the starting point to the endpoint is found in the grid environment to save time. The method is fast for static obstacles and generates feasible routes, but the performance is not optimal. In [27], another constrained A\* algorithm was proposed. In a simulated closed ocean environment, the effects of static and dynamic obstacles are considered to generate a safer route by maintaining a safe distance. It reduces the computation time and improves operational efficiency by optimizing the heuristic function, which adapts to the globally optimal path planning. In [28], an R-RA\* algorithm was proposed. As only a fraction of the grid map, it is possible to significantly reduce the length of the route, saving computational time and improving the operational efficiency of the algorithm. However, the generated paths are not globally optimal. In [29], a rectangular grid instead of a hexagonal grid was presented. With the reduction in intermediate nodes, it makes the path smoother. The optimization is also performed in the path length to ensure the robustness and safety of the ship.
