## 1 Introduction  
In recent years, many scholars and engineers are committed to developing various autonomous underwater vehicles (AUVs) because of the increasing application demands [1], such as marine environment exploration [2], marine resource monitoring [3], pelagic survey [4], seabed resource exploitation [5; 6], military mission [7], and so forth. With the rapid development of more available advanced technologies, such as processing capabilities and high-density power supplies, more and more AUVs are now indeed being used for executing those high risk and repetitive tasks instead of people [8]. With the roles and missions constantly evolving, AUVs, instead of people performing missions in the unknown large-scale complex underwater environment, are an inevitable trend because of AUVs' inherent advantages. However, until recently, limited by its autonomy and acoustic communication abilities, AUVs can only conduct and implement a limited number of tasks in the offshore area in a relatively known environment. AUVs are needed for higher performance on autonomy and intelligence, such as decision-making planning, situational awareness, path planning, and simultaneous localization and mapping (SLAM), etc [9]. Path planning technology of AUVs is a significant technology that improves the AUVs' autonomy and promotes their applications in the large-scale complex marine environment [10]. It is desirable for a path planner to have an effective path planning model and an online learning algorithm to adapt the model's complexity. On the one hand, it is still a challenge to build this effective path planning model that satisfies the various constraints, such as the energy/time consumption, the turning radius limitation, the marine environment, and the ocean current. On the other hand, real-time performance and stability of planning the path is also an important issue. In fact, the autonomous path planning problem can be recognized as a search problem under multiple constraints, which principally includes two sub-questions: How to represent and model the path, and what algorithms efficiently find the optimal path. The following part first summarizes the commonly used path representation methods and then summarizes the various path planning algorithms. There are many ways to represent the motion path of AUVs in the underwater environment. Common representation methods are straight lines, Dubin-curves, polynomial curves, and spline curves. The straight-line representation [11] treats the path as a series of segments that are connected end to end. This representation is simple, but the line segments need to be smoothed for the kinematic constraints and controllability of AUVs. The Dubin-curve representation [12] uses a circle for smoothing straight-lines at the line segment connection, which is widely used in the field of mobile robots [13], but the Dubin-curve representation is computationally intensive and is not suitable for real-time path planning [14]. The polynomial and spline curves can represent more complex and smooth paths [15; 16] using fewer parameters (or control points), which have been increasingly used in robot path representations in recent years. In this paper, the B-spline curve is proposed to represent the smooth path for the requirement of kinematic constraints of AUVs. The path planning algorithm can be simply divided into two categories according to the optimality of the solution result. One class emphasizes the optimality of the solution results. These algorithms are represented by the graph search algorithms, while the other class emphasizes that the optimal feasible solutions are obtained with the greatest possibility under reasonable computational costs, such as sample-based algorithms, artificial potential field (APF), bioinspired meta-heuristics [17], and artificial intelligence based (AI-based) algorithms. [PERSON] et al.