1. Introduction
AUV is a kind of autonomous underwater robot, which is mainly used for ocean exploration and data collection, and has a wide range of applications in the exploration and exploitation of marine resources as well as marine defense and security. AUV carries a variety of sensors to observe and acquire marine information on a large scale, which plays an important role in the development of marine resources and the prevention of disasters [
1]. AUV is an important tool for marine research, which can perform observation missions in the ocean for long periods of time due to their unique mode of operation and efficient energy utilization. Up to now, AUV has been used in the fields of marine biology, chemistry and physics research, including the detection of parameters such as ocean temperature, salinity and oxygen content [
2,
3].
AUV, a new type of underwater robot, utilizes the change in its internal buoyancy system to float and dive, and the change of the center of mass by the internal weight shifting device to control the forward direction. AUV has no conventional propulsion and utilizes the natural flow of the ocean to assist in its movement. This mode of operation significantly reduces energy consumption, so the AUV has the advantages of low energy consumption, low noise, wide range of activities, and long-term continuous observation [
4,
5]. AUV plays a vital role in marine safety and provides accurate real-time measurements for ocean data analysis, prediction, model building, and optimization by collecting complex ocean information [
6,
7,
8].
The underwater environment of the ocean is extremely complex. Complex ocean currents and extreme meteorological conditions may cause the AUV to deviate from its intended route. In the actual observation mission, precise navigation is needed to follow the predetermined route in order to make the AUV arrive at the target sea area accurately for sampling. Path planning is particularly important to ensure that AUV can fulfill their exploration tasks efficiently and accurately [
9,
10]. Reasonable path planning not only improves the detection efficiency of AUVs but also reduces their energy consumption and operating costs.
The development of path planning technology is vital for enhancing the precision, reducing the operational timeframe, and decreasing the energy expenditure of AUVs. Such advancements are particularly important for the standardized use of AUVs in future applications [
11]. At present, AUV path planning methods mainly include traditional algorithms, intelligent optimization algorithms, and multi-algorithm fusion. In practical applications, path planning also needs to take into account the integration and application of key technologies such as environment reconstruction technology, environment sensing technology, intelligent decision-making technology, and underwater localization technology [
12].
The AUV, as an important ocean observation tool, and its path planning research have made remarkable development in recent years. For the complex marine environment, reasonable path planning to ensure that AUVs can accurately and efficiently collect the required data helps AUVs to avoid obstacles to ensure their own safety, and can ensure the quality of the mission completion under the premise of reducing energy consumption and extending the range [
13,
14]. In paper [
15], the principles, advantages and disadvantages of AUV modeling and path search techniques are summarized. In addition, this paper visualizes the experimental environment, real-time performance, and path planning range of AUVs.
In the referenced paper [
16], a comprehensive review of various path planning strategies for AUVs is presented, taking into account the inherent predictability and unpredictability of underwater environments. The paper delves into algorithms designed for both single and multiple AUVs, tailored to operate in environments that can be either predictable or unpredictable. In a particular paper [
17], an advanced algorithm for AUV path planning is introduced, which is founded on the Deep Deterministic Policy Gradient (DDPG) methodology. This sophisticated end-to-end path planning algorithm is designed to directly optimize the decision-making policy. The algorithm operates by processing sensory data it receives as input and subsequently generating output in the form of the vehicle’s travel speed and the angle at which it should navigate through the underwater environment. In paper [
18], a hybrid path planning algorithm considering AUV dynamic constraints based on the improved A* algorithm and Artificial Potential Field (APF) algorithm for AUVs is conducted, highlighting the synergy between traditional algorithms like A* and APF to improve path accuracy, efficiency, and obstacle avoidance by incorporating AUV dynamics and trajectory predictions. Zhang et al. [
19] proposed a multi-AUV full-coverage path-planning algorithm using intuitionistic fuzzy decision-making to address challenges in collaborative search operations. The approach involves constructing a state space model of the search environment using a raster method, and applying intuitionistic fuzzy decision-making to handle uncertain underwater information and plan paths. Fuli Sui et al. [
20] presented a solution for the multi-task path planning problem of AUVs, which is crucial for applications like oil spill detection in complex 3D ocean environments with obstacles. A bi-level multi-objective path planning model was proposed to minimize path length and dangerous distance. The model was solved using a bi-layer hybrid algorithm that combines ant colony optimization (ACO) for task sequencing, particle swarm optimization (PSO) for waypoint generation, and the A* algorithm for creating collision-free paths. Liu et al. [
21] addressed the challenge of path planning for multiple AUVs tasked with missions involving numerous targets in complex underwater environments. A cooperative evolutionary computation algorithm with a bilayer encoding scheme was proposed, representing surface location points and target mission sequences. A multiple populations framework efficiently solved the optimization problem, and a recombination-based sampling strategy improved convergence.
Intelligent algorithms are of great significance to AUV path planning, which can improve the efficiency and accuracy of path planning and adapt to the complex and changing marine environment [
22,
23,
24,
25,
26,
27,
28]. It realizes autonomous path planning and promotes the development of AUV technology. Intelligent algorithms can help AUVs quickly find the optimal or suboptimal paths in complex and changing marine environments, which significantly improves the efficiency of path planning and optimizes the performance parameters of AUVs. It helps AUVs to perform tasks safely and efficiently in complex environments. In this paper, AUV path planning based on the ISSA is proposed for the problems of stability and path length of AUV path planning [
29,
30]. The ISSA not only improves the efficiency and accuracy of path planning, avoids local optimal solutions, and adapts to complex environments but also enhances the scalability and generalization of the algorithm, which is of great significance to the path planning of AUV [
31,
32].
The following improvements can make our work more meaningful: Firstly, the motion model of AUVs and the underwater eddy current model of the ocean are constructed to simulate the motion characteristics and behaviors of AUVs, which can more accurately predict their performance in different environments. Secondly, the SSA is improved. The addition of Levy flight strategy and nonlinear convergence factor can be more applicable to the path planning of AUV. The performance of the improved algorithm, parameter optimization, and path planning is verified by some test functions to evaluate the effectiveness and robustness of the algorithm. Finally, applying the ISSA to the path planning of AUV can make the AUV adapt to the complex and changing marine environment. It not only improves the efficiency and accuracy of path planning but also reduces the errors and deviations in the actual operation and avoids the trap of falling into the optimal solution locally.
The main structure of this paper is as follows: In
Section 2, the modeling of AUVs and ocean eddy is presented. In
Section 3, the SSA is presented, and improvement strategies are added. Then, 2D path planning and 3D path planning for AUVs via the ISSA are simulated in
Section 4. The conclusion is given in
Section 5.
4. Path Planning for AUV
The marine environment is intricate and subject to constant change, with the dynamics of marine organisms exhibiting a wide variety of characteristics, and the ocean currents are unpredictable due to the combined influence of many factors, all of which will increase the difficulty of underwater AUVs in detecting and sensing the marine environment. Obstacle avoidance of the AUV has a great impact on the execution of the mission, so it is of great significance to enhance the path planning technology of the AUV. The information fusion of the improved algorithm with AUV path planning can realize the accuracy, reliability, and resilience of the underwater AUV in navigating the target’s movement, and its own motion dynamics within the intricate marine environment is crucial.
4.1. Path Planning for AUV in 2D Environment
AUV 2D path planning is optimized by using the SSA and ISSA, whose results are investigated. The effectiveness of the proposed method is verified through experiments. A fitness function incorporating constraints is formulated as =, where m denotes the total number of nodes along the path. The term signifies the squared distance between consecutive nodes, effectively measuring the path’s length in a grid-like pattern. In this experiment, the path nodes are progressed sequentially to their subsequent positions. Ultimately, the path is ascertained based on the horizontal coordinates that delineate the trajectory.
The grid map is used for constructing the simulation environment due to its simplicity and efficiency. This method involves dividing a two-dimensional plane into grids of equal length and width, each with a side length of one. In the encoding process, the value one represents obstacles, which are depicted as black areas in the environmental model, while zero represents unobstructed grids, shown as white areas. The grid environment for AUV path planning is illustrated in
Figure 6, with the starting point coordinates at (0, 10) and the endpoint coordinates at (10, 0). The SSA and ISSA are used for 2D path planning of the AUV. The initial overall number is 50, and the maximum number of iterations is 500.
Figure 6a represents the optimal paths of the two algorithms. It is clear to see that the path under the optimization of the ISSA is shorter.
Figure 6b represents the 2D path planning of the AUV under the influence of vortices. Under the influence of eddy currents, the AUV path to the end point has a slight deviation, but the ISSA still shows a clear advantage. The iterative curves of AUV 2D path planning by the SSA and ISSA are shown in
Figure 7.
Table 4 shows the comparison results of the two algorithms for 2D path planning.
As presented in
Table 4, the ISSA outperforms the SSA on several metrics under varying environmental conditions. In the “No Eddy” scenario, the ISSA registers a 102.38% reduction in the number of iterations required (42 vs. 85), a 43.75% reduction in the average path length (32 vs. 46), and a 45.05% decrease in computational time (1.022 s vs. 1.86 s). Additionally, the ISSA demonstrates markedly improved consistency with a 56.01% reduction in the standard deviation of results (0.99556 vs. 2.2631). In the “Existence Eddy” environment, although the gap in iterations narrows with the ISSA showing a modest 4.55% improvement (42 vs. 44), it maintains a significant 50.66% increase in computational efficiency (1.317 s vs. 2.669 s). Crucially, the ISSA achieves a 26.32% decrease in the mean path length (56 vs. 76) relative to the SSA, indicating superior efficacy in navigating to shorter paths. The ISSA also shows considerably enhanced consistency, evidenced by a 63.30% reduction in the standard deviation of results (1.3333 vs. 3.6327). This lower standard deviation suggests that the ISSA outcomes are more reliable and consistent than those of SSA, particularly in complex scenarios. Collectively, these results underscore the comprehensive improvements of the ISSA in efficiency, path length optimization, and consistency across both tested environments, with especially significant enhancements in computational speed and result stability.
4.2. Path Planning for AUVs in 3D Environment
The marine environment is distinguished by its unique features and inherent complexity, predominantly reflected in the shifting nature of maritime weather conditions and the flow of seawater. Additionally, the environment is marked by the intense pressure and frigid temperatures present at great ocean depths, as well as the aggressive corrosiveness of seawater. In addition, there are some unobservable and complex environments in the marine environment, such as reefs and undercurrents. At the same time, some mesoscale and submesoscale eddies are also an important part of the complex environment of the marine environment. The complex marine environment is constructed as shown in
Figure 8, which includes marine sediments, reefs, and eddies.
AUVs face great risks when performing observation and detection missions in complex unsteady environments. In the complex nonstationary environment, the AUV is very susceptible to the influence of eddy currents and deviation from the predetermined route when searching for the target, but the detection mission requires the AUV to move along the target direction and along the predetermined trajectory at all times until it reaches the target point for sampling. Accurate path planning for an AUV in intricate and changing environments is essential for ensuring the successful execution of its mission objectives. High-precision path planning technology requires high stability and robustness of the path planning algorithm.
Regarding setting up the starting point and end point in a complex marine environment, in the 3D path planning simulation, the starting point (denoted by a star) is at coordinates (100, 250, −100), and the endpoint (denoted by a circle) is at coordinates (900, 650, −150). The coordinates of the three obstacles are respectively (300, 350, −100), (400, 600, −100), and (500, 350, −100). Each grid cell in the map is set to a size of 40 × 40 m. Through combining the AUV dynamics model with the intelligent algorithms (ISSA, PSO, WOA, GWO, MVO, GJO, and SSA), the motion trajectories of AUVs under seven intelligent algorithms are obtained as shown in
Figure 9. The iteration curves of 3D path planning for AUV by ISSA, PSO, WOA, GWO, MVO, GJO, and SSAare shown in
Figure 10.
Table 5 shows the comparison results of the seven algorithms for 3D path planning. Different intelligent algorithms have different effects on AUV path planning in complex marine environments. In order to verify the effectiveness of the proposed AUV 3D path planning method based on the improved SSA, the path planning under the influence of eddy currents and obstructions is discussed with seven algorithms. As shown in
Table 5, ISSA consistently outperforms the others across all metrics. It requires the fewest iterations, which is 19. The mean grid path length of the ISSA is the lowest at 32, achieving reductions from 21.88% against GWO to 312.50% against WOA. It also shows the greatest consistency, with a standard deviation of 0.996. ISSA records the best performance at 30, significantly better than competitors, with improvements ranging from 20.00% against GWO to 316.67% against WOA. Moreover, in terms of computational time, ISSA is the quickest at 2.346 s. The comparison shows that the trajectory of the AUV path planning with the improved SSA is more stable and smooth. Furthermore, the ISSA proposed in this paper has the shortest computational time consumption, which is 2.346 s in a 3D scene, and can support real-time AUV path planning in real-world scenarios with regular motion state.
5. Conclusions
In this paper, we investigate the problem of 3D path planning for AUV based on the ISSA. The motion model of the AUV is constructed under the consideration of eddy current influence. The improved salp swarm algorithm is proposed. On the basis of the salp swarm algorithm, the Levy flight strategy and nonlinear convergence factor are added to expand the range of the leader position, which in turn expands the search range of the algorithm. The algorithm is capable of swiftly converging upon the optimal solution. The ISSA is applied to AUV 2D path planning and 3D path planning, which realizes the flexible obstacle avoidance of the AUV. Compared with the other six intelligent algorithms, the ISSA is relatively more stable. Even in the complex marine environment, a route with short distance and high safety can be planned quickly.
In future work, the ISSA-based 3D path planning under the influence of dynamic obstacles will be considered, and the ISSA can be better applied to the problems of path planning tracking and detecting complex ocean information in AUVs. Additionally, we plan to validate and optimize in real ocean environments, while also taking into account path planning considering AUV energy loss.