Multi-Autonomous Underwater Vehicle Full-Coverage Path-Planning Algorithm Based on Intuitive Fuzzy Decision-Making

Abstract

Aiming at the difficulty of realizing full-coverage path planning in a multi-AUV collaborative search, a multi-AUV full-coverage path-planning algorithm based on intuitionistic fuzzy decision-making is proposed. First, the state space model of the search environment was constructed using the raster method to provide accurate environment change data for the AUV. Second, the full-coverage path-planning algorithm for the multi-AUV collaborative search was constructed using intuition-based fuzzy decision-making, and more uncertain underwater information was modeled using the intuition-based fuzzy decision algorithm. A priority strategy was used to avoid obstacles in the search area. Finally, the simulation experiment verified the proposed algorithm. The results demonstrate that the proposed algorithm can effectively realize full-coverage path planning of the search area, and the priority strategy can effectively reduce the generation of repeated paths.

1. Introduction

The ocean occupies 70% of the earth’s surface area. Considering the convenient transportation, rich resources, and important strategic position of the underwater area, in recent years, more and more human activities have been developed to access the deep sea, and the demand for underwater search and rescue, resource exploration, pipeline inspection, and other tasks has been increasing. Therefore, the multi-AUV collaborative search mode has attracted significant attention. On the basis of the traditional single-AUV system, a multi-AUV system can improve task efficiency and fault tolerance through cooperation among the AUVs. When one or more AUVs fail, other AUVs can continue performing the search task, ensuring the continuity and stability of the search. The full-coverage path-planning algorithm is a special path-planning algorithm for specific problems, such as seabed terrain exploration, lost object search, and seabed rescue, and it must realize the search task of the entire search area without dead corners. The information synchronization between different AUVs and a reasonable path-planning algorithm determines whether the full coverage of the search area can be realized and the efficiency of the full-coverage search task.

In recent years, the full-coverage path-planning algorithm has been widely used with UAVs, mobile robots, surface boats, AUVs, and other agents [1,2,3,4]. Inspired by the social behavior of the biological world, Jiao [5] et al. proposed a new multi-agent overlay path-planning algorithm. A new motion model was proposed by introducing behavioral guidance points to guide agents in making decisions. In order to avoid falling into local optima, a cooperative mechanism was designed to improve the adaptability of the system. Simulation results show that the proposed algorithm has advantages over other algorithms in terms of maximum coverage time and coverage repetition rate. Reference [6] introduces an algorithm that uses multiple agents to carry out traversal detection and path coverage of the target region, and plans closed-loop paths in each subregion through the fast-exploration random-tree algorithm to ensure continuous exploration and repeated access to each node of the target region. The final optimization algorithm ensures complete coverage of the target region. The underwater full-coverage path-planning algorithm has also received extensive attention in recent years due to special underwater application scenarios. Zhu [7] et al. proposed a bionic neural network algorithm with improvements, aiming at addressing the shortcomings of the bionic neural network algorithm in robot path planning, such as high computational complexity and long path-planning time, and applied it to the full-coverage path planning of autonomous underwater vehicles. The simulation results showed that the underwater robot could completely cover the entire working space and remove the deadlock immediately without waiting. At the same time, it has the advantages of high-efficiency full-coverage path planning, short path-planning time, and a low overlap coverage rate. Shi [8] et al. proposed a new data-driven coverage path-planning method that automatically updates waypoints intermittently based on objective functions constructed from detection preferences, sonar performance, and coverage efficiency information. The proposed method can be easily adjusted or modified to achieve different coverage objectives. Gan [9] et al. proposed a full-coverage reliability function path-planning algorithm based on a behavior strategy, which enabled AUVs to automatically avoid obstacles while completing the full-coverage task. The simulation results showed that the proposed algorithm not only completed the full-coverage task but also reduced the number of AUVs falling into the dead zone and the traversal repetition rate. Galceran [10] et al. proposed a new method of using autonomous underwater vehicles to plan the detection coverage path of complex seabed structures and a re-planning algorithm based on random trajectory optimization, and proved the effectiveness of the method in marine experiments. Yordanova [11] proposed a coverage path-planning method adapted to the track spacing of underwater vehicles, which was realized through the coverage overlap of the tail of the moving sensor range. Aiming at the path-planning problem of autonomous underwater vehicles searching static targets in marine environments, Yao [12] proposed a layered method based on maximizing the cumulative detection reward or maximizing search efficiency. On this basis, the adaptive elliptic spiral cover strategy was adopted to plan the cover paths within each subregion, and the Dubins paths meeting the AUV motion constraints were taken as the transition paths among the subregions. Through the analysis of the literature described above, it can be seen that the current full-coverage path-planning algorithm is mostly applied to the working conditions of a single underwater vehicle. Considering the high efficiency required by underwater operations, the cooperative operation mode of multiple underwater vehicles has become a better choice for underwater tasks. At present, there are few studies on the application of a full-coverage path-planning algorithm to multiple AUVs, most of which focus on formation keeping, formation reconstruction, and other directions. However, with the increasing demand for underwater full-coverage search tasks in the future, it is of great significance to design a full-coverage path-planning algorithm for multiple AUVs.

The remainder of this article is organized as follows. In Section 2, the construction method of the raster model for a multi-AUV system is described. Basic knowledge about the intuitionistic fuzzy set theory and the design flow of the multi-AUV full-coverage path-planning algorithm based on the intuitionistic fuzzy decision and priority strategy is provided in Section 3. In Section 4, the effectiveness and performance of the proposed algorithm are verified using simulation experiments. Finally, the conclusion is given in Section 5.

2. Spatial Raster Model Construction for a Multi-AUV System

The construction of a raster model can effectively realize information exchange among multiple AUVs and the state simulation of the task space. By dividing the task space into N × N grids, the grid model constructs the information states at different locations. The number of grids depends on the size of the task environment and the demand for task accuracy. More grids increase the working time of the system, and less grids reduce the working accuracy of the system. Therefore, it is important to select a suitable number of grids. Compared with a single-AUV system, information interaction among multiple AUVs is a challenge that needs to be solved. The construction of a reasonable grid model can not only enable each AUV to realize a real-time understanding of the current task environment state but also enable it to know the position of other AUVs in the working process to avoid repeated path planning at the same position and the serious consequences caused by mutual collisions.

Based on a known task environment, this study simulates the state of the workspace using a raster model. The state space can be represented by a raster model as follows:

$$S_k(i,j)=\left\{\begin{array}{l}0\hspace{1em}\mathrm{Unplanned} \mathrm{grid}\\ 1\hspace{1em}\mathrm{Planned} \mathrm{grid}\\ 5\hspace{1em}\mathrm{Obstacle} \mathrm{position}\end{array}\right.,$$

(1)

In the grid model, a value of 0 represents the unplanned search area in the workspace, a value of 1 represents the planned search area in the workspace, and a value of 5 represents the location of obstacles in the workspace, i.e., the area where collision must be avoided during the work of the AUV cluster. The grid model of the workspace can be constructed using this method as follows (see Figure 1):

The blue region is the work area that needs to be covered by the AUVs, and the yellow region is the obstacle area. The grid method effectively simulates the state of the workspace and provides the basis for the subsequent path-planning algorithm.

3. Multi-AUV Full-Coverage Path-Planning Algorithm Based on Intuitive Fuzzy Decision-Making

Intuitionistic fuzzy decision-making is often applied to problems involving inaccurate, uncertain, and fuzzy decision information. An AUV operating environment is located underwater. Compared with a land and air environment, the underwater environment is more complex, and factors such as water flow and quality are complex and variable. Therefore, the application of an intuitionistic fuzzy decision-making algorithm can describe the fuzziness of an AUV operating process in a fuzzy manner.

3.1. Intuitionistic Fuzzy Set Theory

Intuitionistic fuzzy [13,14,15] sets usually refer to three functions to represent membership degree, nonmembership degree, and hesitation degree, and use three kinds of functions to represent the degrees of support, opposition, and hesitation of decision-makers toward decisions. Compared with fuzzy decision-making, the introduction of a nonmembership degree and hesitation degree enables the decision-maker to have a higher degree of freedom in the decision-making process, instead of having to choose between the two absolute attitudes of support and opposition. Atanassov [16] generalized fuzzy set theory and obtained the commonly used definition of an intuitionistic fuzzy set as follows:

Assuming that X is a nonempty classical set, we obtain

$$\stackrel{\sim }{A}=\{〈x,{\mu }_{\stackrel{\sim }{A}}(x),{\nu }_{\stackrel{\sim }{A}}(x)〉|x\in X\},$$

(2)

Here is an intuitionistic fuzzy set on X, where ${\mu }_{\stackrel{\sim }{A}}(x)$ and ${\nu }_{\stackrel{\sim }{A}}(x)$ are the membership and nonmembership degrees of element x belonging to $\stackrel{\sim }{A}$, respectively, i.e.,

$$\begin{array}{l}{\mu }_{\stackrel{\sim }{A}}(x):X\to \left[0,1\right],x\in X\to {\mu }_{\stackrel{\sim }{A}}(x)\in [0,1]\\ {\nu }_{\stackrel{\sim }{A}}(x):X\to \left[0,1\right],x\in X\to {\nu }_{\stackrel{\sim }{A}}(x)\in [0,1]\end{array},$$

(3)

and satisfy

$$0\le {\mu }_{\stackrel{\sim }{A}}(x)+{\nu }_{\stackrel{\sim }{A}}(x)\le 1,x\in X.$$

(4)

For any $x\in X$,

$${\pi }_{\stackrel{\sim }{A}}(x)=1-{\mu }_{\stackrel{\sim }{A}}(x)-{\nu }_{\stackrel{\sim }{A}}(x),$$

(5)

which represents the hesitancy of element X toward $\stackrel{\sim }{A}$. When ${\pi }_{\stackrel{\sim }{A}}(x)$ = 0, the intuitionistic fuzzy set degenerates to the fuzzy set; thus, the fuzzy set is a special case of the intuitionistic fuzzy set.

We define an intuitionistic fuzzy number $\stackrel{\sim }{\alpha }=({\mu }_{\stackrel{\sim }{\alpha }},{\nu }_{\stackrel{\sim }{\alpha }})$, where

$${\mu }_{\stackrel{\sim }{\alpha }}\in [0,1],{\nu }_{\stackrel{\sim }{\alpha }}\in [0,1],{\mu }_{\stackrel{\sim }{\alpha }}+{\nu }_{\stackrel{\sim }{\alpha }}\le 1.$$

(6)

The score of $\stackrel{\sim }{\alpha }$ is given by

$$s(\stackrel{\sim }{\alpha })={\mu }_{\stackrel{\sim }{\alpha }}-{\nu }_{\stackrel{\sim }{\alpha }}.$$

(7)

If ${\stackrel{\sim }{A}}_1=〈{\mu }_j,{\nu }_j〉(j=1,2,\dots ,n)$ is a set of intuitionistic fuzzy numbers, then the intuitionistic fuzzy weighted average operator can be calculated as follows:

$$IFW{A}_{\omega }({\stackrel{\sim }{A}}_1,{\stackrel{\sim }{A}}_2,\dots ,{\stackrel{\sim }{A}}_n)=〈1-{\displaystyle \prod _{j=1}^n{(1-{\mu }_j)}^{{\omega }_j},{\displaystyle \prod _{j=1}^n{({\nu }_j)}^{{\omega }_j}}}〉.$$

(8)

3.2. Multi-AUV Full-Coverage Path-Planning Algorithm Based on Intuitionistic Fuzzy Decision-Making

The complex underwater environment, current eddy current, frequency of unknown obstacles, communication limitations, and other problems pose challenges to the multi-AUV full-coverage path-planning algorithm. The grid model described in the Section 2 of this paper can simulate the position of obstacles well in underwater environments and provides the basis for the multi-AUV full-coverage path-planning algorithm. Underwater communication limitations are also one of the main problems of multi-AUV collaborative algorithms. Underwater communication mainly involves wired and wireless communication; however, wired communication is not suitable for large-scale multi-AUV communication with high mobility because of the large investment in laying wire, difficult construction, and limited scope. However, the absorption losses of electromagnetic and light waves are large underwater, so sonic communication is currently the mainstream underwater AUV communication method. However, compared with terrestrial and sky communication modes, the communication delay is longer because of the limited transmission capacity of sound waves, and communication loss causes uncertainty in the communication quality. At the same time, the underwater environment varies greatly depending on the location; thus, the adaptability of the multi-AUV algorithm is a high requirement. The advantage of intuitionistic fuzzy decision-making lies in the expression of fuzzy information and the ability to make decisions quickly. Therefore, this paper adopts intuitionistic fuzzy decision-making to realize a multi-AUV full-coverage path-planning algorithm.

This section builds an intuitionistic fuzzy function based on two points: collision cost and energy consumption cost. When multiple AUVs are performing full-coverage path planning, the risk of collision among AUVs should be reduced as much as possible to avoid major losses. Considering that the maneuverability of the AUV was lower than that of the UAV and other equipment, 10 m and 1 m were taken as the threshold values. When the distance among the AUVs exceeded 10 m, no collision risk was considered. When the distance among AUVs was between 1 and 10 m, it was considered to have a certain degree of collision risk. When the distances among AUVs were less than 1 m, the AUVs were considered to have a collision risk to a large degree. Based on this, the intuitionistic fuzzy set is constructed as follows (see

Table 1. Intuitionistic fuzzy set based on collision cost.

Distance	Collision Cost
D > 10	<0.8 0.7>
10 ≥ D ≥ 1	<0.5 0.3>
D < 1	<0.2 0.7>

).

Considering the small size of AUVs and their limited battery capacity, the endurance of an AUV is another issue that needs to be considered during an underwater mission. Most AUVs adopt a rudder or differential rudder to realize a change in direction, which causes greater energy loss than going straight. Therefore, the number of turns should be reduced as much as possible in path planning with the full coverage of multiple AUVs. Based on this concept, the intuitionistic fuzzy set is constructed as follows (see

Table 2. Intuitionistic fuzzy set based on energy consumption cost.

Executive Decision	Energy Consumption Cost
Go straight	<0.9 0.05>
Turn left	<0.5 0.3>
Turn right	<0.2 0.7>

).

The backward and inclined directions were not considered to avoid repeated paths. The cow-plowed grass method was used as a reference; that is, turning 90° minimized the number of areas divided by the planned path. As a result, the path that the AUV could select during each movement could be obtained, as shown in Figure 2. The part circled in red is the path away from the obstacle when the current policy is adopted.

The shaded region represents the immovable direction. The values of going straight, turning left, and turning right based on the intuitionistic fuzzy decision algorithm can be calculated using Equation (1), and the maximum value was selected as the next move decision.

3.3. Full-Coverage Path-Planning Algorithm Based on Priority Policy

When there are no obstacles in the task area, the multi-AUV full-coverage path-planning algorithm based on intuitionistic fuzzy decision-making can make fast decisions for multi-AUV clusters. However, when there is an obstacle in the task space, relying only on the intuition-based fuzzy decision algorithm will result in more segmentation subintervals, as shown in Figure 3. In the figure, when AUV1 leaves the obstacle in the circled area, it will choose to continue going straight and divide the lower half of the area into ① and ② zones because of the loss of energy consumption. No matter which zone the search task is completed in first in subsequent path planning, in the process of moving from one subinterval task to another, passing through the duplicate searched paths is inevitable. Therefore, a priority strategy is introduced based on the designed multi-AUV full-coverage path-planning algorithm based on intuitive fuzzy decision-making.

The priority strategy means that when the collision loss is low enough, even if going straight can save a certain amount of energy, to prolong the working time for the generation of a repeated path on the wall, when the AUV anticipates the obstacle, the obstacle is bypassed first, as shown in Figure 3. As can be seen from the figure, when the AUV executes the priority strategy, the number of partitions can be reduced from two to one (Figure 2), thereby avoiding subsequent repeated path planning.

Although the priority strategy can reduce the number of partitions to a certain extent, partitions will inevitably occur during full-coverage path planning for multiple AUVs. That is, there are no selected paths around the AUV, but unsearched areas remain in the entire task area (Figure 4). When AUV1’s path planning completes the search plan of area ②, there is still area ① that is not planned by the path; thus, the memory function is added to the algorithm. When the AUV has no choice of direction during the task execution, it searches the existing memory to find the location nearest to the current location; however, there is still an unplanned area around it. Thus, the AUV moves to this area, as shown in Figure 5. When a path encounters obstacles, the A* algorithm is used to plan the obstacle avoidance path. The A* algorithm will not be described here [17,18,19,20].

3.4. Algorithm Flow

The flow of the proposed multi-AUV full-coverage search path-planning algorithm based on intuitionistic fuzzy decision-making is as follows:

• Step 1: Build the grid model of the workspace;
• Step 2: Determine the AUV entry position and direction;
• Step 3: Determine the intuitionistic fuzzy function set and realize multi-AUV full-coverage path planning based on the intuitionistic fuzzy decision;
• Step 4: When encountering obstacles, if the collision risk is low, execute the priority strategy;
• Step 5: If there is no direction to choose at the current position, the memory function is used to search for other unplanned areas. If obstacles are encountered in the progression process, the A* algorithm is used to realize path planning for avoiding obstacles;
• Step 6: When no unplanned location is present in the entire working range, multi-AUV full-coverage path planning is complete.

The algorithm flow chart is as follows (see Figure 6).

4. Analysis of Experimental Results

The experiment simulated the underwater working environment by simulation and constructed a working environment space model using a grid model. In the experiment, working environments I and II were used as the spatial conditions for multiple AUVs to achieve full-coverage path planning. Working environment I had five obstacles, regular or irregular in shape, and working environment II had four obstacles, regular or irregular in shape. The multi-AUV full-coverage path-planning algorithm based on intuitionistic fuzzy decision-making was used in the simulation experiments. In order to verify the effectiveness of the algorithm for different numbers, simulation tests were carried out on two AUVs and four AUVs in two environments. The experimental conditions were as follows: AUV1 started from the lower left corner of the working area with a heading angle of 90°; AUV2 started from the upper left corner of the working area with a heading angle of −90°. When the number of AUVs was four, the new AUV, AUV3, started from the upper right corner of the working area with a heading angle of −90°; AUV4 started from the lower right corner of the work area with a heading angle of 90°. With the lower left corner as the coordinate origin, the obstacle coordinates of working environment I were (10:20, 9:10), (10:11, 11:15), (13:15, 23:29), (1:14, 42:43), (46:50, 10:26), (30:32, 29:40), and (33:40, 33:35). The obstacle coordinates of working environment II were (9:10, 8:10), (11:12, 10:10), (11:12, 11:15), (31:32, 21:25), (25:32, 24:25), (16:20, 44:45), (14:15, 41:48), (31:32, 36:37), (33:34, 38:39), (35:36, 40:41), and (37:38, 42:43).

It can be seen from Figure 7 and Figure 8 that under the condition of two AUVs or three AUVs, the multi-AUV full-coverage path-planning algorithm based on intuitionistic fuzzy decision-making can effectively make decisions for AUVs and realize full-coverage path planning for the working area under the condition of working environment I, and there is no risk of collision among the two AUVs. The introduction of a priority strategy can effectively avoid known obstacles in the work area and can help reduce the number of partitions. At the same time, it was found that when there was no direction around the AUV during the working process, the introduction of the memory function could help the AUV find the next position at the fastest speed.

Figure 9 shows the multi-AUV full-coverage path-planning algorithm based on intuitive fuzzy decision-making in working environment II under the condition of two AUVs. According to the analysis of Figure 9a, it can be seen that after locating the position by the memory function, obstacles are passed in the process of moving from position ① to position ②. Here, the A* algorithm was adopted to achieve effective obstacle avoidance, and its path results are shown in Figure 9b. Figure 10 shows the multi-AUV full-coverage path-planning algorithm based on intuitive fuzzy decision-making under working environment II with four AUVs. From the graphical analysis, it can be seen that the multi-AUV full-coverage path-planning algorithm based on intuitive fuzzy decision-making is effective in both working conditions, regardless of the presence of two AUVs or four AUVs.

Considering the complexity of the actual water environment, in order to further verify the feasibility of the algorithm, multiple irregular obstacles were added to create working environment III on the basis of working environment II, and four AUVs were used for the test at the same time. The new obstacle coordinates of working environment III were (30, 23), (45, 33), (40, 16), (40, 17), (40, 19), (49, 41), (38, 37), (41, 45), (50, 37), (10, 23), (13, 25), (15, 33), (10, 16), (20, 17), (20, 19), (39, 37), (41, 44), (50, 36), (35, 23), (40, 16), (40, 17), (40, 19), (30, 17), (30, 18), (4, 45), (5, 37), (44, 5), and (45, 10). The experimental results are shown in Figure 11. The results show that the algorithm is feasible and effective even in a complex simulation environment.

5. Conclusions

In this study, intuitionistic fuzzy decision-making is applied to the full-coverage path-planning problem with multi-AUV. First, a grid model is used to describe the state of the working area. Then, an intuitionistic fuzzy set model is established to evaluate the value of path planning for multi-AUV systems. In order to solve the problem of obstacle collision avoidance in this process, a priority strategy is introduced to ensure obstacle collision avoidance and to avoid the generation of more segments as much as possible to prevent more repeated path planning in later stages. When an AUV has no choice of direction during task execution, it searches the existing memory to find a location closest to the current location. When the AUV encounters obstacles in its path to this position, the A* algorithm is used to plan its path. In the experimental analysis, three working environments were used to verify the proposed algorithm. The results show that the multi-AUV full-coverage path-planning algorithm based on intuitionistic fuzzy decision-making is feasible, and there were no collisions among AUVs in the path-planning process. At the same time, the algorithm is effective and feasible for clusters with different numbers of AUVs. In order to further verify the feasibility of this algorithm in the real underwater environment, we will use physical tests to carry out relevant verification in the future.