Research Article  Open Access
Jianjun Ni, Liu Yang, Pengfei Shi, Chengming Luo, "An Improved DSABased Approach for MultiAUV Cooperative Search", Computational Intelligence and Neuroscience, vol. 2018, Article ID 2186574, 13 pages, 2018. https://doi.org/10.1155/2018/2186574
An Improved DSABased Approach for MultiAUV Cooperative Search
Abstract
MultiAUV cooperative target search problem in unknown 3D underwater environment is not only a research hot spot but also a challenging task. To complete this task, each autonomous underwater vehicle (AUV) needs to move quickly without collision and cooperate with other AUVs to find the target. In this paper, an improved dolphin swarm algorithm (DSA) based approach is proposed, and the search problem is divided into three stages, namely, random cruise, dynamic alliance, and team search. In the proposed approach, the Levy flight method is used to provide a random walk for AUV to detect the target information in the random cruise stage. Then the selforganizing map (SOM) neural network is used to build dynamic alliances in real time. Finally, an improved DSA algorithm is presented to realize the team search. Furthermore, some simulations are conducted, and the results show that the proposed approach is capable of guiding multiAUVs to achieve the target search task in unknown 3D underwater environment efficiently.
1. Introduction
Autonomous underwater vehicle (AUV) has a wide range of applications in the field of science, commerce, and military, such as searching missing airplanes and ships wreckage, maritime rescuing, and exploitation of marine resources [1–4]. MultiAUV system attracts more and more attentions recently, due to its high parallelism, robustness, and collaboration of high efficiency [5, 6]. MultiAUV system can complete difficult tasks more rapidly and efficiently than a single AUV, so it is a very important development direction in the research field of AUV [7–9].
Target search is a very important and basic mission in the applications of multiAUVs. Also, it is a very challenging task in the field of multiple AUVs. Lots of work has been done to deal with the target search problem. For example, Xiao et al. [10] presented a cooperative multiagent search algorithm to solve the problem of searching for a target on a 2D plane under multiple constraints. Li and Duan [11] proposed a game theoretic formulation for multiple unmanned aerial vehicle cooperative search and surveillance. Cai and Yang [12] proposed a novel potential fieldbased particle swarm optimization approach for a team of mobile robots to cooperatively search targets in unknown environments. Most of the existed methods are focused on the search problem for the ground mobile robot on 2D environments. However, there are obvious differences between the search tasks for the ground mobile robot and the underwater robot. The underwater environment is threedimensional (3D) and has lots of uncertainties [13–15], which is more complicated than 2D ground environment. So, the general cooperative search approaches for the ground mobile robot cannot be used directly for multiAUVs.
Much research has been done to deal with various tasks in the cooperative search task of multiAUVs. For example, Zhu et al. [16] proposed a biologically inspired selforganizing map method for the dynamic task assignment and path planning of multiAUV system. Cao et al. [17] proposed an integrated algorithm for a cooperative team of MultiAUVs by combining the Glasius bioinspired neural network and bioinspired cascaded tracking control approach to improve search efficiency and reduce tracking errors. Yi et al. [18] studied the task assignment problem of a swarm of robots in 3D dynamic environments, and an improved approach that integrates the advantages and characteristics of biological neural systems is proposed. Li et al. [19] presented a bioinspired geomagnetic navigation method for AUV without using any a priori geomagnetic information. Those methods discussed above are all the key technologies of the multiAUV search task, and the research results provided a good basic for the cooperative search task of multiAUVs. However, few of those methods above considered the cooperative search task as a whole, and the search task for the dynamic targets is often ignored.
To complete the cooperative search task efficiently for multiAUVs, the complexity of the search task in the 3D unknown underwater environment with great uncertainties should be considered. The safety of the AUVs and the cooperative efficiency are two main issues in the search task [20, 21]. Recently, many researchers have done lots of work in this field. For example, Ni et al. [22] proposed a partition and column parallel search strategy and a formation search control algorithm based on an improved spinal neural system in 3D underwater environment with obstacles. Abreu et al. [23] presented a coverage path planning technique for search operations, which takes into account the uncertainties of the vehicle position and detection performance. Cao et al. [24] studied the problem of the target search in 3D underwater environments, and an integrated strategy is proposed including the map building based on the DempsterShafer theory of evidence and the path planning based on a bioinspired neurodynamics model. However, there are still some shortcomings in the existing methods that should be solved, such as the low efficiency of the dynamic targets search in the complex 3D underwater environment.
The methods of cooperative search for multiple AUVs can be divided into two types according to the target information. One is based on known information of target prior distribution, such as heuristic search methods [25, 26]. The other is based on sensor information without any target information, such as the region search methods [27]. This paper is focused on the sensor informationbased cooperative search task based on the swarm intelligence algorithm.
In the proposed approach, a novel integrated search method is proposed, including the random cruise strategy, the dynamic alliance construction, and the method to find the position of target. Firstly, a Levy flightbased random cruise strategy is proposed to give AUV a random walk to cruise in the underwater environment [28, 29]. In this study, the Levy flight algorithm is improved by an adjustment module based on fuzzy rules, to make it suitable for the movement characteristics of AUV and the complexity of the underwater environment [30]. After retrieving the target information, a dynamic alliance for the team search is determined using the SOM neural network algorithm [31, 32]. Then, an improved dolphin swarm algorithm (DSA) based approach is used to plan the path for each AUV to search the target [33, 34]. The cooperative search approach in this paper takes full consideration of the obstacles, making the search task more in line with the actual situation and improving the practicality of the method.
The main contributions of this paper are summarized as follows. (1) A cooperative search task in 3D unknown underwater environment is presented, which is completed by a multiAUVs system. (2) An improved DSAbased method is proposed for multiAUV target search, which is an integration of several methods, such as the fuzzy rulesbased Levy flight algorithm for AUVs cruising and the improved DSAbased team search method. (3) The ability of the DSAbased method is improved. The calculation time of the algorithm is reduced, and the search efficiency and the adaptivity of the algorithm for AUVs in 3D underwater environment are increased. (4) Some simulations are conducted in 3D underwater environments, where the situations of the search task for static targets and dynamic targets are simulated. And the proposed algorithm is compared with the general dolphin swarm algorithm and PSO algorithm in these simulations.
This paper is organized as follows. Section 2 presents the problem statement. The proposed cooperative search approach for multiple AUVs based on the improved DSA is given in Section 3. Section 4 gives out the simulation studies and the result analysis. The performance of the proposed approach is discussed in Section 5. Finally, conclusions are given in Section 6.
2. Problem Statement
In this paper, the multiAUV cooperative target search problem in unknown 3D underwater environment is studied. The technical details are not focused in this study, including the shape and movement of the AUV, environment detection, and communication problems. The search task in this paper is that an AUV system is used to find some targets in this underwater environment. The problems are introduced as follows:(1)The AUVs are labelled as , and the set of targets are denoted as . is the number of the AUVs used in the search task, and is the number of the targets.(2)The target has some information that can be detected by the AUVs (such as the infrared radiation of the heat source, the radiation of the radioactive source, or the odour of the odorous source), and the intensity of the target information in the environment is defined as follows:where represents the intensity of target information; and are the coordinates of the target and a point in the environment, respectively; is the largest information intensity; represents the propagation radius of the target information; and function defines the distance between the position and .(3)Each AUV is considered as an omnidirectional robot, having a visual capability and the abilities to communicate with other AUVs, recognize each other, identify the information of target, detect obstacles, and determine their locations in real time. For simplification without losing generality, the AUV can change the moving direction without delay. The movement speed of the AUV can be changed in a certain range around the standard speed (defined as ).(4)The AUVs have no knowledge about the environment and the locations of targets, except the number of targets to be searched. The closer the AUV is to the target, the bigger the intensity of the target information is. If the target is in the visual range of the AUV (denoted as , which is very small, because the underwater environment is dark), it is found and locked by this AUV.
The search task of the targets based on multiAUVs is shown in Figure 1. The work flow and the proposed solutions for the three main stages in this study are shown in Figure 2, which will be introduced in detail as follows.
3. Proposed Approach
In order to complete the cooperative search task for multiAUV system in an unknown 3D underwater environment, some key problems should be solved efficiently, including the random cruise strategy, the dynamic alliance construction, and the way to find the position of target according to the target information. In this paper, a multiAUV cooperative target search approach based on an improved DSA algorithm is proposed.
Before the introduction of the proposed approach, it is necessary to define some flags. One flag is denoted by , indicating the AUV status as cruising, searching, or locking. Another flag is denoted by , indicating the target status as unknown, known, or locked:
3.1. Levy FlightBased Random Cruise
When the AUV does not find any target information, set . The AUV is cruising randomly in the underwater environment, in which an appropriate random cruise strategy is crucial. In this paper, Levy flight is used to randomly change the position of the AUV. The Levy flight essentially provides a random walk for robots, while the random step length is drawn from a levy distribution [35]:where is an index. Then the next position of the AUV can be decided bywhere is the position of the AUV at the time t; is an adjustment parameter which should be related to the velocity of the AUV; means elementbyelement multiplication; can be calculated by Mantegna’s algorithm as [36]:where and are drawn from normal distributions.
Based on the general Levy flight, the AUV can get a random path to search for target information. However, some important things are not considered by the general Levy flight algorithm, because it is often used in optimization algorithms. For example, the AUV may run out of the search area and collide with the obstacles and other AUVs, and the step length generated by the levy algorithm is not suitable for the movement of AUVs. To deal with these problems above, an adjustment module based on fuzzy rules is introduced into the general Levy algorithm. The structure of it is shown in Figure 3.
One of the inputs of the proposed adjustment module is the environment information (including the distance to the obstacles, the distance to the neighbor AUV, and the distance to the search area boundary, defined as , , and , respectively). To consider the real movement of the AUV, another input of the adjustment module is defined as follows:where is the simulation step length. The outputs of the adjustment module are the adjustment for the step length and the movement direction .
The adjustment module in this paper is based on some fuzzy rules. Considering the complexity of the underwater environment, the membership of the input variables , , and are divided as three fuzzy sets, which are (representing near, middle, and far). The membership of variables and are divided as five fuzzy sets, which are . The membership function used in this paper is Gaussian function. To make the AUV to find the target information efficiently, the is defined as , representing going straight and making a turn (the turning angle is random in the range of ). Based on the experiences, total nine fuzzy rules are summarized for the adjustment module, and the style of these rules is as follows:
In this stage, all AUVs move randomly in the search area to detect the target information until an AUV finds target information. Then it goes to the next stage.
3.2. Dynamic Alliance Based on SOM Neural Network
After the AUV finds the target information, the flag of this AUV is set as and the flag of the detected target is labelled as . Before the detected target is found, the AUV who finds the target information should construct a dynamic AUV alliance to search the target faster and more effectively, which can be seen as a task assignment problem.
In this study, a dynamic alliance assignment strategy based on SOM neural network is proposed. The SOM neural network contains two layers, namely, the input layer and the output layer (Figure 4). Each neuron in the output layer of the neural network gets the opportunity to respond to the input through competition. Finally, only one neuron becomes the winner. SOM neural network is competitive, cooperative, and selforganized, which can be used to solve the task assignment problem for multiAUV system efficiently.
In the proposed SOM neural network, the input layer is made up of a neuron , which represents the coordinate of the AUV in the 3D underwater environment. And the coordinates of the other AUVs are denoted as the output layer neurons: . Every neuron of the output layer is fully connected to the neurons of the input layer, and for an input neuron, there is not only one winner.
Winners are chosen during the iterations, and the number of winners depends on the size of AUV team. For a given goal as an input, the output neurons compete to be the winner in an iteration according to a specified criterion described as [37]:where denotes that the th neuron from the th group of the output neurons is the winner; is the set of neurons that have not been the winner yet in an iteration. If the th neuron is chosen to be a winner, the flag of the related AUV is set as . All the winner AUVs with construct the dynamic alliance.
3.3. Team Search Based on an Improved DSA
In this stage, AUVs in each team will search for the exact location of the target based on the intensity of the information, which is a cooperative search problem by optimal solution. Considering the complex underwater environment and the cooperation between the AUVs in a team, an improved dolphin swarm algorithm (DSA) is proposed for multiAUV cooperative search, which is an efficient global search method to solve various optimization problems, by simulating the dolphin’s actual predatory process [33]. The main reason to use DSA method in this paper is that the DSA has better global search ability, better stability, and higher convergence speed, compared with the conventional evolutionary algorithms. To make the DSA method more efficient for the team search, some improvements are presented in this paper, which are introduced as follows.
In the proposed DSAbased method, each dolphin represents an AUV, in the 3D search space of the underwater environment. The dolphin is defined as , and its position is , which is the same as the coordinate of the AUV . For each dolphin , there are two corresponding variables and , where and represent the optimized solution obtained by the dolphin and by all the dolphins of the group in a single search time, respectively. is the number of the dolphins in one group, namely the size of the AUV team. The fitness function is the basis for judging whether the position is better, which is defined as follows:where is the information intensity of the target ; is the parameter to adjust the effect on targets by obstacles or other AUVs; is a function to check whether there is an obstacle, and is a function to judge whether there are other AUVs too close to be collided. The two functions are defined as follows:where is the safe distance of two AUVs to avoid colliding together.
There are four pivotal phases in DSAbased search process, namely, explore phase (namely, the search phase; to distinguish between the search phase of DSA and the search task of the multiAUVs system, in this paper, we name it as explore phase), call phase, reception phase, and predation phase. The details of each phase are introduced as follows:(1)Explore phase. In this phase, each dolphin explores its nearby area by making sounds , towards random directions, where , and is a constant representing the speed attribute of sound. Within the maximum explore time , the sound that the dolphin makes at the time will search for a new solution :where , and is the total explore times for the dolphin. Then, the value of for the at the time is calculated by
And, the value of for can be obtained:where means the set of the of the dolphin during the explore time .
In the multiAUV target search task, the AUV’s motion characteristic in 3D underwater environment should be considered. In the general DSAbased method, the directions of sound are random, which will reduce the effects of the cooperative search. To deal with this problem, the random directions of sounds in the DSAbased method are replaced by a 3D dynamic moving directions model, which is shown in Figure 5.
In the proposed direction model, the core of it is the position of AUV, is the detection range of the onboard sensors, and represents the sound direction. Since all the possible directions are considered in the direction model, the maximum explore time can be not considered and AUV only needs to search for the optimal direction once in a single explore time. Then, the new solution in equation (11) can be calculated by(2)Call phase and reception phase. In the call phase, each dolphin will make sounds to inform other dolphins of its result in explore phase. In the reception phase, dolphins will determine if they can receive information from other dolphins, according to the transmission time matrix . In this study, for simplification, it is assumed that the communication between AUVs is normal; that means the sounds information from the call phase can be received by all dolphins in reception phase.
Then in these two phases, the of the dolphin is updated as follows:where is the valued of obtained from all the dolphins in the same group.(3)Predation phase. In this phase, the dolphins need to update their position according to calculated by the previous phases. However, the in one group is same based on the general DSA method, which may cause the collision between the AUVs in the same team. To deal with this problem, combined with the AUV’s motion characteristics and the underwater environment, an adaptive reference point () is proposed in this paper as follows:where is a constant; and is an arbitrary unit vector. Then, the updated formula of the proposed algorithm is replaced by
After all the dolphins get their new position , then update by
All the AUV will move towards the new position , until the target is found. Otherwise, the DSAbased method will go to the explore phase again. The pseudocode of the whole proposed approach is shown in Figure 6 and its work flow is summarized as follows.
Step 1. The AUVs cruise in the unknown environment randomly using Levy flight algorithm, and detect the target information.
Step 2. If the target information is detected, a dynamic AUV alliance to search the target is constructed by the SOM neural network algorithm.
Step 3. Each AUV in the dynamic alliance is guided to find the position of the target using the dolphin swarm algorithm.
Step 4. Once a target is found by an AUV, then an AUV in the alliance will follow the tracks of this target, and others in the same alliance go to Step1.
Step 5. If all the targets are found, the search task is ended.
4. Simulation Experiments
To demonstrate the effectiveness of the proposed approach for cooperative target search of multiAUVs in unknown 3D environment, some simulations are carried out by a computer with 4G RAM and i52450M 2.5 GHz CPU at the platform of MATLAB. To simplify the realization, the assumptions in this study are as follows: (1) The AUVs and targets are assumed as points without any shapes. (2) The obstacles are enlarged properly in the simulations to deal with the problem of the real shape and size of AUVs. (3) The targets are assumed to move randomly in the environment and the AUV velocity is greater than the target velocity; otherwise, it will be difficult to find the targets. In the simulations, the step length of AUV is 4 m and the step length of target is 2 m. (4) AUVs, obstacles, and target locations are randomly deployed in the 3D underwater environment.
The parameters in all the simulations are the same and given in Table 1. The size of the environment is . To show the advantages of the proposed improved DSAbased algorithm (IDSA), it is compared with the general PSO search algorithm (PSO) and the general DSA method (GDSA). During the conduction of the target search task, the methods for the cruise stage and the dynamic alliance of the three approaches are same, expect the methods for the final team search are different. In the general PSObased team search method, the main parameters are and , which are the cognitive and social scaling factors [38] and are set as and in this study. The GDSAbased method has the same parameters as the IDSAbased method to have comparability, except that the GDSA generates the directions randomly and has multiple iterations in the updating for .
4.1. The Targets are Static
In order to test the basic performance of the proposed approach, the first simulation of searching for the static targets is conducted. The search process based on the proposed IDSA approach is shown in Figure 7. Figure 7(a) shows the initial positions of AUVs and the targets. The initial positions of the AUVs are , , , , , and . And the initial positions of targets are and . Figure 7(d) shows the final trajectories based on the proposed method. The results of the comparison experiments are shown in Figure 8 and Table 2. In this study, an index is used to compare the comprehensive performance of the search methods, namely, the computation efficiency , which is defined as follows:where is the total time used to find all the targets and is the total steps of all the AUVs used in the search task. The less the value of , the higher computation efficiency of the search method.
(a)
(b)
(c)
(d)
(a)
(b)

The results in Figure 7 show that the proposed method can find the targets effectively. At first time, the AUV knows nothing about the obstacles and targets in underwater environment, so each AUV cruises in the underwater environment randomly. Then, the information of is detected by AUVs, and an alliance searching for is formed by the AUVs , , and (Figure 7(b)). When the target is found and locked by (Figure 7(c)), the other two AUVs in this alliance cruise randomly again to search the other targets. Finally, two targets are found and the search task is finished (Figure 7(d)). The results in Figure 8 and Table 2 show that all the three methods can find the static targets efficiently. Because the targets are static, the GDSA method needs less steps and the length of it is less than the proposed IDSA method. However, the computation efficiency of the GDSA is less than the proposed method.
4.2. The Targets are Dynamic
To further test the performance of the proposed approach in the dynamic targets search task, this simulation is conducted. In this simulation, the targets can move randomly in the underwater environment. The results of the proposed approach are shown in Figure 9 and the initial positions of the AUVs and targets are the same as those of the static simulation (Figure 9(a)). The final trajectories based on the PSO method and the GDSA method in this simulation are shown in Figure 10. The results of this simulation are listed in Table 3.
(a)
(b)
(c)
(d)
(a)
(b)

In the search process based on the proposed method, the target is searched by the alliances , , and firstly. Then, is found and locked by . This process is similar with that of the static simulation (Figure 9(b)). However, the AUVs and will construct a new alliance with to search , when the information of is detected. Meanwhile, moves following (Figure 9(c)). Finally, is found by , the search task finished, and the final positions of targets are and (Figure 9(d)). The results of this simulation show that the proposed approach can search the dynamic targets in unknown environment successfully with a relative smooth path than the GDSA method and the PSO method (Figures 9(d) and 10). In addition, the data in Table 3 show that the proposed approach has greater superiority with the shortest path, the shortest time, and the highest computation efficiency in the dynamic target search task than the other two methods, which shows the proposed method has a higher efficiency in the dynamic target search task.
5. Discussions
The results of the simulations in Section 4 show that the proposed method can achieve the multiAUV cooperative search task effectively in unknown 3D environment and shows great superiority comparing with the general DSA and PSO algorithm. Some performances of the proposed approach are discussed in this section.
In order to test the effect of the proposed approach in searching target under a very complex situation, a simulation is conducted, where the parameters of the proposed approach are the same as those in Section 4, except there are some dynamic obstacles in the environment (the step length of the dynamic obstacle is 3 m). In this simulation, the number of AUVs and targets are 3 and 1, respectively, to show the target search process clearly. The initial positions of AUVs are , , and , and the initial position of target is (Figure 11(a)). The final path generated by the proposed approach is shown in Figure 11(d). In this simulation, the total time for the search task is 15.580 (s), and the path length of all AUVs is 465.19 m. The computational efficiency of the proposed approach in this task is 0.146, which increases obviously compared with the tasks in static environment. The main reason is that the proposed method should compute the environment in realtime during the cruise stage, which need much time in a dynamic environment. In spite of this, the results of this simulation show that the AUVs based on the proposed approach can find the target efficiently and avoid the moving obstacles simultaneously, in a dynamic unknown 3D environment (Figures 11(b)–11(d)).
(a)
(b)
(c)
(d)
To illustrate the extensive applications of the proposed algorithm, a simulation is carried out with much more targets. The environment and the parameters of the proposed approach are the same as those in Section 4, except the number of targets is increased to 4. The initial positions of the AUVs are the same with Section 4, and the initial positions of targets are , , , and (Figure 12(a)). The results of the search process are shown in Figure 12. The total time of the search process is 31.326 (s), and the path length of all AUVs is 851.47 m. The computational efficiency of the proposed approach in this task is 0.181; the main reason is that much time is needed to find the target information, and the cooperative performance will decrease obviously when the ratio of the number of target with the number of AUVs decreases (Figures 12(b)–12(d)). The results of this simulation show that the proposed approach can deal with this challenging task. In addition, this simulation proves that multiple AUVs can increase the search efficiency, and the search efficiency and success rate will be increased greatly if there are much more AUVs joining the task.
(a)
(b)
(c)
(d)
6. Conclusion
The multiAUV cooperative target search problem in unknown 3D underwater environment is studied in this paper, and a novel integrated method is proposed. In the proposed method, an improved Levy flight algorithm is used for the AUV random cruise in the unknown environment and the SOM neural network algorithm is used to construct the dynamic alliance for the AUVs which find the target information. And an improved dolphin swarm algorithm (DSA) is proposed to realize the final team search for targets. The proposed method can deal with the problems in the cooperative search task efficiently under various situations, such as the targets are dynamic and there are some moving obstacles in the environment. Furthermore, the movement characteristics of the AUV are considered in the proposed search method, which make it easy to apply the proposed method for real applications of target search task by multiAUVs. In the future work, the real experiments for multiple AUVs cooperative search will be conducted to test the practical performance of the proposed method. In addition, some other bioinspired methods will be studied, to realize targets search by multiAUVs more efficiently.
Data Availability
The data used to support the findings of this study are included within the article.
Conflicts of Interest
The authors declare that they have no conflicts of interest to this work.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (61873086, 61801169, and 61573128), and the Fundamental Research Funds for the Central Universities (2018B23214).
References
 M. E. A. Alaaeldeen and W. Y. Duan, “Overview on the development of autonomous underwater vehicles (AUVs),” Journal of Ship Mechanics, vol. 20, no. 6, pp. 768–787, 2016. View at: Google Scholar
 J. Ni, L. Wu, P. Shi, and S. X. Yang, “A dynamic bioinspired neural network based realtime path planning method for autonomous underwater vehicles,” Computational Intelligence and Neuroscience, vol. 2017, Article ID 9269742, 16 pages, 2017. View at: Publisher Site  Google Scholar
 B. Allotta, A. Caiti, R. Costanzi et al., “A new AUV navigation system exploiting unscented Kalman filter,” Ocean Engineering, vol. 113, pp. 121–132, 2016. View at: Publisher Site  Google Scholar
 X. Xiang, C. Yu, and Q. Zhang, “On intelligent risk analysis and critical decision of underwater robotic vehicle,” Ocean Engineering, vol. 140, pp. 453–465, 2017. View at: Publisher Site  Google Scholar
 R. Cui, Y. Li, and W. Yan, “Mutual informationbased MultiAUV path planning for scalar field sampling using multidimensional RRT∗,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 46, no. 7, pp. 993–1004, 2016. View at: Publisher Site  Google Scholar
 Y. S. Jung, K. W. Lee, S. Y. Lee, M. H. Choi, and B. H. Lee, “An efficient underwater coverage method for multiAUV with sea current disturbances,” International Journal of Control, Automation and Systems, vol. 7, no. 4, pp. 615–629, 2009. View at: Publisher Site  Google Scholar
 B. Das, B. Subudhi, and B. B. Pati, “Cooperative control coordination of a team of underwater vehicles with communication constraints,” Transactions of the Institute of Measurement and Control, vol. 38, no. 4, pp. 463–481, 2016. View at: Publisher Site  Google Scholar
 Z. Huang, D. Zhu, and B. Sun, “A multiAUV cooperative hunting method in 3D underwater environment with obstacle,” Engineering Applications of Artificial Intelligence, vol. 50, pp. 192–200, 2016. View at: Publisher Site  Google Scholar
 Z. Lichuan, W. Tonghao, Z. Feihu, and X. Demin, “Cooperative localization for multiAUVs based on GMPHD filters and information entropy theory,” Sensors, vol. 17, no. 10, p. 2286, 2017. View at: Publisher Site  Google Scholar
 H. Xiao, R. Cui, and D. Xu, “A samplingbased bayesian approach for cooperative multiagent online search with resource constraints,” IEEE Transactions on Cybernetics, vol. 48, no. 6, pp. 1773–1785, 2018. View at: Publisher Site  Google Scholar
 P. Li and H. Duan, “A potential game approach to multiple UAV cooperative search and surveillance,” Aerospace Science and Technology, vol. 68, pp. 403–415, 2017. View at: Publisher Site  Google Scholar
 Y. Cai and S. X. Yang, “A potential fieldbased PSO approach for cooperative target searching of multirobots,” in Proceedings of the World Congress on Intelligent Control and Automation (WCICA), pp. 1029–1034, Shenyang, China, July 2014. View at: Google Scholar
 D. Zhu, H. Huang, and S. X. Yang, “Dynamic task assignment and path planning of multiAUV system based on an improved selforganizing map and velocity synthesis method in threedimensional underwater workspace,” IEEE Transactions on Cybernetics, vol. 43, no. 2, pp. 504–514, 2013. View at: Publisher Site  Google Scholar
 M. P. Aghababa, “3D path planning for underwater vehicles using five evolutionary optimization algorithms avoiding static and energetic obstacles,” Applied Ocean Research, vol. 38, pp. 48–62, 2012. View at: Publisher Site  Google Scholar
 J. Zhou, D. Ye, J. Zhao, and D. He, “Threedimensional trajectory tracking for underactuated AUVs with bioinspired velocity regulation,” International Journal of Naval Architecture and Ocean Engineering, vol. 10, no. 3, pp. 282–293, 2018. View at: Publisher Site  Google Scholar
 D. Zhu, X. Cao, B. Sun, and C. Luo, “Biologically inspired selforganizing map applied to task assignment and path planning of an AUV system,” IEEE Transactions on Cognitive and Developmental Systems, vol. 10, no. 2, pp. 304–313, 2017. View at: Publisher Site  Google Scholar
 X. Cao, H. Sun, and G. E. Jan, “MultiAUV cooperative target search and tracking in unknown underwater environment,” Ocean Engineering, vol. 150, pp. 1–11, 2018. View at: Publisher Site  Google Scholar
 X. Yi, A. Zhu, S. X. Yang, and C. Luo, “A bioinspired approach to task assignment of swarm robots in 3D dynamic environments,” IEEE Transactions on Cybernetics, vol. 47, no. 4, pp. 974–983, 2017. View at: Publisher Site  Google Scholar
 H. Li, M. Liu, and K. Liu, “Bioinspired geomagnetic navigation method for autonomous underwater vehicle,” Journal of Systems Engineering and Electronics, vol. 28, no. 6, pp. 1203–1209, 2017. View at: Google Scholar
 M. Couillard, J. Fawcett, and M. Davison, “Optimizing constrained search patterns for remote minehunting vehicles,” IEEE Journal of Oceanic Engineering, vol. 37, no. 1, pp. 75–84, 2012. View at: Publisher Site  Google Scholar
 B. Das, B. Subudhi, and B. B. Pati, “Cooperative formation control of autonomous underwater vehicles: an overview,” International Journal of Automation and Computing, vol. 13, no. 3, pp. 199–225, 2016. View at: Publisher Site  Google Scholar
 J. Ni, L. Yang, L. Wu, and X. Fan, “An improved spinal neural systembased approach for heterogeneous AUVs cooperative hunting,” International Journal of Fuzzy Systems, vol. 20, no. 2, pp. 672–686, 2018. View at: Publisher Site  Google Scholar
 N. Abreu, N. Cruz, and A. Matos, “Accounting for uncertainty in search operations using AUVs,” in Proceedings of 2017 IEEE OES International Symposium on Underwater Technology, UT 2017, Haeundae, Busan, Republic of Korea, February 2017. View at: Google Scholar
 X. Cao, D. Zhu, and S. X. Yang, “MultiAUV target search based on bioinspired neurodynamics model in 3D underwater environments,” IEEE Transactions on Neural Networks and Learning Systems, vol. 27, no. 11, pp. 2364–2374, 2016. View at: Publisher Site  Google Scholar
 M. Dadgar, S. Jafari, and A. Hamzeh, “A PSObased multirobot cooperation method for target searching in unknown environments,” Neurocomputing, vol. 177, pp. 62–74, 2016. View at: Publisher Site  Google Scholar
 F. Wu, R. J. Yang, and Q. W. Gao, “Heuristic search for moving underwater targets based on Markov process,” Journal of Electronics and Information Technology, vol. 32, no. 5, pp. 1088–1093, 2010. View at: Google Scholar
 J. Ni and S. X. Yang, “A fuzzylogic based chaos GA for cooperative foraging of multirobots in unknown environments,” International Journal of Robotics and Automation, vol. 27, no. 1, pp. 15–30, 2012. View at: Publisher Site  Google Scholar
 V. Fioriti, F. Fratichini, S. Chiesa, and C. Moriconi, “Levy foraging in a dynamic environment—extending the Levy search,” International Journal of Advanced Robotic Systems, vol. 12, no. 7, p. 98, 2015. View at: Publisher Site  Google Scholar
 D. Sutantyo, P. Levi, C. Moslinger, and M. Read, “Collectiveadaptive Levy flight for underwater multirobot exploration,” in Proceedings of 2013 IEEE International Conference on Mechatronics and Automation, pp. 456–462, Takamastu, Japan, August 2013. View at: Google Scholar
 H. Omrane, M. S. Masmoudi, and M. Masmoudi, “Fuzzy logic based control for autonomous mobile robot navigation,” Computational Intelligence and Neuroscience, vol. 2016, Article ID 9548482, 10 pages, 2016. View at: Publisher Site  Google Scholar
 X. Li and D. Zhu, “An adaptive SOM neural network method for distributed formation control of a group of AUVs,” IEEE Transactions on Industrial Electronics, vol. 65, no. 10, pp. 8260–8270, 2018. View at: Google Scholar
 A. Zhu and S. X. Yang, “A neural network approach to dynamic task assignment of multirobots,” IEEE Transactions on Neural Networks, vol. 17, no. 5, pp. 1278–1286, 2006. View at: Google Scholar
 T. Q. Wu, M. Yao, and J. H. Yang, “Dolphin swarm algorithm,” Frontiers of Information Technology and Electronic Engineering, vol. 17, no. 8, pp. 717–729, 2016. View at: Publisher Site  Google Scholar
 W. Yong, W. Tao, Z. ChengZhi, and H. HuaJuan, “A new stochastic optimization approach: dolphin swarm optimization algorithm,” International Journal of Computational Intelligence and Applications, vol. 15, no. 2, Article ID 1650011, 2016. View at: Publisher Site  Google Scholar
 X. He, J. Huang, Y. Rao, and L. Gao, “Chaotic teachinglearningbased optimization with levy flight for global numerical optimization,” Computational Intelligence and Neuroscience, vol. 2016, Article ID 8341275, 12 pages, 2016. View at: Publisher Site  Google Scholar
 E. Cuevas and A. ReynaOrta, “A cuckoo search algorithm for multimodal optimization,” The Scientific World Journal, vol. 2014, Article ID 497514, 20 pages, 2014. View at: Publisher Site  Google Scholar
 J. Ni, X. Yang, J. Chen, and S. X. Yang, “Dynamic bioinspired neural network for multirobot formation control in unknown environments,” International Journal of Robotics and Automation, vol. 30, no. 3, pp. 256–266, 2015. View at: Publisher Site  Google Scholar
 Q. Tang, L. Ding, F. Yu, Y. Zhang, Y. Li, and H. Tu, “Swarm robots search for multiple targets based on an improved grouping strategy,” IEEE/ACM Transactions on Computational Biology and Bioinformatics, 2017, In press. View at: Publisher Site  Google Scholar
Copyright
Copyright © 2018 Jianjun Ni et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.