Path planning for autonomous underwater vehicle in time‐varying current

IET Intelligent Transport SystemsVolume 13, Issue 8 p. 1265-1271 Research ArticleFree Access Path planning for autonomous underwater vehicle in time-varying current Xiang Cao, Corresponding Author Xiang Cao cxeffort@126.com School of Automation, Southeast University, Nanjin, 210096 People's Republic of China School of Physics and Electronic Electrical Engineering, Huaiyin Normal University, Huaian, 223300 People's Republic of ChinaSearch for more papers by this authorChang-yin Sun, Chang-yin Sun School of Automation, Southeast University, Nanjin, 210096 People's Republic of ChinaSearch for more papers by this authorMing-zhi Chen, Ming-zhi Chen Merchant Marine College, Shanghai Maritime University, Shanghai, 201306 People's Republic of ChinaSearch for more papers by this author Xiang Cao, Corresponding Author Xiang Cao cxeffort@126.com School of Automation, Southeast University, Nanjin, 210096 People's Republic of China School of Physics and Electronic Electrical Engineering, Huaiyin Normal University, Huaian, 223300 People's Republic of ChinaSearch for more papers by this authorChang-yin Sun, Chang-yin Sun School of Automation, Southeast University, Nanjin, 210096 People's Republic of ChinaSearch for more papers by this authorMing-zhi Chen, Ming-zhi Chen Merchant Marine College, Shanghai Maritime University, Shanghai, 201306 People's Republic of ChinaSearch for more papers by this author First published: 23 April 2019 https://doi.org/10.1049/iet-its.2018.5388Citations: 3AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Due to the complexity of underwater environment, the navigation of autonomous underwater vehicle (AUV) is affected by current. Although some traditional methods can plan the non-collision path for AUV to reach the destination, it cannot overcome the influence of current on AUV navigation. In order to solve this problem, a velocity vector synthesis method combining belief function (BF) method is proposed. Among them, the BF method is used to dynamically plan the non-collision path. The velocity vector synthesis method is used to adjust the AUVs movement direction to offset the effect of time-varying current. The simulation results show that the proposed algorithm is effective and can overcome the problem of 'current influence'. At the same time, compared with other methods, the proposed algorithm can guide AUV to achieve more efficient and adaptive path planning. 1 Introduction Autonomous underwater vehicle (AUV) path planning means that the AUV follows non-collision and shortest paths from beginning to end. Path planning is an important element for underwater search, underwater SLAM (simultaneous positioning and mapping) and underwater target hunting. Path planning is one of the key contents of underwater vehicle research [1-4]. Many achievements have been made in the study of AUV path planning. For example, the genetic algorithm (GA) for path planning is widely used. It produces a series of possible paths of iterative evolution, using genetic operators to pursue the best results [5]. However, its disadvantage is that the GA lacks convergence, so the generated path may not be optimal or consistent [6]. Compared with GA, A* search technology and rapid exploration random tree (RRT) [7] have better consistency and convergence, because they use discrete environmental, called grid diagram. For example, Persson et al. [8] extended the classical A* algorithm to the field of motion planning based on sampling. However, due to the non-holonomic constraints of the vehicle, further path smoothing is required. Also, the computation time may be high. The RRT method [9] introduced by LaValle [10] does not need to set any resolution parameters, so the RRT method can use a random scheme to quickly and uniformly detect the environment space [11, 12]. However, RRT methods are not suitable for dynamic path planning because they do not provide globally optimal solutions with minimal distance costs. Potential field algorithms [13-15] are popular in path planning because they can effectively find solutions to mitigate the impact of obstacles and destinations. Wu et al. [16] proposed an improved artificial potential field (APF) method to improve the efficiency of path planning. The local minimum problem is solved by integrating wall tracking method. In addition, due to the global planning capability of ant colony algorithm, it is embedded into the APF algorithm [17, 18]. When a robot meets a moving obstacle or changes in the environment, the combined strategy uses local path planning to re-plan the path so that collisions can be avoided. However, this algorithm adds additional algorithms that increase the computational burden [19]. Therefore, Garrido et al. [20] proposed a fast growing algorithm by simulating the propagation of electromagnetic waves, and used this method to build a potential field. Only the starting point is the global minimum point in the generated potential field, and its value is 0. The path planning of these algorithms is efficient, but they cannot overcome the local minimum problem. It should be noted that most of the above studies focus on the generation of non-collision paths but ignore the impact of other environmental factors (such as currents) on path planning [21-23]. The underwater environment is an uncertain, complex and unstable space. In particular, changing current has a great influence on AUV navigation. Therefore, environmental factors need to be considered when designing the AUV path planning algorithm. Sun et al. [24] used fuzzy control method to deal with three-dimensional (3D) AUV path planning based on sonar model. Compared with the horizontal set method, the improved version of the fuzzy algorithm has higher computational efficiency. In addition, a fuzzy inference system with acceleration/disconnection (A/B) module is developed for real-time navigation, enabling AUV to avoid dynamic obstacles automatically. Yan et al. [25] applied 3D bio-inspired neural network to AUV path planning. AUV attracts its mission globally through exciting neural activity and network transmission. At the same time, it is pushed away by localised inhibitory neural activity to avoid collision. However, these methods only take into account the 3D underwater environment and dynamic obstacles, and do not take into account the current impact. To solve the problem of current's effect, Chow [26] combined the k -means method with the Dubins model to solve the problem of accessing compact interval destinations to multiple AUV in the presence of constant current. The study of the novel lies in the k -means to complete the task allocation and adjusted Dubins model, for each of the AUV planning path, but it doesn't take into account the practical application of our more common variable current. For variable current, Cao et al. [27] solved the environmental impact problem in AUV path planning by using field-based particle swarm optimisation algorithm (PPSO). However, these studies are only applicable to the AUV platform, where only 2D current and collision avoidance limits (with limited distance from obstacles) are studied. For 3D AUV navigation, such as time-varying current needs to be considered. In order to solve this problem, an optimised AUV path planning for underwater environment is studied. In this study, the velocity synthesis (VS) algorithm and the belief function (BF) method are combined to reduce the effects of environmental factors (such as time-varying current).The BF method is used to plan the non-collision path, and the VS algorithm is used to adjust the moving direction of AUV to offset the influence of current. Simulation results show that compared with BF method, the algorithm can guide AUV to implement path planning and has high efficiency and adaptability. It is proved that the proposed method solves the problem of 'current influence'. The rest of the paper is organised as follows. In Section 2, the problem statement is given. Section 3 presents the proposed BF and velocity vector synthesis method based integrated path planning algorithm. The various simulation experiments are given in Section 4. Summary and outlook is given in Section 5. 2 Problem statement In this study, the AUV working environment is a 3D environment with time-varying current. According to the actual situation, there may be obstacles and current, as shown in Fig. 1. On the map, the red dots represent AUV and its location; the green pentagram represents the destination position; the black block shows the stationary obstacle; the blue lines represent the current. In order to realise the AUV path planning in real underwater environment, two key problems need to be solved. The first question is: can algorithm security guide AUV from beginning to end? For example, when an AUV works in an obstacle environment, collision avoidance have the highest priority. The second question is: whether the algorithm can plan the optimal paths in complex underwater environments including time-varying currents? The time-varying current deviates the AUV from the planned path, making the AUV sail to the end of the trajectory longer. Fig. 1Open in figure viewerPowerPoint 3D underwater environment 3 Proposed approach In order to solve the problems and challenges of Section 2, it is necessary to combine the traditional hybrid algorithm. This study proposes a VS method combining BF method. The proposed approach involves two phases. First, the BF is used for path planning. Then VS is added to offset time-varying current effect on AUV to optimise the paths. Thus, if there is no obstacle in the environment, AUV will reach the destination in a straight line. If there are obstacles in the environment, the improved BF method will guide AUVs to avoid obstacles. 3.1 Traditional BF approach In the traditional BF method, the BF is divided into the position BF and the direction BF. The environment is built as a grid map firstly, and the position belief of j th unit will be calculated by formula (1). Direction belief of the j th unit will be calculated by formula (2) [28] (1) (2) where is the angle between two vectors from AUV to the j th unit and to the destination separately. (3) where is the coordinate of the AUV in the 3D coordinate, is the coordinate of the j th unit and is the coordinate of the destination. The overall belief value for each unit j is (4) where c is a constant value between 0 and 1. The next position of AUV sailing is calculated by formula (5) (5) Obviously, the traditional BF algorithm can solve effectively the path planning in the no-current environment. However, there are three disadvantages to the traditional BF algorithm. (i) Since the traditional BF algorithm is based on a grid map, even if there are no obstacles in the environment, the navigation path of the AUV is a polygonal line, which leads to the path growth and consumes more energy. (ii) The traditional BF algorithm cannot complete the path planning in the case of 'dead point'. In the unit adjacent to the AUV, the 'dead point' appears where the number of maximum BF grids is more than one. AUV cannot make the right choices based on traditional BF. (iii) The influence of current on the AUV navigation is not considered. 3.2 Improved BF algorithm In order to improve the shortcomings of the traditional BF algorithm, an improved BF is proposed. The improved BF value of the j th unit is calculated as shown in formula (6) [29, 30]. Compared with the belief function value of the traditional BF algorithm, the improved BF not only considers the Mj and Nj, but also considers the 'dead point' functions and the visited information value Ij. Where indicates whether the j th unit is 'dead point' or not. Ij is the visited information value left in the j th unit, and is decreased as time increases, suppose the j th unit is visited at time , so and if the unit is visited before. d, and are constants, to ensure the belief value of obstacle unit is less than zero. After an AUV finishes a destination, 'dead points' of it are cleared for the next path planning. Same as the traditional BF approach, AUV selects the next navigation position with the maximum BF value of the surrounding units. (6) (7) (8) 3.3 VS method Taking into account the actual underwater environment, this study focuses on the path planning in the presence of current and obstacles. In order to solve the shortcomings of the BF algorithm, an algorithm that combines VS and BF is proposed. The basic idea of the VS algorithm is to control the movement direction of the AUV, counteract the effects of the current on the navigation of the AUV and make the resultant vector point to the destination. The AUV is used as the origin and axes parallel with the map axes to construct the motion coordinate system. The representation of the current velocity vector in the motion coordinate system is shown in Fig. 2, ang 1 represents the angle between V c and 0−xy plane, ang 2 is the angle between projection vector of V c on 0−xy plane and the positive direction of x -axis and anticlockwise direction is set as the positive direction. Fig. 2Open in figure viewerPowerPoint Current velocity As shown in Fig. 3, the synthesis speed is the sum of current and AUVs speed, . In the formulae (9)–(11), vector V auv represents the AUVs velocity whose magnitude is given and can be adjusted according to different requirements, and vector V c denotes the ocean currents. Vector V s is introduced to represent the planned path for the AUV. The angle of synthesis speed V s and current speed V c is defined as ang 3. So the value of synthesis speed V s can be obtained by formula (10) [31]. (9) (10) (11) Fig. 3Open in figure viewerPowerPoint Velocity synthesis 4 Simulation studies In the simulation study, there are AUV, destination, time-varying current and obstacles of different sizes and shapes in the underwater working space. This study aims to study this algorithm, so we make the following assumption: (i) AUV is represented by a point without size; (ii) compared with the underwater work space, the turning radius of AUV is negligible, so AUV is assumed to be able to move in all directions; (iii) the positions of AUV, destination and obstacles are generated randomly. In the simulation, the working space of AUV is put into 80 m × 80 m × 80 m. In order to verify the effectiveness of the algorithm, three different situations, including free environment, obstacle environment and dynamic destination environment, were simulated on the MATLAB R2011a. In all simulation experiments, the proposed algorithm uses the same parameters. The parameter settings are shown in Table 1. Table 1. Control parameters of BF& VS Parameter Value c 0.5 d 0.2 0.3 0.2 4.1 Free environment AUV is always operating in an underwater environment, characterised by complex space–time variations. AUVs ability to overcome currents plays an important role in path planning. To achieve this, current information including size and direction can be measured by sensors on the AUV. AUV automatically re-plans the path when the current changes. At the beginning of the simulation, the initial location of the AUV is (18, 12, 9); the initial location of the destination is (71, 68, 62). In Fig. 4, where the green pentagram represents the destination, the curve represents the motion trajectory of AUV, and the arrow indicates its motion direction. The black note represents the current size, the second represents the angle between the current and the xy -plane, and the third represents the angle between the current and the xz -plane. The coordinates of Location 1 and Location 2 are (25, 19, 28) and (57, 49, 46), respectively. Fig. 4Open in figure viewerPowerPoint AUV path planning for time-varying current in free environment (a) BF algorithm, (b) BF and VS algorithm Then, we use the motion of AUV to describe the time-varying current effect in Fig. 4a, where Location 1 and Location 2 represent the current change at that position and the value is indicated by the black annotation. The black comment Location 1 of the comment is displayed at that location, changing the current size to 0.8. In addition, the first angle (the angle between the current and the xy- plane) is 45°, and the second angle (the angle between the current and xz -plane) is −45°. At first, there was no current in the workplace, AUV could move along the straight path until it reached Location 1. Due to the influence of current, AUV starts to deviate from the planning path at Location 1, as shown in Fig. 4a. As the current changes at Location 2, the motion of AUV changes correspondingly with the current. It is easy to see from Fig. 4a that the BF algorithm cannot make the AUV navigation overcome the influence of current. Fig. 4b shows the path planning results of the proposed algorithm. When there is no obstacle, the proposed algorithm applies VS to overcome the effects of currents, the AUV sails in a straight line. It is easy to see from Fig. 4b that the path planned by the BF and VS algorithm is the shortest of all paths. In addition, Table 2 shows the AUV path length of different algorithms as shown in Figs. 4a and b. From Table 2, we can see that the proposed algorithm has better performance than the traditional BF algorithm in a time-varying current environment. Obviously, the proposed algorithm allows the AUV to access the destination with minimum consumption in the presence of time-varying current. Table 2. Comparison of the path length by two algorithms in free environment Algorithm Path length, m BF 62.37 BF and VS 34.16 4.2 Obstacles environment In the realistic underwater environment, there are many obstacles, including static and dynamic obstacles. The proposed algorithm can avoid not only static obstacles, but dynamic ones also. Fig. 5 shows the initial positions of AUV and obstacles, where O 1 is the dynamic obstacle. Assume that the velocity of the obstacle is lower than the motion of AUV. There is no obstacle between the AUV and the destination at the beginning of the stage. In this simulation, however, the obstacle O 1 moves into the AUVs planned path. If AUV continues to follow the original trajectory, it will collide with O 1. The BF algorithm can solve the collision problem, because it can adjust the next movement position of AUV according to the real-time changing environmental information. Therefore, according to the BF algorithm, AUV can re-plan a path to avoid dynamic obstacle. Fig. 5Open in figure viewerPowerPoint AUV path planning for dynamic obstacle in time-varying current (a) BF algorithm 1, (b) BF and VS algorithm While avoiding obstacles, AUV must overcome the influence of time-varying current. The VS algorithm was introduced to overcome the influence of current by adjusting the AUVs sailing direction. Fig. 5 shows the results of the path planning in a time-varying current environment with static destinations using two different methods. In the simulation, the initial locations of AUV and destination are (30, 20, 8) and (56, 76, 63), respectively; the coordinate of Location 1 is (30, 20, 38), the current parameter at Location 1 is set to (0.3, 0°, 90°); the coordinate of Location 2 is (52, 61, 54), the current parameter at Location 2 is set to (0.4, 35°, 60°). Fig. 5a shows the results of BF algorithm. We can see that the AUVs trajectory changes significantly when it encounters a dynamic obstacle. The BF algorithm guided AUV to avoid obstacle O 1. Due to the influence of current, the AUVs trajectory became bent. In Fig. 5b, similar to BF algorithm, AUV avoids dynamic obstacles by re-planning the path. Due to the application of VS algorithm, the AUVs trajectory does not become bent under the influence of current. No matter how the current changes, VS algorithm will always keep AUV in its desired tracks. Table 3 shows the path lengths of two different algorithms in obstacles environment with variable current. In terms of path length, the BF and VS algorithm is obviously shorter than BF algorithm. Therefore, the proposed algorithm can save energy. In addition, we found that the BF algorithm was farther away than that in the free environment, but there was no significant difference in length through the proposed algorithm. This proves that the proposed integration algorithm has the same operability in different environment. Table 3. Comparison of the path length by two algorithms for obstacle Algorithm Path length, m BF 83.92 BF and VS 42.56 4.3 Dynamic destination environment The algorithm can be used to deal with dynamic destination environment. Due to the principle of competitive learning, the AUV automatically re-plans path whenever the destination position and current changes. In Fig. 6, the initial location of the AUV is (39, 8, 6), the initial location of the destination is (76, 59, 63); the green pentagram represents the destination; the arrow represents the movement direction of the destination; the curve represents the trajectory of AUV, and the yellow dot represents the current changing position. Fig. 6Open in figure viewerPowerPoint AUV path planning for dynamic destination in time-varying current (a) BF algorithm 1, (b) BF and VS algorithm The proposed algorithm can not only realise the path planning of static destination, but also realise the path planning of dynamic destination. The principle is that the BF algorithm can readjust the BF based on the changed environmental information and then re-plan the path. When the destination moves, the value of the BF changes according to (10). According to the weight update result, AUV can be repositioned to the desired position. In this section, there are not only dynamic destination but also changing current in the environment. In the simulation, we set the parameters of current as follows: the coordinate of Location 1 is (28, 15, 21), the current parameter at Location 1 is set to (0.2, 90°, 0°); the coordinate of Location 2 is (23, 21, 38), the current parameter at Location 2 is set to (0.3, 40°, 30°); the coordinate of Location 3 is (70, 38, 55), the current parameter at Location 3 is set to (0.1, 100°, 15°). Similar to the working process of a static destination, AUV begins to move along a non-collision path. However, in 10 s, the destinations leave their original location. Destination moved to (60, 70, 50). Fig. 6 shows the results of two different algorithms for path planning in a dynamic target environment with variable current. Fig. 6a shows the results of BF algorithm. When the destination moves, we see the AUV moving to the new destination position. Due to the influence of current, the AUVs trajectory became bent. Similar to Fig. 6a, the proposed algorithm can control the AUV to move towards the new destination in Fig. 6b. The difference between the two algorithms is that the proposed algorithm is not affected by current. As the adaptation of VS keeps the AUV in its desired tracks, regardless of the current change. Table 4 shows the path lengths of two different algorithms in dynamic destination environment with variable current. The results show that the proposed algorithm is much shorter than BF algorithm in AUV navigation path. Therefore, the proposed algorithm is more energy saving than BF algorithm. There is no doubt that the VS and BF algorithm is better suited to handle path planning in a dynamic destination environment with variable current. Table 4. Comparison of the path length by two algorithms for dynamic destination Algorithm Path length, m BF 98.74 BF and VS 46.35 In order to further prove the effectiveness of the proposed algorithm, the simulation of the dynamic destination changes nearly at all the given time. From the start of the simulation to the arrival of the AUV at the dynamic destination, the dynamic destination is always in a random motion. Assume that the speed of the dynamic destination is less than the speed of the AUV. Fig. 7 shows the process of AUV path planning. Fig. 7a shows the trajectory of the AUV and the destination at the beginning of the path planning. We can see the AUV and the destination move at the same time. After a period of time, the AUV reaches the destination, and its trajectory is shown in Fig. 7b. It can be seen that AUV can always adjust the direction to move towards the destination under the control of the proposed algorithm. The proposed algorithm can handle the situation where the dynamic destination changes nearly all the time. Fig. 7Open in figure viewerPowerPoint AUV path planning for the dynamic destination changes nearly all the time (a) The initial phase, (b) The final path 4.4 Comparison of different algorithms In order to further verify the performance of the proposed algorithm, comparison studies with the biological inspired neural network (BINN) algorithm will be carried out. The steps in the planning path of BINN algorithm are as follows: firstly, topologically organised biological inspired neural network based on underwater map is constructed to represent the dynamic environment. Then, the object attracts AUV globally through the dynamic neural activity landscape of the model, while obstacles push AUV away to avoid collision. Finally, AUV automatically plans the path to the destination through the steepest gradient descent rule. The detailed working process is seen in [23]. The parameters of BINN in the simulation are shown in Table 5. Table 5. Control parameters of BINN Parameters Value Description A 2 the passive decay rate of the neural activity B 1 the upper bounds of the neural activity D 1 the lower bounds of the neural activity μ 0.3 a positive constant The comparison studies involve one dynamic destination, AUV, time-varying current and some obstacles with environments scale of 80 m × 80 m × 80 m. Destination, AUV and obstacle are randomly deployed. Two algorithms are applied to the path planning of AUV. Under these conditions, the two algorithms completed 100 simulation experiments of path planning. In order to clearly distinguish the two algorithms, Table 6 lists the path length, the time of complete the task, the computing time of the two algorithms and the standard deviation statistics. The results in Table 6 show that BF and VS perform better than BINN in the comparison simulation. It has shorter path length and time, and shorter calculation time. Through analysis, BINN algorithm cannot overcome the problems of 'current influence' and 'dead point'. Therefore, BF and VS can not only complete the path planning but also improve the efficiency of the path planning in environments with time-varying currents. Table 6. Performance comparison between BF&VS and BINN Performance Algorithm BF and VS, m BINN, m path length 78.35 ± 18.15 105.79 ± 30.94 task completion time 69.68 ± 10.37 117.81 ± 38.75 computing time 37.45 ± 8.32 89.96 ± 20.74 5 Conclusion In this study, an integration algorithm based on BF algorithm and VS algorithm is proposed. This integration algorithm can control AUV to realise dynamic path planning in 3D time-varying current environment. The BF algorithm is applied to AUV path planning. The VS method is used to optimise the path of AUV. 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Cybern., 2013, 43, (2), pp. 504– 514 Citing Literature Volume13, Issue8August 2019Pages 1265-1271 FiguresReferencesRelatedInformation