The Path Planning and Location Method of Inspection Robot in a Large Storage Tank Bottom

With the development of robot technology, inspection robots have been applied to the defect detection of large tanks. However, the existing path planning algorithm of the tank bottom detection robot is easy to fall into the local minimum, and the path is not smooth. Besides, the positioning of the tank bottom detection robot is not accurate. This article proposes a path planning and location algorithm for the large tank bottom detection robot. Specifically, we design a preset spiral path according to the shape of the tank bottom, and a rotating potential field (RPF) near the obstacle is added to avoid the problem of path planning falling into a local minimum. We obtained accurate and smooth planning results. Compared with the state-of-the-art, the RPF method reduced the average RMSE by 9.49%. In addition, by measuring the acoustic emission distance, the three-point positioning algorithm can be used to achieve the calculation of the robot position detection in the proposed method, and the average positioning error on the spiral path is only 0.0748 ± 0.0032.


Introduction
Oil storage tank is an essential and important infrastructure in the petroleum, chemical, and other industries [1]. And the tank may be deformed or leaked under the action of various gas-liquid corrosion and stress changes [2]. If there are potential safety hazards in the oil storage tank, it may cause huge losses [3]. In the recent years, China oriental chemical plant "6.27," Huangdao oil depot "8.12," Dalian Petrochemical Company "8.29," Shandong Shida Technology Company "7.16," and other accidents indicate that China's oil storage tank accidents are still in a state of multiple occurrences [4]. Terefore, the detection and data collection of oil storage tank is a challenging task.
Te metal oil tank is a vessel welded with a steel plate. High strength low alloy steel is used for large volume oil tanks with a capacity of more than 10,000 m 3 [5]. Te common shapes of metal oil tanks are vertical cylindrical, horizontal cylindrical, and spherical. For the most common vertical cylindrical oil tank, the tank bottom is horizontal and round, and a small part of the area is covered with obstacles such as pipes, valves, and oil sludge. Traditional tank bottom detection methods required professionals to carry special equipment into the tank body [6]. Tis detection method has large potential safety hazards and many processes. To mitigate the risk and simplify the process, Leon-Rodriguez described the design of an umbilical-free mobile nondestructive testing (NDT) climbing robot, and the robot was made transitions between the surfaces [7]. Zhang proposed a new climbing robot with a simplifed motion mode and a strong load capacity [8]. Te designed robot has high mobility and can successfully realize the climbing movement, but it cannot meet the demand of omnidirectional movement. After that, Li developed a novel Mecanum omnidirectional climbing robot for tanks inspection [9]. Nevertheless, the application of climbing robot is limited by the poor adsorption capacity. Zhang investigated an innovative wall-climbing robot system based on magnetic circuit optimization [10]. But manual assistance is required during detection. Subsequently, Feng explored a wall-climbing robot with the fusion welding forming model based on BP neural network for automatic welding of the island spherical tank [11]. However, the motion of the robot at the tank bottom has not been considered. To solve this problem, Chrysalidis introduced and analyzed various robot systems for cleaning residual oil at the tank bottom [12]. But these residual oil cleaning robot systems still need manual assistance. Terefore, Chang established a wheeled robot with a magnetic fux leakage testing device [13]. And yet, the circular motion suitable for the tank bottom shape is not considered. Tus, Mondal proposed an adjustable circular shape robot [14]. Te rotational module is designed to allow the wheels to rotate and be able to go in a circular motion. Nevertheless, obstacle avoidance is not considered in this literature. In summary, how to realize automatic obstacle avoidance and dynamic path planning still needs further improvement.
With the development of intelligent automobile and robot, path planning has attracted more and more attention. Traditional path planning algorithms include A-Star, Dijkstra, D-Star Lite, RRT, neural network, intelligence algorithm, and artifcial potential feld method. A-Star is an efective direct search algorithm and is broadly applied. With the increase of nodes, the efciency decreases signifcantly [15,16]. Dijkstra solved the shortest path problem through constructing a directed graph and the optimal solution was obtained [17,18]. However, the space occupied by Dijkstra is large. D-star Lite searches path nodes by maintaining one priority queue and has dynamic planning capability [19,20]. Te disadvantage is low efciency when the state space is large. In RRT, random spanning trees and searching paths were generated. Although the algorithm principle is simple, the planned path cannot be guaranteed to be the optimal path [21,22]. Te solution was optimized in neural network through designing multiple neurons with nonlinear mapping capability and connecting them with weight coefcients. Here, nonlinear mapping and parallel processing were realized but the training time is too long [23,24]. And path planning based on the intelligence algorithm may avoid the problem of local minimum and they are computationally expensive and difcult to solve the problem of high dimension [25]. In comparison, the artifcial potential feld method is a common method with high efciency and a wide application range for robot path planning [26]. Te path planned by the potential feld method is generally smooth and safe, but this method has local minimum problem. To solve the problem of falling into the minimum, many scholars have done research. Sun presented a dynamic window approach and defned a danger index in the speed feld for moving object avoidance. But the problem of inaccessibility of the target is not considered [27]. On this basis, Liu improved a potential feld path planning method based on the genetic algorithm, where the genetic algorithm was used to optimize the combined potential feld function of gravity and repulsion and found the lowest point of potential energy directly so as to determine the step size and moving direction of the robot [28]. However, the security of path planning results is still insufcient. Orozco-Rosas proposed a membrane evolutionary artifcial potential fled (memEAPF) approach with combined membrane computing with a genetic algorithm and improve the security of planned paths [29]. Nevertheless, the oscillation between obstacles and concave obstacle problems is still not considered. Aiming at these problems, Lin constructed an artifcial potential feld path planning model based on decision tree through utilizing the advantages of decision tree in rule expression and extraction, in which this algorithm realized the real-time and accurate identifcation of current behavior and fast decision-making of next time behavior in path planning [30]. With the complexity of the improved methods, the computational complexity is further increased. Tus, Tian proposed a method to construct a guided potential feld in the virtual guiding pipeline. Te algorithm complexity is reduced and the ability to avoid local minima is improved [31]. However, the path planning results are not smooth. Orozco-Rosas proposed a QAPF learning algorithm combining Q-Learning and the artifcial potential feld to obtain smooth results [32]. In addition, the virtual target (VT) method is also proposed to make the path smoother [33]. Virtual targets are designed according to nearest obstacle and generate additional gravity in the VT method. Although the VT method efectively smooths the paths, many virtual targets need to be designed for spiral path planning, which afects the efciency of path planning. Tus, Zhao proposed an improved artifcial potential feld (IAPF) method (state-of-the-art) with designed additional gravity according to the direction of the local minimum point [34]. Although the IAPF method can efectively jump out of the local minimum point, the cost is that there are redundant path points on some paths, which reduces the smoothness of the planning results and increases unnecessary movement. Terefore, on the basis of avoiding local minimum points, how to consider smoothness and efciency of the path planning algorithm needs to be further studied.
Besides, the accuracy and efectiveness of the positioning algorithm are crucial to move the robot accurately according to the path planning results. Until now, the existing indoor location methods have limited positioning accuracy and diferent costs when applied in oil tanks, such as the methods based on Wi-Fi, WLAN, ZigBee, Bluetooth, and ultrawideband (UWB). Te wireless signal in Wi-Fi is vulnerable to interference and refection, resulting in limited positioning accuracy [35]. Shadow and multipath efect exists in WLAN [36]. ZigBee is easy to cause multipath efect and abnormal signal attenuation due to the infuence of the nearby environment [37]. Bluetooth has a small coverage and its accuracy is afected by beacon density [38]. UWB can ensure the positioning accuracy but the equipment cost is high [39]. As a result, a high-precision and cost-acceptable positioning method needs to be considered.
At present, the storage tank in China has been operating for a long time. Tank maintenance and health status monitoring is an urgent task. Due to the lack of the automatic detection equipment, the detection of tank bottom plate is labor-intensive. And the detection efciency is very low. Furthermore, working for a long time in the sealed space of the storage tank is harmful to the health of the staf.
To raise the inspection efciency of the large storage tank bottom, this article intends to propose the path planning and positioning algorithm of the large-scale tank bottom Te rest of this article is structured as follows: Section 2 describes the proposed method. Te experiment results and discussions are presented in Section 3. Finally, Section 4 is the conclusion.

Proposed Method
To achieve efective path planning and accurate positioning of the detection robot, frst, the spiral preset path is designed according to the shape of the tank bottom. Ten, the fow and parameter setting of the rotating potential feld method are introduced. Finally, the principle of the positioning algorithm is described.

Rotating Potential Field Method Based on the Spiral Path.
Tis work designs a spiral path for detecting the bottom of vertical cylindrical oil storage tanks in order to add the detecting area. Inspired by the motion mode of celestial bodies, we improve the traditional artifcial potential feld method through adding a rotation potential feld (RPF) near the obstacles. Te proposed method increases the ability of the artifcial potential feld method to jump out of local extreme points.
First, the robot motion path is set to the spiral equation to make the detection path cover the bottom of the circular oil tank as much as possible. Te spiral path is shown in Figure 1, and points on the path are expressed by p i (x i , y i ). Points in the spiral path are by where n max is the number of iterations required when the distance between the current position of the robot and the center of the circle is less than the threshold d 0 or the preset maximum number of iterations is reached. Te spiral path equation is written by where R is the radius of oil tank bottom, d is the spiral coil pitch, t is the angular velocity, n is the number of iterations, and n ∈ [0, 2πR/d]. When detecting at the bottom, a point p 0 on the tank wall is a starting point and the end point is p n max . On the spiral path, the traditional artifcial potential feld method is shown in Figure 2Q i is considered as current location, and p i+1 is the target point. Point q i is within the infuence range of obstacles, that is to say, the distance between the point q i and the obstacle is less than ρ 0 , where ρ 0 is the infuence radius of obstacles. Te robot is afected by the gravitational F att and repulsive F rep at the same time, which makes the robot move along the direction of resultant force F and reach the point q i+1 . When the resultant force is approach to zero, the path planning method based on the artifcial potential feld method is easy to fall into local extreme points. Figure 3 shows an example of the case of falling into a local extreme point.
When it falls into the local extreme point on the spiral path, the potential feld method is changing with the number of iterations. And the next target point is changed to a critical position. Although the path planning can jump out of the local extreme point, the robot still deviates from the spiral preset path, resulting in the failure of path planning. Figure 4 is a simulation experiment of the failure of path planning. If the radius of the circular bottom of the oil tank is 10, the starting point of the path planning is (10, 0) and the ending point is (0, 0). Te robot moves counterclockwise according to the spiral path. Te green points in the Figure 4 are the historical trajectory of the robot and the red points Computational Intelligence and Neuroscience are obstacles. When the robot moves to the area marked by the purple box, it falls into local extreme points. Next, the results of multiple iterations are almost unchanged. After the next path point changes to a critical position, the robot jumps out of the local extreme point due to large gravity. But the path planning is a failure because the next path point deviates from the original preset route.
To solve this problem, the traditional artifcial potential feld method is improved in this article. Inspired by the motion mode of celestial bodies, we propose a rotating potential feld method based on the spiral path through adding a rotating potential feld near the obstacles.
Te artifcial potential feld method is easy to fall into local extreme points because the resultant force is 0, which causes the robot to stop moving. Te robot moves from the tank wall to the center of the circular tank bottom according to the spiral path. Similar to the movement of celestial bodies, the center of the circle is regarded as the central star, and the robot is taken as the planet moving around the central star. All obstacles are treated as stars; then, the whole system is a multistar system. If the robot moves along the spiral path, it can be regarded as the existence of orbit attenuation in the planetary orbit. Unlike the multistar system in astronomy, the stars in this system always remain stationary, and the two do not rotate around each other. Te infuence range of the obstacle is regarded as the gravitational range of the star, and the gravitational force is not considered outside the infuence range.
Under this assumption, when the planet enters the gravitational range of another star H around the central star, the planet rotates around H. Te gravity generated by the central star is greater. After turning to a certain degree, the planet leaves the gravitational range of H and re-enter the orbit around the central star, that is, the robot may bypass the obstacles.
In order to simulate this motion around the star, a rotating potential feld is added around the obstacle and it is illustrated in Figure 5. When the current position point q i is in the rotation potential feld formed by the obstacle O j , the tangent direction of the circle with O j as the center and passing through the q i point at q i is the gravitational direction. Since the rotation direction in the rotation potential feld is counterclockwise, the tangent direction is also consistent with the rotation direction. Considering that the smaller the distance between q i and O j , the robot may avoid the obstacle O j as soon as possible and the greater the rotation potential feld force. Tat is to say, the force of the rotating potential feld should be inversely proportional to ρ(q i , O j ). Te gravitational force in the rotating potential feld can be defned as where K rot represents the gain coefcient of gravity in a rotating potential feld and set K rot � K att in the experiment. Te fowchart of the rotating potential feld method based on the spiral path is shown in Figure 6.

Acoustic Emission Localization Algorithm.
Te tank bottom detection robot can sense the environment and its own state through sensors and further realize the target oriented autonomous movement in the environment with obstacles. In this work, we select acoustic emission sensors as the excitation source. Tree base stations with known positions are set. Te distances between the current position of inspection robot and the three base stations are measured through acoustic emission sensors. And then the three-point positioning algorithm is applied to realize the real-time calculation of the robot position.   Computational Intelligence and Neuroscience Te three-point positioning algorithm [40] may adopt the position coordinate information of three known points to calculate the current position information. Here, the three points are not collinear.  y). We can obtain the equation Equation (4) is simplifed as follows: Subtract the third equation from the frst two equations in equation (5) and it is written by Ten, we can obtain the equation

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So far, we may easily solve equation (8) by the least square method.
where β ′ is the approximate value of β.

Experimental Test Results and Discussion
Tis section includes three parts. First, the proposed RPF method is compared quantitatively and qualitatively with the existing methods under diferent obstacle distributions. Next, the impact of diferent parameters in the RPF on the planning results is discussed and analyzed. Finally, the effectiveness of the three-point positioning algorithm is verifed by the positioning experiment.

Path Planning Simulation Experiments.
To verify the efectiveness of the path planning algorithm proposed in this article, the robot path planning simulation experiment is carried out. Te CPU model used in the experiment is Intel (R) core (TM) i7-9750h CPU @ 2.60 GHz, and the simulation software platform version is MATLAB 2016.
In the experiment, we model the tank bottom as a circular surface with a radius of 10. Te center of the circle is the origin of the coordinate axis. Green points are used to represent the robot's motion path. Te motion start point is (10, 0) and the end point is (0, 0). Te robot moves counterclockwise. Te termination condition is that the number of iterations is reached or the distance from the end point is less than the threshold d 0 .
We randomly generate m obstacles to verify the path planning ability of the algorithm under diferent obstacle distributions. Te m obstacles are shown as O j (x j , y j ), j � 1, 2, 3, . . ., m, where x j ∈ (−10, 10), y j ∈ (−10, 10), and x 2 j + y 2 j > d 2 0 . Te common parameter settings of diferent algorithms are the same, where K att � 200, K rep � 200, the step size of each iteration move s is set as 0.2, the pitch of spiral path d � 0.4π, angular velocity t � 0.02, and the distance in termination condition d 0 is 0.2.
In order to quantitatively compare the efectiveness of path planning of diferent algorithms, we defne three quantitative evaluation indexes, namely, precision (P), recall (R), and root mean square error (RMSE). Among them, P and R indexes are originated to machine learning indicators. For the path planning point q i and its corresponding preset path point p i , it is regarded as the correct point at ρ(q i , p i ) ≤ T 0 ; otherwise, it is the wrong point. Te three indicators are designed as follows: Precision (P) [41] is estimated by where TP indicates the total number of correct points in path planning, NP is the total number of error points, and P is the proportion of correct points in all path points in the path planning.
Recall (R) [41] is estimated by where FN is the total number of planned errors on the preset path, and R is the proportion of correct points in all the preset path points in the path planning. RMSE [42] is computed by Multiple groups of obstacles are randomly generated within the given range. Te existing methods and the proposed method are compared on three groups of obstacles with diferent distribution. Te quantitative analysis is listed in Table 1. Both P and R indicators are counted at T 0 = 0.2. Te optimal indicators of each group are written in bold in Table 1. We can see that VT, IAPF (state-of-the-art), and RPF are successful in path planning under the infuence of three groups of the obstacles with diferent distribution. Compared with the other two methods, RPF   Figure 8 in order to further compare the consistency between the path planning of diferent algorithms and the preset path. Among the three methods without the improved repulsion function, the rotating potential feld method is better than the virtual target method. Combined with the IR function, when T 0 � 0, the P and R indexes of all methods are improved. For example, under the distribution of obstacle 1, VT + IR improves the precision of 19.34% and the recall of 16.47%. Tis is because the IR function adds some gravitation, which makes the robot moving closer to the preset path. From the P and R curves, RPF + IR has better performance under diferent T 0 under the three obstacle distributions.
Te spiral path planning results illustrated represent intuitively the obstacle avoidance efect of diferent algorithms under three obstacle distributions. Figure 9 shows the results of diferent algorithms under obstacle distribution 1. In the blue rectangular box, it can be seen that APF failed to consider the local extreme points. While the path planning has been successfully realized in the VT, IAPF, and RPF. In the purple rectangular box, only APF + IR cannot successfully plan the path, but other methods combined with the improved repulsion may successfully plan the path.
From the yellow rectangular box, we can see that the overall planning of VT + IR is successful. But it falls into a local minimum point at trying to pass through the middle of two obstacles for many times before avoiding obstacles. Te robot was not separated from the local extreme point until the gravity of a distant point on the preset path is large enough and a deviation between the obstacle avoidance path and the preset path is large enough. However, IAPF + IR and RPF + IR have efectively avoided the local minimum point. In addition, the planning results of IAPF + IR have redundant path points on both sides of the preset spiral path. And RPF + IR in our work does not have this problem. Figure 10 presents the results of path planning in obstacle distribution 2. By observing the gray rectangular box, we can see that the planning result of the VT is diferent from that of other methods. Tis is caused by the design of virtual points. Under the infuence of the counterclockwise rotating potential feld, RPF maintains an upward detour path. Combined with the IR function, diferent algorithms perform similarly in this local region.
In the purple rectangular region, both APF and APF + IR fail to plan and the other algorithms are successful. VT and VT + IR avoid two obstacles by detour, while IAPF, IAPF + IR, and RPF do not fall into the local minimum point under the action of the rotating potential feld. Tey also cross successfully between the two obstacles, and these methods have better performance in quantitative analysis. Figure 11 displays the path planning results of obstacle distribution 3. In the gray rectangular box, both APF and APF + IR fall into the local minimum point, resulting in the failure of path planning. Other methods may avoid obstacles successfully and complete the path planning. Moreover, the planning results of IAPF + IR have redundant path points on both sides of the preset spiral path. And RPF + IR does not have this problem.   We also analyzed the poor results of RPF in path planning. When the robot's current obstacle avoidance action has not ended and meets other obstacles, the obstacle avoidance path will deviate from the preset spiral path, as shown in Figure 12. When this situation occurs continuously, it will lead to more detection blind areas when the tank bottom detection robot performs the detection task as shown in the yellow rectangle in Figure 12. Obstacle avoidance is equivalent to increasing the distance from the current position to the target position, but the step length of the algorithm is fxed, and so more movements are required and the position of the target point is constantly updated. Terefore, when the obstacle avoidance action occurs repeatedly, the distance between the robot's current position and the target point is large, and the gravitation of the target point to the current position is strong. Tis makes the robot move rapidly towards the target point and cannot maintain the preset spiral path.

Infuence of the Parameter Settings Experiment.
In the proposed RPF method, its performance is afected by the setting parameters. We implement the path planning experiment under obstacle distribution 1 for diferent K att , K rep , K rot, and ρ 0 . Te 4 diferent ρ 0 s and 7 diferent ratios of K att and K rep are set in this experiment. Te quantitative comparison results of diferent ρ 0 are listed in Table 2. Te diference between the best index and the worst index of P is 2.11% (from 88.07% to 85.96%). Te diference between the best index and the worst index of R is 1.53% (from 79.85% to 78.32%). Te diference between the best index and the worst index of RMSE is 0.0377 (from 0.2551 to 0.2928). Tese diferences prove that diferent parameters have little infuence on the success of RPF path planning.

Acoustic Emission Positioning Simulation Experiment.
To verify the efectiveness of the three-point positioning algorithm, the simulation experiment of robot positioning is           Computational Intelligence and Neuroscience carried out in this section. In the experiment, three basis points are set up with the coordinates A (7.5, 0), B (−7.5, 0), and C (0, 7.5). A random point is given as the truth point (x gt , y gt ), and the distance from the point to the three basis points is calculated. We add random disturbances to the three distance values to simulate the error in the actual system. If the distance from the truth point to the base station is l, the distance l e after adding random disturbance is

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where v ∈ [−0.05, 0.05] stands for the random disturbance.
Since the acoustic emission sensor ranging results at the same location are diferent each time in the actual system, this experiment adds diferent random disturbances to the distance between the same truth point and the basis point many times. Te average of the multiple positioning results determined the fnal position (x loc , y loc ). In the experiment, the repetition times are set to 20 times. Te Euclidean distance between the positioning result and the truth point is computed as the error E of the positioning algorithm.
In this experiment, several truth points are randomly generated to verify the efectiveness of the algorithm. 12 test environments (P01 to P12) are constructed for the positioning accuracy test. Each environment contains 50 random points. We implemented the proposed algorithm 30 times for each test with diferent v. Best, mean, worst, standard deviation, and t-test represent the solution over independent 30 runs under each environment, respectively. Te results are displayed in Table 3. Te level 0.05 of signifcance is considered for the t-test. Te results indicate that the three-point positioning algorithm has good accuracy. When |v| ≤ 0.05, the average error in all environments is only 0.0839. At the same time, the p-values are far smaller than the level 0.05 of signifcance. In addition, we also tested the calculation time of the algorithm. Each positioning takes only 6∼10 ms, which meets the needs of the actual project. In order to display intuitively the positioning efect, the positioning visualization results are illustrated in Figure 13. It can be seen that the positioning results of the algorithm are very close to the true value point.
In this article, the positioning simulation is also carried out according to the spiral path in the path planning. Te starting point is still (10, 0), the spiral pitch d � 0.4π and angular velocity t � 0.1, and a total of 500 points are generated. Te three-point positioning algorithm is operated after adding random disturbance. Te results are displayed in Figure 14. Te trend of the algorithm results (blue points) is consistent with that of the preset spiral path (red curve). Under this kind of random disturbance, the average error of all point positioning results is only 0.0744. Te 30 times with diferent random disturbance are run, and the average error is only 0.0748 ± 0.0032.

Conclusion
Tis work has investigated a rotating potential feld method based on the spiral path for detecting the bottom of the tank. First, the preset spiral path was designed according to the shape of the tank bottom, and the rotating potential feld was added on the basis of the artifcial potential feld method to achieve efective planning and obstacle avoidance. Te average RMSE of RPF is 9.49% lower than that of IAPF (state-of-the-art), and the algorithm running time is not signifcantly reduced. After that, the three-point positioning algorithm was utilized to realize the calculation of the inspection robot position through measuring the acoustic emission range. Te positioning error on the spiral path is only 0.0748 ± 0.0032. Te parameters in this article, such as K att , K rot, and K rep , are selected based on experience, but diferent parameters do have certain impacts on the planning results, as discussed in Section 3.2. Terefore, better parameter selection can further improve the performance of RPF, and intelligent algorithms such as the genetic algorithm and the particle swarm optimization can be considered for parameter selection. In addition, we found in the simulation experiment that when the robot's current obstacle avoidance action has not ended and meets other obstacles, the obstacle avoidance path will deviate from the preset spiral path. When this situation occurs continuously, it will lead to more detection blind areas when the tank bottom detection robot performs the detection task. Terefore, how to solve the path deviation caused by the continuous obstacle avoidance action is an important issue to improve the algorithm's scene adaptability. Flexible step size design and direction constraints may solve this problem.

Data Availability
Te datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.

Conflicts of Interest
Te authors declare that they have no conficts of interest.