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- Publisher
- Hindawi Publishing Corporation
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- Copyright © 2019 Hong-Jun Wang 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.
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- 1687-9600
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- 1687-9619
- DOI
- 10.1155/2019/6097591
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Abstract
Hindawi Journal of Robotics Volume 2019, Article ID 6097591, 8 pages https://doi.org/10.1155/2019/6097591 Research Article An Improved Ant Colony Algorithm of Robot Path Planning for Obstacle Avoidance 1 1 2 1 Hong-Jun Wang, Yong Fu , Zhuo-Qun Zhao , and You-Jun Yue Tianjin Key laboratory for Control Theory and Applications in Complicated System, Tianjin University of Technology, Tianjin 300384, China School of Mechanical Engineering, Tianjin Sino-German University of Applied Sciences, Tianjin 300350, China Correspondence should be addressed to Yong Fu; 353269648@qq.com and Zhuo-Qun Zhao; zhuoqunzhao@protonmail.com Received 4 October 2018; Revised 18 January 2019; Accepted 11 February 2019; Published 9 June 2019 Academic Editor: Keigo Watanabe Copyright © 2019 Hong-Jun Wang et al. is Th 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. The obstacle avoidance in path planning, a hot topic in mobile robot control, has been extensively investigated. The existing ant colony algorithms, however, remain as drawbacks including failing to cope with narrow aisles in working areas, large amount of calculation, etc. To address above technical issues, an improved ant colony algorithm is proposed for path planning. In this paper, a new weighted adjacency matrix is presented to determine the walking direction and the narrow aisles therefore are avoided by redesigning the walking rules. Also, the best ant and the worst ant are introduced for the adjustment of pheromone to facilitate the searching process. eTh proposed algorithm guarantees that robots are able to find a satisfying path in the presence of narrow aisles. The simulation results show the effectiveness of the proposed algorithm. 1. Introduction the survival of the tfi test are introduced on the basis of max-min ant system to achieve parameter adjustment and The past decades have witnessed a rapid development of the pheromone update, which accelerates the convergence speed robot control. Nowadays, robots are expected to be capable of of the algorithm. Reviewing existing literature, in spite of various tasks, e.g., collecting the environmental information, the considerable achievement of the ant colony algorithm in avoiding obstacles accurately, fast path planning, etc. At the dealing with path planning, one may notice that some flaws aspect of path planning, much of work concentrates on remain, including exponential explosion [8] and failure of articfi ial potential efi ld method [1], ant colony algorithm bypassing narrow aisle [9]. The exponential explosion refers [2], and genetic algorithm [3]. Aiming at the convergence to the fact that the fine grid division exponentially increases speed of ant colony algorithm and the problem of easy to the search range, resulting in a time-consuming calculation. fall into local optimum, [4] proposes to add artificial local Some articles simply regard robots as a mass point in absence potential optimization algorithm for specific problems in of the consideration of narrow aisles. The problem of narrow the ant colony algorithm search process, which reduces the aisles refers to the fact that the robot cannot pass through blindness of ant colony algorithm and enhances search capa- the narrow aisle due to the limitation of its own volume, bilities. Reference [5] adds the local path information in rigid structure, and trajectory. To address the problem, the environment to initialize pheromone and path selection some articles propose the approaches of environment map probability and the convergence of the algorithm is improved reconstruction, where an obstacle is intentionally mapped to and the premature of algorithm is overcome. In [6], a new occupy one or more grids. Specicfi ally, if it is less than one dynamic search inducing factor is proposed to change the grid, it is counted as one grid. It is also proposed to extend performance of the ant colony algorithm. The dynamic search the boundary of the obstacle outward to the appropriate size model improves the quality of the optimal solution as well as [7, 10]. The approaches of map construction are reasonably increases the convergence speed of the algorithm. Reference effective except some drawbacks. It is reported that when the [7] proposes adaptive model and the evolution strategy of distance between two obstacles is larger than the width of the 2 Journal of Robotics 2 2 2 2 1.5 1.5 1.5 1.5 1 1 1 0.5 0.5 0.5 0.5 0 0 0 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 (a) (b) (c) (d) Figure 1: Obstacle distribution. robot and less than twice width of it, the simulated path works well. When two obstacles, however, are close to each other and the actual distance is less than or equal to the width of the robot itself, the simulation path is invalid. Alternatively, the approach of detours is proposed. Reference [9] constructs a grid map by expanding the obstacle outward, and accordingly the obstacles is avoided by the mean of right-angle bypass and diagonal travel. The approach of right-angle bypass essentially is to stay away from obstacles by walking between the centers of the safety grid only. Reference [11] expands the outward in six selectable directions: up, down, left, right, 0 246 8 10 bottom le,ft and top right. In these six directions, the robot Figure 2: Global motion direction. prefers to move forward obliquely [12, 13]. According to the different positions of the obstacles, the corresponding modes of bypass are den fi ed, respectively. Although both of the methods are aiming at bypassing the narrow aisle, the 2.2. Environmental Formulation. It is well-known that the performance is of conservativeness. It can be observed that distribution of obstacles determines the trafficability for a planned paths by these methods are relatively long. How to robot, which is easily clarified in Figure 1. It is observed that reduce the overall length of paths while effectively avoiding the distributions A, B, and C guarantee the high trafficability of one robot. However, the distribution D is the case with a narrow aisles motivates the investigation of this paper. In this paper, the directions of motion of a robot are expanded to quite narrow aisle for a robot bypassing, which means the low eight and the movement direction of the robot is analyzed traca ffi bility. From a global perspective, the position of the robot in for different positions, an improved ant colony algorithm is proposed by setting new walking rules. the grid is different as well as the direction. Typically, the The contribution of this paper can be summarized as the positions can be categorized into the nine different cases as following aspects. (a) The outwards of grids are extended to Figure 2 shows. eight directions for a better path plan. (b) The new walking According to the positions, the motion of a robot is subdi- rules wereproposed for bypassing thenarrowaisle.(c) The vided into different directions, which eliminates unnecessary amount of calculation is reduced by proposing analytical calculations and accelerates the searching process. calculation method. 3. The Improved Ant Colony Algorithm 2. The Basic Principle of the Algorithm 3.1. The Walking Rules. As aforementioned, there exist dif- 2.1. Grid-Based Environment Map Modeling. In order to ficulties in the existing ant colony algorithms of searching accurately collect the environment and detect the narrow a satisfying path when it has a narrow aisle only to get aisle, the 2D-SDF-SLAM method proposed in [14] is used to through. The solution will be presented in this subsection, construct the map, which can obtain the environmental shape which follows the following two steps. information and ensure the accuracy of the result. The safe zone and the danger zone are defined in the grids, where the Step 1. Consider that the directions of a robot’s motion are safe zones are represented by the areas without the obstacle eight: the upper left, the lower left, the upper right, the lower and the danger zones are represented by the obstacles [15]. right, upper, lower, le,ft and right. When the grid is plotted in rectangular coordinates, the black area represents the crop growing area (dangerous area) and 𝑖 +𝑗 =1 (1) 𝑚 𝑛 the white area represents the open area (safe area). The grid center coordinate of the dangerous area (black part) is the 𝑖 =1 center point of an obstacle, and the grid center point of safe (2) area (white part) is the feasible path point of the robot [16]. 𝑗 =1 𝑛 Journal of Robotics 3 (m-1,n-1) (m-1,n) (m-1,n+1) (m,n-1) (m,n) (m,n+1) (m+1,n-1) (m+1,n) (m+1,n+1) Figure 3: The distance between two grids on the X-axis and Y-axis. Figure 4: An ant’s current position with 8 possibly positions for next. i represents the coordinates of the current grid on X-axis, and j represents the coordinates of the current grid on Y-axis. In order to calculate the distance between arbitrarily two grids, 3.2. The Global Motion Direction. For the ant colony algo- m represents the coordinates of the surrounding grid on X- rithm path planning based on raster graph, there is an expo- axis, and n represents the coordinates of the surrounding grid nential explosion problem when calculating the weighted on Y-axis. When the condition (1) is satisfied, the direction of adjacency matrix, and the meaning of the weighted adja- the next motion will be the upper, or lower, or le,ft or right cencymatrix istoosingle. To addressthe problem, this directions. When condition (2) holds, it will be the upper le,ft paper proposes an analytical calculation method to optimize. lower left, upper right, or lower right directions. Compared with the previous method, the proposed method is more flexible, and different walking principles can be In Figure 3, i represents the distance of arbitrarily two defined according to the requirements and it is also possible gridsonX-axisand j represents the distance of arbitrarily to process and calculate the higher precision grid in the same two grids on Y-axis. When the two safety grids are side by time. side, the lateral distance i is 1 and the longitudinal distance As aforementioned, with the 9 different positions, the j is 0; when the two safety grids are juxtaposed, the lateral movements of the robot are formulated respectively. For distance i is 0; the longitudinal distance j is 1; if the two m n instance, the robot at the position 5 possesses eight different safety grids are diagonal, the lateral distance i is 1, and the directions of motion. According to Figure 1, it can be seen that longitudinal distance j is 1. Both distances are 0. narrow aisle may appear in the upper le,ft upper right, lower left, and lower right directions. When (3)-(6) is true, it means Step 2. According to the robot’s eight directions of motion there is no narrow aisle around; and otherwise a narrow aisle [17], we may mark the eight directions of the current grid, exists. By this mean, the narrow aisle and the nonnarrow aisle see Figure 4, and distinguish the narrow aisle according to are easily identified. formulas (3), (4), (5), and (6). Then we may calculate the To calculate the distance between adjacent two safety distance in each direction. grids in raster, the following equation is necessary: The following equations give the criteria for the existence of narrow aisle: 0.5 2 2 (7) 𝐷 ((𝑖−1 ) ∗𝑙+𝑗, (𝑚−1 ) ∗𝑙+ 𝑛 ) = (𝑖 +𝑗 ) , 𝑚 𝑛 𝐺 (𝑚, 𝑛 − 1 ) =1‖𝐺 ̸ (𝑚− 1,𝑛 ) =1 ̸ (3) where matrix 𝐷 is used to store the distance between the 𝐺 (𝑚, 𝑛 − 1 ) =1‖𝐺 ̸ (𝑚+ 1,𝑛 ) =1 ̸ (4) grids; 𝑙 represents the size of the environment matrix. The right side of (7) is the distance formula, and the left side 𝐺 𝑚, 𝑛 + 1 =1‖𝐺 ̸ 𝑚+ 1,𝑛 =1 ̸ ( ) ( ) (5) is the new additive group adjacency matrix, where the horizontal and vertical coordinates of the matrix represent a 𝐺 (𝑚, 𝑛 + 1 ) =1‖𝐺 ̸ (𝑚− 1,𝑛 ) =1 ̸ (6) grid of the environmental matrix defined by the numbering method. where the scalar G(m,n) ∈ R denotes an indicator of obstacles which is also an element in the environmental matrix. It indicates an obstacle, when its value is 1; it equals 0, other- 3.3. Design of the Heuristic Function. It is a common knowl- wise. edge that, in the basic ant colony algorithm, the direction of When the condition in (3) is met, it shows that a narrow the next step is locally solved without the consideration of the aisle is in the upper left direction. Likewise, the condition overall information. As a result, it yields the locally optimal in (4) is corresponding to the lower le;ft (5) is correspond- solution rather than the globally optimal solution. ing to the right lower; (6) is corresponding to the upper In order to use the global information, the objective right. guidance factor is introduced into the heuristic function. 4 Journal of Robotics The probability of robot-k from the grid-i to grid-j can be where 𝜌 (𝜏 (i,j)) is the global pheromone volatilization coef- obtained by ficient; l is the length of the best path of the robot; l is gb gw the length of the worst path taken by the ant; and Q is the pheromone increasing strength. 𝛼 𝛽 𝛾 [𝜏 (𝑡 )] [𝜂 (𝑡 )] [𝜆 (𝑡 )] { 𝑗𝑜 { (8) ,𝑗 ∈ {𝑁 − 𝑎𝑏 𝑇 𝑢 } 𝑘 3.5. The Flow of the Proposed Algorithm. Specifically, the steps 𝛼 𝛽 𝛾 ∑ [𝜏 (𝑡 )] [𝜂 (𝑡 )] [𝜆 (𝑡 )] { 𝑘∈{−𝑇𝑁 𝑎𝑏𝑢 } 𝑗𝑜 { of the improved ant colony algorithm can be concluded as 0, other follows. where 𝜏 (t) denotes pheromone concentration on the path ij Step 1. Collect the environment information and get the grid (i,j) at time t; 𝜂 denotes the visibility to from grid-i to grid- ij map of the environment. Then, set the starting point and the j; 𝜆 denotes the grid-j proceeds to the extent desired target jo ending point; initialize the ant colony parameters. point o; 𝛼 denotes the information heuristic factor coefficient; 𝛽 denotes the expected heuristic factor coefficient; 𝛾 denotes Step 2. From (1)-(6), determine the current location and the guiding factor coefficient; Tabu denotes the Tabu list of whether there is a narrow aisle around the grid. ant-k. For more information about the Tabu list, see [18]. {𝑁 -𝑢 } represents a collection of grids that ant-k can Step 3. Calculate the distance between all the grids and the currently select, where N represents a collection of all rasters surrounding grids according to the dieff rent positions of the [19]. grids in Figure 2 and the corresponding walking rules and The objective guidance factor is obtained by to the ant in construct a new weighted adjacency matrix. the path planning process, according to the current position from the global direction of the next step. The formula of the Step 4. Set m ants at the start and choose the next node-j target guidance factor is obtained by basing on the distance of the new weighted adjacency matrix with the pheromone distribution in different positions in Figure 2. 𝜆 = (9) 𝑗𝑜 𝑗𝑜 Step 5. Add node-j into the Tabu list of ant-k. where S represents the shortest safe distance between the jo Step 6. Repeat Steps 4 to 5. The ant reaches the target point, current grid-j and the target grid-o, obtained by searching and saves the pathrouth (n, m) and the path length (n, m) for a new weighted adjacency matrix D. 𝜆 represents the jo of each ant, from which the optimal pathrouth (n,m) and reciprocal of the shortest safe distance between the current the optimal path length (length) are selected, and the average grid and the target grid. The larger the shortest safe distance is, the smaller the guidance factor is, the smaller the shortest path length average n. of m ants in this cycle is calculated. safe distance is, the larger the guidance factor is, and the Step 7. Update path pheromones according to formula (10), greater the possibility of selection is. (11), and (12). 3.4. Design of the Optimal Worst Pheromone Update Func- Step 8. Determine whether the algorithm reaches the maxi- tion. In the process of the path searching, pheromones mum number of iterations, then the algorithm terminates and on the path will not only volatilize and decrease with outputs the optimal path routh best, otherwise repeat Steps 3 time but also increase with the number of ants passing to 7. through the path. Because the pheromone in the ant colony algorithm is aeff cted by all the ants, many ants have an The o fl wchart of the improved ant colony algorithm path impact on pheromone updating, which will accelerate the planning is shown in Figure 5. evolution process and accelerate the search speed. Therefore, pheromone updating function is designed, as shown in formulas (10), (11), and (12). 4. The Simulation Result 𝜏 (𝑖, )𝑗 = (1 − 𝜌 (𝜏 (𝑖, ))) 𝑗 ∗ 𝜏 (𝑖, )𝑗 + 𝜓 (𝑖, )𝑗 To verify the effectiveness and superiority of the proposed (10) algorithm, the following simulation is conducted by Matlab ∗Δ𝜏(𝑖,)𝑗 platform. In this simulation, the number of robots per gen- eration, M, is set to be 30; the iterating time K=200; besides ,𝑄 (𝑖, )𝑗 ∈ 𝑜𝑏𝑎𝑙𝐺𝑙 𝑡𝑝𝑖𝑚𝑢𝑚𝑜 parameters in (8, 11) are set to be 𝛼 =1, 𝛽 =7, 𝜌 =0.43, 𝛾 =3, and Q=100. The considered surrounding in this simulation is with 𝜓(𝑖, )𝑗 = (11) −𝑄, (𝑖, 𝑗) ∈ 𝑜𝑏𝑎𝑙𝐺𝑙 𝑤𝑜𝑟𝑠𝑡 a narrow aisle. 0, (𝑖, )𝑗 ∈ 𝑜𝑡ℎ𝑒𝑟 The simulation results are shown in Figures 6–9. It can be observed from Figure 6(a) that three paths generated by three −1 different algorithms are different in the same environment (𝑙 ) , (𝑖, )𝑗 ∈ 𝑜𝐺𝑏𝑎𝑙𝑙 𝑡𝑝𝑖𝑚𝑢𝑚𝑜 𝑔𝑏 Δ𝜏 (𝑖, 𝑗) = (12) with narrow aisle. Through the comparison of the proposed −1 (𝑙 ) ,(𝑖, )𝑗 ∈ 𝑜𝐺𝑏𝑎𝑙 𝑙 𝑤𝑜𝑠𝑟𝑡 algorithm and its counterpart in [7], one may see that the path 𝑔𝑤 𝑇𝑎𝑏 𝑖𝑗 𝑖𝑗 𝑖𝑗 𝑖𝑗 𝑖𝑗 Journal of Robotics 5 Start This paper [7] [11] Build a grid map and determine the start and the target point The corresponding weighted adjacency matrix is calculated based on grid map and formula. Set m ants at the start point Choose node-j basing on the new heuristic function, pheromone distribution and new weighted adjacency matrix 0 5 10 15 20 Add node-j into the Tabu list of ant-k (a) Path planning contrast Convergence curve (minimum path length) Whether current the node is the target node or not. Record all the information of the ant's path Whether the maximum iterations are reached End Figure 5: Algorithm flowchart. 0 50 100 150 200 Number of iterations This paper planned by the method of this paper bypasses two narrow [11] aisles and reaches the target point, but [7] fails to avoid [7] the narrow aisles. Compared with [11], both paths of the (b) Comparison of convergence curves of path planning proposed method and [11] avoid narrow aisles but the former is relatively short. Figure 6: Results of path planning. For the comparison of the convergence speed, two work- ing environments without narrow aisle are chosen. From Figure 7, onemay seethat thepath of thethree algorithms Table 1: Comparison of calculation time. is basically the same in Figure 7(a) graph. From Figure 7(b), Experiment Global Calculation (t/s) Analytical calculation (t/s) however, it can be observed that the proposed algorithm converges around the point of 20 generations. The algorithm 1 0.0038 8.4192e-04 of [7] converges around 40-generation and [11] around 30 - 2 0.0037 8.9884e-04 generation. Based on the simulation, one may conclude that 3 0.0037 8.3912e-04 the convergence of the proposed algorithm is faster than the 4 0.0037 8.2730e-04 counterparts in the [7, 11]. Besides, the environment used in [7] is also employed for 5 0.0038 8.2637e-04 simulation. Figure 8(a) shows that the paths generated by the 6 0.0037 8.4752e-04 proposed algorithm and [11] are identical. The convergence 7 0.0037 8.4223e-04 speeds of them, however, are different; the former is faster which can be seen from Figure 8(b). 8 0.0037 9.9027e-04 Select the same size of the environmental information 9 0.0037 8.9479e-04 matrix as 20∗20. Now, compare the two methods for calculat- 10 0.0037 9.6508e-04 ing a new adjacency matrix. Different methods cost different average 0.0037 8.7734e-04 duration. The results are shown in Table 1. path length 6 Journal of Robotics Convergence curve (minimum path length) [11] [7] This paper 0 50 100 150 200 05 10 15 20 Number of iterations [11] [7] This paper (a) Path planning contrast (b) Comparison of convergence curves of path planning Figure 7: Results of path planning. 20 Convergence curve (minimum path length) [11] [7] This paper 0 50 100 150 200 0 5 10 15 20 Number of iterations [11] [7] This paper (a) Path planning contrast (b) Comparison of convergence curves of path planning Figure 8: Results of path planning. In order to further verify the superiority of the proposed increases proportionally with a smaller coefficient, which is analytical calculation method, a comparison of the different more efficient and less time-consuming. size of the environmental matrix is given in Figure 9. It can be seen from Figure 9 that the analysis method 5. Conclusion proposed in this paper consumes less time than the global method. And with the increase of the environment matrix, With the help of 2D-SDF-SLAM, taking the narrow aisles the consumption time of the global method increases expo- into account, this paper realizes the collection of environ- nentially, while the time consumed by the analysis method mental information; a precise environmental raster map is path length path length Journal of Robotics 7 0.14 References [1] S. S. Ge and Y. J. Cui, “New potential functions for mobile robot 0.12 path planning,” IEEE Transactions on Robotics and Automation, vol.16,no. 5,pp.615–620, 2000. 0.1 [2] M. 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Published: Jun 9, 2019