A Novel Integrated Path Planning Algorithm for Warehouse AGVs

Chinese Journal of ElectronicsVolume 30, Issue 2 p. 331-338 Original Research PaperFree Access A Novel Integrated Path Planning Algorithm for Warehouse AGVs Wen Tao, School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing, 100044 ChinaSearch for more papers by this authorYang Daichuan, School of Automation, Hangzhou Dianzi University, Hangzhou, 310018 ChinaSearch for more papers by this authorLiu Weifeng, School of Automation, Hangzhou Dianzi University, Hangzhou, 310018 ChinaSearch for more papers by this authorWen Chenglin, School of Automation, Hangzhou Dianzi University, Hangzhou, 310018 ChinaSearch for more papers by this authorCai Baigen, School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing, 100044 ChinaSearch for more papers by this author Wen Tao, School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing, 100044 ChinaSearch for more papers by this authorYang Daichuan, School of Automation, Hangzhou Dianzi University, Hangzhou, 310018 ChinaSearch for more papers by this authorLiu Weifeng, School of Automation, Hangzhou Dianzi University, Hangzhou, 310018 ChinaSearch for more papers by this authorWen Chenglin, School of Automation, Hangzhou Dianzi University, Hangzhou, 310018 ChinaSearch for more papers by this authorCai Baigen, School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing, 100044 ChinaSearch for more papers by this author First published: 01 March 2021 https://doi.org/10.1049/cje.2021.02.002 This work was supported by the National Key Research and Development Program (No.2020YFB1313301) and the National Natural Science Foundation of China (No.61806064, No.61751304, No.61933013). AboutSectionsPDF 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 onEmailFacebookTwitterLinked InRedditWechat Abstract We propose an integrated path planning method for multiple automated guided vehicles performing logistics delivery within a real-world warehouse environment considering obstacles. By applying it on each vehicle, this proposed method enables the vehicle the vehicles have the capabilities for autonomous path planning. The path planning consists of three parts, K-means algorithm based task points clustering, genetic algorithm based task points ordering, and the probabilistic road map based best path search. Vehicle conflict resolution is depending on implementing the probabilistic road map construction considering the realistic map with obstacles. The simulations result validate that the clustering and ordering are necessary for the path planning, both the path planning time and the Automated guided vehicles (AGVs) running time can be dramatically reduced. I. Introduction With the rapid development of modern industries, automated warehouses is becoming the mainstream among many giant enterprises, including Amazon in USA and Jingdong in China, and in these automated warehouses, instead of manpower, the main labor is taken by logistics robots. The one of the most primary applications of the logistics robots is to utilize the mobile Automated guided vehicles (AGVs) for delivering or loading goods in warehouses or storage facilities. In this application, how to allocate the multiple tasks to the AGVs efficiently is the one of the most challenging parts. There is plenty of proposed work related to task scheduling in the manufacturing field and other applications, such as K-Nearest neighbor (K-NN)[1], Decision Tree[2], Mixed integer linear programming (MILP)[3], and the heuristics algorithms, including fish swarm algorithm[4], Simulated annealing (SA)[5] and Genetic algorithm (GA)[6], all these algorithms can solve the task allocation problem. In logistics distribution applications, AGVs path planning or routing is another important issue. In Ref.[7], a time window based routing method is proposed for the multiple AGV control system, by using that, the shortest path problem can be dynamically solved with avoiding AGV conflicts; in Ref.[8], a time window method based task assignment and the A-star algorithm Ref.[9] based path planning are jointly proposed, the conflict problem of AGVs has been solved, but, the path environment is just formulated through using a very simply way, which is unrealistic and reduces the capability of the work; in Ref.[10], an algebraic algorithm is used to plan the path for the AGVs, however, in this paper, task assignment has not been considered and the path environment is just presented by using an acyclic graph; in Ref.[11], Petri Net is applied to analyze and design the AGV systems, but the downside of this research work is that only an ideal warehoused environment is considered, this kind of formulation makes this planning method incapable to the real-world applications. It is worthy to mention that all the aforementioned research schedule all the tasks as a whole, no clustering is considered, which may result in a low efficiency with the number of tasks increasing. Therefore, to achieve the maximum efficiency for the AGVs logistics distribution, we have a strong motivation to find out a new combinational method that can integrate the task clustering and scheduling with the path planning, meanwhile, take the real-world environment into consideration. The following sections are arranged: Section II gives the knowledge about how to cluster the task maps in a build a raster with constraints; in Section III, the Genetic algorithm (GA) will be introduced to order the task points in each cluster; to achieve a better path planning in real maps with obstacles, an improved Probabilistic road map (PRM) algorithm is utilized, and the simulation examples are illustrated to prove the validity of this algorithm in Section IV; the conclusion is drawn in Section V. II. Problem Statement The aim of the warehouse logistics distribution is to arrange the AGVs collaboratively complete the whole goods delivery tasks in a most efficiency way. To achieve this aim, the following requirements should be fulfilled: 1) Task clustering, all the task points need to be clustered into different groups depending on their geographical locations on the map, the tasks in each group will be assigned to a dedicated AGV; 2) In each task group, the delivery order must be well planned, in this paper, GA is employed to find out the order; 3) Once the order is defined, the delivery path should be also carefully analyzed, the path is supposed to be the shortest and obstacle-free from the initial to the final; 4) Instead of just using directed acyclic graph to present the warehouse plant layout, in this paper we formulate the AGV working space based on a real-world map. 1. Objective function In this part, the object function of the task scheduling is introduced. We assume that the whole goods is expressed by V, which is V = V q × Q ( 1 ) (1) where Vq is the unit volume of the whole goods, Q is the quantity of the whole goods. We assume there are N AGVs, each AGV has a serial code m, the quantity of the units taken by an AGV m is noted as Qm, therefore, the overall load of the AGV m is expressed as, V m = V q × Q m ( 2 ) (2) In order to deliver all the goods in a high-efficiency way, Q and V should fulfil the following requirements, ∑ m = 1 N Q m = Q ∑ m = 1 N V m = V ( 3 ) (3) In practice, the task points are predefined, each AGV robot starts from a task point to another following a specific order and path. Assume that there are z task points, AGV m needs to deliver goods to i task points following a sorted order, which is expressed as: P 0 , P 1 , ⋯ , P i , ⋯ , P z , ( i ≤ z ) ( 4 ) (4) where the starting point is P 0 ( X P 0 , Y P 0 ) , the final point is P i ( X P i ( m ) , Y P i ( m ) ) . The AGV robot travels from P0 to Pi and then return. As a result, the overall travel distance of the AGV robot m is, S m = ( X P 1 ( m ) - X P 0 ) 2 + ( ( Y P 1 ( m ) - Y P 0 ) 2 + ∑ j = 1 i - 1 ( X P j + 1 ( m ) - X P j ( m ) ) 2 + ( ( Y P j + 1 ( m ) - Y P j ( m ) ) 2 + ( X P i ( m ) - X P 0 ) 2 + ( ( Y P i ( m ) - Y P 0 ) 2 ( 5 ) (5) We suppose that for each meter the consumption of the AGV robot m is C, therefore, for all the N AGV robots, the cost function for accomplishing the whole mission will be, T = ∑ m = 1 N ( S m × C ) ( 6 ) (6) The objective is to minimize the cost function. 2. Map modelling Map modelling is the most fundamental part for the AGV logistic distribution. In many prior research, directed acyclic graph is used to present the warehouse plant layout, but this method is difficult to formulate the obstacles and will result in a infeasible path planning. To overcome this drawback, we will formulate the AGV working space depending on a real-world map. Three types of map formulation methods are popular in the logistic navigation, namely feature map[12], topological map[13] and raster map[14]. For the small-scale space considering obstacles, the raster map has more advantages in path planning[15]. To create a raster map, firstly, we need to process the real-world map[16]. In this paper, the map of the Hangzhou Dianzi University shown in Figure II-B(a) is used as the example, in which the roads are considered as the passable area, the buildings and gardens are defined as obstacles. Then, we divide the map into a number of girds as shown in Figure II-B(b). For each grid, there is a possibility matrix represented as [a, b, U, c], where [a, b] is the configuration of the central point of the grid; U = [0, 1] is a binary variable indicating whether this area is passable or not; c represents the passing cost, for an obstacle, the cost will be ∞. To balance the accuracy and the computational cost, the raster map is divided into 100 × 100 grids, as a result, there will be 10000 sampling points indicating whether these area is passable or not. Fig. 1Open in figure viewerPowerPoint (a) The actual map; (b) The original PRM; (c) The improved PRM after being processed by the Map-Lean method 3. Map leaning The aforementioned method used to process the actual map is known as the Probabilistic Road Map (PRM)[17]. However, in the PRM, due to the location of the grids is presented by the configuration of their central points, some passable paths may be considered as impassable, this is called the narrow passage problem[18-20]. The narrow problem can dramatically decrease the path planning efficiency, to overcome this drawback, one of the solution is to thin the objects on the original PRM[21], we call it Map-Lean method. By using the Map-Lean method, an improved PRM is generated like Figure II-B(c). The main concept of the Map-Lean method is to isotropically lean the obstacles in an equal proportion, therefore, the passable area is expanded, more sampling points will be on the passable area. However, there is a drawback of the Map-Lean method, if the shapes of the obstacles are too complicated, excessively lean the obstacles may lead to the false passage problem, a passable path will be considered in an impassable area. As the actual map selected in this paper is not too complicated, the false passage problem is not likely to happen. In the Map-Lean method, we use i and j to control the leaning ratio λ. For a triangle obstacle, as shown in Figure II-C(a), h is the number of the grids at the height of the obstacle, l is the number of the grids at the bottom of the obstacle; for a rectangle obstacle, as shown in Figure II-C(b), h is the number of the grids at the short edge of the obstacle, l is the number of the grids at the long edge of the obstacle. For the leaning ratio, there is, λ = 1 - ( h - i ) ( l - j ) h l (1) For the obstacles with more complex shapes, we can decompose them into a combination of triangles and rectangles, by which the leaning ration will be achievable. For the map used in this paper, if we adopt a conservative obstacle leaning strategy, let i = 1, j = 0, we can derive that the obstacle leaning ratio is about 16%. Fig. 2Open in figure viewerPowerPoint Diagram for Map-Lean III. Task Points Clustering and Ordering To improve the path planning efficiency in AGV logistics distribution, we will conduct clustering and ordering for these task points. 1. Task Points Clustering There are many existing methods that can be used to do task points clustering, such as K-Nearest Neighbor[22], K-Means[23], Shared Nearest Neighbor[24]. Due to the map used in this paper is not very complicated, K-Means is employed to carry out the clustering work, which is considered as an effective and fast enough method for dealing with simple scenarios. The K-Means algorithm is adopted to find K clusters in a given dataset, the dataset contains I randomly generated task points, each point in the dataset needs to be assigned to a cluster. In this paper, Manhattan distance[25] is adopted as the distance metric, the objective of clustering is to find the minimum J, which is expressed as[26], J = ∑ i = 1 I ∑ k = 1 K r k i | P i - μ k | 2 ( 8 ) (8) where Pi is the i-th task point, μk is randomly generated for the k-th cluster, rki is a binary variables indicating whether the Pi has been assigned to the cluster k or not. After finishing the clustering, the configurations of the centroid in each cluster will be updated as the average of the task points in the cluster. Here is an indicative example, it is assumed that there are 26 task points need to be assigned to 3 clusters, the detailed configurations of each task point are shown in Fig.3 and Table 1 respectively. The clustering result is drawn in Fig.4 and Table 2. In Fig.4 we can see that the task points in each cluster are marked by different colors, cluster I and cluster III have 8 task points respectively, cluster II has 10 task points. Fig. 3Open in figure viewerPowerPoint The locations of the task points 2. Task points ordering by genetic algorithm After clustering these task points, in this part we will investigate how to plan the delivery order in each cluster. Considering the convenience and efficiency, the Genetic Algorithm (GA) will be a good option to undertake this work. Table 1. The Coordinate of the Task Points on the Map P1(42,4) P2(12,30) P3(84,35) P4(50,90) P5(96,96) P6(40,70) P7(95,60) P8(10,55) P9(5,80) P10(40,40) P11(70,10) P12(70,80) P13(21,21) P14(5,40) P15(45,26) P16(65,23) P17(89,19) P18(68,73) P19(13,97) P20(43,66) P21(67,53) P22(80,80) P23(3,75) P24(94,26) P25(41,90) P26(53,15) GA is a very popular optimization method, it is based random search and inspired by the biological evolution, known as the survival of the fittest. By means of the genetic operators, it produces a population through crossover and mutation which could lead to the next generation of population become better than the previous generations[27]. After the GA processing, the best individual in the population will be seen as the approximate optimal solution of the problem. The process of the GA is: Fig. 4Open in figure viewerPowerPoint The task points clustering result Table 2. The Task Points Clustering Result No. Type I Type II Type III 1 D(50,90) A(42,4) F(40,70) 2 L(70,80) C(84,35) H(10,55) 3 G(95,60)) J(40,40) I(5,80) 4 E(96,96) K(70,10) S(13,97) 5 R(68,73) M(21,21) T(43,66) 6 U(67,53) O(45,26) W(3,75) 7 V(80,80) P(65,23) B(12,30) 8 Y(41,90) Q(89,19) N(5,40) 9 X(94,26) 10 Z(53,15) 1) Randomly generate M individuals as the population, evaluate the fitness f(xi) for each individual based on the travel distance, i = 1, 2, 3…M; 2) Calculate the selection probability P(xi) for each individual, 3) Based on the fitness of each individual, use the round robin selection to select the individuals 4) Generate the next generation population of solutions from those selected individuals through a combination of genetic operators: crossover and mutation. 5) Repeat the Step 3 and Step 4 until reaches the iteration limit; 6) Output the individual solutions. P ( x i ) = f ( x i ) ∑ j = 1 M f ( x j ) ( 9 ) (9) Before implementing the ordering process, we need to find out which task point is the initial task point P1. Assume a point P0, the P1 will be able to minimize the Euclidean distance to P0, the AGV will deliver the goods P0 at first. The Euclidean distance between P0 and P1 is ( x P 0 - x P 1 ) 2 + ( y P 0 - y P 1 ) 2 . In this paper, we set the configuration of P0 to as (70, 0), therefore, the P1 in Type I, II and III will be U(67, 53), K(70, 10) and B(12, 30) respectively. By implementing the GA, the optimised task points delivery order in each cluster can be drawn. The optimization result is in Fig.5. IV. Path Planning Problem In the preceding part of the paper, the combination of multiple algorithms, including tasks points clustering and ordering, has been analyzed. In terms of how to plan the delivery path between the successive task points, there are a number of ready-to-use methods, such as the PRM method[28], the improved PRM method and IDA*[29], D* Lite[30] and Bug2 algorithm[31]. In this section, we will introduce and implement the PRM-based path planning methods as the example, then, to state the necessity of the combination of clustering and ordering, conduct the path planning without doing task points clustering and ordering as the contrast. Fig. 5Open in figure viewerPowerPoint The task points delivery ordering resut 1. PRM-Based path planning The PRM method is proposed by Kavraki et al. This method can be applied to determine the most suitable path between a starting point and a goal point. The PRM-based path planning consists of two steps: roadmap construction and path searching. In the first step, the PRM method uses random sampling to obtain the free space information of the map. Firstly, v collision-free configurations are randomly chosen on the map G, all these configurations form dataset V; then, we set a distance radius r, generally it should be 0.3 times of the matrix size, for each configuration in V, connect its neighbors with the distance less than r as an edge in G, all these edges form dataset E; finally, a PRM G = (V, E) is achieved. The detailed process of the PRM construction is shown in Algorithm 1. In the second step, we can a local planner, such as the Dijkstra algorithm, to search the shortest path on G = (V, E). The complexity of this PRM method is O(|E| + |V|log|V|) Obviously, if we want the PRM method has an excellent result, just need to increase the quantity of the sampling points on the map, you can learn more free space information of the map. However, when the number of the sampling points increase, more vertices and edges will casus the computational complexity grows exponentially. Therefore, to recieve a better result, we need to carefully set the radius r[30]. In order to prove the efficiency of the PRM method, we take the task points in Cluster I as the example. We select 150 sampling points and the radius v is set to as 22. The path planning result for Cluster I is shown in Fig.6. Algorithm 1 PRM Construction Input: v and r Output: PRM G = (V;E) V ← ∅ E ← ∅ while |V| < v do repeat q ← a random configuration in the map until q is collision-free V ← V ∪ {q} end while for all q ∈ V do Nq ← the neighbors of q chosen from V and dist < r for all q* ∈ Ng do if (q, q*) ∉ E and (q, q*) is collision-free then E ← E ∪ {(q, q*)} end if end for end for 2. Effectiveness simulations on other common approaches In order to prove the effectiveness of the proposed integrated path planning method in this paper, we will conduct the simulations for other common path planning approaches and take the result as the contrast. As can be seen from Table 4, after clustering the task points and applying the genetic algorithm to order the task points in clusters, the path planning performance, no matter for what approaches, is substantially improved, especially for the travel distance, and the delivery consuming time. All these can prove the significance of the clustering and ordering. Fig. 6Open in figure viewerPowerPoint PRM method for map path finding of Type I clusters In a contrast, when we cancel the ordering in the clusters, for each approach, the delivery completion time is increased significantly. The main reason is that there is no intra-cluster ordering, the AGV can only randomly select which task point to deliver in its own cluster, due to the lack of pre-ordering, AGVs can not find the shortest to travel, as a result, the completion time increases. Then, when the clustering and ordering are canceled together, the worse scenarios happen, the AGVs randomly select which task to do from more options, even though the work can still be accomplished by the AGVs, the overall time consuming is severely increased. From the result, the IDA* algorithm, the D* algorithm and the Bug2 algorithm can complete the tasks in a shorter time then PRM-based approaches, however, as all these time need more complicated map construction process, a longer calculation time is required. Moreover, it is worthy to mention that the bug2 algorithm's planning has a failure problem, as shown in Fig.6. The reason is that the obstacle is irregular with a protruding corner, which causes the failure for the path planning between U(67, 53) to G(95, 60). This failure shows this approach has defects Due to the increase of sampling points, the improved PRM algorithm can achieve better path planning result than the PRM algorithm with only adding a small amount of computation. Meanwhile, compared with other approaches algorithms, the improved PRM algorithm is more time-saving. For the PRM-based path planning methods, the planning time is much shorter than other approaches, which can compensate the inferiors on the running time. Fig. 7Open in figure viewerPowerPoint Path Planning Failure of the bug2 Algorithm Table 3. Three path planning simulations result for different algorithms and parameters Radius Sampling Task cluster sorted Task clustered Calculation time (s) Distance Algorithm Time on running 30 100 Y Y 0.011 S PRM 3.729 22 150 Y Y 0.016 S IPRM 3.656 n/a n/a Y Y 4.711 S IDA* 3.126 n/a n/a Y Y 6.055 S D* Lite 3.211 n/a n/a Y Y 1.110 S Bug2 n/a 30 100 N Y 0.012 M PRM 5.015 22 150 N Y 0.015 M IPRM 5.001 n/a n/a N Y 4.831 M IDA* 4.690 n/a n/a N Y 5.523 M D* Lite 4.719 n/a n/a N Y 4.491 M Bug2 4.860 30 100 N N 0.021 L PRM 10.585 22 150 N N 0.021 L IPRM 10.424 n/a n/a N N 5.366 L IDA* 9.862 n/a n/a N N 6.816 L D* Lite 9.037 n/a n/a N N 4.932 L Bug2 9.593 Note: Probabilistic Road Map (PRM); Improved Probabilistic Road Map(IPRM); Iterative deepening A* (IDA*); Short (S); Medium (M); Long (L). V. Conclusions Most of the existing research work[32, 33] mainly work on the path planning between two points in a small-scale map with obstacles, or just consider the straightly connected paths between the multiple points[34]. In this paper, we propose an integrated method to plan the pathes for the AGVs in logistics distribution considering real-world map and realistic obstacles, multiple task points and multiple AGVs, and realistic working environment simultaneously. In this proposed method, the task points clustering, ordering and path searching are engaged, which makes the path planning more efficient. The situation result validate that this integration of the task points clustering and ordering can help the path planning achieve a better performance, in terms of both the planning time and the logistics time. In our future work, we will generalise the proposed method, try to adapt it to more other fields, such as wayside base stations placement in intelligent transportation, railway transportation scheduling and navigation[35, 36], wireless sensor network optimization[37], more popular techniques, such as Interacting Multiple Model[38], Fuzzy-based Algorithms[39] and evolutionary-based optimization methods[40], will be also applied in out future research. Biography WEN Tao (corresponding author) received the B.Eng degree in computer science from Hangzhou Dianzi University, Hangzhou, China, MSc. degree from the University of Bristol, Bristol, UK, and Ph.D degree from the University of Birmingham, Birmingham, UK, in 2011, 2013 and 2018, respectively. Now, he works at Beijing Jiaotong University. His research interests include the radio-based train control systems optimization, path planning, digital filter design and its application in transportation systems. References 1Gongde Guo, Hui Wang, David Bell, Yaxin Bi, and Kieran Greer Knn model-based approach in classification. In Robert Meersman, Zahir Tari, and Douglas C. Schmidt, editors, On The Move to Meaningful Internet Systems 2003: CoopIS, DOA, and ODBASE, pages 986— 996, Berlin, Heidelberg, 2003. Springer Berlin Heidelberg. CrossrefGoogle Scholar 2J.R. Quinlan. Induction of decision trees. Mach. Learn., Vol. 1, No. 1, pp. 81— 106, March 1986. CrossrefGoogle Scholar 3Peter Brucker Scheduling algorithms. 10.1007/978-3-662-04550-3. Google Scholar 4Taixiong Zheng and Jiongqiu Li. Multi-robot task allocation and scheduling based on fish swarm algorithm. In 2010 8th World Congress on Intelligent Control and Automation, pp. 6681— 6685, July 2010. Google Scholar 5Kap Hwan Kim and Kyung Chan Moon Berth scheduling by simulated annealing. Transportation Research Part B, Vol. 37, No. 6, pp. 0— 560. Google Scholar 6H. Zhang, H. Luo, Z. Wang, Y. Liu, and Y. Liu Multi-robot cooperative task allocation with definite path-conflict-free handling. IEEE Access, 7: 138495— 138511, 2019. CrossrefWeb of Science®Google Scholar 7N. Smolic-Rocak, S. Bogdan, Z. Kovacic, and T. Petrovic Time windows based dynamic routing in multi-agv systems. IEEE Transactions on Automation Science and Engineering, Vol. 7, No. 1, pp. 151— 155, Jan 2010. CrossrefWeb of Science®Google Scholar 8W. Zhang, Y. Peng, W. Wei, and L. Kou Real-time conflict-free task assignment and path planning of multi-agv system in intelligent warehousing. In 2018 37th Chinese Control Conference (CCC), pp. 5311— 5316, July 2018. Google Scholar 9W. Seo, S. Ok, J. Ahn, S. Kang, and B. Moon An efficient hardware architecture of the a-star algorithm for the shortest path search engine. In 2009 Fifth International Joint Conference on INC, IMS and IDC, pp. 1499— 1502, Aug 2009. Google Scholar 10L. Xin, H. Xiangyuan, Y. Ziqi, Q. Xiaoning, and D. Yingkui The algebraic algorithm for path planning problem of agv in flexible manufacturing system. In 2018 37th Chinese Control Conference (CCC), pp. 2396— 2399, July 2018. Google Scholar 11T. Nishi and R. Maeno Petri net decomposition approach to optimization of route planning problems for agv systems. IEEE Transactions on Automation Science and Engineering, Vol. 7, No. 3, pp. 523— 537, July 2010. CrossrefWeb of Science®Google Scholar 12Se Jin Lee, Dong Woo Cho, Wan Kyun Chung, Jong Hwan Lim, and Chul Ung Kang Feature based map building using sparse sonar data. In 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 1648— 1652, Aug 2005. Google Scholar 13W. Yuan, Z. Cao, M. Tan, and J. Liu Topological mapping and navigation based on visual sensor network. In 2014 IEEE International Conference on Mechatronics and Automation, pp. 1686— 1690, Aug 2014. Google Scholar 14X. Wang, Y. Jin, and Zhaohong Ding A path planning algorithm of raster maps based on artificial potential field. In 2015 Chinese Automation Congress (CAC), pp. 627— 632, Nov 2015. Google Scholar 15Daichuan Yang and Chenglin Wen Multiple targets robot path planning based on ant colony and improved probabilistic road map. Journal of Hangzhou Dianzi University, 2017. Google Scholar 16Kai-bo Xu, Hai-yan Lu, Yang Huang, and Shi-juan Hu Robot path planning based on double-layer ant colony optimization algorithm and dynamic environment. Chinese Journal of Electronics, Vol. 47, No. 10, pp. 2166— 2176, 2019. Google Scholar 17L.E. Kavraki, P. Svestka, J. Latombe, and M.H. Overmars Probabilistic roadmaps for path planning in high-dimensional configuration spaces. IEEE Transactions on Robotics and Automation, Vol. 12, No. 4, pp. 566— 580, Aug 1996. CrossrefWeb of Science®Google Scholar 18Zheng Sun, D. Hsu, Tingting Jiang, H. Kurniawati, and J. H. Reif Narrow passage sampling for probabilistic roadmap planning. IEEE Transactions on Robotics, Vol. 21, No. 6, pp. 1105— 1115, 2005. CrossrefWeb of Science®Google Scholar 19Korbinian Nottensteiner, Mikel Sagardia, Andreas Stemmer, and Christoph Hermann Borst Narrow passage sampling in the observation of robotic assembly tasks. In IEEE International Conference on Robotics and Automation, pp. 130— 137, 2016. Google Scholar 20Changan, CHANG, Jingang, and Chunyang Path planning for mobile robot based on an improved probabilistic roadmap method. Chinese Journal of Electronics, Vol. 18, No. 3, pp. 395— 399, 2009. Web of Science®Google Scholar 21Mitul Saha, Jean Claude Latombe, Yu Chi Chang, and Friedrich Prinz Finding narrow passages with probabilistic roadmaps: The small-step retraction method. Autonomous Robots, Vol. 19, No. 3, pp. 301— 319, 2005. CrossrefWeb of Science®Google Scholar 22Leif Peterson K-nearest neighbor. Scholarpedia, Vol. 4, No. 2, 2009. CrossrefGoogle Scholar 23J.A. Hartigan and M. A. Wong Algorithm as 136: A k-means clustering algorithm. Journal of the Royal Statistical Society, Vol. 28, No. 1, pp. 100— 108, 1979. Wiley Online LibraryGoogle Scholar 24Partha Pratim Kundu and Sushmita Mitra Multi-objective optimization of shared nearest neighbor similarity for feature selection. Applied Soft Computing, Vol. 37, No. C, pp. 751— 762, 2015. CrossrefGoogle Scholar 25W. Chiu, G.G. Yen, and T. Juan Minimum manhattan distance approach to multiple criteria decision making in multiobjective optimization problems. IEEE Transactions on Evolutionary Computation, Vol. 20, No. 6, pp. 972— 985, Dec 2016. CrossrefWeb of Science®Google Scholar 26Tangkai Zhang, Jie Luo, and Longjun Li Path planning method based on k-means and svm combination grid partition. Microcomputer & Its Applications, 2016. Google Scholar 27Yong Wang, Heng Zhou, and Ying Wang Mobile robot dynamic path planning based on improved genetic algorithm. In Green Energy and Sustainable Development I: Proceedings of the International Conference on Green Energy and Sustainable Development, pp. 020046, 2010. Google Scholar 28L.E. Kavraki, M.N. Kolountzakis, and J. Latombe Analysis of probabilistic roadmaps for path planning. IEEE Transactions on Robotics and Automation, Vol. 14, No. 1, pp. 166— 171, Feb 1998. CrossrefGoogle Scholar 29Richard E. Korf Iterative-deepening-a*: An optimal admissible tree search. In International Joint Conference on Artificial Intelligence, pp. 1034— 1036, 2010. Google Scholar 30Sven Koenig and Maxim Likhachev D*lite. In Eighteenth National Conference on Artificial Intelligence and Fourteenth Conference on Innovative Applications of Artificial Intelligence, July 28 - August 1, 2002, Edmonton, Alberta, Canada, pp. 476— 483, 2002. Google Scholar 31V. Lumelsky and A. Stepanov Dynamic path planning for a mobile automaton with limited information on the environment. IEEE Transactions on Automatic Control, Vol. 31, No. 11, pp. 1058— 1063, November 1986. CrossrefWeb of Science®Google Scholar 32Jingang Cao Robot global path planning based on an improved ant colony algorithm. Journal of Computer & Communications, Vol. 04, No. 2, pp. 11— 19, 2016. CrossrefGoogle Scholar 33Jianhua Liu, Jianguo Yang, Huaping Liu, Xingjun Tian, and Meng Gao An improved ant colony algorithm for robot path planning. Soft Computing, Vol. 1, No. 11, pp. 1— 11, 2016. Google Scholar 34Qianjie Lu, Zhiping Chen, Linjia Zhang, Haonan Wang, and Chunlu Liu Multi-sources and multi-destinations route search in community bus service based on ant colony algorithm. Journal of Hangzhou Dianzi University, 2016. Google Scholar 35T. Wen, C. Constantinou, L. Chen, Z. Li, and C. Roberts A practical access point deployment optimization strategy in communication-based train control systems. IEEE Transactions on Intelligent Transportation Systems, Vol. 20, No. 8, pp. 3156— 3167, Aug 2019. CrossrefWeb of Science®Google Scholar 36T. Wen, Q. Ge, X. Lyu, L. Chen, C. Constantinou, C. Roberts, and Cai A cost-effective wireless network migration planning method supporting high-security enabled railway data communication systems. Journal of the Franklin Institute, 2019. DOI:10.1016/j.jfranklin.2019.01.037. PubMedWeb of Science®Google Scholar 37T. Wen, C. Wen, C. Roberts, and B. Cai Distributed filtering for a class of discrete-time systems over wireless sensor networks. Journal of the Franklin Institute, Vol. 35, No. 5, pp. 3038— 3055, 2020. CrossrefGoogle Scholar 38G. Xie, L. Sun, T. Wen, X. Hei, and F. Qian Adaptive transition probability matrix-based parallel imm algorithm. IEEE Transactions on Systems, Man, and Cybernetics: Systems, pp. 1— 10, 2019. Google Scholar 39Wei-dong Chen and Qi-guang Zhu Mobile robot path planning based on fuzzy algorithms. Chinese Journal of Electronics, Vol. 39, No. 4, pp. 971— 974. Google Scholar 40Chang-an Liu, Xiao-hu Yan, Chun-yang Liu, and Hua Wu Dynamic path planning for mobile robot based on improved ant colony optimization algorithm. Chinese Journal of Electronics, Vol. 39, No. 5, pp. 238— 242, 2011. Google Scholar Volume30, Issue2March 2021Pages 331-338 FiguresReferencesRelatedInformation