Solving path planning problem based on logistic beetle algorithm search–pigeon‐inspired optimisation algorithm

Electronics LettersVolume 56, Issue 21 p. 1105-1108 Control engineeringFree Access Solving path planning problem based on logistic beetle algorithm search–pigeon-inspired optimisation algorithm Ang Liu, Corresponding Author Ang Liu liuang96@163.com School of Automation and Electronic Information, Xiangtan University, Xiangtan, People's Republic of ChinaSearch for more papers by this authorJin Jiang, Jin Jiang School of Automation and Electronic Information, Xiangtan University, Xiangtan, People's Republic of ChinaSearch for more papers by this author Ang Liu, Corresponding Author Ang Liu liuang96@163.com School of Automation and Electronic Information, Xiangtan University, Xiangtan, People's Republic of ChinaSearch for more papers by this authorJin Jiang, Jin Jiang School of Automation and Electronic Information, Xiangtan University, Xiangtan, People's Republic of ChinaSearch for more papers by this author First published: 14 September 2020 https://doi.org/10.1049/el.2020.1895Citations: 5AboutSectionsPDF 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 Mobile robot path planning is an important part of the mobile robot field. The swarm intelligence optimisation algorithm has certain advantages in solving such multi-objective optimisation problems, so this Letter proposes to apply the pigeon-inspired optimisation (PIO) algorithm to the path planning problem. However, the traditional PIO algorithm is suffering from the problems of easy to get into local optimisation, low stability and premature convergence. To overcome its shortcomings, this Letter proposes a logistic beetle algorithm search–PIO (LBAS-PIO) algorithm. In the optimisation process of the LBAS-PIO algorithm, the PIO algorithm is initialised by the logistic mapping, making the search space more extensive. Learning from the idea of the beetle algorithm search, each pigeon has its own judgment of the environment and the number of iterations and search time are reduced. Further, the path evaluation function of the algorithm and the execution order of the operators are optimised to make the algorithm smoother and easier to find the global optimal solution. Simulation and experimental results illustrated the superiority of the LBAS-PIO algorithm and the LBAS-PIO algorithm better meets the needs of mobile robots for the optimal path planning. Introduction Currently, path planning has been the most popular and important part in the field of mobile robot control. For the path planning of mobile robots, it is required to find an optimal path from the starting point to the target point in the planning space under given constraints [1, 2 ]. The robot path planning problem can be modelled as a multi-objective optimisation problem and the robot path planning method mainly include A* algorithm [3 ], particle swarm optimisation [4 ], etc. In recent years, many swarm intelligence optimisation algorithms have been proposed to solve the problem of robot path planning. Notable ones include particle swarm optimisation algorithm, ant colony optimisation algorithm, pigeon-inspired optimisation (PIO) algorithm, etc. In these algorithms, PIO is a new type of swarm intelligence optimisation algorithm. With its excellent navigation capabilities and group flight mechanism, PIO has achieved good results in solving multi-objective problems. However, PIO has problems of easy to get into the position of the local optimal solution and premature convergence. Lin et al. [5 ] introduced the adaptive weight coefficient to the map operator of the PIO algorithm to increase the search efficiency. Li and Duan [6 ] adopted a mechanism of probability selection to distinguish map operators and landmark operators of the PIO algorithm, which improved the global search ability of the algorithm. However, these improvement strategies have some problems, such as not initialise the algorithm, considering only the impact between pigeon populations, etc. In this Letter, the traditional PIO is first introduced and the shortages of it are analysed. Then, we combine the PIO algorithm with logistic mapping and beetle algorithm search (BAS) to solve the path planning problem. The logistic mapping is used to initialise the PIO, so that the PIO can search the entire space. However, we use the idea of individual search in the BAS to combine it with PIO, so that the PIO can not only consider the influence of group factors, but also have individual judgment, which effectively overcomes the problems of easy to fall into the local optimal solution and low execution efficiency. Finally, the evaluation function of the algorithm and the sequence of operators are appropriately improved to make the path smoother and easier to get into the position of the global optimal solution. Traditional PIO algorithm The PIO is composed of a map and a compass operator and landmark operator. At the map and compass operator, in the D-dimensional space, assuming that the number of pigeons is , the speed and position update formula of the ith pigeon at the tth iteration is as follows: (1) (2) where is the speed of the ith pigeon after the tth iteration, is the position of the ith pigeon after the tth iteration, R is the map and compass factor, denotes the global best position of all the pigeons, rand signifies a random number within [0, 1]. At the later stage, using the landmark operator to guarantee that the pigeons are flying towards the optimal position, and the speed and the update formula are as follows: (3) (4) (5) where the number of pigeons at the tth iteration, refers to the position of the pigeons, f is the fitness value. This Letter proposes to apply the PIO algorithm to the robot path planning, but the traditional PIO algorithm has some problems, such as the algorithm is not initialised and only considers the influence between groups, the resulting path is not smooth enough, etc. These problems will make the algorithm easy to fall into local optimisation and lead to lower execution efficiency under a complex environment. Path evaluation function The evaluation function of the path performance of the mobile robot is as follows: (6) where is safety evaluation function, is path length evaluation function, is the smooth evaluation function, are the weight ratios of the three functions and . Safety evaluation function represents the threat cost caused by obstacles. If the path segment is divided into ten parts, and the five points on the path segment are taken to represent the cost of the threat source to the path of the segment, then the calculation formula of the cost of the threat source to the segment i is (7) where represents the length of the path, is the number of obstacles, represents the threat factor, indicating the influence degree of the obstacle, and represents the distance between the point at and the kth obstacle. is path length evaluation function, and the evaluation function in the A* algorithm is used to improve it as follows: (8) where represents the distance between the node i and the node , and represents the distance between the node and the target point e. For the smooth evaluation function , it represents the smoothness index of the entire path (9) where is expressed as the vector angle formed by the road segment i and the road segment . When gets smaller, the sum of the vector angle between two adjacent road segments becomes smaller and the path will be smoother. Chaos initialisation The traditional PIO algorithm does not initialise the initial path during path planning, which leads to a low efficiency of the final algorithm. This Letter proposes to use the chaos mapping method to initialise the PIO algorithm, using the randomness and ergodicity of chaotic thought to search and jump out of the local optimal solution. The logistic mapping is used for initialisation here, and its mathematical model is (10) where is the logistic parameter. When , the logistic mapping is in a chaotic state, and when , the entire system is completely chaotic. Fig. 1 is the initial solution set of pseudorandom distribution generated by 300 iterations when . Fig. 1Open in figure viewerPowerPoint Pseudorandom distribution sequence generated by logistic mapping BAS-PIO algorithm In the iterative process of the PIO algorithm, the focus is more on the influence between the groups of pigeons. The BAS algorithm is only for individuals, and does not consider the connections between groups [7 ]. This Letter combines the BAS algorithm with the PIO algorithm to propose the BAS-PIO algorithm. When updating the position of the pigeons, the idea of the beetle algorithm search was added. The BAS-PIO algorithm can well overcome the problems of easy to fall into the local optimal solution and poor stability in the PIO algorithm. The updated location of the map operator is as follows: (11) (12) where represents a positive constant, represents position increment function. The function is defined as follows: (13) where is the step size at the kth iteration, represent the fitness values of the left and right whiskers of the ith pigeon at this iteration, respectively. For : (14) where x is the coordinate of the centroid, is the distance between the two whiskers of the pigeon, and the position of the left and right whiskers can be determined by the following formula: Cross running operator In the traditional PIO algorithm, the map and compass operator is used in the early stage of the iteration to search, and the landmark operator is used in the later stage of the iteration. The operation of the map and compass operator and the landmark operator separately will cause the algorithm to converge in advance. In this Letter, the two-stage operator is used in a cross-running method. Both operators are used in the two iteration stages. The specific iteration order is as follows: (15) where t is the number of iterations, and represent the maximum number of iterations of the map and compass operator and landmark operator in the traditional PIO algorithm. Through the mutual restriction of the two operators, the PIO algorithm can be effectively avoided from falling into local optimality and premature convergence. Results and discussion To validate the performance of LBAS-PIO on robot path planning, comparative experiments are performed on the PIO, PSO, and LBAS-PIO under different environments. Matlab 2017b platform is employed for modelling and path simulation analysis under the Windows10 operating system. In the simulation experiment, the number of pigeons is 200, the number of iterations is 50, is 150. Scenario 1: Unexpected obstacles. Scenario 2: Simple obstacle environments. Scenario 3: Complex obstacle environment. To test the superiority of the LBAS-PIO in path planning, we compared the LBAS-PIO with PIO and PSO in three environments. Fig. 2 shows the path planned under unexpected obstacles, Fig. 3 shows the path planned from (0, 0) along the way to the target point (70,100) under simple obstacle environments, Fig. 4 shows the path planned from (0, 0) along the way to the target point (35, 50) under complex obstacle environments. Fig. 2Open in figure viewerPowerPoint Results for scenario 1 with three different algorithms a PIO in three scenario b PSO in three scenario c LBAS-PIO in three scenario Fig. 3Open in figure viewerPowerPoint Results for scenario 2 with three different algorithms a PIO in three scenario b PSO in three scenario c LBAS-PIO in three scenario Fig. 4Open in figure viewerPowerPoint Results for scenario 3 with three different algorithms a PIO in three scenario b PSO in three scenario c LBAS-PIO in three scenario The three algorithms are executed separately 100 times. Table 1 records the average performance of the three algorithms in different environments. It can be seen that all performance of LBAS-PIO is better than PIO and PSO. Table 1. Comparison of three pathfinding algorithms Algorithm Length, km Time, s Cost scenario 1 PIO 51.885 1.475 2.665 PSO 53.407 1.593 2.694 LBAS-PIO 51.618 1.123 2.356 scenario 2 PIO 141.938 2.987 60.634 PSO 140.267 3.194 62.831 LBAS-PIO 128.699 2.126 55.023 scenario 3 PIO 63.708 4.243 73.801 PSO 65.295 5.325 79.231 LBAS-PIO 61.718 3.731 68.325 Convergence curves of the cost values in scenario 1 and scenario 2 are displayed in Fig. 5. We can see that the LBAS-PIO algorithm has lower cost values in these two different environments and can converge more steadily and quickly. Fig. 5Open in figure viewerPowerPoint Comparative curves of iteration of cost values Conclusion The LBAS-PIO algorithm for multi-objective optimisation-based mobile robot path planning is proposed in this Letter. The standard PIO algorithm has the problems of easy to fall into the local optimal solution and low execution efficiency. By using the logic method to initialise, the ergodicity of pigeon is improved, and the algorithm is less likely to fall into the local optimal. Furthermore, the idea of the BAS algorithm is used in combination with the PIO algorithm, so that the pigeon can not only consider the influence of group factors, but also have individual judgment. Finally, the evaluation function and the execution order of LBAS-PIO algorithm is improved to make the path smoother and easier to get into the position of the global optimal solution. Simulation results show that the LBAS-PIO algorithm better meets the needs of a mobile robot for the optimal path planning. References 1Han J. Seo Y.: 'Mobile robot path planning with surrounding point set and path improvement ', Appl. Soft Comput., 2017, 57, pp. 35– 47, (doi: 10.1016/j.asoc.2017.03.035 ) 2Jeddisaravi K. Alitappeh R.A. 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