A Multi-Agent Path Planning Method Based on Adaptive Meme Algorithm

Abstract

A multi-agent path planning method based on an adaptive meme algorithm addresses the immaturity and slow convergence speed of current multi-agent path planning methods. This method employs a structure combining global optimization and local search, utilizing chromosomes as generated paths in a two-dimensional grid map and optimizing their fitness values ​​through strategies such as "selection" and "crossing." A hill-climbing algorithm is used as a sub-algorithm for local optimization to prevent generated solutions from getting trapped in local optima, thereby improving the accuracy of multi-agent motion control and enhancing the algorithm's convergence speed and optimization efficiency. This solves the problems of slow convergence speed and low path optimization accuracy that are difficult to address in current multi-agent path planning methods. Experimental results show that this method can accurately optimize multi-objective paths for multiple agents, and the average length of each path converges to the globally optimal path length with population iterations, achieving the expected results.

Description

TECHNICAL FIELD

[0001] The application realizes multi-agent path-based cooperative scheduling by using a path planning method based on an adaptive meme algorithm, which is a meta-heuristic optimization algorithm combining global heuristic algorithm and local search, and has wide application prospects in solving multi-objective optimization models with complex constraints. Multi-agent cooperative scheduling, i.e. by adding a constraint model, makes multiple agents travel along the planned path and avoid conflicts between agents. The study of this problem can improve the efficiency of the scheduling system and is a research hotspot in the field of multi-agent. BACKGROUND

[0002] With the development of intelligent manufacturing technology, mobile robots are now used in many industrial workshops to realize the scheduling and transportation of goods, which helps to promote the unmanned operation and automatic operation of the workshop. With the continuous expansion of the market, single-agent systems are difficult to meet the needs of complex tasks, and multi-agent cooperative systems have emerged, which have stronger robustness and environmental adaptability and promote the flexibility and fault tolerance of the system. Therefore, the research results of the application have broad application prospects.

[0003] The key challenge of path planning problem is that the optimization algorithm is not mature enough and the convergence speed of the algorithm is slow, so that the robot cannot adapt to a more complex working scene. Most scholars divide the optimization algorithm into two types: centralized planning method and distributed planning method. However, the designed algorithm has low universal quality and efficiency in solving the model, and needs to collect more complete map information and communication information of adjacent agents, so a large amount of computing resources is consumed. When the algorithm processes a model with complex map information or agent conflict, the algorithm is prone to fall into local optimum in the iterative calculation process, which will cause the robot to be easily locked at the local optimum point in the process of path obstacle avoidance. Therefore, it is necessary to establish a path planning optimization algorithm with stronger search ability to improve the convergence speed and optimization efficiency of the algorithm in solving the multi-agent path planning model.

[0004] The application designs a multi-agent path planning method based on memes, which realizes the solution of the multi-agent path planning model by constructing a path length optimization model. SUMMARY

[0005] In order to solve the above practical problems, the application is a multi-agent path planning method based on an adaptive meme algorithm, which adds an optimization operator combining global optimization and local optimization, and improves the strategy of local optimization to solve the multi-agent path planning model. Compared with the traditional path planning method, the algorithm has improved convergence speed and control accuracy, and improved the optimization efficiency of solving the multi-agent path planning problem.

[0006] A multi-agent path planning method based on adaptive meme algorithm, characterized by establishing a fitness function based on steering cost, designing a chromosome selection strategy based on improved roulette operation, designing a chromosome optimization strategy based on crossover and mutation, establishing a continuous path function and a local optimization strategy, and realizing the optimization of the "shortest path length" target, comprising the following steps:

[0007] (1) Establish a fitness function based on steering cost

[0008] The generated path in the two-dimensional grid map is represented by a binary string format, the distance between the center points of the two-dimensional grid map is used to represent the adjacent distance of the grid, the steering cost is used to measure the state of the robot in the adjacent grid, and the fitness function is used to encode the steering cost. The steering cost fitness function F i k is as follows:

[0009]

[0010] Where F i k represents the fitness value of the kth chromosome in the population at the ith grid, and the fitness value is calculated by represents the decoded horizontal coordinate of the kth chromosome in the population at the ith grid, represents the decoded vertical coordinate of the kth chromosome in the population at the ith grid. If the robot performs a straight steering, the steering cost function value is encoded as 1; if it performs an oblique steering, the steering cost function value is encoded as If it performs other forms of steering, i.e. jumping grids or crossing obstacles, the steering cost function value is encoded as 100;

[0011] (2) Design a chromosome selection strategy based on improved roulette operation

[0012] ① First, a set of initial solutions in the form of chromosomes is randomly generated as an initial population, and the fitness F i k of the chromosomes contained in the initial population is calculated. The inverse of the fitness is taken as the roulette fitness, and the roulette fitness V′ k of the kth chromosome in the population is calculated as follows:

[0013]

[0014] ② The roulette fitness V′ k of the chromosome is linearly mapped to the range [0,1], and the normalized value P k is taken as the selection probability, and the kth individual in the population is randomly selected with the selection probability Pk The calculation formula is as follows:

[0015]

[0016] Among them, F i k This represents the fitness value of the k-th chromosome individual in the i-th grid. The number of chromosome individuals in the population, m, is set to 200, and the number of genes on the individual chromosome, n, is set to 20.

[0017] ③ Individuals selected by each chromosome in the population according to the roulette wheel selection probability Gr are retained.

[0018] ④ In process ③, chromosomes that were not selected select a certain size of individuals from the population according to the random selection probability Rr;

[0019] ⑤ The chromosome individuals selected in processes ③ and ④ are combined to form a new generation population that is preserved;

[0020] Here, Gr represents the probability of an individual making a choice through a roulette wheel strategy, and its value is set to 0.7; Rr represents the probability of an individual making a choice through a random search strategy, and its value is set to 0.3.

[0021] (3) Design chromosome optimization strategies based on crossover and mutation

[0022] A strategy based on single-point crossover is constructed to achieve global optimization of chromosomes. `cp` represents the probability of each chromosome in the population participating in crossover, and its value is set to 0.4.

[0023] ① First, select a chromosome population of a certain size from the new generation population according to the crossover probability cp, and then use P... k and P k+1 Represents the parent chromosome, which satisfies the sequence... and in This represents the undecoded binary value of the k-th chromosome in the i-th grid.

[0024] ② Use pointer indexes to randomly select positions on the parent chromosome P k and P k+1 Two crossover points are selected in the sequence, and the gene sequences of the chromosomes are interchanged at the crossover points, so that the offspring chromosomes after the crossover all carry the gene sequences of their parent chromosomes. The offspring chromosome C generated by this crossover strategy... k and C k+1 The formula is as follows:

[0025] C k =P k ×a+P k+1×(1-a) (4)

[0026] C k+1 =P k ×(1-a)+P k+1 ×a (5)

[0027] Where 'a' represents a cross-random number that determines the pointer index position, and its value will be linearly assigned within the range of [0,1] according to the pointer index position;

[0028] ③ Use point mutation strategy to generate offspring chromosome C k and C k+1 To perform mutation optimization, first, a progeny chromosome is randomly selected, and a mutation point is randomly chosen using the pointer index. The gene at the mutation point on the chromosome will undergo allelic mutation. Each individual in the population undergoes mutation according to the mutation probability mp, which is set to 0.3. The mutation strategy calculation formula is as follows:

[0029]

[0030] in, This represents the undecoded binary value of the k-th chromosome in the i-th grid, where R is the direction of binary mutation flipping.

[0031] (4) Establish continuous path function

[0032] ① Select parameter list C[] to store continuous paths that meet the requirements, and use equations (7) and (8) to decode the chromosomes in the population into rectangular coordinates of the center point of each grid, and determine whether there are obstacles around the inserted grid and whether the position jumps out of the grid map area, and compare whether the inserted grid is in the path stored in list C[]. If there are no obstacles around the inserted grid and it is not on the existing path, then the grid coordinates of the next state will be inserted. and The formula for calculating the inserted raster coordinates is as follows:

[0033]

[0034] in, This represents the floor function. and F represents the grid coordinates of the previous state. i k This represents the fitness value of the individual with chromosome k in the i-th grid. This represents the undecoded binary value of the k-th chromosome in the i-th grid.

[0035] ② Use formulas (9) and (10) to determine whether the raster coordinates of the current point on this path are continuous with the coordinates of the inserted raster point, where This indicates the rounding up operation;

[0036]

[0037] If the coordinates of the current grid center and the center point of the inserted grid are... and If less than or equal to 1, then two adjacent grid points and If the result is continuous, the next grid point will be inserted according to equations (9) and (10). If the coordinates of the current grid center and the center point of the inserted grid are... and If the value is greater than 1, then two adjacent grid points and If the paths are discontinuous, use the filter function to filter them out.

[0038] (5) Design a local search strategy based on the hill climbing algorithm

[0039] ① By constructing a local search operator to perform local optimization of the population, first, a pointer i is randomly selected in the population, and the fitness of chromosomes in its neighborhood is compared; where q represents the value of the selected neighboring individuals, and its value is set to 2, then the algorithm will compare the fitness F corresponding to the (i-1), i, and i+1th chromosome individuals. i-1 F i F i+1 ;

[0040] ② Use list P[] to store the better chromosomes after local optimization. That is, keep the individuals with smaller fitness values ​​compared in ① in this list. Then, the pointer traverses the entire population, repeats the fitness comparison process in ①, and updates list P[] as the pointer traverses.

[0041] ③ In the P[] list, randomly generate l chromosome paths with the lowest fitness according to the fitness function, and decode the chromosome corresponding to each path into raster rectangular coordinates to perform path conflict constraints, which satisfy the following conditions: and Make This ensures that the various motion trajectories do not collide, enabling the generation of multiple optimal robot paths in the grid map;

[0042] ④ The path planning environment is modeled using the grid map method. The grid simulation map size is set to 20×20, the number of obstacles in the grid is set to 20, the number of paths generated by the algorithm is set to l=3, and the maximum number of iterations N=200 or less than the optimal solution error limit δ≤0.05 is added as the algorithm termination condition. If the algorithm termination condition is reached, the algorithm will stop iterating and generate the population with the best fitness, thus realizing the solution of multi-agent path planning. Attached Figure Description

[0043] Figure 1 The flowchart of the algorithm design of this invention is shown below.

[0044] Figure 2 The grid simulation map of the present invention

[0045] Figure 3 The simulation effect diagram of the present invention

[0046] Figure 4 This is an optimized effect diagram of the present invention. Detailed Implementation

[0047] This invention designs a meme-based multi-agent path planning method. By constructing a path length optimization model, the method solves the multi-agent path planning model. The proposed algorithm model can be deployed to multiple robots to achieve collaborative scheduling.

[0048] A multi-agent path planning method based on an adaptive meme algorithm is characterized by establishing a fitness function based on turning costs, designing a chromosome selection strategy based on an improved roulette wheel operation, designing a chromosome optimization strategy based on crossover and mutation, establishing a continuous path function and a local optimization strategy, and achieving the objective of optimizing the "shortest path length". The method includes the following steps:

[0049] (1) Establish a fitness function based on steering cost

[0050] The generated paths in a 2D grid map are represented using chromosomes in binary string format. The adjacency distance of a grid cell is represented by the distance between the center points of the 2D grid map. Turning cost is used to measure the robot's travel state in adjacent grid cells, and a fitness function is used to encode the turning cost. The established turning cost fitness function F i k as follows:

[0051]

[0052] Among them, F i k This represents the fitness value of the k-th chromosome in the i-th grid, using... This represents the Cartesian x-coordinate of the k-th chromosome in the i-th grid after decoding. This represents the Cartesian ordinate of the k-th chromosome in the i-th grid after decoding. If the robot makes a straight turn, the turning cost function value is encoded as 1; if it makes an oblique turn, the turning cost function value is numerically encoded as... If other forms of turning are performed, such as jumping grids or crossing obstacles, the turning cost function value is encoded as 100;

[0053] (2) Design a chromosome selection strategy based on improved roulette wheel operation

[0054] ① First, a set of initial solutions is randomly generated in the form of chromosomes as the initial population. The fitness F corresponding to the chromosome individuals in the initial population is set. i k Take the reciprocal as the roulette wheel fitness, where V is the roulette wheel fitness of the individual with the kth chromosome in the population. k The formula for calculating ′ is as follows:

[0055]

[0056] ②The fitness V corresponding to the chromosome is determined by roulette wheel selection. k Linearly map to the range [0,1], and normalize the value P. k The selection is randomized using the probability of being selected, where the probability P of the k-th individual in the population being selected is... k The calculation formula is as follows:

[0057]

[0058] Among them, F i k This represents the fitness value of the k-th chromosome individual in the i-th grid. The number of chromosome individuals in the population, m, is set to 200, and the number of genes on the individual chromosome, n, is set to 20.

[0059] ③ Individuals selected by each chromosome in the population according to the roulette wheel selection probability Gr are retained.

[0060] ④ In process ③, chromosomes that were not selected select a certain size of individuals from the population according to the random selection probability Rr;

[0061] ⑤ The chromosome individuals selected in processes ③ and ④ are combined to form a new generation population that is preserved;

[0062] Here, Gr represents the probability of an individual making a choice through a roulette wheel strategy, and its value is set to 0.7; Rr represents the probability of an individual making a choice through a random search strategy, and its value is set to 0.3.

[0063] (5) Design chromosome optimization strategies based on crossover and mutation

[0064] A strategy based on single-point crossover is constructed to achieve global optimization of chromosomes. `cp` represents the probability of each chromosome in the population participating in crossover, and its value is set to 0.4.

[0065] ① First, select a chromosome population of a certain size from the new generation population according to the crossover probability cp, and then use P...k and P k+1 Represents the parent chromosome, which satisfies the sequence... and in This represents the undecoded binary value of the k-th chromosome in the i-th grid.

[0066] ② Use pointer indexes to randomly select positions on the parent chromosome P k and P k+1 Two crossover points are selected in the sequence, and the gene sequences of the chromosomes are interchanged at the crossover points, so that the offspring chromosomes after the crossover all carry the gene sequences of their parent chromosomes. The offspring chromosome C generated by this crossover strategy... k and C k+1 The formula is as follows:

[0067] C k =P k ×a+P k+1 ×(1-a) (4)

[0068] C k+1 =P k ×(1-a)+P k+1 ×a (5)

[0069] Where 'a' represents a cross-random number that determines the pointer index position, and its value will be linearly assigned within the range of [0,1] according to the pointer index position;

[0070] ③ Use point mutation strategy to generate offspring chromosome C k and C k+1 To perform mutation optimization, first, a progeny chromosome is randomly selected, and a mutation point is randomly chosen using the pointer index. The gene at the mutation point on the chromosome will undergo allelic mutation. Each individual in the population undergoes mutation according to the mutation probability mp, which is set to 0.3. The mutation strategy calculation formula is as follows:

[0071]

[0072] in, This represents the undecoded binary value of the k-th chromosome in the i-th grid, where R is the direction of binary mutation flipping.

[0073] (6) Establish continuous path function

[0074] ① Select parameter list C[] to store continuous paths that meet the requirements, and use equations (7) and (8) to decode the chromosomes in the population into rectangular coordinates of the center point of each grid, and determine whether there are obstacles around the inserted grid and whether the position jumps out of the grid map area, and compare whether the inserted grid is in the path stored in list C[]. If there are no obstacles around the inserted grid and it is not on the existing path, then the grid coordinates of the next state will be inserted. and The formula for calculating the inserted raster coordinates is as follows:

[0075]

[0076] in, This represents the floor function. and F represents the grid coordinates of the previous state. i k This represents the fitness value of the individual with chromosome k in the i-th grid. This represents the undecoded binary value of the k-th chromosome in the i-th grid.

[0077] ② Use formulas (9) and (10) to determine whether the raster coordinates of the current point on this path are continuous with the coordinates of the inserted raster point, where This indicates the rounding up operation;

[0078]

[0079] If the coordinates of the current grid center and the center point of the inserted grid are... and If less than or equal to 1, then two adjacent grid points and If the result is continuous, the next grid point will be inserted according to equations (9) and (10). If the coordinates of the current grid center and the center point of the inserted grid are... and If the value is greater than 1, then two adjacent grid points and If the paths are discontinuous, use the filter function to filter them out.

[0080] (5) Design a local search strategy based on the hill climbing algorithm

[0081] ① By constructing a local search operator to perform local optimization of the population, first, a pointer i is randomly selected in the population, and the fitness of chromosomes in its neighborhood is compared; where q represents the value of the selected neighboring individuals, and its value is set to 2, then the algorithm will compare the fitness F corresponding to the (i-1), i, and i+1th chromosome individuals. i-1 F i Fi+1 ;

[0082] ② Use list P[] to store the better chromosomes after local optimization. That is, keep the individuals with smaller fitness values ​​compared in ① in this list. Then, the pointer traverses the entire population, repeats the fitness comparison process in ①, and updates list P[] as the pointer traverses.

[0083] ③ In the P[] list, randomly generate l chromosome paths with the lowest fitness according to the fitness function, and decode the chromosome corresponding to each path into raster rectangular coordinates to perform path conflict constraints, which satisfy the following conditions: and Make This ensures that the various motion trajectories do not collide, enabling the generation of multiple optimal robot paths in the grid map;

[0084] ④ The path planning environment is modeled using the grid map method. The grid simulation map size is set to 20×20, the number of obstacles in the grid is set to 20, the number of paths generated by the algorithm is set to l=3, and the maximum number of iterations N=200 or less than the optimal solution error limit δ≤0.05 is added as the algorithm termination condition. If the algorithm termination condition is reached, the algorithm will stop iterating and generate the population with the best fitness, thus realizing the solution of multi-agent path planning.

[0085] Table 1 shows the parameter values ​​of the present invention.

[0086]

Claims

1. A multi-agent path planning method based on an adaptive meme algorithm, characterized in that, The method comprises the following steps: (1) Establish a fitness function based on steering cost; use a binary string format chromosome to represent the generated path in the two-dimensional grid map, represent the adjacency distance of the grid with the distance between the center points of the two-dimensional grid map, use the steering cost to measure the travel state of the robot in the adjacent grid, and use the fitness function to encode the steering cost. The steering cost fitness function F i k The steering cost fitness function F i k is as follows: where F i k represents the fitness value of the kth chromosome in the population at the ith grid, which is calculated by represents the decoded abscissa of the kth chromosome in the population at the ith grid, represents the decoded ordinate of the kth chromosome in the population at the ith grid; if the robot performs straight steering, the steering cost function value is encoded as 1; if it performs diagonal steering, the steering cost function value is encoded as if it performs other forms of steering, i.e., jumping grids or crossing obstacles, the steering cost function value is encoded as 100; (2) design a chromosome selection strategy based on improved roulette operation; (3) designing a chromosome optimization strategy based on crossover and mutation; (4) establishing a continuous path function; (5) designing a local search strategy based on a hill climbing algorithm; ① a local search operator is constructed to perform local optimization on the population, first, a pointer i is randomly selected in the population, and the fitness of the chromosome in its neighborhood is compared; wherein q represents the number of selected neighborhood individuals, and is set to 2, the algorithm will compare the fitness F of the i-1, i, i+1 chromosome individuals i-1 i i+1 ;​​ ② a list P[] is used to store the better chromosomes after local optimization, that is, the individuals with smaller fitness values in step ① are retained in the list, then the pointer traverses the entire population, and the fitness comparison process in step ① is repeated, and the list P[] is updated with the traversal of the pointer; ③ In the P[] list, randomly generate l minimum fitness chromosome paths according to the fitness function, and decode each path into a grid rectangular coordinate to constrain the path collision, which satisfies the constraint and So that So that each motion trajectory does not collide with each other, and the optimal path of multiple robots is generated in the grid map. ④ the grid map method is used for path planning environment modeling, the size of the grid simulation map is set to 20*20, the number of obstacles in the grid is set to 20, the number of paths generated by the algorithm is set to l=3, and the maximum number of iterations N=200 or the error limit δ≤0.05 is set as the termination condition of the algorithm, if the termination condition of the algorithm is reached, the algorithm will stop iteration, and the population with the optimal fitness is generated.

2. The method of claim 1, wherein, Step (2) is specifically: ①First, a set of initial solutions is randomly generated in the form of chromosomes as an initial population, and the fitness F i k The reciprocal is taken as the roulette fitness, where the roulette fitness V k of the kth chromosome individual in the population is calculated as follows: (ii) the roulette wheel fitness value V corresponding to the chromosome is calculated k linearly mapped to the range [0, 1], the normalized value P k is randomly selected as the selected probability, where the probability P that the kth individual in the population is selected k The calculation formula is as follows: wherein F i k indicates the fitness value of the kth chromosome individual at the ith grid, the number of chromosome individuals m of the population is set to 200, and the number of genes n of the individual chromosome is set to 20; ③ each chromosome in the population is selected by the roulette strategy according to the roulette selection probability Gr; ④ the chromosomes not selected in process ③ are selected according to the random selection probability Rr to form a population of a certain size; ⑤ the selected chromosomes in processes ③ and ④ are combined to form a new generation of population; wherein Gr is the probability of individual selection by the roulette strategy, and is set to 0.7, and Rr is the probability of individual selection by the random search strategy, and is set to 0.

3.

3. The method of claim 2, wherein, Step (3) is specifically: A strategy based on single-point crossover is constructed to realize global optimization of the chromosome, and cp represents the probability of each chromosome in the population participating in crossover, and is set to 0.4, k and P k+1 denote the parent chromosomes, which satisfy the sequence and wherein denotes the kth chromosome in the ith grid undecoded binary value;​ ②The position of the pointer index is randomly selected in the parent chromosome P k and P k+1 Two crossover points are selected in the sequence of the parent chromosome, and the gene sequence of the chromosome is exchanged at the crossover points, so that the child chromosomes after the crossover carry the gene sequence of the parent chromosome, wherein the child chromosomes C k and C k+1 generated by the crossover strategy are as follows: C k = P k x a + P k+1 x (1 - a) (4) C k+1 = P k × (1 - a) + P k+1 × a (5) wherein a represents a crossover random number for determining the index position of the pointer, and the value is linearly assigned in the range of [0, 1] according to the index position of the pointer; ③ The point mutation strategy is used to generate offspring chromosomes C k and C k+1 Mutation optimization is performed by first randomly selecting an offspring chromosome and randomly selecting a mutation point using a pointer index. The genes of the chromosome at the mutation point will undergo allelic mutation. Each population individual is mutated according to a mutation probability mp, which is set to 0.

3. The mutation strategy calculation formula is as follows: wherein, Rk i represents the undecoded binary value of the kth chromosome at the ith grid, R is the direction of binary mutation flip.

4. The method of claim 3, wherein, Step (4) is specifically: ①Parameter list C[] is selected to store the continuous path meeting the requirements, and formulas (7) and (8) are used to decode the chromosomes in the population into the rectangular coordinates of the center points of the grids, and it is judged whether the surrounding of the inserted grid is an obstacle and whether the position jumps out of the area of the grid map, and it is compared whether the inserted grid is in the path stored in list C[], if the surrounding of the inserted grid is not an obstacle and is not in the existing path, then the grid coordinates of the next state are inserted and The iterative calculation formula of the inserted grid coordinates is as follows: wherein, represents a floor operation, and denotes the grid coordinates of the previous state, F i k denotes the fitness value of the kth chromosome individual at the ith grid, denotes the undecoded binary value of the kth chromosome at the ith grid; (9) and (10) to determine whether the grid coordinates of the current point of the path and the coordinates of the inserted grid point are continuous, wherein represents a rounding-up operation; If the current grid center and the inserted grid center point coordinate values and are less than or equal to 1, then the two adjacent grid points and are continuous, and the next grid point to be inserted is continued according to the equations (9) and (10) If the current grid center and the inserted grid center point coordinate values and are greater than 1, then the two adjacent grid points and are discontinuous, and the path is filtered out using the filter function.

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