Mobile robot path planning method based on improved artificial bee colony algorithm

Abstract

The application discloses a mobile robot path planning method based on an improved artificial bee colony algorithm, and the optimal solution generated by each iteration of the artificial bee colony algorithm is substituted into the hunting stage of a grey wolf optimization algorithm, and a new honey source position is generated by using the grey wolf optimization algorithm; the honey source is introduced in the neighborhood search in the employed bee stage, so that the local search capability of the artificial bee colony is improved; the global optimal solution is substituted into the scout bee stage, the honey source search equation is improved, and the algorithm is more easily to get rid of the local optimum; the improved algorithm GW-ABC is applied to the mobile robot path planning, and the experimental results show that the search capability of the improved algorithm is stronger, and the convergence speed is faster.

Description

TECHNICAL FIELD

[0001] The present application relates to a robot path planning method, in particular to a mobile robot path planning method based on an improved artificial bee colony algorithm. BACKGROUND

[0002] The artificial bee colony algorithm (ABC) was proposed by Karaboga in 2005. Inspired by the foraging behavior of honey bees, the artificial bee colony algorithm divides the bee colony into three types of bees, simulating the process of honey bees searching for honey sources and the mutual cooperation between honey bees in collecting honey sources. The ABC algorithm has few control parameters and is easy to implement, and has been successfully applied to various practical problems, such as pattern recognition, magnetism, neural network control, etc.

[0003] In recent years, a large number of scholars have studied the improvement of the ABC algorithm to achieve better results. M.S. Kiran et al. proposed a multi-search equation strategy, allowing bees to select the optimal search equation for adaptive update while considering multiple benchmark characteristics. M.S. Kiran and O. FindiK record the update direction of individuals, and if an individual is successfully updated, the recorded update direction is used in the next generation; Zhou Xinyu et al. added a neighborhood search mechanism to the search formula of the artificial bee colony, exploiting better neighbor honey sources from the ring neighborhood topology of the current honey source, balancing the exploration and exploitation capabilities of the algorithm, and saving the search experience of the scout bee in the form of generating the reverse solution of the discarded honey source with the general reverse learning strategy to improve search efficiency; Zhu and Kwong introduced global optimal information into ABC to improve its development ability and achieve higher solution accuracy. Gao et al. divided the entire colony into several sub-colonies and proposed two communication mechanisms among them to promote optimization performance. Li Yancang et al. used information entropy to change the search process to improve search efficiency. Akay and Karaboga proposed a new frequency perturbation strategy to avoid falling into local minima. In order to better balance the coarse search and precise search capabilities of ABC, Gao proposed a new update equation that uses two randomly selected food sources and adopts an orthogonal learning strategy. Kuang et al. introduced chaotic distribution into the scout bee stage to enhance its global search capability. Gao et al. defined a new search mechanism to overcome the oscillation phenomenon in employed bees, and proposed an intelligent learning mechanism to speed up the convergence speed of the worst employed bee. The above-mentioned ABC algorithms have strong global search capability, but researchers have found that they often face problems such as slow convergence speed and easy falling into local optimum. SUMMARY

[0004] To solve the above technical problems, the present application provides a mobile robot path planning method based on an improved artificial bee colony algorithm, which has fast convergence speed and strong local search capability.

[0005] The technical scheme for solving the above technical problem is: a mobile robot path planning method based on an improved artificial bee colony algorithm, comprising the following steps:

[0006] Step one: initialize the parameters related to the honey source;

[0007] Step two: generate an initial solution and calculate the fitness of the honey source, and start iteration;

[0008] Step three: substitute the optimal solution generated by the artificial bee colony algorithm ABC in each iteration into the hunting stage of the grey wolf optimization algorithm GWO, generate a new honey source position using the grey wolf optimization algorithm, introduce the new honey source during neighborhood search in the employed bee stage, and perform neighborhood search; the onlooker bee selects the path corresponding to the better honey source according to the greedy algorithm;

[0009] Step four: substitute the global optimal solution into the scout bee stage, improve the honey source search equation, and if the solution path is not updated for limit times, the employed bee becomes a scout bee, discards the old solution, randomly generates a new solution path, and starts iteration again;

[0010] Step five: determine whether the number of iterations reaches the maximum number of iterations t max , if so, output the optimal path node, connect the nodes in turn to obtain the optimal path, otherwise return to step three and continue execution.

[0011] The above mobile robot path planning method based on the improved artificial bee colony algorithm, in step two, the artificial bee colony algorithm is a group life optimization algorithm inspired by the behavior of a bee colony, and the algorithm is executed in three stages, namely the employed bee stage, the onlooker bee stage and the scout bee stage; the artificial bee colony algorithm simulates the honey collecting behavior of bees, where the position of a honey source represents a candidate solution, and the amount of nectar in each honey source is considered as fitness; the number of employed bees and onlooker bees is equal, which is half of the size of the whole population; the employed bees update the current honey source according to the position in memory and share information about new honey sources with onlooker bees; according to this information, the scout bees perform neighborhood search; the specific process is as follows:

[0012] (1) Initialization

[0013] In the initialization stage, a set of possible solutions is randomly generated by the following equation:

[0014]

[0015] where x i,j represents the set of solutions, i = 1, 2, …, N, N is the population size, j = 1, 2, …, Dim, and Dim represents the dimension; and upper and lower bounds of the jth variable; rand(0,1) is a random number between 0 and 1;

[0016] (2) Employed bee phase

[0017] In this phase, a new food source is generated from the old food source in the memory of the employed bee, i.e. a new candidate solution is generated:

[0018]

[0019] where v ij is the position of the new food source, is a random number between -1 and 1, and k is a randomly generated integer, k = 1, 2,..., N, and k ≠ i;

[0020] (3) Onlooker bee phase

[0021] In the onlooker bee phase, the onlooker bees select the probability P i from the employed bees according to the roulette wheel selection method, and then randomly generate a random number between 0 and 1 and compare it with the probability P i . If P i is greater than the generated random number, the food source is selected according to equation (3), and then the new solution generated by the employed bee and the onlooker bee is selected according to the greedy algorithm, i.e. the better solution is selected by comparing the fitness values of the food sources:

[0022]

[0023] where P i represents the probability of the ith set of solutions being selected, and f i is the fitness of the ith set of solutions,

[0024]

[0025] where fitness i is the objective function value of the i solutions, and abs(fitness i ) represents the absolute value of fitness i ;

[0026] (4) Scout bee phase

[0027] In the scout bee phase, once a food source cannot be further improved within a predetermined period, it is replaced by a new food source, and the employed bees associated with it subsequently become scout bees;

[0028] The new food source is randomly generated according to equation (1), and steps 2 to 4 are repeated until the termination condition is met.

[0029] In the above-mentioned mobile robot path planning method based on the improved artificial bee colony algorithm, in step two, the gray wolf algorithm imitates the democratic social behavior of a group of gray wolves when chasing and hunting prey. There are four levels in the gray wolf social hierarchy, with the highest level, which is the optimal solution, being α wolf, the second-best solutions being β wolf and δ wolf, and the other solutions being ω wolf.

[0030] The hunting behavior of gray wolf packs includes three stages: approaching the prey, surrounding the prey, and attacking the prey. The mathematical expression for surrounding the prey is:

[0031] X(t+1)=X p (t)-A·D (5)

[0032] D = |C·X p (t)-X(t)| (6)

[0033] In the formula, t is the current iteration number, X(t) represents the current position of the gray wolf, and X p Let A represent the current location of the prey, D represent the distance between the individual gray wolf and the prey, and A and C be coefficient vectors; where,

[0034] A = 2ar1 - a (7)

[0035] C = 2r² (8)

[0036]

[0037] In the formula, a is the convergence factor, and r1 and r2 are random numbers in the interval [0, 1].

[0038] The mathematical model for the gray wolf's attack on its prey is as follows:

[0039] D a =|C1·X α (t)-X(t)| (10)

[0040] D β =|C2·X β (t)-X(t)| (11)

[0041] D δ =|C3·X δ (t)-X(t)| (12)

[0042] D a D β and D δ Let X represent the distances between α, β, and δ and other individuals, respectively. a (t), X β (t) and X δ(t) respectively represent the positions of α, β and δ at time t, the coefficient vectors A1, A2 and A3 are generated by formula (7), C1, C2 and C3 are random vectors, generated by formula (8);

[0043] X1 = X α (t)-A1·D α (13)

[0044] X2 = X β (t)-A2·D β (14)

[0045] X3 = X δ (t)-A3·D δ (15)

[0046] X(t+1) = (X1+X2+X3) / 3 (16)

[0047] X1, X2, X3 respectively represent the positions of α, β and δ with other individuals.

[0048] The mobile robot path planning method based on the improved artificial bee colony algorithm, in step two, in order to increase the local search ability and accelerate the convergence speed, the search formula of the employed bee stage is modified:

[0049]

[0050] generated by the hunting stage of GWO algorithm, representing the position of the honey source at time t, representing the position of the honey source searched by GWO algorithm at time t, r is a random number between [-1, 1];

[0051] The artificial bee colony algorithm calculates the fitness value of the solution every iteration, and the artificial bee colony algorithm is applied to path planning, and the fitness value is equivalent to the path length, and the minimum fitness value every iteration corresponds to an optimal solution X gbest In order to improve the search accuracy of the algorithm, the current optimal solution X gbest is introduced into the GWO algorithm:

[0052] D a ′ = |C1·X α -X gbest | (18)

[0053] D β ′ = |C2·X β -X gbest | (19)

[0054] D δ ′ = |C3·Xδ X gbest | (20)

[0055] wherein D a ', D β ' and D δ ' represent the distance between alpha, beta and delta and the best individual respectively;

[0056] X1′=X α (t)-A1·D α ' (21)

[0057] X2′=X β (t)-A2·D β ' (22)

[0058] X3′=X δ (t)-A3·D δ ' (23)

[0059] X′(t+1)=(X1′+X2′+X3′) / 3 (24)

[0060] X′1, X′2, X3′ represent the positions of alpha, beta and delta in the wolf pack advancing towards the current best individual respectively, and X′(t+1) is the position of the grey wolf at time t+1 in the optimization process;

[0061] In the GWO algorithm, the value of a in equation (9) is linearly decreased from 2 to 0, but the process of optimizing the honey source is not linear in reality. In order to adapt to the diversity of the algorithm and speed up the convergence, equation (9) is changed to

[0062]

[0063] wherein f best is the fitness value of the current best solution X gbest , and L is the straight-line distance from the starting point.

[0064] In the fourth step, the search equation is improved in order to improve the ability to get rid of local optimum.

[0065]

[0066] wherein Q is an adaptive adjustment coefficient,

[0067]

[0068] wherein f best is the fitness value of the current best honey source, and f iThe fitness value of the solution of the i-th group is a honey source, limitNum represents the number of experimental failures, and the initial value is 0; limitNum is increased by 1 if the honey source i is not updated each time; if the honey source i is not updated for limit times, the honey source is abandoned, and a new honey source is generated according to formula (26).

[0069] The application has the beneficial effects that the optimal solution generated by the artificial bee colony algorithm in each iteration is substituted into the hunting stage of the grey wolf optimization algorithm, and a new honey source position is generated by using the grey wolf optimization algorithm; the honey source is introduced in the neighborhood search in the employed bee stage, so as to improve the local search ability of the artificial bee colony; the global optimal solution is substituted into the scout bee stage, the honey source search equation is improved, and the algorithm is more easily out of the local optimum; the improved algorithm GW-ABC is applied to the mobile robot path planning, and the experimental results show that the search ability of the improved algorithm is stronger, and the convergence speed is faster. BRIEF DESCRIPTION OF DRAWINGS

[0070] Figure 1 The flowchart of the application.

[0071] Figure 2 The schematic diagram of the first test environment in the simulation experiment.

[0072] Figure 3 The schematic diagram of the second test environment in the simulation experiment.

[0073] Figure 4 The shortest path result diagram generated by four algorithms in the first environment.

[0074] Figure 5 The convergence diagram of four algorithms in the first environment.

[0075] Figure 6 The shortest path result diagram generated by four algorithms in the second environment.

[0076] Figure 7 The convergence diagram of four algorithms in the second environment. DETAILED DESCRIPTION

[0077] The application will be further described below in combination with the drawings and examples.

[0078] As shown in the drawings, Figure 1 An improved artificial bee colony algorithm-based mobile robot path planning method includes the following steps:

[0079] Step 1: initialize the honey source related parameters.

[0080] Step 2: generate an initial solution, calculate the fitness of the honey source, and start iteration.

[0081] Artificial bee colony algorithm is a kind of swarm life optimization algorithm, inspired by the behavior of bee colony, the algorithm is executed in three stages, namely the employed bee stage, the onlooker bee stage and the scout bee stage; Artificial bee colony algorithm simulates the foraging behavior of bees, where the position of a honey source represents a candidate solution, the amount of nectar in each honey source is considered as fitness, the number of employed bees and onlooker bees is equal, which is half of the population size, the employed bees update the current honey source according to the position in memory, and share information about new honey sources with onlooker bees, according to these information, the scout bees carry out neighborhood search; The specific process is as follows:

[0082] (1) Initialization

[0083] In the initialization stage, a set of possible solutions is randomly generated by the following equation:

[0084]

[0085] Where x i,j represents the set of solutions, i = 1, 2, …, N, N is the population size, j = 1, 2, …, Dim, Dim represents the dimension; And represent the upper and lower bounds of the jth variable; rand(0, 1) is a random number between [0, 1];

[0086] (2) Employed bee stage

[0087] In this stage, the old honey source in the memory of the employed bee is used to generate a new honey source, that is, a new candidate solution is generated:

[0088]

[0089] Where v ij is the position of the new honey source, is a random number between [-1, 1], k is a randomly generated integer, k = 1, 2, …, N, and k ≠ i;

[0090] (3) Onlooker bee stage

[0091] In the onlooker bee stage, the onlooker bee selects the individual with larger probability P i in the employed bee group according to the roulette wheel form, then generates a random number between (0, 1) and compares it with the probability P i , if P i is greater than the generated random number, then the honey source is selected according to formula (3), then the new solution generated by the employed bee and the onlooker bee selects the better honey source according to the greedy algorithm, that is, the better solution is selected by comparing the fitness value of the honey source:

[0092]

[0093] In the formula, Pi Pi represents the probability that the i-th solution is selected, f i is the fitness of the i-th solution,

[0094]

[0095] where fitness i is the objective function value of the i-th solution, abs(fitness i ) represents the absolute value of fitness i ;

[0096] (4) Scout bee phase

[0097] In the scout bee phase, once a certain honey source cannot be further improved within a predetermined period, it is replaced with a new honey source, and the employed bees related to it subsequently become scout bees;

[0098] The new honey source is randomly generated according to formula (1), and steps 2 to 4 are repeated until the termination condition is met.

[0099] The grey wolf algorithm simulates the democratic social behavior exhibited by a group of grey wolves when chasing and hunting prey. In the social hierarchy of grey wolves, there are four levels, with the highest level being the optimal solution, which is the alpha wolf, the suboptimal solution being the beta wolf and the delta wolf, and the other solutions being the omega wolf.

[0100] The grey wolf pack hunting behavior includes three stages: approaching the prey, surrounding the prey, and attacking the prey. The mathematical expression for surrounding the prey is:

[0101] X(t+1)=X p (t)-A·D (5)

[0102] D=|C·X p (t)-X(t)| (6)

[0103] In the formula, t is the current iteration number, X(t) represents the current position of the grey wolf, X p represents the current position of the prey, D represents the distance between the grey wolf individual and the prey, and A and C are coefficient vectors; wherein,

[0104] A=2ar1-a (7)

[0105] C=2r2 (8)

[0106]

[0107] In the formula, a is the convergence factor, r1 and r2 are random numbers between 0 and 1;

[0108] The mathematical model of the grey wolf attacking the prey stage is:

[0109] D a = |C1 · X α (t) - X(t) | (10)

[0110] D β = |C2 · X β (t) - X(t) | (11)

[0111] D δ = |C3 · X δ (t) - X(t) | (12)

[0112] D a , D β and D δ represent the distance between α, β and δ and other individuals respectively, X α (t), X β (t) and X δ (t) represent the position of α, β and δ at t time respectively, the coefficient vector A1, A2 and A3 are generated by formula (7), C1, C2 and C3 are random vectors, generated by formula (8);

[0113] X1= X α (t) - A1 · D α (13)

[0114] X2= X β (t) - A2 · D β (14)

[0115] X3= X δ (t) - A3 · D δ (15)

[0116] X(t+1) = (X1+X2+X3) / 3 (16)

[0117] X1, X2, X3 represent the position of α, β and δ and other individuals respectively.

[0118] In order to increase the local search ability and accelerate the convergence speed, the search formula of honey source in the hired bee stage is modified:

[0119]

[0120] Generated by the hunting stage of GWO algorithm, represents the position of honey source at t time, represents the position of honey source searched by GWO algorithm at t time, r is a random number between [-1, 1].

[0121] The Artificial Bee Colony Algorithm (APA) calculates the fitness value of a solution in each iteration. When applied to path planning, the fitness value is analogous to the path length, and the minimum fitness value in each iteration corresponds to an optimal solution X. gbest To improve the search accuracy of the algorithm, the current optimal solution X is... gbest Introduced into the GWO algorithm:

[0122] D a ′=|C1·X α -X gbest | (18)

[0123] D β ′=|C2·X β -X gbest | (19)

[0124] D δ ′=|C3·X δ -X gbest | (20)

[0125] In the formula, D a ′、D β ′ and D δ ′ represent the distances between α, β, and δ and the optimal individual, respectively;

[0126] X1′=X α (t)-A1·D α ' (twenty one)

[0127] X2′=X β (t)-A2·D β ' (twenty two)

[0128] X3′=X δ (t)-A3·D δ ' (twenty three)

[0129] X′(t+1)=(X1′+X2′+X3′) / 3 (24)

[0130] X′1, X′2, and X3′ represent the positions of α, β, and δ in the wolf pack as they move toward the current best individual, respectively, and X′(t+1) is the position of the gray wolf at time t+1 during the optimization process.

[0131] In the GWO algorithm, the value of 'a' in equation (9) decreases linearly from 2 to 0. However, the optimization process of honey sources is not actually linear. To adapt to the diversity of algorithms and accelerate the convergence speed, equation (9) is changed to...

[0132]

[0133] In the formula f best It is the current optimal solution Xgbest Corresponding nectar source fitness value, L is the starting point straight distance.

[0134] Step three: the optimal solution produced by artificial bee colony algorithm ABC each iteration is substituted into the hunting stage of grey wolf optimization algorithm GWO, and a new nectar source position is generated by using grey wolf optimization algorithm. The new nectar source is introduced in the neighborhood search in the employed bee stage, and the neighborhood search is performed. The scout bee selects the path corresponding to the better nectar source according to the greedy algorithm.

[0135] Step four: the global optimal solution is substituted into the scout bee stage, and the nectar source search equation is improved. If the solution path is not updated for limit times, the employed bee becomes a scout bee, the old solution is discarded, a new solution path is randomly generated, and iteration is restarted.

[0136] The purpose of the scout bee stage of the ABC algorithm is to get rid of the local optimum, but the search equation of the updated nectar source in the scout bee stage has great randomness, which is not conducive to getting rid of the local optimum. In order to improve the ability to get rid of the local optimum, the search equation is improved:

[0137]

[0138] In the formula, Q is an adaptive adjustment coefficient,

[0139]

[0140] Where, f best is the fitness value of the current optimal nectar source, f i is the nectar source fitness value of the i-th solution, limitNum represents the number of experimental failures, and its initial value is 0. If the nectar source i is not updated each time, limitNum is increased by 1. If the nectar source i is not updated for limit times, the nectar source is abandoned, and a new nectar source is generated by formula (26).

[0141] Step five: judge whether the iteration number reaches the maximum iteration number t max , if so, output the optimal path node, connect the nodes in turn to get the optimal path, otherwise return to step three and continue to execute.

[0142] Simulation

[0143] In order to verify the practicability of the algorithm, the improved algorithm GW-ABC is applied to the path planning problem of mobile robot. The matlabR2016a software is used to test in two kinds of environments shown in Figure 2 , Figure 3 The starting point of the scene shown in Figure 2 is (0, 0), the end point is (25, 40), and the obstacles are randomly distributed. Figure 3The starting point of the shown scenario is (1, 11) and the end point is (26, 14), with a U-shaped and a V-shaped obstacle. The shortest paths planned by the ABC algorithm, the particle swarm optimization (PSO) algorithm, the glowworm swarm optimization (GSO) algorithm and the GW-ABC algorithm in the test environment are tested. Each algorithm is run 30 times in each environment, with 300 iterations and 3 dimensions, and the shortest paths obtained after each iteration of each algorithm are recorded and averaged.

[0144] As Figure 4 shown is a shortest path result graph generated by the four algorithms in the second environment, Figure 5 the convergence graphs of the four algorithms, and Table 1 is a comparison of the experimental results of the four algorithms. As can be seen from the comparison of the path planning simulation experimental results in Table 1, compared with the traditional ABC algorithm, the average path obtained by the improved GW-ABC algorithm is shortened by 12.70%, and compared with the GSO algorithm and the PSO algorithm, the average path is shortened by 14.25% and 7.17% respectively, effectively improving the optimization performance of the algorithm. As Figure 2 can be seen from the convergence graphs of the four algorithms, the classic ABC algorithm tends to be stable after 110 iterations, while the GW-ABC algorithm tends to be stable after 35 iterations, reaching the optimal value. Compared with the PSO algorithm and the GSO algorithm, the convergence speed of the GW-ABC algorithm is obviously faster.

[0145] Table 1

[0146] Algorithm Shortest path length / m Longest path length / m Average path length / m ABC 56.38 69.91 63.30 GSO 58.69 74.45 64.44 PSO 55.97 66.18 59.53 GW-ABC 54.41 57.33 55.26

[0147] As Figure 6 shown is a shortest path result graph generated by the four algorithms in the second environment, Figure 7 the convergence graphs of the four algorithms, and Table 2 is a comparison of the experimental results of the four algorithms. As can be seen from the comparison of the path planning simulation experimental results in Table 2, compared with the traditional ABC algorithm, the average path obtained by the improved GW-ABC algorithm is shortened by 16.72%, and compared with the GSO algorithm and the PSO algorithm, the average path is shortened by 21.97% and 7.85% respectively, effectively improving the optimization performance of the algorithm. As Figure 5 can be seen from the convergence graphs of the four algorithms, the GW-ABC algorithm tends to be stable after 30 iterations, while the classic ABC algorithm tends to be stable after 50 iterations. Compared with the PSO algorithm and the GSO algorithm, obviously, the GW-ABC algorithm is easier and faster to approach the optimal value.

[0148] Table 2

[0149] Algorithm Shortest path length / m Longest path length / m Average path length / m ABC 36.97 29.27 33.98 GSO 41.45 31.74 36.27 PSO 32.26 28.73 30.71 GW-ABC 30.62 27.86 28.30

[0150] The classic ABC algorithm is easy to fall into local optimum, while the improved GW-ABC algorithm can effectively avoid falling into local optimum, has stronger search ability and faster convergence speed. Compared with the other three algorithms, the improved GW-ABC algorithm can find the shortest path more effectively and has faster convergence speed.

Claims

1. A path planning method for a mobile robot based on an improved artificial bee colony algorithm, characterized in that, Includes the following steps: Step 1: Initialize honey source related parameters; Step 2: Generate an initial solution and calculate the fitness of the nectar source, then begin iteration; Step 3: Substitute the optimal solution generated by each iteration of the artificial bee colony algorithm ABC into the hunting phase of the gray wolf optimization algorithm GWO. Use the gray wolf optimization algorithm to generate new nectar source locations. Introduce the new nectar source during the neighborhood search in the hired bee phase and perform a neighborhood search. The observer bees select the path corresponding to the better nectar source according to the greedy algorithm. The Gray Wolf Algorithm mimics the democratic social behavior exhibited by a pack of gray wolves when chasing and hunting prey. There are four levels in the gray wolf social hierarchy, with the highest level, which is the optimal solution, being α wolf; the second-best solutions are β wolf and δ wolf; and the other solutions are ω wolf. The hunting behavior of gray wolf packs includes three stages: approaching the prey, surrounding the prey, and attacking the prey. The mathematical expression for surrounding the prey is: X(t+1)=X p (t)-A·D (5) D=|C·X p (t)-X(t)| (6) In the formula, t is the current iteration number, X(t) represents the current position of the gray wolf, and X p Let A represent the current location of the prey, D represent the distance between the individual gray wolf and the prey, and A and C be coefficient vectors; where, A = 2ar1 - a (7) C＝2r2 (8) In the formula, a is the convergence factor, and r1 and r2 are random numbers in the interval [0, 1]. The mathematical model for the gray wolf's attack on its prey is as follows: D a =|C1·X α (t)-X(t)| (10) D β =|C2·X β (t)-X(t)| (11) D δ =|C3·X δ (t)-X(t)| (12) D a D β and D δ Let X represent the distances between α, β, and δ and other individuals, respectively. α (t), X β (t) and X δ (t) represent the positions of α, β and δ at time t, respectively. The coefficient vectors A1, A2 and A3 are generated by formula (7), and C1, C2 and C3 are random vectors generated by formula (8). X1=X α (t)-A1·D α (13) X2=X β (t)-A2·D β (14) X3=X δ (t)-A3·D δ (15) X(t+1)=(X1+X2+X3) / 3 (16) X1, X2, and X3 represent the positions of α, β, and δ relative to other individuals, respectively; Step 4: Substitute the global optimal solution into the scout bee stage, improve the honey source search equation. If the solution path is not updated for a consecutive limit number of times, the hired bee becomes a scout bee, discards the old solution, randomly generates a new solution path, and restarts the iteration. To improve the ability to escape local optima, the search equation is improved as follows: In the formula, Q is the adaptive adjustment coefficient. Among them, f best f is the fitness value of the current optimal nectar source. i Let be the fitness value of the honey source in the i-th solution, and limitNum represent the number of failed experiments. Its initial value is 0. If the honey source i is not updated in each iteration, limitNum is incremented by 1. If the honey source i is not updated for a consecutive limit number of times, the honey source is abandoned and a new honey source is generated by equation (26). Step 5: Determine if the number of iterations has reached the maximum number of iterations t. max If the optimal path node is reached, the nodes are connected sequentially to obtain the optimal path; otherwise, return to step three to continue execution.

2. The mobile robot path planning method based on the improved artificial bee colony algorithm according to claim 1, characterized in that, In step two, the artificial bee colony algorithm is a population life optimization algorithm inspired by bee colony behavior. This algorithm is executed in three phases: the hired bee phase, the observer bee phase, and the scout bee phase. The artificial bee colony algorithm simulates the nectar-gathering behavior of bees. The location of a nectar source represents a candidate solution, and the amount of nectar in each nectar source is considered fitness. The number of hired bees and observer bees is equal, representing half the total population size. The hired bees update the current nectar source based on their memory of its location and share information about new nectar sources with the observer bees. Based on this information, the scout bees perform a neighborhood search. The specific process is as follows: (1) Initialization During the initialization phase, a set of possible solutions is randomly generated using the following equation: Where x i,j Let i = 1, 2, ..., N, where N is the population size, and j = 1, 2, ..., Dim, where Dim represents the dimension. and This represents the upper and lower bounds of the j-th variable; rand(0,1) is a random number between [0,1]. (2) Hired bee stage In this stage, new nectar sources are generated using the memories of old nectar sources held by the hired bees, i.e., new candidate solutions are generated: Where v ij It is a new honey source location. It is a random number between [-1, 1], where k is a randomly generated integer, k = 1, 2, ..., N, and k ≠ i; (3) Observer bee stage During the observer bee phase, the observer bee selects a probability P from the hired bee colony based on a roulette-like method. i For larger individuals, a random number between (0, 1) with probability P is then randomly generated. i Comparison, if P i If the value is greater than the generated random number, the nectar source is selected according to equation (3). Then, the new solutions generated by the hired bees and the observer bees are selected according to the greedy algorithm to select the better nectar source, that is, the fitness value of the nectar source is compared to select the better solution: In the formula, P i f represents the probability that the i-th solution is selected. i Let be the fitness of the nectar source for the i-th solution. Among them, fitness i Let abs(fitness) be the objective function value for i solutions. i ) represents fitness i The absolute value; (4) Scout Bee Stage During the scout bee phase, if a nectar source cannot be further improved within a predetermined period, it is replaced by a new nectar source, and the bees associated with it subsequently become scout bees. New nectar sources are randomly generated according to formula (1), and steps 2 to 4 are repeated until the termination condition is met.

3. The mobile robot path planning method based on the improved artificial bee colony algorithm according to claim 2, characterized in that, In step two, to enhance local search capabilities and accelerate convergence, the formula for searching nectar sources during the hired bee phase is modified: Generated by the hunting phase of the GWO algorithm. Indicates the location of the nectar source at time t. Let r represent the location of the honey source searched by the GWO algorithm at time t, where r is a random number between [-1, 1]. The Artificial Bee Colony Algorithm (APA) calculates the fitness value of a solution in each iteration. When applied to path planning, the fitness value is analogous to the path length, and the minimum fitness value in each iteration corresponds to an optimal solution X. gbest To improve the search accuracy of the algorithm, the current optimal solution X is... gbest Introduced into the GWO algorithm: D a ′=|C1·X α -X gbest | (18) D β ′=|C2·X β -X gbest | (19) D δ ′=|C3·X δ -X gbest | (20) In the formula, D a ′、D β ′ and D δ ′ represent the distances between α, β, and δ and the optimal individual, respectively; X1′=X α (t)-A1·D α ′ (21) X2′=X β (t)-A2·D β ’ (22) X3′=X δ (t)-A3·D δ ′ (23) X′(t+1)=(X1′+X2′+X3′) / 3 (24) X′1, X′2, and X3′ represent the positions of α, β, and δ in the wolf pack as they move toward the current best individual, respectively, and X′(t+1) is the position of the gray wolf at time t+1 during the optimization process; In the GWO algorithm, the value of 'a' in equation (9) decreases linearly from 2 to 0. However, the optimization process of honey sources is not actually linear. To adapt to the diversity of algorithms and accelerate the convergence speed, equation (9) is changed to... In the formula f best It is the current optimal solution X gbest The corresponding nectar source fitness value, where L is the straight-line distance from the starting point.

Images