A robot path planning method based on improved harris hawk algorithm

Abstract

The application discloses a robot path planning method based on an improved Harris hawk optimization algorithm, the Harris hawk optimization algorithm is improved and optimized first, and an improved Harris hawk optimization algorithm is obtained, then Harris hawk position optimization in the improved Harris hawk optimization algorithm is corresponding to robot path planning, optimal Harris hawk positions obtained by using the improved Harris hawk optimization algorithm are used as various nodes of robot path planning, and the various nodes, a path starting point and a path ending point are connected to realize robot path planning, wherein, the specific improvement and optimization measures of the improved Harris hawk optimization algorithm are as follows: 1, an escape energy formula is improved by using a natural constant e; 2, an elite cooperation guiding global search strategy is adopted to replace a random Harris hawk guiding global search strategy; and 3, an intraspecific competition strategy is introduced in the Harris hawk optimization algorithm development stage, and the method has the advantages of high precision and high efficiency.

Description

Technical Field

[0001] This invention relates to robot path planning methods, and more particularly to a robot path planning method based on an improved Harris Eagle algorithm. Background Technology

[0002] Mobile robot path planning is a crucial technology in mobile robot research. Its goal is to find a collision-free and low-cost route from the starting point to the target point; this route is often referred to as the shortest. Planning an efficient and obstacle-avoiding route has always been a challenging problem. With increasingly complex engineering problems and the growing prevalence of automation, mobile robot path planning must be adaptable to its environment.

[0003] Path planning is typically based on classical and heuristic algorithms. Classical algorithms, such as A*Star and artificial potential fields, offer simple implementation concepts but suffer from low efficiency and high perturbation. Heuristic algorithms, such as the Grey Wolf Optimization Algorithm, Artificial Bee Colony Optimization Algorithm, Bat Algorithm, and Harris Eagle Optimization Algorithm, are robust and offer significant advantages in path planning. However, they also have common drawbacks, such as getting trapped in local optima and slow convergence. To address these issues with robot path planning methods employing either classical or heuristic algorithms, some researchers have proposed combining improved heuristics with classical algorithms. However, this combination increases computational complexity, impacting the efficiency of robot path planning and leading to lower robot performance and increased wear and tear. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a robot path planning method based on the improved Harris Eagle algorithm that has high accuracy and high efficiency.

[0005] The technical solution adopted by this invention to solve the above-mentioned technical problems is as follows: a robot path planning method based on an improved Harris Eagle optimization algorithm. First, the Harris Eagle optimization algorithm is improved and optimized to obtain an improved Harris Eagle optimization algorithm. Then, the Harris Eagle position optimization in the improved Harris Eagle optimization algorithm is correlated with robot path planning. The optimal Harris Eagle position is obtained using the improved Harris Eagle optimization algorithm. The optimal Harris Eagle position is used as each node in the robot path planning. Each node, the path start point, and the path end point are connected sequentially to realize robot path planning. The specific improvement and optimization measures for the Harris Eagle optimization algorithm are: 1. Improving the escape energy formula using the natural constant e; 2. Replacing the random Harris Eagle-guided global search strategy with an elite cooperative global search strategy; 3. Introducing an intraspecific competition strategy during the development stage of the Harris Eagle optimization algorithm.

[0006] The improved Harris Eagle optimization algorithm is used to find the optimal Harris Eagle position, which is then used as the position of each node in the robot path planning. The specific process of connecting each node, the path start point, and the path end point in sequence to achieve robot path planning is as follows:

[0007] Step 1: Determine the relevant parameters for path planning. Specifically, establish a continuous coordinate system two-dimensional plane map of the area requiring path planning. At each obstacle in the continuous coordinate system two-dimensional plane map, fit a circle in an inscribed manner, and count the number of fitted circles, denoted as W. Obtain the center coordinates and radius of each circle, and mark the center coordinates of the v-th circle as... Let the radius of the v-th circle be denoted as Get the starting point coordinates, ending point coordinates, and maximum x-coordinate of a 2D plane map in a continuous coordinate system (ub). x , Maximum value of the y-axis ub y Minimum value of x-axis lb x and the minimum value of the ordinate lb y Let the starting point coordinates be (x start ,y start The endpoint coordinates are (x end ,y end ), set the upper limit ub = (ub x ,ub y ), set the lower limit lb = (lb x ,lb y Let the area of ​​a two-dimensional plane map in a continuous coordinate system be S, where S = (ub) x -lb x )×(ub y -lb y Let the number of path nodes be n, where n is an integer greater than or equal to 2;

[0008] Step 2: Construct a Harris Eagle population, where the population size is set to N, where N is an integer greater than or equal to 4, and the maximum number of iterations is set to T, where T is an integer greater than or equal to 50. Initialize N Harris Eagle individuals in the population using formula (1) to obtain the initial population, i.e., the 0th generation population:

[0009]

[0010] In equation (1), Let the coordinate of the i-th Harris Eagle individual in the 0th generation population be denoted as j-th coordinate, where The x-axis is... Using the ordinate as the vertical axis, each individual Harris Eagle has n coordinates. Each Harris Eagle is represented by a coordinate set consisting of its n coordinates, where i = 1, 2, ..., N, j = 1, 2, ..., n. and These are random numbers generated by a random function, and

[0011] Step 3: Evaluate each Harris Eagle individual in the 0th generation population. The specific process for evaluating the i-th Harris Eagle individual in the 0th generation population is as follows:

[0012] S3-1, Settings in for The 0th coordinate in the middle, for The (n+1)th coordinate in the middle, (x i j (0),y i j (0)) is The j-th coordinate;

[0013] S3-2, Settings The number of intersection points between the line connecting the l-th and (l+1)-th coordinates and the W circles is . Will Initialize to 0; initialize l to 0;

[0014] S3-3. Set variable m and initialize m to equal 1;

[0015] S3-4, Settings The shortest distance between the line connecting the l-th and (l+1)-th coordinates and the center of the m-th circle is:

[0016] S3-5, calculated using formula (2)

[0017]

[0018] In equation (2), || represents the absolute value sign;

[0019] S3-6, Judgment Is it less than or equal to? If less than or equal to Then adopt The sum of the current value plus 1 is updated. otherwise The current value remains unchanged;

[0020] S3-7. Determine if the current value of m is equal to W. If the current value of m is equal to W, then determine if the current value of l is equal to n. If the current value of l is equal to n, then set the current value as n. The value is assigned to w i (0), proceed to step S3-8. If the current value of l is not equal to n, then... Assign the current value to Then, the value of l is updated by adding 1 to the current value of l, and the process returns to step S3-3. If the current value of m is not equal to W, the value of m is updated by adding 1 to the current value of m, and the process returns to step S3-4.

[0021] S3-8, w i (0) and Substituting each coordinate into the fitness function shown in equation (3), the fitness value of the i-th Harris Hawk individual in the 0th generation population is calculated:

[0022]

[0023] In equation (3), This represents the fitness value of the i-th Harris Hawk individual in the 0th generation population;

[0024] S3-9. Sort the N Harris Eagle individuals in the 0th generation population according to their fitness values ​​from smallest to largest, and select the Harris Eagle individual with the smallest fitness value in the 0th generation population as the best Harris Eagle individual X in the 0th generation. best (0), let X be the optimal state of the 0th generation population. a (0), X best (0) Assign the value to X a (0), let X be the Harris Eagle individual with the second smallest fitness value in the 0th generation population. b (0); Let X be the Harris Eagle individual with the third smallest fitness value in the 0th generation population. c (0) Select the Harris Eagle individual with the lowest fitness value in the 0th generation population as the 0th generation prey X. a (0);

[0025] Step 4: Set the iteration variable t and initialize t to 1;

[0026] Step 5: Perform the t-th iteration on the Harris Eagle population to obtain the t-th generation population. The specific iteration process is as follows:

[0027] S5-1. For each Harris Eagle individual in the (t-1)th generation population, determine whether it has crossed the boundary to obtain the updated (t-1)th generation population. The specific determination process for the i-th Harris Eagle individual in the (t-1)th generation population is as follows:

[0028] like Then let Soon Updated to equal lb x ,like Then let Soon Updated to equal ub x ,like but If remain unchanged, Then let Soon Updated to equal lb y ,like Then let Soon Updated to equal ub y , but Remain unchanged;

[0029] S5-2. Calculate the mean coordinates of the updated (t-1)th generation population. The specific process is as follows:

[0030] set up Let be the mean of the j-th coordinate of the (t-1)-th generation population after the update, where for x-coordinate for The ordinate is calculated using equation (4). and

[0031]

[0032] In equation (4), Let x be the x-coordinate of the j-th coordinate of the i-th Harris Eagle individual in the updated (t-1)-th generation population. Let j be the ordinate of the j-th coordinate of the i-th Harris Eagle individual in the updated t-1 generation population;

[0033] S5-3. Let E(t) be the escape energy of the t-th generation prey. Calculate the escape energy of the t-th generation prey using equation (5). Set coefficients A(t), B(t), and C(t). Calculate the coefficients A(t), B(t), and C(t) according to equations (6), (7), and (8):

[0034]

[0035]

[0036]

[0037]

[0038] E0(t) is generated using a random function, and -1≤E0(t)≤1. The convergence factor of the t-th generation is set to be equal to |E(t)|; || is the absolute value symbol, and e is the natural constant with a value of 2.7182818284. X represents a The fitness value of (t-1), X represents b The fitness value of (t-1), X represents c The fitness value of (t-1);

[0039] S5-4. Let X be the i-th Harris Eagle individual in the updated t-1 generation population. i (t-1), X i (t-1) is transformed into an n×2 type matrix, denoted as X. i (t-1), X i In (t-1), the first column is the x-axis and the second column is the y-axis. The j-th coordinate of the i-th Harris Eagle individual in the updated (t-1)-th generation population corresponds to X. i The 1×2 type vector in the j-th row of (t-1) is denoted as... X a Each coordinate of (t-1) is transformed into a 1×2 type vector with the first column being the x-coordinate and the second column being the y-coordinate, where X a The 1×2 type vector obtained by transforming the j-th coordinate of (t-1) is denoted as... X b Each coordinate of (t-1) is transformed into a 1×2 type vector with the first column being the x-coordinate and the second column being the y-coordinate. b The 1×2 type vector obtained by transforming the j-th coordinate of (t-1) is denoted as... X c Each coordinate of (t-1) is transformed into a 1×2 type vector with the first column being the x-coordinate and the second column being the y-coordinate. c The 1×2 type vector obtained by transforming the j-th coordinate of (t-1) is denoted as...

[0040] Let X be the i-th Harris Eagle individual in the t-th generation population. i (t), X i (t) is transformed into an n×2 type matrix X i (t), X i In (t), the first column is the x-axis, and the second column is the y-axis, representing the i-th Harris Eagle individual in the t-th generation population. i The j-th coordinate of (t) corresponds to X iThe 1×2 type vector in the j-th row of (t) is denoted as...

[0041] We determine the convergence factor |E(t)| for the t-th generation. If |E(t)| < 1, we proceed to step S5-5 first, then to step S5-6. Based on steps S5-5 and S5-6, we obtain... If |E(t)|≥1, then first use random functions to generate... and in Then determine Is it greater than or equal to 0.5? Then, the result is obtained by using equation (9). Then proceed directly to step S5-7; otherwise, calculate using equation (10). Then proceed directly to steps S5-7;

[0042]

[0043]

[0044] S5-5. Let J(t) be the jumping intensity of the t-th generation prey. First, calculate the jumping intensity J(t) according to equation (11), and then calculate the jumping intensity X respectively. i Replace each row vector of (t-1), where X i The process of replacing the j-th row vector of (t-1) is as follows:

[0045] S5-5-1. Define four 1×2 type vectors for pre-replacement, namely... and The results were obtained by using equations (12) to (17). and

[0046] J(t)=2(1-r4(t)) (11)

[0047]

[0048]

[0049]

[0050]

[0051]

[0052] Where D is a 2-dimensional unit vector, β equals 1.5, and Γ represents the gamma function; random numbers μ(t), ν(t), and r4(t) are generated using random functions, and 0≤μ(t)≤1, 0≤ν(t)≤1, and 0≤r4(t)≤1;

[0053] S5-5-2, X i Replace the j-th row vector of (t-1) with After converting to a coordinate set, a Harris Hawk individual is obtained. The fitness value of this Harris Hawk individual is obtained using the same method as for each Harris Hawk individual in the 0th generation population. This obtained fitness value is denoted as...

[0054] X i Replace the j-th row vector of (t-1) with After converting to a coordinate set, a Harris Hawk individual is obtained. The fitness value of this Harris Hawk individual is obtained using the same method as for each Harris Hawk individual in the 0th generation population. This obtained fitness value is denoted as...

[0055] X i Replace the j-th row vector of (t-1) with After converting to a coordinate set, a Harris Hawk individual is obtained. The fitness value of this Harris Hawk individual is obtained using the same method as for each Harris Hawk individual in the 0th generation population. This obtained fitness value is denoted as...

[0056] X i Replace the j-th row vector of (t-1) with After converting to a coordinate set, a Harris Hawk individual is obtained. The fitness value of this Harris Hawk individual is obtained using the same method as for each Harris Hawk individual in the 0th generation population. This obtained fitness value is denoted as...

[0057] S5-6. Generate a random number rand(t) using a random function, where 0 ≤ rand(t) ≤ 1. Select a strategy based on the random number rand(t) and the convergence factor |E(t)| of the t-th generation.

[0058] S5-6-1. If rand(t)≥0.5 and 0.5≤|E(t)|<1, the result is obtained by using equation (17).

[0059] If rand(t)≥0.5 and 0≤|E(t)|<0.5, the result is obtained using equation (18).

[0060] If rand(t) < 0.5 and 0.5 ≤ |E(t)| < 1, first determine... Is it less than If satisfied, then Assign to If not satisfied, then judge. Is it less than If satisfied, then Assign to If not satisfied, Assign to

[0061] If rand(t) < 0.5 and 0 ≤ |E(t)| < 0.5, first determine... Is it less than If satisfied, then Assign to If not satisfied, then judge. Is it less than If satisfied, then Assign to If not satisfied, Assign to

[0062] After the operation is completed, you will get to

[0063] S5-6-2, The currently obtained to Converting a 1×2 type vector back to coordinates to The transformed coordinates form a coordinate set containing n coordinates, thus yielding a Harris Hawk individual. The fitness value of this Harris Hawk individual is calculated using the same method as for each Harris Hawk individual in the 0th generation population, denoted as .

[0064] S5-6-3, Set a 1×2 type vector for pre-replacement. The result is obtained by using equation (19). After converting the Harris Eagle individual obtained in step S5-6-2 into an n×2 type matrix using the same method as before, replace the j-th row vector of this n×2 type matrix with... The results are then transformed into a coordinate set, yielding a Harris Hawk individual. The fitness value of this individual is calculated using the same method as for each Harris Hawk individual in the 0th generation population. This fitness value is then denoted as... like Less than Then Assign to otherwise Remain unchanged;

[0065]

[0066]

[0067]

[0068] S5-7, The currently obtained to Following the same method as before, convert them to coordinates, and you will get... to The corresponding n coordinates form a coordinate set, which is the i-th Harris Eagle individual in the t-th generation population. Thus, the N Harris Eagle individuals in the t-th generation population are obtained.

[0069] S5-8. Determine if the current value of t is equal to T. If not, evaluate the t-th generation population using the same method as in step 3 to obtain the fitness value of each Harris eagle individual in the t-th generation population and the Harris eagle individual X with the smallest fitness value in the t-th generation population. best (t), the optimal state X of the t-th generation population a (t), the Harris Eagle individual X, which has the second smallest fitness value in the t-th generation population. b (t), the Harris Eagle individual X, which has the third smallest fitness value in the t-th generation population. c (t) and the tth generation prey X a (t), then update the value of t by adding 1 to the current value of t, and return to step S5.1 for the next iteration. If it equals T, the iteration ends and the optimal state X is output. best (T) represents the optimal position for the Harris Hawk;

[0070] Step 6: Locate X on the two-dimensional plane map in the continuous coordinate system. best The positions of each coordinate in (T), i.e., the node positions, are connected sequentially from the starting point to the ending point, connecting the starting point coordinates (x, y, y) to the ending point. start ,y start ), X best Each coordinate in (T) and the endpoint coordinate (x) end ,y end This yields the optimal path for the robot to move.

[0071] Compared with existing technologies, the advantages of this invention are as follows: First, the Harris Eagle optimization algorithm is improved and optimized. Then, the Harris Eagle position optimization in the improved Harris Eagle optimization algorithm is correlated with robot path planning. The optimal Harris Eagle position is obtained using the improved Harris Eagle optimization algorithm, and this optimal Harris Eagle position is used as each node in the robot path planning. Each node, the path start point, and the path end point are connected sequentially to achieve robot path planning. Compared with the original Harris Eagle optimization algorithm, the improved Harris Eagle optimization algorithm uses the natural constant e to improve the escape energy formula, thereby increasing the global search probability in the early stages of the algorithm and improving its optimization ability. An elite cooperative global search strategy is adopted instead of the random Harris Eagle-guided global search strategy, improving the algorithm's search performance and efficiency. An intraspecific competition strategy is introduced during the Harris Eagle optimization algorithm development stage to enhance the Harris Eagle's ability to escape local optima. Therefore, this invention reduces the algorithm's tendency to get trapped in local optima and improves the convergence speed, achieving both high accuracy and high efficiency. Attached Figure Description

[0072] Figure 1 The figure shows an example of the robot path planning results in scenario one, comparing the robot path planning method based on the improved Harris Eagle optimization algorithm of the present invention with five existing comparative algorithms.

[0073] Figure 2 The figure shows an example of the robot path planning results in scenario two, comparing the robot path planning method based on the improved Harris Eagle optimization algorithm of the present invention with five existing comparative algorithms. Detailed Implementation

[0074] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0075] Example 1: A robot path planning method based on an improved Harris Eagle optimization algorithm. First, the Harris Eagle optimization algorithm is improved to obtain an improved Harris Eagle optimization algorithm. Then, the Harris Eagle position optimization in the improved Harris Eagle optimization algorithm is correlated with robot path planning. The optimal Harris Eagle position is obtained using the improved Harris Eagle optimization algorithm. The optimal Harris Eagle position is used as each node in the robot path planning. Each node, the path start point, and the path end point are connected sequentially to achieve robot path planning. The specific improvement and optimization measures for the improved Harris Eagle optimization algorithm are: 1. Improving the escape energy formula using the natural constant e; 2. Replacing the random Harris Eagle-guided global search strategy with an elite cooperative global search strategy; 3. Introducing an intraspecific competition strategy during the development stage of the Harris Eagle optimization algorithm.

[0076] Example 2: This example is basically the same as Example 1, except that: In this example, the optimization of the Harris Eagle position in the improved Harris Eagle optimization algorithm is correlated with robot path planning. The improved Harris Eagle optimization algorithm is used to obtain the optimal Harris Eagle position, and the optimal Harris Eagle position is used as the position of each node in the robot path planning. The specific process of connecting each node, the path start point, and the path end point in sequence to realize the robot path planning is as follows:

[0077] Step 1: Determine the relevant parameters for path planning. Specifically, establish a continuous coordinate system two-dimensional plane map of the area requiring path planning. At each obstacle in the continuous coordinate system two-dimensional plane map, fit a circle in an inscribed manner, and count the number of fitted circles, denoted as W. Obtain the center coordinates and radius of each circle, and mark the center coordinates of the v-th circle as... Let the radius of the v-th circle be denoted as Get the starting point coordinates, ending point coordinates, and maximum x-coordinate of a 2D plane map in a continuous coordinate system (ub). x , Maximum value of the y-axis ub y Minimum value of x-axis lb x and the minimum value of the ordinate lb y Let the starting point coordinates be (x start ,y start The endpoint coordinates are (x end ,y end ), set the upper limit ub = (ub x ,ub y ), set the lower limit lb = (lb x ,lb y Let the area of ​​a two-dimensional plane map in a continuous coordinate system be S, where S = (ub) x -lb x )×(ub y -lb y Let the number of path nodes be n, where n is an integer greater than or equal to 2;

[0078] Step 2: Construct a Harris Eagle population, where the population size is set to N, where N is an integer greater than or equal to 4, and the maximum number of iterations is set to T, where T is an integer greater than or equal to 50. Initialize N Harris Eagle individuals in the population using formula (1) to obtain the initial population, i.e., the 0th generation population:

[0079]

[0080] In equation (1), Let the coordinate of the i-th Harris Eagle individual in the 0th generation population be denoted as j-th coordinate, where The x-axis is... Using the ordinate as the vertical axis, each individual Harris Eagle has n coordinates. Each Harris Eagle is represented by a coordinate set consisting of its n coordinates, where i = 1, 2, ..., N, j = 1, 2, ..., n. and These are random numbers generated by a random function, and

[0081] Step 3: Evaluate each Harris Eagle individual in the 0th generation population. The specific process for evaluating the i-th Harris Eagle individual in the 0th generation population is as follows:

[0082] S3-1, Settings in for The 0th coordinate in the middle, for The (n+1)th coordinate in the middle, (x i j (0),y i j (0)) is The j-th coordinate;

[0083] S3-2, Settings The number of intersection points between the line connecting the l-th and (l+1)-th coordinates and the W circles is . Will Initialize to 0; initialize l to 0;

[0084] S3-3. Set variable m and initialize m to equal 1;

[0085] S3-4, Settings The shortest distance between the line connecting the l-th and (l+1)-th coordinates and the center of the m-th circle is:

[0086] S3-5, calculated using formula (2)

[0087]

[0088] In equation (2), || represents the absolute value sign;

[0089] S3-6, Judgment Is it less than or equal to? If less than or equal to Then adopt The sum of the current value plus 1 is updated. otherwise The current value remains unchanged;

[0090] S3-7. Determine if the current value of m is equal to W. If the current value of m is equal to W, then determine if the current value of l is equal to n. If the current value of l is equal to n, then set the current value as n. The value is assigned to w i (0), proceed to step S3-8. If the current value of l is not equal to n, then... Assign the current value to Then, the value of l is updated by adding 1 to the current value of l, and the process returns to step S3-3. If the current value of m is not equal to W, the value of m is updated by adding 1 to the current value of m, and the process returns to step S3-4.

[0091] S3-8, w i (0) and Substituting each coordinate into the fitness function shown in equation (3), the fitness value of the i-th Harris Hawk individual in the 0th generation population is calculated:

[0092]

[0093] In equation (3), This represents the fitness value of the i-th Harris Hawk individual in the 0th generation population;

[0094] S3-9. Sort the N Harris Eagle individuals in the 0th generation population according to their fitness values ​​from smallest to largest, and select the Harris Eagle individual with the smallest fitness value in the 0th generation population as the best Harris Eagle individual X in the 0th generation. best (0), let X be the optimal state of the 0th generation population. a (0), X best (0) Assign the value to X a (0), let X be the Harris Eagle individual with the second smallest fitness value in the 0th generation population. b (0); Let X be the Harris Eagle individual with the third smallest fitness value in the 0th generation population. c (0) Select the Harris Eagle individual with the lowest fitness value in the 0th generation population as the 0th generation prey X. a (0);

[0095] Step 4: Set the iteration variable t and initialize t to 1;

[0096] Step 5: Perform the t-th iteration on the Harris Eagle population to obtain the t-th generation population. The specific iteration process is as follows:

[0097] S5-1. For each Harris Eagle individual in the (t-1)th generation population, determine whether it has crossed the boundary to obtain the updated (t-1)th generation population. The specific determination process for the i-th Harris Eagle individual in the (t-1)th generation population is as follows:

[0098] like Then let Soon Updated to equal lb x ,like Then let Soon Updated to equal ub x ,like but If remain unchanged, Then let Soon Updated to equal lb y ,like Then let Soon Updated to equal ub y , but Remain unchanged;

[0099] S5-2. Calculate the mean coordinates of the updated (t-1)th generation population. The specific process is as follows:

[0100] set up Let be the mean of the j-th coordinate of the (t-1)-th generation population after the update, where for x-coordinate for The ordinate is calculated using equation (4). and

[0101]

[0102] In equation (4), Let x be the x-coordinate of the j-th coordinate of the i-th Harris Eagle individual in the updated (t-1)-th generation population. Let j be the ordinate of the j-th coordinate of the i-th Harris Eagle individual in the updated t-1 generation population;

[0103] S5-3. Let E(t) be the escape energy of the t-th generation prey. Calculate the escape energy of the t-th generation prey using equation (5). Set coefficients A(t), B(t), and C(t). Calculate the coefficients A(t), B(t), and C(t) according to equations (6), (7), and (8):

[0104]

[0105]

[0106]

[0107]

[0108] E0(t) is generated using a random function, and -1≤E0(t)≤1. The convergence factor of the t-th generation is set to be equal to |E(t)|; || is the absolute value symbol, and e is the natural constant with a value of 2.7182818284. X represents a The fitness value of (t-1), X represents b The fitness value of (t-1), X represents c The fitness value of (t-1);

[0109] S5-4. Let X be the i-th Harris Eagle individual in the updated t-1 generation population. i (t-1), X i (t-1) is transformed into an n×2 type matrix, denoted as X. i (t-1), X i In (t-1), the first column is the x-axis and the second column is the y-axis. The j-th coordinate of the i-th Harris Eagle individual in the updated (t-1)-th generation population corresponds to X. i The 1×2 type vector in the j-th row of (t-1) is denoted as... X a Each coordinate of (t-1) is transformed into a 1×2 type vector with the first column being the x-coordinate and the second column being the y-coordinate, where X a The 1×2 type vector obtained by transforming the j-th coordinate of (t-1) is denoted as... X b Each coordinate of (t-1) is transformed into a 1×2 type vector with the first column being the x-coordinate and the second column being the y-coordinate. b The 1×2 type vector obtained by transforming the j-th coordinate of (t-1) is denoted as... X c Each coordinate of (t-1) is transformed into a 1×2 type vector with the first column being the x-coordinate and the second column being the y-coordinate. c The 1×2 type vector obtained by transforming the j-th coordinate of (t-1) is denoted as...

[0110] Let X be the i-th Harris Eagle individual in the t-th generation population. i (t), X i (t) is transformed into an n×2 type matrix X i (t), X i In (t), the first column is the x-axis, and the second column is the y-axis, representing the i-th Harris Eagle individual in the t-th generation population. i The j-th coordinate of (t) corresponds to X iThe 1×2 type vector in the j-th row of (t) is denoted as...

[0111] We determine the convergence factor |E(t)| for the t-th generation. If |E(t)| < 1, we proceed to step S5-5 first, then to step S5-6. Based on steps S5-5 and S5-6, we obtain... If |E(t)|≥1, then first use random functions to generate... and in Then determine Is it greater than or equal to 0.5? Then, the result is obtained by using equation (9). Then proceed directly to step S5-7; otherwise, calculate using equation (10). Then proceed directly to steps S5-7;

[0112]

[0113]

[0114] S5-5. Let J(t) be the jumping intensity of the t-th generation prey. First, calculate the jumping intensity J(t) according to equation (11), and then calculate the jumping intensity X respectively. i Replace each row vector of (t-1), where X i The process of replacing the j-th row vector of (t-1) is as follows:

[0115] S5-5-1. Define four 1×2 type vectors for pre-replacement, namely... and The results were obtained by using equations (12) to (17). and

[0116] J(t)=2(1-r4(t)) (11)

[0117]

[0118]

[0119]

[0120]

[0121]

[0122] Where D is a 2-dimensional unit vector, β equals 1.5, and Γ represents the gamma function; random numbers μ(t), ν(t), and r4(t) are generated using random functions, and 0≤μ(t)≤1, 0≤ν(t)≤1, and 0≤r4(t)≤1;

[0123] S5-5-2, X i Replace the j-th row vector of (t-1) with After converting to a coordinate set, a Harris Hawk individual is obtained. The fitness value of this Harris Hawk individual is obtained using the same method as for each Harris Hawk individual in the 0th generation population. This obtained fitness value is denoted as...

[0124] X i Replace the j-th row vector of (t-1) with After converting to a coordinate set, a Harris Hawk individual is obtained. The fitness value of this Harris Hawk individual is obtained using the same method as for each Harris Hawk individual in the 0th generation population. This obtained fitness value is denoted as...

[0125] X i Replace the j-th row vector of (t-1) with After converting to a coordinate set, a Harris Hawk individual is obtained. The fitness value of this Harris Hawk individual is obtained using the same method as for each Harris Hawk individual in the 0th generation population. This obtained fitness value is denoted as...

[0126] X i Replace the j-th row vector of (t-1) with After converting to a coordinate set, a Harris Hawk individual is obtained. The fitness value of this Harris Hawk individual is obtained using the same method as for each Harris Hawk individual in the 0th generation population. This obtained fitness value is denoted as...

[0127] S5-6. Generate a random number rand(t) using a random function, where 0 ≤ rand(t) ≤ 1. Select a strategy based on the random number rand(t) and the convergence factor |E(t)| of the t-th generation.

[0128] S5-6-1. If rand(t)≥0.5 and 0.5≤|E(t)|<1, the result is obtained by using equation (17).

[0129] If rand(t)≥0.5 and 0≤|E(t)|<0.5, the result is obtained using equation (18).

[0130] If rand(t) < 0.5 and 0.5 ≤ |E(t)| < 1, first determine... Is it less than If satisfied, then Assign to If not satisfied, then judge. Is it less than If satisfied, then Assign to If not satisfied, Assign to

[0131] If rand(t) < 0.5 and 0 ≤ |E(t)| < 0.5, first determine... Is it less than If satisfied, then Assign to If not satisfied, then judge. Is it less than If satisfied, then Assign to If not satisfied, Assign to

[0132] After the operation is completed, you will get to

[0133] S5-6-2, The currently obtained to Converting a 1×2 type vector back to coordinates to The transformed coordinates form a coordinate set containing n coordinates, thus yielding a Harris Hawk individual. The fitness value of this Harris Hawk individual is calculated using the same method as for each Harris Hawk individual in the 0th generation population, denoted as .

[0134] S5-6-3, Set a 1×2 type vector for pre-replacement. The result is obtained by using equation (19). After converting the Harris Eagle individual obtained in step S5-6-2 into an n×2 type matrix using the same method as before, replace the j-th row vector of this n×2 type matrix with... The results are then transformed into a coordinate set, yielding a Harris Hawk individual. The fitness value of this individual is calculated using the same method as for each Harris Hawk individual in the 0th generation population. This fitness value is then denoted as... like Less than Then Assign to otherwise Remain unchanged;

[0135]

[0136]

[0137]

[0138] S5-7, The currently obtained to Following the same method as before, convert them to coordinates, and you will get... to The corresponding n coordinates form a coordinate set, which is the i-th Harris Eagle individual in the t-th generation population. Thus, the N Harris Eagle individuals in the t-th generation population are obtained.

[0139] S5-8. Determine if the current value of t is equal to T. If not, evaluate the t-th generation population using the same method as in step 3 to obtain the fitness value of each Harris eagle individual in the t-th generation population and the Harris eagle individual X with the smallest fitness value in the t-th generation population. best (t), the optimal state X of the t-th generation population a (t), the Harris Eagle individual X, which has the second smallest fitness value in the t-th generation population. b (t), the Harris Eagle individual X, which has the third smallest fitness value in the t-th generation population. c (t) and the tth generation prey X a (t), then update the value of t by adding 1 to the current value of t, and return to step S5.1 for the next iteration. If it equals T, the iteration ends and the optimal state X is output. best (T) represents the optimal position for the Harris Hawk;

[0140] Step 6: Locate X on the two-dimensional plane map in the continuous coordinate system. best The positions of each coordinate in (T), i.e., the node positions, are connected sequentially from the starting point to the ending point, connecting the starting point coordinates (x, y, y) to the ending point. start ,y start ), X best Each coordinate in (T) and the endpoint coordinate (x) end ,y end This yields the optimal path for the robot to move.

[0141] To verify the effectiveness, stability, and superiority of the robot path planning method based on the improved Harris Hawks optimization algorithm of this invention in robot path planning, the improved Harris Hawks optimization algorithm (AAHHO) of this invention was compared with five other algorithms in the same environment: the HSCA algorithm disclosed in the literature "Robot Path Planning Based on Improved Sine and Cosine Algorithms", the TGWO algorithm disclosed in the literature "Mobile Robot Path Planning Using Improved Gray Wolf Algorithms", the IHHO algorithm disclosed in the literature "An Improved Harris Hawks Optimizer for Job-Shop Scheduling Problem", the CHHO algorithm disclosed in the literature "Chaotic Harris Hawks Optimization Algorithm", and the original Harris Hawks optimization algorithm (HHO). Simulation experiments were conducted to highlight the optimization performance of the improved Harris Hawks algorithm through these five comparison algorithms. This invention selected two scenarios for robot path planning: a simpler scenario, such as... Figure 1 As shown, another type is a more complex scenario, such as... Figure 2 As shown. The maximum number of iterations T is set to 50. In Scenario 1, due to fewer obstacles, the number of path nodes is set to 2, the Harris Eagle population size N is 4, the endpoint coordinates are (4,4), and the starting coordinates are (0,0). The robot path planning results of the 6 algorithms in Scenario 1 are as follows. Figure 1 As shown. Scenario 2 has many obstacles, so we assume the number of path nodes is 3, the Harris Eagle population size N is 6, the endpoint coordinates are (6,6), and the starting coordinates are (0,0). The six algorithms for robot path planning in Scenario 2 are as follows: Figure 2 As shown in Table 1, each comparison algorithm was tested 20 times for robot path planning. The best, worst, average, and variance of each of the 20 experiments were recorded. The path comparison data of the six algorithms in different scenarios are shown in Table 1.

[0142] Table 1: Path Comparison Data of Six Algorithms in Different Scenarios

[0143]

[0144]

[0145] Analysis of the data in Table 1 shows that, while the improved Harris Eagle optimization algorithm of this invention is not the best in terms of optimal value, it is not significantly different from the minimum optimal value. The difference is only 0.0014 in scenario one and 0.0095 in scenario two. In terms of worst-case, average, and variance, the improved Harris Eagle optimization algorithm of this invention is the best compared to the other five algorithms. Overall, the data in Table 1 demonstrates that the improved Harris Eagle optimization algorithm of this invention performs better than the other five algorithms in terms of search performance and stability, exhibiting the best overall performance.

Claims

1. A robot path planning method based on an improved Harris Eagle optimization algorithm, characterized in that... First, the Harris Eagle optimization algorithm is improved to obtain an improved Harris Eagle optimization algorithm. Then, the Harris Eagle position optimization in the improved Harris Eagle optimization algorithm is correlated with robot path planning. The optimal Harris Eagle position is obtained using the improved Harris Eagle optimization algorithm. The optimal Harris Eagle position is used as each node in the robot path planning. Each node, the path start point, and the path end point are connected sequentially to realize the robot path planning. The specific improvement and optimization measures of the Harris Eagle optimization algorithm are as follows:

1. Improve the escape energy formula using the natural constant e; 2. Replace the random Harris Eagle-guided global search strategy with an elite cooperative global search strategy; 3. Introduce an intraspecific competition strategy during the development stage of the Harris Eagle optimization algorithm. The improved Harris Eagle optimization algorithm is used to find the optimal Harris Eagle position, which is then used as the position of each node in the robot path planning. The specific process of connecting each node, the path start point, and the path end point in sequence to achieve robot path planning is as follows: Step 1: Determine the relevant parameters for path planning. Specifically, establish a continuous coordinate system two-dimensional plane map of the area requiring path planning. At each obstacle in the continuous coordinate system two-dimensional plane map, fit a circle in an inscribed manner, and count the number of fitted circles, denoted as W. Obtain the center coordinates and radius of each circle, and mark the center coordinates of the v-th circle as... Let the radius of the v-th circle be denoted as v = 1, 2, ..., W; This retrieves the starting coordinates, ending coordinates, and maximum x-coordinate ub of a two-dimensional plane map in a continuous coordinate system. x , Maximum value of the y-axis ub y Minimum value of x-axis lb x and the minimum value of the ordinate lb y Let the starting point coordinates be (x start ,y start The endpoint coordinates are (x end ,y end ), set the upper limit ub = (ub x ,ub y ), set the lower limit lb = (lb x ,lb y Let the area of ​​a two-dimensional plane map in a continuous coordinate system be S, where S = (ub) x -lb x )×(ub y -lb y Let the number of path nodes be n, where n is an integer greater than or equal to 3; Step 2: Construct a Harris Eagle population, where the population size is set to N, where N is an integer greater than or equal to 4, and the maximum number of iterations is set to T, where T is an integer greater than or equal to 50. Initialize N Harris Eagle individuals in the population using formula (1) to obtain the initial population, i.e., the 0th generation population: In equation (1), Let the coordinate of the i-th Harris Eagle individual in the 0th generation population be denoted as j-th coordinate, where The x-axis is... Using the ordinate as the vertical axis, each individual Harris Eagle has n coordinates. Each Harris Eagle is represented by a coordinate set consisting of its n coordinates, where i = 1, 2, ..., N, j = 1, 2, ..., n. and These are random numbers generated by a random function, and Step 3: Evaluate each Harris Eagle individual in the 0th generation population. The specific process for evaluating the i-th Harris Eagle individual in the 0th generation population is as follows: S3-1, Settings in for The 0th coordinate in the middle, for The (n+1)th coordinate in the middle, for The j-th coordinate; S3-2, Settings The number of intersection points between the line connecting the l-th and (l+1)-th coordinates and the W circles is . Will Initialize to 0; initialize l to 0; S3-3. Set variable m and initialize m to equal 1; S3-4, Settings The shortest distance between the line connecting the l-th and (l+1)-th coordinates and the center of the m-th circle is: S3-5, calculated using formula (2) In equation (2), || represents the absolute value sign; S3-6, Judgment Is it less than or equal to? If less than or equal to Then adopt The sum of the current value plus 1 is updated. otherwise The current value remains unchanged; S3-7. Determine if the current value of m is equal to W. If the current value of m is equal to W, then determine if the current value of l is equal to n. If the current value of l is equal to n, then set the current value as n. The value is assigned to w i (0), proceed to step S3-8. If the current value of l is not equal to n, then... Assign the current value to Then, the value of l is updated by adding 1 to the current value of l, and the process returns to step S3-3. If the current value of m is not equal to W, the value of m is updated by adding 1 to the current value of m, and the process returns to step S3-4. S3-8, w i (0) and Substituting each coordinate into the fitness function shown in equation (3), the fitness value of the i-th Harris Hawk individual in the 0th generation population is calculated: In equation (3), This represents the fitness value of the i-th Harris Hawk individual in the 0th generation population; S3-9. Sort the N Harris Eagle individuals in the 0th generation population according to their fitness values ​​from smallest to largest, and select the Harris Eagle individual with the smallest fitness value in the 0th generation population as the best Harris Eagle individual X in the 0th generation. best (0), let X be the optimal state of the 0th generation population. a (0), X best (0) Assign the value to X a (0), let X be the Harris Eagle individual with the second smallest fitness value in the 0th generation population. b (0); Let X be the Harris Eagle individual with the third smallest fitness value in the 0th generation population. c (0) Select the Harris Eagle individual with the lowest fitness value in the 0th generation population as the 0th generation prey X. a (0); Step 4: Set the iteration variable t and initialize t to 1; Step 5: Perform the t-th iteration on the Harris Eagle population to obtain the t-th generation population. The specific iteration process is as follows: S5-1. For each Harris Eagle individual in the (t-1)th generation population, determine whether it has crossed the boundary to obtain the updated (t-1)th generation population. The specific determination process for the i-th Harris Eagle individual in the (t-1)th generation population is as follows: like Then let Soon Updated to equal lb x ,like Then let Soon Updated to equal ub x ,like but If remain unchanged, Then let Soon Updated to equal lb y ,like Then let Soon Updated to equal ub y , but Remain unchanged; S5-2. Calculate the mean coordinates of the updated (t-1)th generation population. The specific process is as follows: set up Let be the mean of the j-th coordinate of the (t-1)-th generation population after the update, where for x-coordinate for The ordinate is calculated using equation (4). and In equation (4), Let x be the x-coordinate of the j-th coordinate of the i-th Harris Eagle individual in the updated (t-1)-th generation population. Let j be the ordinate of the j-th coordinate of the i-th Harris Eagle individual in the updated t-1 generation population; S5-3. Let E(t) be the escape energy of the t-th generation prey. Calculate the escape energy of the t-th generation prey using equation (5). Set coefficients A(t), B(t), and C(t). Calculate the coefficients A(t), B(t), and C(t) according to equations (6), (7), and (8): E0(t) is generated using a random function, and -1≤E0(t)≤1. The convergence factor of the t-th generation is set to be equal to |E(t)|; || is the absolute value symbol, and e is the natural constant with a value of 2.7182818284. X represents a The fitness value of (t-1), X represents b The fitness value of (t-1), X represents c The fitness value of (t-1); S5-4. Let X be the i-th Harris Eagle individual in the updated t-1 generation population. i (t-1), X i (t-1) is transformed into an n×2 type matrix, denoted as X. i (t-1), X i In (t-1), the first column is the x-axis and the second column is the y-axis. The j-th coordinate of the i-th Harris Eagle individual in the updated (t-1)-th generation population corresponds to X. i The 1×2 type vector in the j-th row of (t-1) is denoted as... X a Each coordinate of (t-1) is transformed into a 1×2 type vector with the first column being the x-coordinate and the second column being the y-coordinate, where X a The 1×2 type vector obtained by transforming the j-th coordinate of (t-1) is denoted as... X b Each coordinate of (t-1) is transformed into a 1×2 type vector with the first column being the x-coordinate and the second column being the y-coordinate. b The 1×2 type vector obtained by transforming the j-th coordinate of (t-1) is denoted as... X c Each coordinate of (t-1) is transformed into a 1×2 type vector with the first column being the x-coordinate and the second column being the y-coordinate. c The 1×2 type vector obtained by transforming the j-th coordinate of (t-1) is denoted as... Let X be the i-th Harris Eagle individual in the t-th generation population. i (t), X i (t) is transformed into an n×2 type matrix X i (t), X i In (t), the first column is the x-axis, and the second column is the y-axis, representing the i-th Harris Eagle individual in the t-th generation population. i The j-th coordinate of (t) corresponds to X i The 1×2 type vector in the j-th row of (t) is denoted as... We determine the convergence factor |E(t)| for the t-th generation. If |E(t)| < 1, we proceed to step S5-5 first, then to step S5-6. Based on steps S5-5 and S5-6, we obtain... If |E(t)|≥1, then first use random functions to generate... and in Then determine Is it greater than or equal to 0.5? Then, the result is obtained by using equation (9). Then proceed directly to step S5-7; otherwise, calculate using equation (10). Then proceed directly to steps S5-7; S5-5. Let J(t) be the jumping intensity of the t-th generation prey. First, calculate the jumping intensity J(t) according to equation (11), and then calculate the jumping intensity X respectively. i Replace each row vector of (t-1), where X i The process of replacing the j-th row vector of (t-1) is as follows: S5-5-1. Define four 1×2 type vectors for pre-replacement, namely... and The results were obtained by using equations (12) to (17). and J(t)=2(1-r4(t)) (11) Where D is a 2-dimensional unit vector, β equals 1.5, and Γ represents the gamma function; random numbers μ(t), ν(t), and r4(t) are generated using random functions, and 0≤μ(t)≤1, 0≤ν(t)≤1, and 0≤r4(t)≤1; S5-5-2, X i Replace the j-th row vector of (t-1) with After converting to a coordinate set, a Harris Hawk individual is obtained. The fitness value of this Harris Hawk individual is obtained using the same method as for each Harris Hawk individual in the 0th generation population. This obtained fitness value is denoted as... X i Replace the j-th row vector of (t-1) with After converting to a coordinate set, a Harris Hawk individual is obtained. The fitness value of this Harris Hawk individual is obtained using the same method as for each Harris Hawk individual in the 0th generation population. This obtained fitness value is denoted as... X i Replace the j-th row vector of (t-1) with After converting to a coordinate set, a Harris Hawk individual is obtained. The fitness value of this Harris Hawk individual is obtained using the same method as for each Harris Hawk individual in the 0th generation population. This obtained fitness value is denoted as... X i Replace the j-th row vector of (t-1) with After converting to a coordinate set, a Harris Hawk individual is obtained. The fitness value of this Harris Hawk individual is obtained using the same method as for each Harris Hawk individual in the 0th generation population. This obtained fitness value is denoted as... S5-6. Generate a random number rand(t) using a random function, where 0 ≤ rand(t) ≤ 1. Select a strategy based on the random number rand(t) and the convergence factor |E(t)| of the t-th generation. S5-6-1. If rand(t)≥0.5 and 0.5≤|E(t)|<1, the result is obtained by using equation (17). If rand(t)≥0.5 and 0≤|E(t)|<0.5, the result is obtained using equation (18). If rand(t) < 0.5 and 0.5 ≤ |E(t)| < 1, first determine... Is it less than If satisfied, then Assign to If not satisfied, then judge. Is it less than If satisfied, then Assign to If not satisfied, Assign to If rand(t) < 0.5 and 0 ≤ |E(t)| < 0.5, first determine... Is it less than If satisfied, then Assign to If not satisfied, then judge. Is it less than If satisfied, then Assign to If not satisfied, Assign to After the operation is completed, you will get to S5-6-2, The currently obtained to Converting a 1×2 type vector back to coordinates to The transformed coordinates form a coordinate set containing n coordinates, thus yielding a Harris Hawk individual. The fitness value of this Harris Hawk individual is calculated using the same method as for each Harris Hawk individual in the 0th generation population, denoted as . S5-6-3, Set a 1×2 type vector for pre-replacement. The result is obtained by using equation (19). After converting the Harris Eagle individual obtained in step S5-6-2 into an n×2 type matrix using the same method as before, replace the j-th row vector of this n×2 type matrix with... The results are then transformed into a coordinate set, yielding a Harris Hawk individual. The fitness value of this individual is calculated using the same method as for each Harris Hawk individual in the 0th generation population. This fitness value is then denoted as... like Less than Then Assign to otherwise Remain unchanged; S5-7, The currently obtained to Following the same method as before, convert them to coordinates, and you will get... to The corresponding n coordinates form a coordinate set, which is the i-th Harris Eagle individual in the t-th generation population. Thus, the N Harris Eagle individuals in the t-th generation population are obtained. S5-8. Determine if the current value of t is equal to T. If not, evaluate the t-th generation population using the same method as in step 3 to obtain the fitness value of each Harris eagle individual in the t-th generation population and the Harris eagle individual X with the smallest fitness value in the t-th generation population. best (t), the optimal state X of the t-th generation population a (t), the Harris Eagle individual X, which has the second smallest fitness value in the t-th generation population. b (t), the Harris Eagle individual X, which has the third smallest fitness value in the t-th generation population. c (t) and the tth generation prey X a (t), then update the value of t by adding 1 to the current value of t, and return to step S5.1 for the next iteration. If it equals T, the iteration ends and the optimal state X is output. best (T) represents the optimal position for the Harris Hawk; Step 6: Locate X on the two-dimensional plane map in the continuous coordinate system. best The positions of each coordinate in (T), i.e., the node positions, are connected sequentially from the starting point to the ending point, connecting the starting point coordinates (x, y, y) to the ending point. start ,y start ), X best Each coordinate in (T) and the endpoint coordinate (x) end ,y end This yields the optimal path for the robot to move.

Images