Robot smooth path planning method based on improved harris hawk optimization algorithm

Abstract

This invention discloses a robot smooth path planning method based on an improved Harris Eagle optimization algorithm. The improved Harris Eagle algorithm optimizes the position of control points on a Bezier curve to find the shortest and smoothest path. The improved Harris Eagle algorithm introduces the concept of spiral search to improve the early update strategy, increase population diversity, and enhance the algorithm's global search capability. Sine chaotic mapping is used to improve the escape energy E, better balancing global search and local exploitation. An elite differential mutation strategy is used to mutate and recombine partial solutions in the search space, improving the algorithm's ability to escape local optima. Simulation experiments were conducted on two different grid maps. Simulation data demonstrate that this invention can more accurately find the collision-free shortest path, and the path curvature and its derivative are sufficiently small, satisfying the smoothness requirements of higher-order continuity.

Description

Technical Field

[0001] This invention relates to the field of mobile robot technology, specifically to the field of mobile robot path planning, and particularly to a smooth path planning method for robots based on an improved Harris Eagle optimization algorithm. Background Technology

[0002] Path planning is a crucial research area in mobile robotics. Its goal is to generate a collision-free path from a starting point to an end point. Common path generation criteria include distance, time, smoothness, and safety. Depending on the environmental information, path planning can be categorized into global path planning and local path planning. In global path planning, the environmental information is known, and the robot finds an optimal path within an established environmental model. Local path planning is performed in an unknown environment, optimizing the path based on the robot's current local environmental information. Robots are widely used in modern production and daily life, such as in underwater exploration, express delivery, and disaster relief. Therefore, research on mobile robot path planning has significant practical implications.

[0003] Traditional path planning methods include grid-based methods, artificial potential field methods, visual graph methods, and A* algorithms. These methods often suffer from computational complexity, low efficiency, and path unreachability issues, which can significantly hinder the solution of global path planning problems. In recent years, swarm intelligence algorithms have demonstrated increasing advantages and attracted growing attention. Many swarm intelligence algorithms have already been applied to mobile robot path planning with promising results, such as the whale optimization algorithm, the gray wolf optimization algorithm, and the moth-to-a-flame algorithm.

[0004] The Harris Eagle Optimization Algorithm (HAE) is a population-based metaheuristic algorithm proposed by Heidari et al. in 2019. It mimics the cooperative hunting behavior of Harris Eagles in nature, combining it with a Levy flight strategy to achieve global optimization for complex, multidimensional problems. The algorithm consists of three stages: a global search stage, a transition stage from search to development, and a local development stage. The HAE has advantages such as simple structure, few parameters, and strong local development capabilities. However, it also has some problems in path planning: collisions with obstacles during the optimization process; and the generated paths are not smooth enough, causing difficulties for robot movement. Summary of the Invention

[0005] This invention provides a robot smooth path planning method based on an improved Harris Eagle optimization algorithm, which solves or at least partially solves the technical problem of poor path planning performance in the prior art.

[0006] To address the aforementioned technical problems, this invention provides a robot smooth path planning method based on an improved Harris Eagle optimization algorithm, comprising:

[0007] S1: Construct an environment map in a two-dimensional plane coordinate system using the grid method based on the working environment of the mobile robot, and set the starting point and the ending point;

[0008] S2: Initialize the population position and set the relevant parameters of the Harris Eagle optimization algorithm, including population size N, maximum number of iterations T, individual dimension dim, and upper and lower bounds of the spatial range;

[0009] S3: Determine the control points of the Bézier curve based on the population location, and calculate the path curve of each Harris Eagle individual from the starting point to the ending point on the environmental map using the Bézier equation and control points;

[0010] S4: Calculate the length, curvature, and derivative of curvature of the path curve, and calculate the fitness value. Select the individual with the smallest fitness value as the current prey position.

[0011] S5: Introduce the Sine chaotic mapping to calculate the escape energy E of the prey. Based on the value of E, determine whether to enter the global search phase or the local exploration phase. When |E|≥1, enter the global search phase and execute step S6; when |E|<1, enter the local exploration phase and execute step S7. The formula for calculating the escape energy E is as follows:

[0012] E0 = 2*Cm-1

[0013] E = 2E0(1-t / T)

[0014] Where Cm is the chaos number generated by the Sine chaotic mapping, t is the current iteration number, T is the maximum iteration number, and E0 is the initial value of the escape energy;

[0015] S6: In the global search phase, the concept of a spiral search strategy is introduced. Two different search methods with equal probability are used to update the position of the Harris Eagle. When q < 0.5, the Harris Eagle chooses a landing and ambush location based on the positions of other members of the flock and the position of the prey. When q ≥ 0.5, the individual flies in a spiral pattern within the search space to search for prey. The specific formula is as follows:

[0016]

[0017]

[0018] xr(i)=r(i)*sin(θ(i)),yr(i)=r(i)*cos(θ(i))

[0019] θ(i)=a*π*rand

[0020] r(i)=θ(i)+R*rand

[0021] Among them, X i(t+1) represents the position vector of the i-th individual in the (t+1)-th iteration, X rabbit (t) represents the position vector of the current optimal solution, X m (t) is the average position of all individuals in the current population, ub and lb are the upper and lower bounds of the search space, r1, r2 and q are random numbers between (0,1), and X i (t) is the position vector of the i-th individual in the current population, X i+1 (t) represents the position of the (i+1)th individual at the (t+1)th iteration, x(i) and y(i) are the positions of the eagle individuals in polar coordinates, θ(i) and r(i) are the polar angle and polar radius of the spiral equation, a and R are the parameters that control the spiral trajectory, a takes values ​​in the range of (5,10), R takes values ​​in the range of (0.5,2), rand is a random number in the range of (0,1), xr and yr are the two coordinate values ​​of the individual in the rectangular coordinate system, and xr(i) and yr(i) are the two coordinate values ​​of the ith individual in the rectangular coordinate system.

[0022] S7: In the local development phase, based on the prey's escape energy E and whether the prey escapes the encirclement r, four different attack strategies with equal probability are adopted to pursue and capture the prey and update the population position.

[0023] S8: After the Harris Eagle's individual position update, an elite differential mutation strategy will be added, specifically including:

[0024] a. Mutation: Select a random solution and an elite solution from the search space, and mutate them using the following formula to produce a solution similar to the one in the search space.

[0025] The mutation solution V associated with the pre-optimal solution i :

[0026] V i =X elite +(GS num )*(C sp -X rand )

[0027] Among them, X elite GS represents the current optimal solution, i.e., the elite solution. num These are random numbers generated by Gaussian mutation, with the parameters of Gaussian mutation set to u = 0 and σ = 1; C sp Indicates the center location of the search space; X rand It is a solution vector randomly selected from the search space.

[0028] b. Cross-recombination: The mutation solution and the current optimal solution are cross-recombined. The mathematical model is as follows:

[0029]

[0030] Among them, U ij This represents the new solution generated by the crossover and recombination operation; i represents the i-th individual, j represents the j-th dimension; CR is the adaptive crossover rate; j rand The value is a random value in [1, dim], which means randomly selecting a dimension from the solution vector, where dim represents the dimension of the problem space;

[0031] c. Selection: Using a greedy strategy, select the new solution U generated by mutation and recombination. i and the original solution X i The mathematical model for selecting the most dominant individuals to enter the next generation is as follows:

[0032]

[0033] Where f() represents the fitness function, X i t+1 Let represent the position vector of the i-th individual at the (t+1)-th iteration;

[0034] S9: Calculate the updated Bessel path curve and fitness value of the population, and select the individual with the lowest fitness value to update the prey location X. rabbit ;

[0035] S10: Determine if the maximum number of iterations has been reached. If yes, proceed to step S12; otherwise, return to step S5.

[0036] S11: The individual with the smallest fitness value is taken as the optimal solution for the mobile robot path planning, and the Bezier curve corresponding to this individual is the optimal path curve.

[0037] In one implementation, the formula for initializing the population position in step S2 is:

[0038] Positions=rand(N,dim)×(ub-lb)+lb

[0039] Where Positions represents the population positions, rand() is the random number generation function, and ub and lb are the upper and lower bounds of the search space, respectively.

[0040] In one implementation, the Bezier curve described in step S3 is defined by the following formula:

[0041]

[0042] Where P(t) represents the Bezier curve; t represents the motion time normalization variable; p i =(x i ,y i ) TB is a coordinate vector composed of the coordinate components of the i-th control point; i,n (t)(i=0,1,...,n) is an nth-degree Bernstein polynomial, defined as:

[0043]

[0044] The curvature formula for a Bezier curve in a two-dimensional plane is as follows:

[0045]

[0046] in, Let be the coordinate components of the first derivative of the Bezier curve. Let $\mathbf{a}$ be the coordinate component of the second derivative of the Bezier curve. The expressions for the first and second derivatives of the Bezier curve are as follows:

[0047]

[0048]

[0049] In one implementation, the fitness value in step S4 is calculated using a fitness function, specifically as follows:

[0050] min f=w1×Len+w2×max|Cur(x,y)|+w3×max|Der(x,y)|+Pe(x,y)

[0051] Where Len is the length of the curve path, Cur(x,y) is the curvature of any point (x,y) on the path, Der(x,y) is the derivative of curvature at point (x,y), Pe(x,y) is the penalty factor at point (x,y), and the penalty factor is 0 when a point on the path does not collide with an obstacle; otherwise, the penalty factor is set to a preset value, and w1, w2, w3 are the weight coefficients of each part.

[0052] In one implementation, the four update strategies in step S7 specifically include:

[0053] 1) Soft siege strategy: When r≥0.5 and |E|≥0.5, the mathematical model is as follows:

[0054] X(t+1)=ΔX(t)-E|JX rabbit (t)-X(t)|ΔX(t)=X rabbit (txt)

[0055] Where ΔX(t) represents the positional difference between the Harris Eagle and its prey in the t-th iteration, X rabbitX(t) represents the position vector of the prey in the t-th iteration, X(t) represents the position vector of the individual Harris Hawk in the t-th iteration, J = 2(1-r3) is a random number in the interval (0,2), representing the random jump intensity of the prey, and r3 is a random number in the range (0,1).

[0056] 2) Hard-hitting strategy: When r≥0.5 and |E|<0.5, update the position of the Harris Hawk using the following formula:

[0057] X(t+1)=X rabbit (t)-E|ΔX(t)|

[0058] X(t+1) represents the position vector of an individual Harris Hawk in the (t+1)th iteration;

[0059] 3) A gradual, rapid dive-and-surround soft encirclement strategy: When r < 0.5 and |E| ≥ 0.5, update the Harris Hawk's position using the following formula:

[0060]

[0061] Y = X rabbit (t)-E|JX rabbit (t)-X(t)|

[0062] Z = Y + S × LF(D)

[0063] Where F is the fitness function, D is the problem dimension, S is a 1×D dimensional random vector, Y and Z represent two different dive modes, and LF is levy flight, the expression of which is as follows:

[0064]

[0065] Where u and v are random numbers in the range (0,1), and β is a default constant;

[0066] 4) Gradual, rapid dive-and-attack strategy: When r < 0.5 and |E| < 0.5, the position of the Harris Hawk is updated using the following formula:

[0067]

[0068] Y = X rabbit (t)-E|JX rabbit (t)-X m (t)|

[0069] Z = Y + S × LF(D)

[0070] Among them, X m (t) is the average position of all individuals in the current population.

[0071] In one implementation, the crossover rate in step S8 is described by the following formula:

[0072]

[0073] Where rand(-1,1) is a random number in the range [-1,1]; t is the current iteration number of the algorithm; and T is the maximum number of iterations.

[0074] Compared with the prior art, the advantages and beneficial technical effects of the present invention are as follows:

[0075] 1. This invention provides an optimized solution to the smooth path planning problem for mobile robots, and this technical solution can be applied to other similar practical problems. It finds a better path, effectively solving the problem of mobile robots colliding with obstacles during path optimization. Simultaneously, the generated path meets the smoothness requirements of high-order continuity, and its curvature and derivative are sufficiently small, avoiding the problem of the robot making sharp, large-angle turns. This improves the accuracy and precision of mobile robots in multi-obstacle path planning.

[0076] 2. This invention introduces a novel strategy to improve the Harris Eagle optimization algorithm. Inspired by the Bald Eagle optimization algorithm, the concept of spiral search is introduced to improve the early update strategy of the Harris Eagle optimization algorithm, increasing population diversity and enhancing the algorithm's global search capability. Sine chaotic mapping is used to improve the escape energy E, better balancing global search and local exploitation. An elite differential mutation strategy is used to mutate and recombine partial solutions within the search space, improving the algorithm's ability to escape local optima. The improved algorithm shows a significant performance improvement compared to the basic Harris Eagle optimization algorithm.

[0077] 3. This invention uses continuous high-order Bezier curves instead of connecting several low-order Bezier curve segments. The generated path meets the smoothness requirements of high-order continuity, which plays an important role in the motion control of the robot. Attached Figure Description

[0078] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0079] Figure 1 This is a flowchart of a robot smooth path planning method based on an improved Harris Eagle optimization algorithm provided in an embodiment of the present invention;

[0080] Figure 2This is a flowchart of the improved Harris Eagle optimization algorithm used in this embodiment of the invention;

[0081] Figure 3 This is a comparison chart of the path results of the method of this invention and three other algorithms in a 40×40 environment map;

[0082] Figure 4 This is a comparison chart of the fitness value change curves of the method of this invention and three other algorithms in a 40×40 environment map;

[0083] Figure 5 This is a comparison chart of the path curvature change curves of the method of this invention and three other algorithms in a 40×40 environment map;

[0084] Figure 6 This is a comparison chart of the path curvature derivative changes of the method of this invention and three other algorithms in a 40×40 environment map. Detailed Implementation

[0085] The Harris Eagle Optimization Algorithm, proposed by Heidari et al. in 2019, is a population-based metaheuristic algorithm. It mimics the cooperative hunting behavior of Harris Eagles in nature, combining it with a Levy flight strategy to achieve global optimization for complex, multidimensional problems. It boasts advantages such as simple structure, few parameters, and strong local optimization capabilities. However, this algorithm also suffers from some problems in path planning: collisions with obstacles during the optimization process; and the generated paths are not smooth enough, causing difficulties for robot movement, thus resulting in poor path planning performance.

[0086] To solve the above-mentioned technical problems, the main concept of the present invention is as follows:

[0087] An improved Harris Eagle optimization algorithm is employed to optimize the location of control points on the Bezier curve, thereby finding the shortest and smoothest path. The improved algorithm introduces the concept of spiral search to refine the early update strategy, increasing population diversity and enhancing global search capabilities. Sine chaotic mapping is used to improve the escape energy E, better balancing global search and local exploitation. An elite differential mutation strategy is used to mutate and recombine partial solutions within the search space, improving the algorithm's ability to escape local optima. Simulation experiments on two different grid maps demonstrate that this invention can more accurately find the collision-free shortest path, with sufficiently small path curvature and curvature derivatives, satisfying the smoothness requirements of higher-order continuity.

[0088] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0089] Example 1

[0090] This invention provides a robot smooth path planning method based on an improved Harris Eagle optimization algorithm, comprising:

[0091] S1: Construct an environment map in a two-dimensional plane coordinate system using the grid method based on the working environment of the mobile robot, and set the starting point and the ending point;

[0092] S2: Initialize the population position and set the relevant parameters of the Harris Eagle optimization algorithm, including population size N, maximum number of iterations T, individual dimension dim, and upper and lower bounds of the spatial range;

[0093] S3: Determine the control points of the Bézier curve based on the population location, and calculate the path curve of each Harris Eagle individual from the starting point to the ending point on the environmental map using the Bézier equation and control points;

[0094] S4: Calculate the length, curvature, and derivative of curvature of the path curve, and calculate the fitness value. Select the individual with the smallest fitness value as the current prey position.

[0095] S5: Introduce the Sine chaotic mapping to calculate the escape energy E of the prey. Based on the value of E, determine whether to enter the global search phase or the local exploration phase. When |E|≥1, enter the global search phase and execute step S6; when |E|<1, enter the local exploration phase and execute step S7. The formula for calculating the escape energy E is as follows:

[0096] E0 = 2*Cm-1

[0097] E = 2E0(1-t / T)

[0098] Where Cm is the chaos number generated by the Sine chaotic mapping, t is the current iteration number, T is the maximum iteration number, and E0 is the initial value of the escape energy;

[0099] S6: In the global search phase, the concept of a spiral search strategy is introduced. Two different search methods with equal probability are used to update the position of the Harris Eagle. When q < 0.5, the Harris Eagle chooses a landing and ambush location based on the positions of other members of the flock and the position of the prey. When q ≥ 0.5, the individual flies in a spiral pattern within the search space to search for prey. The specific formula is as follows:

[0100]

[0101]

[0102] xr(i)=r(i)*sin(θ(i)),yr(i)=r(i)*cos(θ(i))

[0103] θ(i)=a*π*rand

[0104] r(i)=θ(i)+R*rand

[0105] Among them, X i (t+1) represents the position vector of the i-th individual in the (t+1)-th iteration, X rabbit (t) represents the position vector of the current optimal solution, X m (t) is the average position of all individuals in the current population, ub and lb are the upper and lower bounds of the search space, r1, r2 and q are random numbers between (0,1), and X i (t) is the position vector of the i-th individual in the current population, X i+1 (t) represents the position of the (i+1)th individual at the (t+1)th iteration, x(i) and y(i) are the positions of the eagle individuals in polar coordinates, θ(i) and r(i) are the polar angle and polar radius of the spiral equation, respectively, a and R are the parameters that control the spiral trajectory, a takes values ​​in the range of (5,10), R takes values ​​in the range of (0.5,2), and rand is a random number in the range of (0,1);

[0106] S7: In the local development phase, based on the prey's escape energy E and whether the prey escapes the encirclement r, four different attack strategies with equal probability are adopted to pursue and capture the prey and update the population position.

[0107] S8: After the Harris Eagle's individual position update, an elite differential mutation strategy will be added, specifically including:

[0108] a. Mutation: Select a random solution and an elite solution from the search space, and mutate them using the following formula to produce a solution similar to the one in the search space.

[0109] The mutation solution V associated with the pre-optimal solution i :

[0110] V i =X elite +(GS num )*(C sp -X rand )

[0111] Among them, X elite GS represents the current optimal solution, i.e., the elite solution.num These are random numbers generated by Gaussian mutation, with the parameters of Gaussian mutation set to u = 0 and σ = 1; C sp Indicates the center location of the search space; X rand It is a solution vector randomly selected from the search space;

[0112] b. Cross-recombination: The mutation solution and the current optimal solution are cross-recombined. The mathematical model is as follows:

[0113]

[0114] Among them, U ij This represents the new solution generated by the crossover and recombination operation; i represents the i-th individual, j represents the j-th dimension; CR is the adaptive crossover rate; j rand The value is a random value in [1, dim], which means randomly selecting a dimension from the solution vector, where dim represents the dimension of the problem space;

[0115] c. Selection: Using a greedy strategy, select the new solution U generated by mutation and recombination. i and the original solution X i The mathematical model for selecting the most dominant individuals to enter the next generation is as follows:

[0116]

[0117] Where f() represents the fitness function, X i t+1 Let represent the position vector of the i-th individual in the (t+1)-th iteration.

[0118] S9: Calculate the updated Bessel path curve and fitness value of the population, and select the individual with the lowest fitness value to update the prey location X. rabbit ;

[0119] S10: Determine if the maximum number of iterations has been reached. If yes, proceed to step S12; otherwise, return to step S5.

[0120] S11: The individual with the smallest fitness value is taken as the optimal solution for the mobile robot path planning, and the Bezier curve corresponding to this individual is the optimal path curve.

[0121] Please see Figure 1 and Figure 2 ,in, Figure 1 This is a flowchart of a robot smooth path planning method based on an improved Harris Eagle optimization algorithm provided in an embodiment of the present invention. Figure 2 This is a flowchart of the improved Harris Eagle optimization algorithm used in this embodiment of the invention.

[0122] In S6, the subscript m represents the average, rabbit represents the prey, and i represents the i-th Harris Hawk individual. In S8, the current optimal solution is the elite solution, and an elite differential mutation strategy is used to mutate and recombine the elite solution. The method for calculating the updated population's Bessel path curve and fitness value in S10 is the same as in steps S3 and S4, and will not be repeated here.

[0123] Specifically, the improved Harris Eagle optimization algorithm adopted in this invention mainly includes improving the escape energy E by Sine chaotic mapping, introducing the concept of spiral search, and improving the early update strategy of the Harris Eagle optimization algorithm; using the elite differential mutation strategy to perform mutation recombination selection on some solutions in the search space, which is specifically reflected in steps S5, S6 and S8.

[0124] In the original Harris Eagle algorithm, the escape energy E decreases linearly, and its calculation formula is E = 2E0(1-t / T), where E0 = 2*rand()-1. This invention replaces the random number rand() with a chaotic number generated by a Sine chaotic map, which better balances global search and local exploitation. The concept of spiral search is introduced to improve the early update strategy of the algorithm, increasing population diversity and enhancing the algorithm's global search capability. An elite differential mutation strategy is used to mutate and recombine partial solutions within the search space, improving the algorithm's ability to escape local optima.

[0125] In one implementation, the formula for initializing the population position in step S2 is:

[0126] Positions=rand(N,dim)×(ub-lb)+lb

[0127] Where Positions represents the population positions, rand() is the random number generation function, and ub and lb are the upper and lower bounds of the search space, respectively.

[0128] In one implementation, the Bezier curve described in step S3 is defined by the following formula:

[0129]

[0130] Where P(t) represents the Bezier curve; t represents the motion time normalization variable; p i =(x i ,y i ) T B is a coordinate vector composed of the coordinate components of the i-th control point; i,n (t)(i=0,1,...,n) is an nth-degree Bernstein polynomial, defined as:

[0131]

[0132] The curvature formula for a Bezier curve in a two-dimensional plane is as follows:

[0133]

[0134] in, Let be the coordinate components of the first derivative of the Bezier curve. Let $\mathbf{a}$ be the coordinate component of the second derivative of the Bezier curve. The expressions for the first and second derivatives of the Bezier curve are as follows:

[0135]

[0136]

[0137] In one implementation, the fitness value in step S4 is calculated using a fitness function, specifically as follows:

[0138] min f=w1×Len+w2×max|Cur(x,y)|+w3×max|Der(x,y)|+Pe(x,y)

[0139] Where Len is the length of the curve path, Cur(x,y) is the curvature of any point (x,y) on the path, Der(x,y) is the derivative of curvature at point (x,y), Pe(x,y) is the penalty factor at point (x,y), and the penalty factor is 0 when a point on the path does not collide with an obstacle; otherwise, the penalty factor is set to a preset value, and w1, w2, w3 are the weight coefficients of each part.

[0140] Specifically, the preset values ​​can be set according to the actual situation, for example, to a large value, such as 200. The weight coefficients of each part can be set to 10, 100, and 100.

[0141] In one implementation, the four update strategies in step S7 specifically include:

[0142] 1) Soft siege strategy: When r≥0.5 and |E|≥0.5, the mathematical model is as follows:

[0143] X(t+1)=ΔX(t)-E|JX rabbit (t)-X(t)|ΔX(t)=X rabbit (txt)

[0144] Where ΔX(t) represents the positional difference between the Harris Eagle and its prey in the t-th iteration, X rabbitX(t) represents the position vector of the prey in the t-th iteration, X(t) represents the position vector of the individual Harris Hawk in the t-th iteration, J = 2(1-r3) is a random number in the interval (0,2), representing the random jump intensity of the prey, and r3 is a random number in the range (0,1).

[0145] 2) Hard-hitting strategy: When r≥0.5 and |E|<0.5, update the position of the Harris Hawk using the following formula:

[0146] X(t+1)=X rabbit (t)-E|ΔX(t)|

[0147] X(t+1) represents the position vector of an individual Harris Hawk in the (t+1)th iteration;

[0148] 3) A gradual, rapid dive-and-surround soft encirclement strategy: When r < 0.5 and |E| ≥ 0.5, update the Harris Hawk's position using the following formula:

[0149]

[0150] Y = X rabbit (t)-E|JX rabbit (t)-X(t)|

[0151] Z = Y + S × LF(D)

[0152] Where F is the fitness function, D is the problem dimension, S is a 1×D dimensional random vector, Y and Z represent two different dive modes, and LF is levy flight, the expression of which is as follows:

[0153]

[0154] Where u and v are random numbers in the range (0,1), and β is a default constant;

[0155] 4) Gradual, rapid dive-and-attack strategy: When r < 0.5 and |E| < 0.5, the position of the Harris Hawk is updated using the following formula:

[0156]

[0157] Y = X rabbit (t)-E|JX rabbit (t)-X m (t)|

[0158] Z = Y + S × LF(D)

[0159] Among them, X m (t) is the average position of all individuals in the current population.

[0160] In one implementation, the crossover rate in step S8 is described by the following formula:

[0161]

[0162] Where rand(-1,1) is a random number in the range [-1,1]; t is the current iteration number of the algorithm; and T is the maximum number of iterations.

[0163] To verify the effectiveness and feasibility of the method provided in this invention, a 40×40 environment map was constructed using a grid method. Simulation experiments were conducted under the same conditions using the improved Harris Eagle optimization algorithm of this invention, the classic Harris Eagle optimization algorithm, the Gray Wolf optimization algorithm, and the Whale optimization algorithm. The population size was set to 50, the maximum number of iterations was 100, and each algorithm was run independently 50 times. Images were plotted using data where the fitness value was at the median. The experimental results are as follows: Figure 3 , 4 As shown in Figures 5 and 6, among which, Figure 3 This is a comparison chart of the path results of the method of this invention and three other algorithms in a 40×40 environment map. Figure 3 (a) is a schematic diagram of the path results using the improved Harris Eagle optimization algorithm, (b) is a schematic diagram of the path results using the classic Harris Eagle optimization algorithm, (c) is a schematic diagram of the path results using the Gray Wolf optimization algorithm, and (d) is a schematic diagram of the path results using the Whale optimization algorithm. Figure 4 This is a comparison chart of the fitness value change curves of the method of this invention and three other algorithms in a 40×40 environment map; Figure 5 This is a comparison chart of the path curvature change curves of the method of this invention and three other algorithms in a 40×40 environment map; Figure 6 This is a comparison chart of the path curvature derivative variation curves of the method of this invention and three other algorithms in a 40×40 environment map. HHO, IHHO, GWO, and WOA represent the classic Harris Eagle optimization algorithm, the improved Harris Eagle optimization algorithm, the Gray Wolf optimization algorithm, and the Whale optimization algorithm, respectively.

[0164] Simulation results show that this invention can effectively solve the problem of smooth path planning for mobile robots. Furthermore, compared to paths generated by the basic Harris Eagle, Gray Wolf, and Whale optimization algorithms, the paths obtained by this invention have shorter distances, smaller curvature and curvature derivatives, and satisfy the smoothness requirements of higher-order continuity, making it an accurate and efficient path planning algorithm.

[0165] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0166] Obviously, those skilled in the art can make various modifications and variations to the embodiments of the present invention without departing from the spirit and scope of the embodiments of the present invention. Thus, if these modifications and variations to the embodiments of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention also intends to include these modifications and variations.

Claims

1. A robot smooth path planning method based on an improved Harris Eagle optimization algorithm, characterized in that, include: S1: Build an environment map and set the start and end points; S2: Initialize the population location and set the relevant parameters for the Harris Eagle optimization algorithm; S3: Determine the control points of the Bezier curve based on the population location, and calculate the path curve of each individual from the starting point to the ending point of the environmental map; S4: Calculate the length, curvature, and derivative of the path curve, calculate the fitness value, and select the individual with the smallest fitness value as the current prey position; S5: Calculate the escape energy E of the prey, when... When the global search phase begins, step S6 is executed; when At this point, the partial development phase begins, and step S7 is executed. The formula for calculating E is: It is the chaos number generated by the Sine chaotic mapping, where t is the current iteration number and T is the maximum iteration number. The initial value of the escape energy; S6: When At that time, based on the positions of other members of the flock and the location of the prey, they choose a landing and ambush location. At that time, it searches for prey by flying in a spiral motion within the search space, using the following formula: Let represent the position vector of the i-th individual in the (t+1)-th iteration. This represents the position vector of the current optimal solution. It is the average position of all individuals in the current population. and For the upper and lower bounds of the search space, q is a random number between (0,1). Let be the position vector of the i-th individual. Let represent the position of the (i+1)th individual at the (t+1)th iteration, and let x(i) and y(i) be the polar coordinate representations of the eagle's position. and Here, represents the polar angle and polar radius of the helical equation, respectively. 'a' and 'R' are parameters controlling the helical trajectory, with 'a' ranging from (5,10) and 'R' ranging from (0.5,2). 'rand' is a random number within the range (0,1). , These are the two coordinate values ​​of the individual in a rectangular coordinate system. , These are the two coordinate values ​​of the i-th individual in the rectangular coordinate system; S7: Based on the prey's escape energy E and whether the prey escapes the encirclement r, four different attack strategies with equal probability are adopted to pursue and capture the prey and update the population position. S8: Incorporate an elite differential mutation strategy, including: a. Mutation, the mutation solution is generated through the following formula. : This represents the current optimal solution; These are random numbers generated by Gaussian mutation, with the parameters of Gaussian mutation set to... ; Indicates the center location of the search space; It is a solution vector randomly selected from the search space; b. Crossover and recombination, the mathematical model is: This represents the new solution generated by the crossover and recombination operation; i represents the i-th individual, j represents the j-th dimension; CR is the adaptive crossover rate; for The random value in the problem space, dim represents the dimension of the problem space; c. Choose the mathematical model: , These are the new solution and the original solution, respectively. Represents the fitness function. Let represent the position vector of the i-th individual at the (t+1)-th iteration; S9: Calculate the updated path curves and fitness values ​​of the population, and select the individual with the lowest fitness value to update the prey location. ; S10: Determine if the maximum number of iterations has been reached. If so, proceed to step S12. Otherwise, return to step S5; S11: Select the individual with the smallest fitness value as the optimal solution for the mobile robot path planning.

2. The robot smooth path planning method based on the improved Harris Eagle optimization algorithm as described in claim 1, characterized in that, The formula for initializing the population position in step S2 is: in, For the location of the population, This is a random number generation function. and These are the upper and lower bounds of the search space, respectively.

3. The robot smooth path planning method based on the improved Harris Eagle optimization algorithm as described in claim 1, characterized in that, The Bezier curve mentioned in step S3 is defined by the following formula: in, Represents the Bezier curve; t represents the motion time normalization variable; It is a coordinate vector composed of the coordinate components of the i-th control point; Let n be a Bernstein polynomial, defined as: The curvature formula for a Bezier curve in a two-dimensional plane is as follows: in, , Let be the coordinate components of the first derivative of the Bezier curve. , Let $\mathbf{a}$ be the coordinate components of the second derivative of the Bezier curve. The expressions for the first and second derivatives of the Bezier curve are as follows: 。 4. The robot smooth path planning method based on the improved Harris Eagle optimization algorithm as described in claim 1, characterized in that, In step S4, the fitness value is calculated using the fitness function, specifically as follows: Where Len is the length of the curved path, Cur(x,y) is the curvature of any point (x,y) on the path, Der(x,y) is the derivative of curvature at point (x,y), and Pe(x,y) is the penalty factor at point (x,y). The penalty factor is 0 when a point on the path does not collide with an obstacle; otherwise, the penalty factor is set to a preset value. These are the weighting coefficients for each part.

5. The robot smooth path planning method based on the improved Harris Eagle optimization algorithm as described in claim 1, characterized in that, The four update strategies in step S7 specifically include: 1) Soft siege strategy: When r≥0.5 and |E|≥0.5, the mathematical model is as follows: in, This represents the positional difference between the Harris Eagle and its prey in the t-th iteration. This represents the position vector of the prey in the t-th iteration. This shows the position vector of an individual Harris Eagle in the t-th iteration. It is a random number within the interval (0,2), representing the random jump intensity of the prey. It is a random number in the range (0,1); 2) Hard-hitting strategy: When r≥0.5 and |E|<0.5, update the position of the Harris Hawk using the following formula: This represents the position vector of an individual Harris Eagle in the (t+1)th iteration; 3) A gradual, rapid dive-and-surround soft encirclement strategy: When r < 0.5 and |E| ≥ 0.5, update the Harris Hawk's position using the following formula: Where F is the fitness function, D is the problem dimension, S is a 1×D dimensional random vector, Y and Z represent two different dive modes, and LF is levy flight, the expression of which is as follows: Where u and v are random numbers in the range (0,1), and β is a default constant; 4) Gradual, rapid dive-and-attack strategy: When r < 0.5 and |E| < 0.5, the position of the Harris Hawk is updated using the following formula: in, It is the average position of all individuals in the current population.

6. The robot smooth path planning method based on the improved Harris Eagle optimization algorithm as described in claim 1, characterized in that, The crossover rate mentioned in step S8 is described by the following formula: Where rand(-1,1) is a random number in the range [-1,1]; t is the current iteration number of the algorithm; and T is the maximum number of iterations.

Images