A mobile robot path planning method based on improved grey wolf optimization algorithm

Abstract

The application discloses a mobile robot path planning method based on an improved grey wolf optimization algorithm, constructs a two-dimensional orchard environment model, discretizes the two-dimensional orchard environment model into a grid map, determines coordinate values of a motion starting point and a motion target point of the mobile robot, and predicts a motion state of the mobile robot at each path node; redundant nodes on a path between the motion starting point and the motion target point are merged until an integrated planning path is formed; the improved grey wolf optimization algorithm is used to regenerate a new motion state of the mobile robot when passing through each path node; the improved grey wolf optimization algorithm is used to generate new position coordinates in a neighborhood of position coordinates of each path node, and the optimized position coordinates are connected to form an optimal path, so that the mobile robot can move at the shortest time and the lowest energy consumption; and the application can comprehensively optimize path length and energy consumption in path planning, ensure the moving efficiency, and reduce energy consumption to the maximum extent.

Description

Technical Field

[0001] This invention relates to the field of robot path planning technology, specifically to a mobile robot path planning method based on an improved gray wolf optimization algorithm. Background Technology

[0002] Path planning for mobile robots is a crucial issue in robotic agriculture. Proper path planning can significantly reduce energy consumption and travel time in orchards, improving operational efficiency. Furthermore, rational path planning can prevent dangerous behaviors such as collisions and tree crashes during movement, ensuring the safety of both the robot and the fruit trees. Swarm intelligence algorithms, as a novel optimization algorithm, have been widely applied in path planning.

[0003] Mobile robot path planning in orchards refers to dividing the orchard into regions and planning the path for the robot to move through the orchard without colliding with or missing any fruit trees. Traditional path planning algorithms, such as particle swarm optimization and genetic algorithms, suffer from slow convergence speed and are prone to getting trapped in local optima when solving complex problems. Furthermore, they only use path length as a constraint for path selection, neglecting the robot's energy consumption. Summary of the Invention

[0004] The purpose of this invention is to provide a mobile robot path planning method based on an improved gray wolf optimization algorithm, in order to solve the problems of slow convergence speed and easy getting trapped in local optima in the complex problem-solving process of the prior art, and the technical problem of robot energy consumption that is ignored by using only path length as a constraint condition for path selection.

[0005] To solve the above-mentioned technical problems, the present invention specifically provides the following technical solution:

[0006] A mobile robot path planning method based on an improved gray wolf optimization algorithm includes the following steps:

[0007] Step 100: Construct a two-dimensional orchard environment model, discretize the two-dimensional orchard environment model into a grid map, and mark bounded obstacle grid cells and non-obstacle grid cells in the grid map.

[0008] Step 200: Determine the coordinates of the starting point and target point of the mobile robot in the two-dimensional orchard environment model, construct the mobile robot motion model, and predict the motion state of the mobile robot at each path node between the starting point and the target point.

[0009] Step 300: Merge some redundant nodes on the path between the starting point and the target point of the movement. In the process of merging some redundant nodes, select path nodes according to the fitness evaluation results until an integrated planning path is formed.

[0010] Step 400: Without changing the node positions of the integrated planning path, based on energy consumption considerations, the improved gray wolf optimization algorithm is used to regenerate the new motion state of the mobile robot when it passes through each path node.

[0011] Step 500: Optimize the position coordinates of each path node. Use the improved Grey Wolf Optimization Algorithm to generate new position coordinates in the neighborhood of the position coordinates of each path node, and connect the optimized position coordinates to synthesize the optimal path, so as to ensure that the mobile robot moves from the starting point to the target point in the shortest time and with the lowest energy consumption.

[0012] As a preferred embodiment of the present invention, in step 200, the motion state of the mobile robot at each path node between the starting point and the target point includes the position, direction, speed and acceleration of the mobile robot at each path node, wherein the position of the mobile robot is represented by a triple q = (x, y, θ).

[0013] In step 200, the formula for constructing the motion model of the mobile robot is:

[0014] X i =u d cosθ;

[0015] Y i =u d sinθ;

[0016] θ i =u ai ;

[0017] The predicted state when the mobile robot arrives at each of the path nodes is the working state of the mobile robot when the parent node of each path node points to that path node.

[0018] X i Y represents the x-coordinate value of the mobile robot in the two-dimensional orchard environment model. i Let θ be the ordinate value of the mobile robot in the two-dimensional orchard environment model. i The angle between the direction of movement of the mobile robot and the X-axis is the forward direction of the mobile robot.

[0019]

[0020] When u dWhen u = 1, it indicates that the mobile robot is moving forward; when u = 1, it indicates that the mobile robot is moving forward. d When the value is -1, it indicates that the mobile robot is moving backward; This represents the maximum turning angle of the mobile robot at each path node of the initially planned path. Then u ai ∈[-1, 1].

[0021] As a preferred embodiment of the present invention, in step 300, the implementation step of merging some redundant nodes using the improved Grey Wolf optimization algorithm is as follows:

[0022] Step 301: Check the height difference between each pair of adjacent path nodes in the starting point and target point of the movement. If the two path nodes are in the same row or adjacent rows, then connect the two path nodes directly; otherwise, go to step 302.

[0023] Step 302: If the difference in the number of rows between two path nodes is greater than 1, generate a continuous path between the two path nodes and check whether all grids between the two path nodes are free. If so, generate a straight line directly between the two path nodes; otherwise, go to step 303.

[0024] Step 303: Locate the faulty object between two path nodes and determine whether all grids between the faulty object and the next path node moving along the path are free. If so, connect the two path nodes by bypassing the obstacle. If not, proceed to step 304.

[0025] Step 304: Find a point without obstacles between the two path nodes and replan the path. If there are obstacles between the two path nodes and no path can be found to bypass them, proceed to step 305.

[0026] Step 305: Move the next path node up or down, repeat steps 301 to 304, and start searching for the path again;

[0027] Step 306: Compare the fitness evaluation results of the current path node with the fitness evaluation results of its surrounding path nodes, and select the node with the largest fitness evaluation result as the new path node.

[0028] In a preferred embodiment of the present invention, the optimization process of the improved gray wolf optimization algorithm in steps 400 to 500 includes the following steps:

[0029] ① Initially, create a random gray wolf population and initialize the position and speed of each individual gray wolf;

[0030] ② Calculate the initial fitness of each gray wolf individual according to the designed fitness function, and save the top 3 gray wolf individuals with the highest fitness α, β, δ;

[0031] ③ Update the current position of all gray wolf individuals in real time according to the improved gray wolf encirclement prey stage function relationship, and calculate the fitness of all gray wolf individuals. The top 3 gray wolf individuals with the highest fitness are α, β, and δ.

[0032] ④ Repeat step ③ until the maximum number of iterations is reached, and output the gray wolf individual with the highest fitness.

[0033] ⑤ Calculate the fitness of individual gray wolves after they move to the next path node based on the functional relationship of the gray wolf surrounding prey stage. Repeat steps ③ to ④ until all gray wolf individuals move to the last path node before the target point.

[0034] 5. A mobile robot path planning method based on an improved gray wolf optimization algorithm according to claim 4, characterized in that,

[0035] The improved gray wolf optimization algorithm consists of three stages: approaching the prey, surrounding the prey, and attacking the prey. Specifically, the functional relationship for each individual gray wolf in the surrounding prey stage is as follows:

[0036] X(k+1)=X P (k)-A×D;(1)

[0037] D = |C × X P (k)-X(k)|;(2)

[0038] In the formula, k is the current iteration number, X(k) represents the current position of the gray wolf, and X p A represents the current location of the prey, D represents the distance between the individual gray wolf and the prey, and A and C are coefficient vectors;

[0039] Among them, A=2a×r1-a; (3)

[0040] C = 2r²; (4)

[0041] The coefficient vector A determines whether the Grey Wolf Optimization Algorithm performs a global search or a local search. The value of the convergence factor a affects the update of A, which in turn affects the search method of the Grey Wolf Optimization Algorithm. The convergence factor a is improved by using a nonlinear approach.

[0042] The improved formula for the convergence factor α is as follows:

[0043]

[0044] In the formula, a is the convergence factor, and r1 and r2 are random numbers in the interval [0, 1].

[0045] In the formula, l represents the iteration time parameter, and k max This indicates the maximum number of iterations.

[0046] As a preferred embodiment of the present invention, the overall improvement of the improved gray wolf optimization algorithm is to combine the particle swarm optimization (PSO) algorithm with the gray wolf optimization algorithm to further improve the search capability and convergence performance of the gray wolf optimization algorithm.

[0047] The gray wolf individual is randomly selected based on the fitness value of different gray wolf individuals at each path node using a roulette wheel method, wherein the probability of the gray wolf individual being selected is positively correlated with the fitness value of the gray wolf individual;

[0048] Finally, the fitness calculation and position update of each individual gray wolf are performed in parallel to speed up the algorithm's operation.

[0049] As a preferred embodiment of the present invention, the specific implementation method of combining the particle swarm optimization (PSO) algorithm with the gray wolf optimization algorithm is as follows:

[0050] Initialize the position and velocity of the particle swarm;

[0051] Set the fitness value for each particle and the current optimal solution X. ipbest and initializing the global optimal solution X igbest The positions and velocities of the gray wolf swarm and the particle swarm are updated through iterative search.

[0052] The fitness values ​​of improved gray wolf individuals and particle individuals are calculated using the update strategies of the improved gray wolf optimization algorithm and the particle swarm optimization algorithm.

[0053] Based on the fitness values ​​of the wolf pack and the particle pack at the same position, the optimal solution is selected as the current solution. If the fitness value of the wolf pack is better, the optimal solution in the wolf pack replaces the worst solution in the particle pack; otherwise, the optimal solution in the particle pack replaces the worst solution in the wolf pack.

[0054] Repeat the above steps until the predetermined number of iterations is reached or the stopping condition is met, then proceed to the gray wolf attacking prey phase.

[0055] As a preferred embodiment of the present invention, the mathematical expression for the gray wolf attacking its prey phase is:

[0056] D α ′=|C1×X α -X igbest |

[0057] D β ′=|C2×X β -X igbest |

[0058] D δ ′=|C3×X δ -X igbest |

[0059] In the formula, D α '、D β 'and D δ ' represents the distances between α, β, and δ and other individuals, respectively, X igbest This represents the initial global optimal solution, where C1, C2, and C3 are random vectors;

[0060] X1′=X α (k)-A1×D α ′

[0061] X2′=X β (k)-A2×D β ′

[0062] X3′=X δ (k)-A3×D δ ′

[0063]

[0064] In the formula, X1', X2', and X3' represent the positions of α, β, and δ relative to other individuals, respectively, and X i (k+1) represents the position of the gray wolf at time k+1 during the optimization process, X α (k), X β (k) and X δ (k) represents the positions of α, β and δ at time k, respectively, and the coefficient vectors A1, A2 and A3 are generated by formula (3) and formula (5).

[0065] In a preferred embodiment of the present invention, in step 500, when synthesizing the optimal path, the path nodes other than the starting point and the target point of the movement are processed in the following order according to the sequence of the integrated planning path obtained by the improved Grey Wolf optimization algorithm:

[0066] Step 501: Starting from the first path node after the starting point of the movement, generate an initial gray wolf population based on the neighborhood of the current path node. The starting point of all gray wolf population individuals at this time is the position of the current node.

[0067] Step 502: Perform an optimization process of the improved gray wolf optimization algorithm according to the fitness function to obtain the optimal gray wolf individual of the current path node. The fitness function takes into account both path length and energy consumption.

[0068] Step 503: Replace the position parameters of the optimal gray wolf individual in the current path node with the original position parameters of the current path node;

[0069] Step 504: Repeat steps 501 to 503 until the current path node is the last path node closest to the moving target point;

[0070] Step 505: Connect the locations of the optimal gray wolf individuals at each path node to form the optimal path for the mobile robot with low path length and low energy consumption.

[0071] As a preferred embodiment of the present invention, the function expression for calculating the fitness is:

[0072] F = α1L + β1E;

[0073] in,

[0074] E = E + A i ×v i 2 ×S i +B i ×a i 2 ×S i +C i ×mu×S i +D i ×load×S i ;

[0075] Where L represents path length; E represents energy consumption; α1 and β1 are weight coefficients, and α1 and β1 are the directions of optimization. If α1 is greater than β1, the improved gray wolf optimization algorithm will focus more on path length; if β1 is greater than α1, the improved gray wolf optimization algorithm will focus more on energy consumption.

[0076] A i B i C i D i All are coefficients, A i B represents the energy consumption weight of speed. i C represents the energy consumption weight of acceleration. i D represents the energy consumption weight of road surface friction. i Indicates the energy consumption weight of the load;

[0077] v i Indicates velocity, a i For acceleration, mu is the coefficient of friction between the mobile robot and the orchard road surface, used to adjust the energy consumption weight of road surface friction, and load is the load of the mobile robot.

[0078] S iLet be the distance between node i and node i+1.

[0079] Compared with the prior art, the present invention has the following advantages:

[0080] (1) The present invention achieves path planning by introducing a hybrid objective function of energy consumption and path length. The function uses the weighted sum of total path length and energy consumption as the fitness value. In the step of updating the position of the gray wolf in the gray wolf optimization algorithm, the energy consumption and path length information are introduced. The gray wolf will tend to select the grid cell that can shorten the path and reduce energy consumption as the next movement target. While ensuring the movement efficiency, it can also minimize energy consumption.

[0081] (2) The improved gray wolf optimization algorithm of this invention can effectively avoid getting trapped in local optima, has stronger search capabilities, and has a faster convergence speed. It can find the shortest path more effectively and has a faster convergence speed. Attached Figure Description

[0082] To more clearly illustrate the embodiments of the present invention or the technical solutions in 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 merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0083] Figure 1 This is a flowchart of a mobile robot path planning optimization method based on the improved gray wolf algorithm according to an embodiment of the present invention.

[0084] Figure 2 This is a path comparison diagram of the improved gray wolf optimization algorithm and other algorithms in a 40*40 orchard environment grid map according to embodiments of the present invention. Detailed Implementation

[0085] 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, and 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.

[0086] like Figure 1As shown, this invention provides a mobile robot path planning method based on an improved gray wolf optimization algorithm, which specifically incorporates considerations of path length and energy consumption. During path planning, the gray wolf optimization algorithm is used not only to select the point with the highest fitness to construct a grid map, but also path length and energy consumption are considered simultaneously in the fitness evaluation. By adding corresponding energy consumption information to each grid cell, the energy consumption of the orchard mobile robot can be fully considered during path planning. This method's fitness evaluation considers not only minimizing the total path length but also minimizing energy consumption. Specifically, it includes the following steps:

[0087] Step 100: Construct a two-dimensional orchard environment model, discretize the two-dimensional orchard environment model into a grid map, and mark bounded obstacle grid cells and non-obstacle grid cells in the grid map.

[0088] Each grid cell in the grid map represents a specific area and includes both obstacle and non-obstacle cells. The grid map contains several bounded obstacle and non-obstacle grid cells. In the grid map, the starting point and target point of the orchard mobile robot are set, and the optimal path is found by improving the Grey Wolf optimization algorithm to achieve efficient orchard environment modeling and path planning.

[0089] Step 200: Determine the coordinates of the starting point and target point of the mobile robot in the two-dimensional orchard environment model, construct the mobile robot motion model, and predict the motion state of the mobile robot at each path node between the starting point and the target point.

[0090] The predicted state when the mobile robot arrives at each of the path nodes is the working state of the mobile robot when the parent node of each path node points to that path node.

[0091] The predicted state includes information such as the mobile robot's position, orientation, speed, and acceleration, in order to assess the reliability of path planning and make adjustments accordingly.

[0092] Each blank grid cell is considered a potential path node. Predicting the robot's motion state at each path node aims to avoid collisions and optimize the robot's path. By combining the predicted motion state information, the improved Grey Wolf optimization algorithm can more fully consider the robot's motion state and behavior at path nodes during selection and adjustment, leading to a more accurate search and optimization process. This better guides the algorithm's iteration and updates, improving its convergence, search efficiency, and performance.

[0093] The motion model for the mobile robot is constructed as follows:

[0094] The movement of a mobile robot can be considered as rigid body motion, and its configuration space in a two-dimensional plane and a rotation angle can be represented by C=R. 2 The position of the orchard mobile robot can be represented by a triple q = (x, y, θ) ×S.

[0095] In this motion model, it is assumed that the robot's origin is located at the center of its rear wheel axle, and the x-axis is along the robot's main axis. Meanwhile, v... i To represent the robot's speed, a i The acceleration is represented by the steering angle, which is defined as... The distance between the front and rear wheels is defined as l. When the steering angle... When fixed in place, the robot will move along a circular path. The radius ρ of this path can be determined by the intersection of the front and rear axles, and the angles between these axles are...

[0096] Based on the above description, the robot's motion can be described by the following equation:

[0097] X i =f1(x,y,θ,v) i ,a i );

[0098] Y i =f2(x,y,θ,v) i ,a i );

[0099] Θ i =f3(x,y,θ,v) i ,a i );

[0100] Assume the robot will move along the rear wheel axis. When Δt approaches zero, the constraint becomes -sinθ + cosθ = 0. If we assume v... i If the scaling factor is equal to sinθ, then this constraint will be satisfied. Furthermore, any scalar multiple of this solution will also satisfy this condition, where the scaling factor is directly related to the robot's velocity v. i Related.

[0101] Let w be the distance the robot travels, and ρ be the radius of the circle traversed by the center of the rear wheel axle under a fixed steering angle. There exists a relationship: dw = ρdθ. At this point, dθ can be expressed as dθ=dw / ρ.

[0102] For both equations, we can divide by dt simultaneously and then subtract v. i Substituting dw / dt into the equation, we get dθ = v i / ρ.

[0103] At this point, if v i and a i Defined as an action variable, using u vi and u ai Instead, the equations of the simplified mobile robot model can be expressed as:

[0104] X i =u vi cosθ;

[0105] Y i =u vi sinθ;

[0106] Θ i =u ai ;

[0107] Furthermore, a description of the mobile robot's direction of motion can be added. Assuming the robot's speed is constant, the model can be further simplified to:

[0108] X i =cosθ;

[0109] Y i =sinθ;

[0110] Θ i =u ai ;

[0111] However, this simplified model cannot clearly indicate whether the robot is moving forward or backward, so an action variable u needs to be added. d To represent direction, the model becomes:

[0112] X i =u d cosθ;

[0113] Y i =u d sinθ;

[0114] Θ i =u ai ;

[0115] The first action variable u d Indicates forward (u d =1) or backward (u) d =-1), to simplify the model, assume u ai ∈[-1, 1], this result applies

[0116] In this model, two new parameters are also introduced: mu, which represents the road surface friction coefficient, and will be used to adjust the impact of road surface friction on energy consumption; and load, which represents the size of the robot's load, and will affect the robot's acceleration and speed. These parameters can further improve the robot's action model and make it more adaptable to the actual working environment.

[0117] Step 300: Merge some redundant nodes on the path between the starting point and the target point of the movement. In the process of merging some redundant nodes, select path nodes according to the fitness evaluation results until an integrated planning path is formed.

[0118] In step 300, the implementation steps of merging some redundant nodes using the improved Grey Wolf optimization algorithm are as follows:

[0119] Step 301: Check the height difference between each pair of adjacent path nodes in the starting point and target point of the movement. If the two path nodes are in the same row or adjacent rows, then connect the two path nodes directly; otherwise, go to step 302.

[0120] Step 302: If the difference in the number of rows between two path nodes is greater than 1, generate a continuous path between the two path nodes and check whether all grids between the two path nodes are free. If so, generate a straight line directly between the two path nodes; otherwise, go to step 303.

[0121] Step 303: Locate the faulty object between two path nodes and determine whether all grids between the faulty object and the next path node moving along the path are free. If so, connect the two path nodes by bypassing the obstacle. If not, proceed to step 304.

[0122] Step 304: Find a point without obstacles between the two path nodes and replan the path. If there are obstacles between the two path nodes and no path can be found to bypass them, proceed to step 305.

[0123] Step 305: Move the next path node up or down, repeat steps 301 to 304, and start searching for the path again;

[0124] Step 306: Compare the fitness evaluation results of the current path node with the fitness evaluation results of its surrounding path nodes, and select the node with the largest fitness evaluation result as the new path node.

[0125] In this embodiment, the purpose of this step is to reduce the path length by merging some redundant nodes, and to plan the path by judging the height difference between nodes, the state of the grid, and the presence of obstacles, ultimately finding a feasible path with the shortest time. Simultaneously, based on the fitness evaluation of the current node and a comparison with surrounding nodes, the node with the highest fitness is selected as the new node to further optimize the path.

[0126] The fitness evaluation function measures the contribution of path nodes to the overall path planning objective. In this step, fitness is assessed by calculating distances between path nodes and the target point, and distances between path nodes and obstacles. During the merging of redundant nodes, the path is optimized by selecting path nodes with higher fitness based on the fitness evaluation results.

[0127] The functional expression for calculating the fitness is:

[0128] F = α1L + β1E;

[0129] in,

[0130] E = E + A i ×v i 2 ×S i +B i ×a i 2 ×S i +C i ×mu×S i +D i ×load×S i ;

[0131] Where L represents path length; E represents energy consumption; α1 and β1 are weight coefficients, and α1 and β1 are the directions of optimization. If α1 is greater than β1, the improved gray wolf optimization algorithm will pay more attention to path length; if β1 is greater than α1, the improved gray wolf optimization algorithm will pay more attention to energy consumption.

[0132] A i B i C i D i All are coefficients, A i B represents the energy consumption weight of speed. i C represents the energy consumption weight of acceleration. i D represents the energy consumption weight of road surface friction. i Indicates the energy consumption weight of the load;

[0133] v i Indicates velocity, a iFor acceleration, mu is the coefficient of friction between the mobile robot and the orchard road surface, used to adjust the energy consumption weight of road surface friction, and load is the load of the mobile robot.

[0134] S i Let be the distance between node i and node i+1.

[0135] In step 300, fitness evaluation is performed on each path node, and some redundant path nodes between the starting point and the target point are merged until an integrated planning path is formed. That is, the improved gray wolf optimization algorithm is used to evaluate the fitness of each path node. The fitness evaluation function is used to measure the contribution of the path node to the overall path planning goal.

[0136] In this step, fitness is evaluated by calculating the distance between path nodes and the target point, the distance between path nodes and obstacles, etc. During the process of merging some redundant nodes, the path is optimized by selecting path nodes with higher fitness based on the fitness evaluation results.

[0137] Step 400: Without changing the node positions of the integrated planning path, based on energy consumption considerations, the improved gray wolf optimization algorithm is used to regenerate the new motion state of the mobile robot when it passes through each path node.

[0138] Step 500: Optimize the position coordinates of each path node. Use the improved Grey Wolf Optimization Algorithm to generate new position coordinates in the neighborhood of the position coordinates of each path node, and connect the optimized position coordinates to synthesize the optimal path, so as to ensure that the mobile robot moves from the starting point to the target point in the shortest time and with the lowest energy consumption.

[0139] In steps 300 to 500, the optimization process of the improved gray wolf optimization algorithm includes the following steps:

[0140] ① Initially, create a random gray wolf population and initialize the position and speed of each individual gray wolf;

[0141] ② Calculate the initial fitness of each gray wolf individual according to the designed fitness function, and save the top 3 gray wolf individuals with the highest fitness α, β, δ;

[0142] ③ Update the current position of all gray wolf individuals in real time according to the improved gray wolf encirclement prey stage function relationship, and calculate the fitness of all gray wolf individuals. The top 3 gray wolf individuals with the highest fitness are α, β, and δ.

[0143] ④ Repeat step ③ until the maximum number of iterations is reached, and output the gray wolf individual with the highest fitness.

[0144] ⑤ Calculate the fitness of individual gray wolves after they move to the next path node based on the functional relationship of the gray wolf surrounding prey stage. Repeat steps ③ to ④ until all gray wolf individuals move to the last path node before the target point.

[0145] The improvements to the gray wolf optimization algorithm in this embodiment are as follows:

[0146] Firstly, by improving the convergence factor, the adaptability and convergence speed are further enhanced. In the Improved Gray Wolf Optimization Algorithm (IGWO), a convergence factor is introduced to control the convergence speed of the gray wolf swarm. By refining the calculation formula of the convergence factor, the IGWO algorithm enables individuals to better adapt to environmental changes and converge to the global optimum more quickly.

[0147] Secondly, the particle swarm optimization (PSO) algorithm is combined with the gray wolf optimization (GWO) algorithm to further improve the search capability and convergence performance of the gray wolf optimization algorithm.

[0148] Third, IGWO also introduces the roulette wheel method, which selects gray wolf individuals for crossover and mutation operations. The roulette wheel method is a method of randomly selecting individuals, and the probability of each gray wolf being selected is proportional to its fitness value. This can increase the diversity of the algorithm and avoid getting trapped in local optima.

[0149] The specific implementation method of improving the convergence factor is as follows:

[0150] The Gray Wolf Algorithm mimics the democratic social behavior exhibited by a pack of gray wolves when chasing and hunting prey. The gray wolf social hierarchy has four levels, with the highest level, which is the optimal solution, being α wolf, the second-best solutions being β wolf and δ wolf, and the other solutions being ω wolf.

[0151] The improved gray wolf optimization algorithm consists of three stages: approaching the prey, surrounding the prey, and attacking the prey. Specifically, the functional relationship for each individual gray wolf in the surrounding prey stage is as follows:

[0152] X(k+1)=X P (k)-A×D;(1)

[0153] D = |C × X P (k)-X(k)|;(2)

[0154] In the formula, k is the current iteration number, X(k) represents the current position of the gray wolf, and X p A represents the current location of the prey, D represents the distance between the individual gray wolf and the prey, and A and C are coefficient vectors;

[0155] Among them, A=2a×r1-a; (3)

[0156] C = 2r²; (4)

[0157] The coefficient vector A determines whether the Grey Wolf Optimization Algorithm performs a global search or a local search. The value of the convergence factor a affects the update of A, which in turn affects the search method of the Grey Wolf Optimization Algorithm. The convergence factor a is improved by using a nonlinear approach.

[0158] The improved formula for the convergence factor α is as follows:

[0159]

[0160] In the formula, a is the convergence factor, and r1 and r2 are random numbers in the interval [0, 1].

[0161] In the formula, l represents the iteration time parameter, and k max Indicates the maximum number of iterations;

[0162] The sigmoid function is used to map the value of l from 0 to the maximum number of iterations, transforming it to the range of 0 to 1, and then mapping it to the range of -1 to 2. This mapping method controls the convergence factor 'a' in the algorithm to accelerate convergence and improve efficiency. A larger 'a' in the initial stage helps the algorithm explore more effectively, while a smaller 'a' gradually decreases later to utilize experience more fully, prompting the algorithm to converge to a better solution faster. By adjusting the convergence factor, the degree of exploration and utilization can be balanced at different stages of the algorithm, improving both efficiency and performance.

[0163] Furthermore, the overall improvement method of the improved gray wolf optimization algorithm provided in this embodiment includes:

[0164] (1) By combining the particle swarm optimization (PSO) algorithm with the gray wolf optimization algorithm, the search capability and convergence performance of the gray wolf optimization algorithm are further improved.

[0165] The specific implementation method of combining the Particle Swarm Optimization (PSO) algorithm with the Grey Wolf Optimization algorithm is as follows:

[0166] Initialize the position and velocity of the particle swarm;

[0167] Set the fitness value for each particle and the current optimal solution X. ipbest and initializing the global optimal solution X igbest The positions and velocities of the gray wolf swarm and the particle swarm are updated through iterative search.

[0168] The fitness values ​​of improved gray wolf individuals and particle individuals are calculated using the update strategies of the improved gray wolf optimization algorithm and the particle swarm optimization algorithm.

[0169] Based on the fitness values ​​of the wolf pack and the particle pack at the same position, the optimal solution is selected as the current solution. If the fitness value of the wolf pack is better, the optimal solution in the wolf pack replaces the worst solution in the particle pack; otherwise, the optimal solution in the particle pack replaces the worst solution in the wolf pack.

[0170] Repeat the above steps until the predetermined number of iterations is reached or the stopping condition is met, then proceed to the gray wolf attacking prey phase.

[0171] The mathematical expression for the gray wolf's attack on its prey phase is as follows:

[0172] D α ′=|C1×X α -X igbest |;

[0173] D β ′=|C2×X β -X igbest |;

[0174] D δ ′=|C3×X δ -X igbest |;

[0175] In the formula, D α '、D β 'and D δ ' represents the distances between α, β, and δ and other individuals, respectively, X igbest This represents the initial global optimal solution, where C1, C2, and C3 are random vectors;

[0176] X1′=X α (k)-A1×D α ′;

[0177] X2′=X β (k)-A2×D β ′;

[0178] X3′=X δ (k)-A3×D δ ′;

[0179]

[0180] In the formula, X1', X2', and X3' represent the positions of α, β, and δ relative to other individuals, respectively, and X i (k+1) represents the position of the gray wolf at time k+1 during the optimization process, X α (k), X β (k) and X δ(k) represents the positions of α, β and δ at time k, respectively, and the coefficient vectors A1, A2 and A3 are generated by formula (3) and formula (5).

[0181] In this improved algorithm, the update strategy of the PSO algorithm is introduced into the Grey Wolf Optimization Algorithm, which enhances the algorithm's global search capability and convergence performance. In each iteration, the grey wolf swarm and the particle swarm update their positions and velocities respectively, and select the optimal solution. Through this iterative process, the algorithm can fully utilize the swarm search capability of the Grey Wolf Optimization Algorithm and the local search capability of the Particle Swarm Optimization Algorithm.

[0182] (2) Using the roulette wheel method, the gray wolf individual is randomly selected based on the fitness value of different gray wolf individuals at each path node, wherein the probability of the gray wolf individual being selected is positively correlated with the fitness value of the gray wolf individual.

[0183] The roulette wheel selection algorithm randomly selects individuals based on their fitness values. Individuals with higher fitness values ​​have a greater probability of being selected, while individuals with lower fitness values ​​also have a chance of being selected. Introducing the roulette wheel selection algorithm may increase the selection opportunities for individuals, even those with lower fitness values. This can maintain population diversity, avoid getting trapped in local optima, and help to search the solution space more comprehensively. The roulette wheel selection algorithm uses probability to select individuals based on fitness values, with individuals with higher fitness values ​​having a greater probability of being selected. This selection method can adjust selection pressure, potentially causing the algorithm to focus more on individuals with high fitness values, thereby accelerating convergence. Through random selection, the roulette wheel selection algorithm can increase the exploratory nature of the algorithm, helping it to explore the search space more comprehensively and helping to discover better solutions.

[0184] (3) Finally, the fitness calculation and position update of each individual gray wolf are performed in parallel to speed up the algorithm.

[0185] By assigning tasks to multiple processing units for simultaneous execution, multiple solution vectors can be processed in parallel, thereby speeding up the search process.

[0186] In step 500, when synthesizing the optimal path, the integrated planning path obtained according to the improved gray wolf optimization algorithm is processed in the following order for the path nodes other than the starting point and the target point:

[0187] Step 501: Starting from the first path node after the starting point of the movement, generate an initial gray wolf population based on the neighborhood of the current path node. The starting point of all gray wolf population individuals at this time is the position of the current node.

[0188] Step 502: Perform an optimization process of the improved gray wolf optimization algorithm according to the fitness function to obtain the optimal gray wolf individual of the current path node. The fitness function takes into account both path length and energy consumption.

[0189] Step 503: Replace the position parameters of the optimal gray wolf individual in the current path node with the original position parameters of the current path node;

[0190] Step 504: Repeat steps 501 to 503 until the current path node is the last path node closest to the moving target point;

[0191] Step 505: Connect the locations of the optimal gray wolf individuals at each path node to form the optimal path for the mobile robot with low path length and low energy consumption.

[0192] In evaluating the movement path of a mobile robot, not only is path length optimization considered, but also energy consumption minimization. Therefore, in the step of updating the gray wolf's position in the gray wolf optimization algorithm, energy consumption information is introduced to adjust the gray wolf's search direction. The gray wolf will tend to select grid cells with lower energy consumption as its next movement target to minimize energy consumption. By comprehensively considering the optimization objectives of path length and energy consumption in path planning, the method of this invention can achieve high efficiency and energy utilization in mobile robot path planning in agricultural orchards.

[0193] To verify the practicality of the algorithm, the improved Grey Wolf algorithm was applied to the path planning problem of a mobile robot. The results were obtained using MATLAB R2020a software. Figure 2 The test was conducted in the environment shown, in which... Figure 2 In the scenario shown, the starting point is (0,0) and the ending point is (39.5,39.5), with obstacles randomly distributed. Four algorithms—Grey Wolf Optimization (GWO), Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO), and Improved Grey Wolf Optimization (IGWO)—were tested to plan the shortest paths in the test environment. Each algorithm was run 30 times, with 500 iterations and a dimension of 2. The shortest paths obtained after each iteration were recorded and their average value was calculated.

[0194] like Figure 2 The results generated by the four algorithms are shown in Table 1, which compares the path results of the four algorithms. As can be seen from the comparison of the path planning simulation results in Table 1, compared with the traditional Grey Wolf optimization algorithm, the improved Grey Wolf optimization algorithm shortens the average path by 10.90%, and compared with the ACO algorithm and PSO algorithm, the average path is shortened by 15.75% and 11.27% respectively, effectively improving the optimization performance of the algorithm.

[0195] Table 1

[0196]

[0197] like Figure 2 The results generated by the five algorithms are shown in Table 2, which compares the energy consumption of the four algorithms. Table 2 shows the comparison of path planning simulation results. As can be seen from the comparison of path planning simulation results in Table 2, compared with the traditional GWO algorithm, the improved IGWO algorithm reduces the average energy consumption by 7.63%, and compared with the ACO and PSO algorithms, the average energy consumption is reduced by 11.14% and 9.07%, respectively. This effectively improves the optimization performance of the algorithms.

[0198] Table 2

[0199]

[0200] The classic GWO algorithm is prone to getting trapped in local optima, while the improved IGWO algorithm effectively avoids this, exhibiting stronger search capabilities and faster convergence. Compared to the other three algorithms, the improved IGWO algorithm finds the shortest path more efficiently and has a faster convergence speed.

[0201] This implementation method specifically incorporates considerations of path length and energy consumption. During the path planning process, not only is the Grey Wolf optimization algorithm used to select the point with the highest fitness to construct the grid map, but path length and energy consumption are also considered in the fitness evaluation.

[0202] By adding corresponding energy consumption information to each grid cell, the energy consumption of the orchard mobile robot can be fully considered during the path planning process. This method's fitness evaluation considers not only minimizing the total path length but also minimizing energy consumption.

[0203] Specifically, this is achieved by introducing a hybrid objective function that considers both energy consumption and path length. This function uses the weighted sum of total path length and energy consumption as the fitness value. In the step of updating the gray wolf's position in the gray wolf optimization algorithm, energy consumption and path length information are incorporated. The gray wolf will then tend to select grid cells that can both shorten the path and reduce energy consumption as its next movement target. In this way, while ensuring movement efficiency, energy consumption can be minimized. By comprehensively optimizing path length and energy consumption in path planning, this method can achieve high efficiency and energy utilization efficiency in the path planning of orchard mobile robots.

[0204] The above embodiments are merely exemplary embodiments of this application and are not intended to limit this application. The scope of protection of this application is defined by the claims. Those skilled in the art can make various modifications or equivalent substitutions to this application within its substance and scope of protection, and such modifications or equivalent substitutions should also be considered to fall within the scope of protection of this application.

Claims

1. A mobile robot path planning method based on an improved gray wolf optimization algorithm, characterized in that, Includes the following steps: Step 100: Construct a two-dimensional orchard environment model, discretize the two-dimensional orchard environment model into a grid map, and mark bounded obstacle grid cells and non-obstacle grid cells in the grid map. Step 200: Determine the coordinates of the starting point and target point of the mobile robot in the two-dimensional orchard environment model, construct the mobile robot motion model, and predict the motion state of the mobile robot at each path node between the starting point and the target point. Step 300: Merge some redundant nodes on the path between the starting point and the target point of the movement, evaluate the fitness of the merged path nodes, and select the path nodes to form an integrated planning path. In step 300, the implementation steps of merging some redundant nodes using the improved Grey Wolf optimization algorithm are as follows: Step 301: Check the height difference between each pair of adjacent path nodes in the starting point and target point of the movement. If the two path nodes are in the same row or adjacent rows, then connect the two path nodes directly; otherwise, go to step 302. Step 302: If the difference in the number of rows between two path nodes is greater than 1, generate a continuous path between the two path nodes and check whether all grids between the two path nodes are free. If so, generate a straight line directly between the two path nodes; otherwise, go to step 303. Step 303: Locate the faulty object between two path nodes and determine whether all grids between the faulty object and the next path node moving along the path are free. If so, connect the two path nodes by bypassing the obstacle. If not, proceed to step 304. Step 304: Find a point without obstacles between the two path nodes and replan the path. If there are obstacles between the two path nodes and no path can be found to bypass them, proceed to step 305. Step 305: Move the next path node up or down, repeat steps 301 to 304, and start searching for the path again; Step 306: Compare the fitness evaluation results of the current path node with the fitness evaluation results of its surrounding path nodes, select the node with the largest fitness evaluation result as the new path node, and select new path nodes in turn to form an integrated planning path. Step 400: Without changing the path node positions of the integrated planning path, based on energy consumption considerations, the improved gray wolf optimization algorithm is used to regenerate the new motion state of the mobile robot when it passes through each path node. Step 500: Optimize the position coordinates of each path node. Use the improved Grey Wolf Optimization Algorithm to generate new position coordinates in the neighborhood of the position coordinates of each path node, and connect the optimized position coordinates to synthesize the optimal path, so as to ensure that the mobile robot moves from the starting point to the target point in the shortest time and with the lowest energy consumption.

2. The mobile robot path planning method based on the improved gray wolf optimization algorithm according to claim 1, characterized in that, In step 200, the motion state of the mobile robot at each path node between the starting point and the target point includes the position, direction, velocity, and acceleration of the mobile robot at each path node, wherein the triplet q=(x, y, ... () indicates the location of the mobile robot; In step 200, the formula for constructing the motion model of the mobile robot is: X i = u d cosθ; AND i = u d sinθ; i = u ai； The predicted state when the mobile robot arrives at each of the path nodes is the working state of the mobile robot when the parent node of each path node points to that path node. X i Y represents the x-coordinate value of the mobile robot in the two-dimensional orchard environment model. i This represents the ordinate value of the mobile robot in the two-dimensional orchard environment model. i The angle between the direction of movement of the mobile robot and the X-axis is the forward direction of the mobile robot. you d ∈{-1,1},u ai ∈[-tan max tan max ]; When u d When u = 1, it indicates that the mobile robot is moving forward; when u = 1, it indicates that the mobile robot is moving forward d When the value is -1, it indicates that the mobile robot is moving backward; max This represents the maximum turning angle of the mobile robot at each path node of the initially planned path. max ∈ (0, π / 2), then u ai ∈[-1, 1].

3. The mobile robot path planning method based on the improved gray wolf optimization algorithm according to claim 1, characterized in that, In steps 300 to 500, the optimization process of the improved gray wolf optimization algorithm includes the following steps: ① Initially, create a random gray wolf population and initialize the position and speed of each individual gray wolf; ② Calculate the initial fitness of each gray wolf individual according to the designed fitness function, and save the top 3 gray wolf individuals with the highest fitness α, β, δ; ③ Update the current position of all gray wolf individuals in real time according to the improved gray wolf encirclement prey stage function relationship, and calculate the fitness of all gray wolf individuals. The top 3 gray wolf individuals with the highest fitness are α, β, and δ. ④ Repeat step ③ until the maximum number of iterations is reached, and output the gray wolf individual with the highest fitness. ⑤ Calculate the fitness of individual gray wolves after they move to the next path node based on the functional relationship of the gray wolf surrounding prey stage. Repeat steps ③ to ④ until all gray wolf individuals move to the last path node before the target point.

4. The mobile robot path planning method based on the improved gray wolf optimization algorithm according to claim 3, characterized in that, The improved gray wolf optimization algorithm consists of three stages: approaching the prey, surrounding the prey, and attacking the prey. Specifically, the functional relationship for each individual gray wolf in the surrounding prey stage is as follows: ；（1） ；（2） In the formula, k is the current iteration number, X(k) represents the current position of the gray wolf, and X p A represents the current location of the prey, D represents the distance between the individual gray wolf and the prey, and A and C are coefficient vectors; in, (3) ；（4） The coefficient vector A determines whether the Grey Wolf Optimization Algorithm performs a global search or a local search. The value of the convergence factor a affects the update of A, which in turn affects the search method of the Grey Wolf Optimization Algorithm. The convergence factor a is improved by using a nonlinear approach. The improved formula for the convergence factor α is as follows: ；（5） In the formula, a is the convergence factor, and r1 and r2 are random numbers in the interval [0, 1]. In the formula, l represents the iteration time parameter, and k max This indicates the maximum number of iterations.

5. A mobile robot path planning method based on an improved gray wolf optimization algorithm according to claim 4, characterized in that, The overall improvement of the Gray Wolf Optimization Algorithm is achieved by combining the Particle Swarm Optimization (PSO) algorithm with the Gray Wolf Optimization Algorithm, thereby further improving the search capability and convergence performance of the Gray Wolf Optimization Algorithm. The gray wolf individual is randomly selected based on the fitness value of different gray wolf individuals at each path node using a roulette wheel method, wherein the probability of the gray wolf individual being selected is positively correlated with the fitness value of the gray wolf individual; Finally, the fitness calculation and position update of each individual gray wolf are performed in parallel to speed up the algorithm's operation.

6. A mobile robot path planning method based on an improved gray wolf optimization algorithm as described in claim 5. The specific implementation method of combining the Particle Swarm Optimization (PSO) algorithm with the Grey Wolf Optimization algorithm is as follows: Initialize the position and velocity of the particle swarm; Set the fitness value for each particle and the current optimal solution X. ipbest and initializing the global optimal solution X igbest The positions and velocities of the gray wolf swarm and the particle swarm are updated through iterative search. The fitness values ​​of improved gray wolf individuals and particle individuals are calculated using the update strategies of the improved gray wolf optimization algorithm and the particle swarm optimization algorithm. Based on the fitness values ​​of the wolf pack and the particle pack at the same position, the optimal solution is selected as the current solution. If the fitness value of the wolf pack is better, the optimal solution in the wolf pack replaces the worst solution in the particle pack; otherwise, the optimal solution in the particle pack replaces the worst solution in the wolf pack. Repeat the above steps until the predetermined number of iterations is reached or the stopping condition is met, then proceed to the gray wolf attacking prey phase.

7. A mobile robot path planning method based on an improved gray wolf optimization algorithm according to claim 6, characterized in that: The mathematical expression for the gray wolf's attack on its prey phase is as follows: ； ； ； In the formula, D α '、D β 'and D δ ' represents the distances between α, β, and δ and other individuals, respectively, X igbest This represents the initial global optimal solution, where C1, C2, and C3 are random vectors; ； ； ； ； In the formula, X1', X2', and X3' represent the positions of α, β, and δ relative to other individuals, respectively, and X i (k+1) represents the position of the gray wolf at time k+1 during the optimization process, X α (k), X β (k) and X δ (k) represents the positions of α, β and δ at time k, respectively, and the coefficient vectors A1, A2 and A3 are generated by formula (3) and formula (5).

8. A mobile robot path planning method based on an improved gray wolf optimization algorithm according to claim 7, characterized in that: In step 500, when synthesizing the optimal path, the integrated planning path obtained according to the improved gray wolf optimization algorithm is processed in the following order for the path nodes other than the starting point and the target point: Step 501: Starting from the first path node after the starting point of the movement, generate an initial gray wolf population based on the neighborhood of the current path node. The starting point of all gray wolf population individuals at this time is the position of the current node. Step 502: Perform an optimization process of the improved gray wolf optimization algorithm according to the fitness function to obtain the optimal gray wolf individual of the current path node. The fitness function takes into account both path length and energy consumption. Step 503: Replace the position parameters of the optimal gray wolf individual in the current path node with the original position parameters of the current path node; Step 504: Repeat steps 501 to 503 until the current path node is the last path node closest to the moving target point; Step 505: Connect the locations of the optimal gray wolf individuals at each path node to form the optimal path for the mobile robot with low path length and low energy consumption.

9. A mobile robot path planning method based on an improved gray wolf optimization algorithm according to any one of claims 2-8, characterized in that: The functional expression for calculating the fitness is: F = α1L+β1E; in, ; ； Where L represents path length; E represents energy consumption; α1 and β1 are weight coefficients, and α1 and β1 are the directions of optimization. If α1 is greater than β1, the improved gray wolf optimization algorithm will focus more on path length; if β1 is greater than α1, the improved gray wolf optimization algorithm will focus more on energy consumption. A i B i C i D i All are coefficients, A i B represents the energy consumption weight of speed. i C represents the energy consumption weight of acceleration. i D represents the energy consumption weight of road surface friction. i Indicates the energy consumption weight of the load; v i Indicates velocity, a i For acceleration, mu is the coefficient of friction between the mobile robot and the orchard road surface, used to adjust the energy consumption weight of road surface friction, and load is the load of the mobile robot. S i Let be the distance between node i and node i+1.

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