Low-altitude airspace unmanned aerial vehicle three-dimensional path planning method based on improved electric eel algorithm

Abstract

The invention discloses a low-altitude airspace unmanned aerial vehicle three-dimensional path planning method based on an improved electric eel algorithm, and relates to the technical field of intelligent control. Firstly, a good point set method is adopted to optimize the initial population quality, it is ensured that the population has higher diversity and coverage in the initial stage of search, and therefore the search efficiency of the overall algorithm is improved. Secondly, a chaos disturbance mechanism is introduced to optimize the foraging behavior of the electric eels, the algorithm can be effectively prevented from falling into local optimum, and the global search capability is improved. In order to further balance global exploration and local development, the rest and hunting behaviors of the electric eels are adjusted by using nonlinear decreasing weights, so that the algorithm is more adaptive in different stages. And finally, introducing the dynamic weight coefficient into the migration behavior of the electric eel so as to enhance the diversity of the population and prevent premature convergence. Through the improvement measures, the method remarkably improves the three-dimensional path planning performance of the unmanned aerial vehicle in the low-altitude airspace, and can effectively obtain a shorter, safer and more reliable optimal path.

Description

Technical Field

[0001] The present invention relates to the field of intelligent control technology, and in particular to a three-dimensional path planning method (IEEFO) for a low-altitude unmanned aerial vehicle based on an improved electric eel algorithm. Background Art

[0002] The development of low-altitude economy has promoted the application of drones in low-altitude complex environments such as cities, and drone path planning, as an important technology to ensure its flight safety and economic efficiency, is particularly critical. In general, this technology requires drones to plan a safe and feasible flight path from a specified starting point to a destination in a specific area based on a cost function as the evaluation criterion and under the premise of meeting constraints. For tasks such as aerial photography and aerial mapping, the evaluation criterion for path planning is the shortest track distance to reduce energy consumption and time; in search and tracking tasks, the evaluation criterion is the probability of dynamic search targets; for rescue tasks, the evaluation criterion is the rescue time. In addition, the path planning problem must also meet multiple constraints and flight safety requirements. These constraints include the maximum tilt angle, turning rate, steering angle, climb angle, flight time, flight altitude and fuel consumption of drones. Flight safety involves drones having to avoid threats such as tall buildings, overhead cables, no-fly airspace, and even aerial missiles and radar detection, which requires drones to have effective environmental threat avoidance capabilities when performing tasks. Therefore, the path planning problem of drones in low-altitude airspace is a very challenging problem.

[0003] At present, the path planning problem of UAVs in low-altitude airspace is generally implemented by the electric eel algorithm (EEFO), which mainly abstracts some biological behaviors of electric eels into mathematical language and transforms a series of formulas to realize the path planning of UAVs in low-altitude airspace. Although the electric eel algorithm (EEFO) performs well in development and utilization, exploration balance and avoiding local optimality, it also faces some problems similar to other swarm intelligence optimization algorithms. For example, problems such as initial population quality, convergence stability, search accuracy and local optimality will cause problems such as too long path length, too high energy consumption or too long planning time in the path planning process of UAVs in low-altitude airspace. In addition, when UAVs perform tasks in complex terrain or dynamic environments, the robustness and adaptability of path planning may decrease, and they cannot avoid threats or respond to environmental changes in time, thereby increasing the risk of mission failure. Summary of the invention

[0004] In view of the shortcomings of the existing technology, the present invention optimizes and improves the traditional electric eel algorithm to ensure that the drone can obtain the optimal path.

[0005] The present invention provides a three-dimensional path planning method for a low-altitude UAV based on an improved electric eel algorithm. First, a three-dimensional environment modeling is performed on the UAV moving space to simulate the threat areas and peaks in the UAV operating environment in real life; then, the improved electric eel algorithm is used to obtain the optimal path of the UAV in the modeled three-dimensional environment;

[0006] Furthermore, the three-dimensional environment modeling of the drone moving space is specifically as follows: setting the size of the drone moving space, setting the starting point and target point of the drone, and randomly generating a cylindrical threat area in the drone moving space by generating random numbers and using a column function;

[0007] Furthermore, the specific steps of using the improved electric eel algorithm to obtain the optimal path of the drone in the modeled three-dimensional environment include:

[0008] S1: introducing a good point set to initialize the population and obtain an initial population; the initial population includes a number of electric eel individuals, each of which represents a flight trajectory of a UAV in a three-dimensional environment, each of which includes a number of coordinate points, each of which includes the spatial coordinates (x, y, z) of the UAV and the state information of the UAV;

[0009] Specifically: First, define the search space G s , which is an s-dimensional unit cube, and the value of each dimension is in [0,1], and then the good point generation formula is used to generate the good point r, and then a good point set including n good points is obtained, and the good points are mapped to the feasible domain where the population is located according to the preset lower bound low of the population and the upper bound up of the population, and n electric eel individuals are obtained, and then the initial population is obtained;

[0010] The optimal point is: r = (r1, r2, ..., r k ,…,r s ), where r k is the kth dimension of the good point r:

[0011] r k ={2cos(2πk / p),1≤k≤s}

[0012] Where p is the smallest prime number satisfying (p-3) / 2≥s;

[0013] The good point set is expressed as:

[0014]

[0015] Among them, P n (l) represents the good point set, l is the number of the good point, n is the number of good points, and {} represents the decimal part;

[0016] The deviation of the good point set satisfies:

[0017] φ(n)=C(r,ε)n -1+ε

[0018] Among them, φ(n) represents the deviation of the good point set, ε represents a positive number; C(r,ε) represents a constant related only to r and ε;

[0019] S2: Set the maximum number of iterations T;

[0020] S3: Set the current number of iterations to 0;

[0021] S4: Construct a total cost function, calculate the total cost function value of the electric eel individuals in the current population as the fitness value, find the best fitness value BestF and the position of the corresponding electric eel individual as the current best position x prey ; The best fitness value BestF is the minimum fitness value;

[0022] Assume that the set of all threat areas is Q. Each cylindrical threat area is projected onto the horizontal plane as a circle, with its center at Indicated by R. q Indicates that q is the number of the threat area, and the spatial coordinates of the current position of the drone are set to The spatial coordinates of the next position are The Euclidean distance between two locations is expressed as The path from the current position of the drone to the next position is expressed as Among them, x ij Indicates the coordinate of the current position on the x-axis, y ij Indicates the coordinate of the current position on the y-axis, z ij represents the coordinate of the current position on the z-axis, i represents the drone number, and j represents the time step;

[0023] The cost function of the set Q of all threat areas that the drone crosses during its movement, that is, the threat avoidance cost, is expressed as:

[0024]

[0025] Among them, F1(X i ) indicates drone X i The threat avoidance cost, X i represents the i-th drone, m is the number of time steps, q Max represents the number of threat areas, Indicates the path The threat avoidance cost function, L represents the cost value, d q represents the distance between the current position of the UAV and the center of the threat area, and S represents the distance between the current position of the UAV and the boundary of the threat area;

[0026] The calculation formula for the track height cost of a drone position is as follows:

[0027]

[0028] Among them, H ij h is the track height cost of a UAV position, Max is the maximum flight altitude, h Min is the safety height, h ij is the flight height of the UAV relative to the ground, σ and λ are weight coefficients;

[0029] The track height cost H of all the positions of the UAV ij The total track height cost is accumulated:

[0030]

[0031] Among them, F2(X i ) is drone X i Total track height cost;

[0032] A transformation method based on Cartesian coordinates is introduced as a smoothness constraint to optimize the smoothness of the path under the constraint condition. The smoothness constraint is:

[0033]

[0034] in, represents the amplitude of the track, γ ij represents the elevation angle, χ ij Indicates the heading angle; x ij-1 Indicates the coordinate of the previous position on the x-axis; y ij-1 Indicates the coordinate of the previous position on the y-axis; z ij-1 Indicates the coordinate of the previous position on the z-axis;

[0035] Heading angle χ ij The calculation formula is:

[0036]

[0037] in, Indicates the path The projection on the horizontal plane, Indicates the path projection on the horizontal plane;

[0038]

[0039] in, is the unit vector in the height direction;

[0040] The pitch angle is the angle between the horizontal plane and the path, and its calculation formula is:

[0041]

[0042] Among them, z i,j+2 Indicates that the drone is The coordinate on the z axis, z i,j+1 Indicates that the drone is The coordinate on the z axis when

[0043] The path smoothing cost is:

[0044]

[0045] Among them, F3(X i ) is drone X i The path smoothing cost; β1 and β2 represent the penalty coefficients of heading angle and pitch angle respectively; the final total cost function is expressed as:

[0046]

[0047] Among them, F(X i ) indicates drone X i The total cost function, f represents the cost number, μ f Indicates the weight coefficients of different costs;

[0048] The weight coefficients of different costs are dynamically adjusted by using an adaptive weight adjustment mechanism as follows:

[0049]

[0050] Among them, Nor f is the weight coefficient;

[0051]

[0052] Among them, F f is the cost of number f, F min is the maximum of the three costs, F min is the minimum of the three costs;

[0053] S5: Determine whether the current number of iterations reaches the set maximum number of iterations. If yes, output the current best fitness value BestF and the current best position x prey , get the optimal path of the UAV, otherwise execute S6;

[0054] S6: Calculate the energy factor E. If E>1, execute S7. If E>1 is not satisfied, if rand<1 / 3, execute S8. If rand>2 / 3, execute S9. Otherwise, execute S10. Rand is a random number between (0,1).

[0055] S7: The electric eel individuals in the population perform interactive behaviors, update the positions of the electric eel individuals, and select the updated best position. If the updated best position is better than the current best position, the updated best position is used as the current best position, the current iteration number is increased by 1 and returns to S5;

[0056] First, generate a chaotic variable X T , and then use X T Generate two chaotic perturbation variables;

[0057]

[0058] Among them, x t represents a random number uniformly distributed in the interval (0,1), t represents the current number of iterations, and x ∈ (t) represents the position of the ∈th electric eel individual in the current population, ∈ is the number of the electric eel individual, is the first chaotic disturbance variable of the ∈th electric eel individual, is the second chaotic disturbance variable of the ∈th electric eel individual, is the global average, and x r (t) is the position of the reference individual, and x r =Low+rand×(Up-Low);

[0059] Finally, according to the obtained chaotic disturbance variable, the position of the electric eel individual is updated, and its expression is:

[0060]

[0061] Among them, x ∈ (t) and x ∈′ (t) is the position of two interacting electric eels randomly selected from the current population, and ∈≠∈′; x ∈ (t+1) represents the updated position of the electric eel individual; p1 and p2 are random numbers in (0,1); fit() represents the fitness value; C is the position adjustment factor;

[0062] C=n1×B

[0063] B=[b1,b2,…b dim ,…,b Dim ]

[0064]

[0065] Where n1 is a randomly generated value from the normal distribution N(0,1), B is a vector, and b dim is the element of the dimth dimension in vector B, where Dim is the total dimension of vector B; randperm(d) means returning a random permutation in the range from 1 to Dim;

[0066] S8: The electric eel individuals in the population perform resting behavior, update the positions of the electric eel individuals, and select the updated best position. If the updated best position is better than the current best position, the updated best position is used as the current best position, the current iteration number is increased by 1 and returns to S5;

[0067] Before performing the resting behavior, the electric eel individual first establishes a resting area and performs the resting behavior based on the nonlinear decreasing weight λ. The method for updating the position of the electric eel individual is:

[0068] x ∈ (t+1)=R′ ∈ (t+1)+n2×(R′ ∈ (t+1)round(rand)×x ∈ (t))

[0069] R′ ∈ (t+1)=Z(t)+α′×|Z(t)-x prey (t)|

[0070] Z(t)=Low+z(t)×(Up-Low)

[0071] α′=λ′×α0×sin(2πrand)

[0072]

[0073] Among them, round(rand) means rounding a random number from 0 to 1, n2 is a randomly generated value from the normal distribution N(0,1), and R′ ∈ (t+1) represents the resting position that the electric eel will obtain in the resting area before performing the resting behavior, α′ is the scale of the current resting area, and x prey (t) represents the current optimal position, α0 represents the initial size of the rest area, and λ′ is a nonlinear decreasing weight, and z(t) is the normalized number; Indicates the random position dimension of an electric eel randomly selected from the current population; Low rand(d) Indicates the lower bound of the currently randomly selected position dimension; Up rand(d)Indicates the upper bound of the current randomly selected position dimension;

[0074] S9: The electric eel individuals in the population perform hunting behavior, update the positions of the electric eel individuals, and select the updated best position. If the updated best position is better than the current best position, the updated best position is used as the current best position, the current iteration number is increased by 1 and returns to S5;

[0075] The electric eel will establish a hunting area before performing hunting behavior. The method to update the location of the electric eel individual is:

[0076] x ∈ (t+1)=H′ prey (t+1)+η′×(H′ prey (t+1)-round(rand)×x ∈ (t))

[0077]

[0078] β′=λ′×β0×sin(2πrand)

[0079] Among them, H′ prey (t+1) is the hunting position that the electric eel will obtain in the resting area before executing the hunting behavior, η′ is the curling factor, β′ is the size of the current hunting area; β0 represents the initial size of the hunting area;

[0080] S10: The electric eel individuals in the population perform migration behavior, update the positions of the electric eel individuals, and select the updated best position. If the updated best position is better than the current best position, the updated best position is used as the current best position, the current iteration number is increased by 1 and returns to S5;

[0081] The dynamic weight strategy coefficient is introduced into the electric eel algorithm. The specific expression is:

[0082]

[0083] ζ4=ζ1-ζ2+ζ3

[0084] Where c is a constant; ζ1, ζ2, ζ3 and ζ4 represent dynamic weight strategy factors;

[0085] After optimization, the migration behavior is performed and the method for updating the position of the electric eel individuals is as follows:

[0086]

[0087] Among them, H′ r (t+1) is an arbitrary position in the hunting area, indicating that the electric eel individuals move to the hunting area through migration behavior. represents the Levy flight function, u, v represent randomly generated values ​​from the normal distribution N(0,1), Γ represents the standard Gamma function.

[0088] Compared with the prior art, the beneficial effects of the present invention are:

[0089] The present invention proposes a three-dimensional path planning method for UAVs in low-altitude airspace based on the improved electric eel optimization algorithm (IEEFO), and significantly improves the effect of path planning through the improvement of multiple key technologies. First, the initial population quality is optimized by the good point set method to ensure that the population has higher diversity and coverage in the early stage of the search, thereby improving the search efficiency of the overall algorithm. Secondly, the introduction of a chaotic perturbation mechanism to optimize the foraging behavior of electric eels can effectively prevent the algorithm from falling into local optimality and improve the global search capability. In order to further balance global exploration and local development, the resting and hunting behaviors of electric eels are adjusted using nonlinear decreasing weights, making the algorithm more adaptable at different stages. Finally, a dynamic weight coefficient is introduced into the migration behavior of electric eels to enhance the diversity of the population and prevent premature convergence. Through these improvement measures, this method significantly improves the three-dimensional path planning performance of UAVs in low-altitude airspace, and can effectively obtain a shorter, safer and more reliable optimal path. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] Figure 1 It is a flow chart of a three-dimensional path planning method for a low-altitude UAV based on an improved electric eel algorithm in an embodiment of the present invention;

[0091] Figure 2 A comparison diagram of three-dimensional path planning of various algorithms in scenario 1 in an embodiment of the present invention (front view);

[0092] Figure 3 A comparison diagram (top view) of the path planning of each algorithm in scenario 1 in an embodiment of the present invention;

[0093] Figure 4 is the convergence curve of each algorithm in scenario 1 in the embodiment of the present invention;

[0094] Figure 5 A comparison diagram of three-dimensional path planning of various algorithms in scenario 2 in an embodiment of the present invention (front view);

[0095] Figure 6 A comparison diagram (top view) of the path planning of each algorithm in scenario 2 in an embodiment of the present invention;

[0096] Figure 7 is the convergence curve of each algorithm in scenario 2 in the embodiment of the present invention;

[0097] Figure 8A comparison diagram of three-dimensional path planning of various algorithms in scenario 3 in an embodiment of the present invention (front view);

[0098] Fig. 9 A comparison diagram (top view) of the path planning of each algorithm in scenario 3 in an embodiment of the present invention;

[0099] Fig.10 is the convergence curve of each algorithm in scenario 3 in the embodiment of the present invention;

[0100] Among them, 1-WOA algorithm; 2-NGO algorithm; 3-BDO algorithm; 4-EEEF algorithm; 5-IEEFO algorithm. DETAILED DESCRIPTION

[0101] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. In order to enable other relevant technical personnel in the field to better understand the implementation of the present invention, the present invention provides simulation verification results of three-dimensional path planning of unmanned aerial vehicles using MATLAB2022b software.

[0102] The present invention proposes a three-dimensional path planning method for low-altitude UAV based on the improved electric eel algorithm. Figure 1 As shown, the following steps are included:

[0103] Firstly, a three-dimensional environment model is built for the UAV's mobile space to simulate the threat areas and mountains in the real-life UAV operating environment. Then, the improved electric eel algorithm is used to obtain the optimal path of the UAV in the modeled three-dimensional environment.

[0104] The three-dimensional environment modeling of the drone moving space is specifically as follows: setting the size of the drone moving space, setting the starting point and target point of the drone, and randomly generating a cylindrical threat area in the drone moving space by generating random numbers and using a column function;

[0105] The specific steps of using the improved electric eel algorithm to obtain the optimal path of the drone in the modeled three-dimensional environment include:

[0106] S1: Introduce a good point set to initialize the population, increase the diversity of the population, and make the population more evenly distributed, so as to obtain an initial population; the initial population includes a number of electric eel individuals, each of which represents a flight trajectory of a drone in a three-dimensional environment, and each flight trajectory includes a number of coordinate points, each of which includes the spatial coordinates (x, y, z) of the drone and the state information of the drone (such as flight speed, angle, etc.). In this way, the initial population has better distribution and representativeness, which lays a good foundation for the subsequent optimization process;

[0107] Specifically: First, define the search space G s, which is an s-dimensional unit cube, and the value of each dimension is in [0,1], and then the good point generation formula is used to generate the good point r, and then a good point set including n good points is obtained, and the good points are mapped to the feasible domain where the population is located according to the preset lower bound low of the population and the upper bound up of the population, and n electric eel individuals are obtained, and then the initial population is obtained;

[0108] The optimal point is: r = (r1, r2, ..., r k ,…,r s ), where r k is the kth dimension of the good point r:

[0109] r k ={2cos(2πk / p),1≤k≤s}

[0110] Where p is the smallest prime number satisfying (p-3) / 2≥s;

[0111] The good point set is expressed as:

[0112]

[0113] Among them, P n (l) represents the good point set, l is the number of the good point, n is the number of good points, and {} represents the decimal part;

[0114] The deviation of the good point set satisfies:

[0115] φ(n)=C(r,ε)n -1+ε

[0116] Among them, φ(n) represents the deviation of the good point set, ε represents a small positive number, which controls the convergence rate of the deviation function and ensures that the generated points gradually tend to be evenly distributed; C(r,ε) represents a constant related only to r and ε;

[0117] In this embodiment, s is set to 15, that is, the flight trajectory represented by each electric eel individual includes 15 coordinate points, and n is set to 90, that is, there are 90 electric eel individuals in the initial population;

[0118] S2: Set the maximum number of iterations T;

[0119] In this implementation, the maximum number of iterations T is set to 200;

[0120] S3: Set the current number of iterations to 0;

[0121] S4: Construct a total cost function, calculate the total cost function value of the electric eel individuals in the current population as the fitness value, find the best fitness value BestF and the position of the corresponding electric eel individual as the current best position x prey; The best fitness value BestF is the minimum fitness value;

[0122] The cost function is constructed based on three evaluation indicators: threat avoidance, track height, and track smoothness:

[0123] For the convenience of research, all threats are assumed to be cylinders, and the set of all threat areas is set to Q. Since there are various sources of threats in reality, in order to better describe them, this invention abstracts all threat areas into the form of cylinders, whose projection on the horizontal plane is a circle, and its center is denoted by Indicated by R. q Indicates that q is the number of the threat area, and the spatial coordinates of the current position of the drone are set to The spatial coordinates of the next position are The Euclidean distance between two locations is expressed as The path from the current position of the drone to the next position is expressed as Among them, x ij Indicates the coordinate of the current position on the x-axis, y ij Indicates the coordinate of the current position on the y-axis, z ij Indicates the coordinate of the current position on the z-axis, i indicates the drone number, j indicates the time step, the x-axis indicates the left-right direction, the y-axis indicates the front-back direction, and the z-axis indicates the up-down direction;

[0124] The cost function of the set Q of all threat areas that the drone crosses during its movement, that is, the threat avoidance cost, is expressed as:

[0125]

[0126] Among them, F1(X i ) indicates drone X i The threat avoidance cost, X i represents the i-th drone, m is the number of time steps, q Max represents the number of threat areas, Indicates the path The threat avoidance cost function, L represents the cost value, d q represents the distance between the current position of the UAV and the center of the threat area, and S represents the distance between the current position of the UAV and the boundary of the threat area;

[0127] Since drones are low-altitude flying devices, they generally have a maximum flight altitude during mission execution, which is called the maximum flight altitude h. Max It should also be considered that the drone should maintain a safe height above the ground. Min The calculation formula of the track height cost of a UAV position is as follows:

[0128]

[0129] Among them, H ij h is the track height cost of a UAV position, Max is the maximum flight altitude, h Min is the safety height, h ij is the flight height of the UAV relative to the ground, σ and λ are weight coefficients;

[0130] The track height cost H of all the positions of the UAV ij The total track height cost is accumulated:

[0131]

[0132] Among them, F2(X i ) is drone X i Total track height cost;

[0133] The pitch angle γ and heading angle χ of the drone are also crucial to the path planning task of the drone during its trajectory. It ensures the smoothness of the drone during its trajectory. In order to ensure the smoothness of the drone on its flight trajectory, a conversion method based on Cartesian coordinates is introduced as a smoothness constraint to optimize the smoothness of the path under the constraint conditions. The smoothness constraint is:

[0134]

[0135] in, represents the amplitude of the track, γ ij represents the elevation angle, χ ij Indicates the heading angle; x ij-1 Indicates the coordinate of the previous position on the x-axis; y ij-1 Indicates the coordinate of the previous position on the y-axis; z ij-1 Indicates the coordinate of the previous position on the z-axis;

[0136] Heading angle χ ij The calculation formula is:

[0137]

[0138] in, Indicates the path The projection on the horizontal plane, Indicates the path projection on the horizontal plane;

[0139]

[0140] in, is the unit vector in the height direction;

[0141] The pitch angle is the angle between the horizontal plane and the path, and its calculation formula is:

[0142]

[0143] Among them, z i,j+2 Indicates that the drone is The coordinate on the z axis, z i,j+1 Indicates that the drone is The coordinate on the z axis when

[0144] The final path smoothing cost is:

[0145]

[0146] Among them, F3(X i ) is drone X i Path smoothing cost; β1 and β2 represent the penalty coefficients of heading angle and pitch angle respectively;

[0147] In summary, the path planning problem of the UAV considers three evaluation indicators: threat avoidance, track height, and track smoothness. The final total cost function can be expressed as:

[0148]

[0149] Among them, F(X i ) indicates drone X i The total cost function, f represents the cost number, μ f Indicates the weight coefficients of different costs;

[0150] The weight coefficients of different costs are dynamically adjusted by using an adaptive weight adjustment mechanism, which can be expressed as:

[0151]

[0152] Among them, Nor f is the weight coefficient;

[0153]

[0154] Among them, F f is the cost of number f, F min is the maximum of the three costs, F min is the minimum of the three costs;

[0155] S5: Determine whether the current number of iterations reaches the set maximum number of iterations. If yes, output the current best fitness value BestF and the current best position x prey , get the optimal path of the UAV, otherwise execute S6;

[0156] S6: Calculate the energy factor E. If E>1, execute S7. If E>1 is not satisfied, if rand<1 / 3, execute S8. If rand>2 / 3, execute S9. Otherwise, execute S10. Rand is a random number between (0,1).

[0157] S7: The electric eel individuals in the population perform interactive behaviors, update the positions of the electric eel individuals, and select the updated best position. If the updated best position is better than the current best position, the updated best position is used as the current best position, the current iteration number is increased by 1 and returns to S5;

[0158] The present invention combines the operation of chaotic disturbance in the interactive behavior of electric eels to enhance the ability to improve the best candidate solution;

[0159] First, generate a chaotic variable X T , and then use X T Generate two chaotic perturbation variables;

[0160]

[0161] Among them, x t represents a random number uniformly distributed in the interval (0,1), t represents the current number of iterations, and x ∈ (t) represents the position of the ∈th electric eel individual in the current population, ∈ is the number of the electric eel individual, is the first chaotic disturbance variable of the ∈th electric eel individual, is the second chaotic disturbance variable of the ∈th electric eel individual, is the global average, and x r (t) is the position of the reference individual, and x r =Low+rand×(Up-Low);

[0162] Finally, according to the obtained chaotic disturbance variable, the position of the electric eel individual is updated, and its expression is:

[0163]

[0164] Among them, x ∈ (t) and x ∈′ (t) is the position of two interacting electric eels randomly selected from the current population, and ∈≠∈′; x ∈ (t+1) represents the updated position of the electric eel individual; p1 and p2 are random numbers in (0,1); fit() represents the fitness value; C is the position adjustment factor;

[0165] C=n1×B

[0166] B=[b1,b2,…b dim ,…,b Dim ]

[0167]

[0168]

[0169] Where n1 is a random value generated from the normal distribution N(0,1), representing a random factor used to introduce randomness, B is a vector, b dim is the element of the dimth dimension in vector B, where Dim is the total dimension of vector B; randperm(d) means returning a random permutation in the range from 1 to Dim;

[0170] S8: The electric eel individuals in the population perform resting behavior, update the positions of the electric eel individuals, and select the updated best position. If the updated best position is better than the current best position, the updated best position is used as the current best position, the current iteration number is increased by 1 and returns to S5;

[0171] Before performing the resting behavior, the electric eel individual first establishes a resting area. α represents the scale of the resting area, and α will decrease as the number of iterations increases, where α0 represents the initial scale of the resting area. Since the resting behavior of the electric eel individual is related to the established resting area, the scale of the resting area of ​​the electric eel individual does not change much during the iteration process, so it is likely to miss the global optimal value. Therefore, a nonlinear decreasing weight λ' is introduced in the improved electric eel algorithm to change the scale of the electric eel's resting area, thereby improving the exploration ability during the entire iteration process;

[0172] The method of performing rest behavior based on the nonlinear decreasing weight λ and updating the position of the electric eel individual is:

[0173] x ∈ (t+1)=R′ ∈ (t+1)+n2×(R′ ∈ (t+1)round(rand)×x ∈ (t))

[0174] R′ ∈ (t+1)=Z(t)+α′×|Z(t)-x prey (t)|

[0175] Z(t)=Low+z(t)×(Up-Low)

[0176] α′=λ′×α0×sin(2πrand)

[0177]

[0178] Among them, round(rand) means rounding a random number from 0 to 1, n2 is a randomly generated value from the normal distribution N(0,1), and R′ ∈ (t+1) represents the resting position that the electric eel will obtain in the resting area before performing the resting behavior, α′ is the scale of the current resting area, and x prey (t) represents the current optimal position, α0 represents the initial size of the rest area, and λ′ is a nonlinear decreasing weight, and z(t) is the normalized number; Indicates the random position dimension of an electric eel randomly selected from the current population; Low rand(d) Indicates the lower bound of the currently randomly selected position dimension; Up rand(d) Indicates the upper bound of the current randomly selected position dimension;

[0179] In the early iterations, the resting positions of the electric eels are updated by nonlinear decreasing weights, with larger weights, and the electric eels have stronger global exploration capabilities. This helps the electric eels explore unknown areas and avoid falling into local optimality too early. As the number of iterations increases, the value of λ′ decreases. In the later iterations, the weights become smaller and smaller, and the exploration range of the electric eels becomes smaller and smaller, which is conducive to a meticulous local search to find the best candidate solution. This exploration can improve the convergence speed and accuracy.

[0180] S9: The electric eel individuals in the population perform hunting behavior, update the positions of the electric eel individuals, and select the updated best position. If the updated best position is better than the current best position, the updated best position is used as the current best position, the current iteration number is increased by 1 and returns to S5;

[0181] Similarly, when the electric eel is in hunting behavior, it will establish the size of the hunting area before executing the hunting behavior. β0 represents the initial size of the hunting area, β represents the size of the hunting area, and the size of the hunting area β will make the range of the hunting area smaller over time. However, hunting behavior also involves curling behavior, and curling behavior is affected by the curling factor, which is defined as η. Therefore, the hunting behavior is improved according to the optimization of the electric eel's resting behavior. The method for updating the position of the electric eel individual is:

[0182] x ∈ (t+1)=H′ prey (t+1)+η′×(H′ prey (t+1)-rand(rand)×x ∈ (t))

[0183]

[0184]

[0185] β′=λ′×β0×sin(2πrand)

[0186] Among them, H′ prey (t+1) is the hunting position that the electric eel will obtain in the resting area before executing the hunting behavior, η′ is the curling factor, β′ is the size of the current hunting area; β0 represents the initial size of the hunting area;

[0187] S10: The electric eel individuals in the population perform migration behavior, update the positions of the electric eel individuals, and select the updated best position. If the updated best position is better than the current best position, the updated best position is used as the current best position, the current iteration number is increased by 1 and returns to S5;

[0188] Although adding Levy function to the migration behavior of the electric eel algorithm avoids it from falling into the local optimum during the development stage, its convergence speed and convergence accuracy are still relatively weak. Therefore, the dynamic weight strategy coefficient is introduced into the electric eel algorithm. Its characteristic is that it can be adjusted adaptively according to the characteristics of the optimization problem and the current number of iterations, so as to better balance the global search and local development capabilities of the algorithm, thereby better improving the convergence speed and optimization accuracy of the algorithm. The specific expression is:

[0189]

[0190] ζ4=ζ1-ζ2+ζ3

[0191] Where c is a constant; ζ1, ζ2, ζ3 and ζ4 represent dynamic weight strategy factors;

[0192] After optimization, the migration behavior is performed and the method for updating the position of the electric eel individuals is as follows:

[0193]

[0194]

[0195] Among them, H′ r (t+1) is an arbitrary position in the hunting area, indicating that the electric eel individuals move to the hunting area through migration behavior. represents the Levy flight function, u, v represent randomly generated values ​​from the normal distribution N(0,1), Γ represents the standard Gamma function;

[0196] In order to verify the correctness and effectiveness of this method, Matlab2022b software was used in the simulation scenario, and the experimental parameters were set as follows: in this implementation, the size of the UAV moving space is 100km×150km×3km, the starting point is set to (10km, 90km, 1.1km), and the target point is set to (130km, 10km, 1.3km); the maximum number of iterations T is set to 200, and the threats are shown in Table 1; the path planning results obtained by WOA, NGO, DBO, and EEFO algorithms in the above scenarios are compared to evaluate the feasibility and effectiveness of the IEEFO algorithm.

[0197] Figure 2 The path planning effects and convergence curves of the five algorithms in scenario 1 are shown. Figure 2 and Figure 3 It can be clearly seen that the path obtained by the IEEFO algorithm is smoother and more convincing than that of the other four algorithms. Figure 4 It shows that the convergence results of WOA and NGO algorithms are not ideal. The reason for this phenomenon is that as the number of iterations increases, the diversity of population solutions decreases, resulting in the algorithm being unable to fully explore the unknown area of ​​the entire search space, thus falling into a local optimal solution. In contrast, the effect of the DBO algorithm is better than other algorithms, but there is still room for improvement compared with the IEEFO algorithm. Scenario 2 is set to verify the path planning capabilities of the five algorithms in complex environments. Figure 5 and Figure 6 The three-dimensional path planning comparison of each algorithm in scenario 2 is shown. Figure 7 The path planning results and convergence curves of these algorithms in scenario 2 are shown. It can be observed that the WOA algorithm falls into a local optimal state very early, and the generated path is not smooth enough. This situation may cause higher costs for the drone when performing tasks in engineering problems. The EEFO algorithm did not show good optimization capabilities when facing threat areas. The costs of the remaining algorithms in path planning are much higher than that of the IEEFO algorithm. Only the IEEFO algorithm obtained better path planning results, which further shows that the IEEFO algorithm can better balance the global and local search capabilities, thereby ensuring the improvement of the algorithm's optimization performance and convergence speed. According to Figure 8-10 The path planning results in show that in scenario 3, except for the IEEFO algorithm and the DBO algorithm, the paths generated by other algorithms are tortuous and fail to effectively avoid obstacles, so they fail to obtain more accurate path planning results. In contrast, the IEEFO algorithm shows good performance and can obtain the optimal path in different scenarios.

[0198] Table 1 Threat area parameters

[0199]

[0200]

Claims

1. A three-dimensional path planning method for low-altitude UAV based on improved electric eel algorithm, characterized in that: Firstly, a three-dimensional environment model is built for the UAV's moving space to simulate the threat areas and mountains in the real-life UAV operating environment. Then, the improved electric eel algorithm is used to obtain the optimal path of the UAV in the modeled three-dimensional environment.

2. The three-dimensional path planning method for low-altitude UAV based on the improved electric eel algorithm according to claim 1 is characterized in that: The three-dimensional environment modeling of the drone moving space is specifically as follows: setting the size of the drone moving space, setting the starting point and target point of the drone, and randomly generating a cylindrical threat area in the drone moving space by generating random numbers and using a column function.

3. The three-dimensional path planning method for low-altitude UAV based on the improved electric eel algorithm according to claim 1 is characterized in that: The specific steps of using the improved electric eel algorithm to obtain the optimal path of the drone in the modeled three-dimensional environment include: S1: introducing a good point set to initialize the population and obtain an initial population; the initial population includes a number of electric eel individuals, each of which represents a flight trajectory of a UAV in a three-dimensional environment, each of which includes a number of coordinate points, each of which includes the spatial coordinates (x, y, z) of the UAV and the state information of the UAV; S2: Set the maximum number of iterations T; S3: Set the current number of iterations to 0; S4: Construct a total cost function, calculate the total cost function value of the electric eel individuals in the current population as the fitness value, find the best fitness value BestF and the position of the corresponding electric eel individual as the current best position x prey ; The best fitness value BestF is the minimum fitness value; S5: Determine whether the current number of iterations reaches the set maximum number of iterations. If yes, output the current best fitness value BestF and the current best position x prey , get the optimal path of the UAV, otherwise execute S6; S6: Calculate the energy factor E. If E>1, execute S7. If E>1 is not satisfied, if rand<1 / 3, execute S8. If rand>2 / 3, execute S9. Otherwise, execute S10. Rand is a random number between (0,1). S7: The electric eel individuals in the population perform interactive behaviors, update the positions of the electric eel individuals, and select the updated best position. If the updated best position is better than the current best position, the updated best position is used as the current best position, the current iteration number is increased by 1 and returns to S5; S8: The electric eel individuals in the population perform resting behavior, update the positions of the electric eel individuals, and select the updated best position. If the updated best position is better than the current best position, the updated best position is used as the current best position, the current iteration number is increased by 1 and returns to S5; S9: The electric eel individuals in the population perform hunting behavior, update the positions of the electric eel individuals, and select the updated best position. If the updated best position is better than the current best position, the updated best position is used as the current best position, the current iteration number is increased by 1 and returns to S5; S10: The electric eel individuals in the population perform migration behavior, update the positions of the electric eel individuals, and select the updated best position. If the updated best position is better than the current best position, the updated best position is used as the current best position, the current number of iterations is increased by 1 and returns to S5.

4. The three-dimensional path planning method for low-altitude UAV based on the improved electric eel algorithm according to claim 3 is characterized in that: The specific S1 is: first define the search space G s , which is an s-dimensional unit cube, and the value of each dimension is in [0,1], and then the good point generation formula is used to generate the good point r, and then a good point set including n good points is obtained, and the good points are mapped to the feasible domain where the population is located according to the preset lower bound low of the population and the upper bound up of the population, and n electric eel individuals are obtained, and then the initial population is obtained; The optimal point is: r = (r1, r2, ..., r k ,…,r s ), where r k is the kth dimension of the good point r: r k ={2cos(2πk / p),1≤k≤s} in, p is the smallest prime number satisfying (p-3) / 2≥s; The good point set is expressed as: Among them, P n (l) represents the good point set, l is the number of the good point, n is the number of good points, and {} represents the decimal part; The deviation of the good point set satisfies: φ(n)=C(r,ε)n -1+ε Among them, φ(n) represents the deviation of the good point set, ε represents a positive number; C(r,ε) represents a constant that is only related to r and ε.

5. The three-dimensional path planning method for low-altitude UAV based on the improved electric eel algorithm according to claim 4 is characterized in that: The total cost function described in S4 is specifically: Assume that the set of all threat areas is Q. Each cylindrical threat area is projected onto the horizontal plane as a circle, with its center at Indicated by R. q Indicates that q is the number of the threat area, and the spatial coordinates of the current position of the drone are set to The spatial coordinates of the next position are The Euclidean distance between two locations is expressed as The path from the current position of the drone to the next position is expressed as Among them, x ij Indicates the coordinate of the current position on the x-axis, y ij Indicates the coordinate of the current position on the y-axis, z ij represents the coordinate of the current position on the z-axis, i represents the drone number, and j represents the time step; The cost function of the set Q of all threat areas that the drone crosses during its movement, that is, the threat avoidance cost, is expressed as: Among them, F1(X i ) indicates drone X i The threat avoidance cost, X i represents the i-th drone, m is the number of time steps, q max represents the number of threat areas, Indicates the path The avoidance threat cost function, L represents the cost value, d q represents the distance between the current position of the UAV and the center of the threat area, and S represents the distance between the current position of the UAV and the boundary of the threat area; The calculation formula for the track height cost of a drone position is as follows: Among them, H ij h is the track height cost of a UAV position, Max is the maximum flight altitude, h Min is the safety height, h ij is the flight height of the UAV relative to the ground, σ and λ are weight coefficients; The track height cost H of all the positions of the UAV ij The total track height cost is accumulated: Among them, F2(X i ) is drone X i Total track height cost; A transformation method based on Cartesian coordinates is introduced as a smoothness constraint to optimize the smoothness of the path under the constraint condition. The smoothness constraint is: in, represents the amplitude of the track, γ ij represents the elevation angle, χ ij Indicates the heading angle; x ij-1 Indicates the coordinate of the previous position on the x-axis; y ij-1 Indicates the coordinate of the previous position on the y-axis; z ij-1 Indicates the coordinate of the previous position on the z-axis; Heading angle χ ij The calculation formula is: in, Indicates the path The projection on the horizontal plane, Indicates the path projection on the horizontal plane; in, is the unit vector in the height direction; The pitch angle is the angle between the horizontal plane and the path, and its calculation formula is: Among them, z i,j+2 Indicates that the drone is The coordinate on the z axis, z i,j+1 Indicates that the drone is The coordinate on the z axis when The path smoothing cost is: Among them, F3(X i ) is drone X i Path smoothing cost; β1 and β2 represent the penalty coefficients of heading angle and pitch angle respectively; The final total cost function is expressed as: Among them, F(X i ) indicates drone X i The total cost function, f represents the cost number, μ f Indicates the weight coefficients of different costs; The weight coefficients of different costs are dynamically adjusted by using an adaptive weight adjustment mechanism as follows: Among them, Nor f is the weight coefficient; Among them, F f is the cost of number f, F min is the maximum of the three costs, F min is the minimum of the three costs.

6. The three-dimensional path planning method for low-altitude UAV based on the improved electric eel algorithm according to claim 5 is characterized in that: The S7 is specifically: First, generate a chaotic variable X T , and then use X T Generate two chaotic perturbation variables; Among them, x t represents a random number uniformly distributed in the interval (0,1), t represents the current number of iterations, and x ∈ (t) represents the position of the ∈th electric eel individual in the current population, ∈ is the number of the electric eel individual, is the first chaotic disturbance variable of the ∈th electric eel individual, is the second chaotic disturbance variable of the ∈th electric eel individual, is the global average, and x r (t) is the position of the reference individual, and x r =Low+rand×(Up-Low); Finally, according to the obtained chaotic disturbance variable, the position of the electric eel individual is updated, and its expression is: Among them, x ∈ (t) and x ∈′ (t) is the position of two interacting electric eels randomly selected from the current population, and ∈≠∈′; x ∈ (t+1) represents the updated position of the electric eel individual; p1 and p2 are random numbers in (0,1); fit() represents the fitness value; C is the position adjustment factor; C=n1×B B=[b1,b2,…b dim ,…,b Dim ] Where n1 is a randomly generated value from the normal distribution N(0,1), B is a vector, and b dim is the element of the dimth dimension in vector B, where Dim is the total dimension of vector B; randperm(d) means returning a random permutation in the range from 1 to Dim.

7. The low-altitude UAV three-dimensional path planning method based on the improved electric eel algorithm according to claim 6 is characterized in that: The S8 is specifically: Before performing the resting behavior, the electric eel individual first establishes a resting area and performs the resting behavior based on the nonlinear decreasing weight λ. The method for updating the position of the electric eel individual is: x ∈ (t+1)=R′ ∈ (t+1)+n2×(R′ ∈ (t+1)round(round)×x ∈ (t)) R′ ∈ (t+1)=Z(t)+α′×|Z(t)-x prey (t)| Z(t)=Low+z(t)×(up-Low) α′=λ′×α0×sin(2πrand) Among them, round(rand) means rounding a random number from 0 to 1, n2 is a randomly generated value from the normal distribution N(0,1), and R′ ∈ (t+1) represents the resting position that the electric eel will obtain in the resting area before performing the resting behavior, α′ is the scale of the current resting area, xprey(t) represents the current optimal position, α0 represents the initial scale of the resting area, and λ′ is a nonlinear decreasing weight, and z(t) is the normalized number; Indicates the random position dimension of an electric eel randomly selected from the current population; Low rand(d) Indicates the lower bound of the currently randomly selected position dimension; Up rand(d) Indicates the upper bound of the dimension of the currently randomly selected position.

8. The three-dimensional path planning method for low-altitude UAV based on the improved electric eel algorithm according to claim 7 is characterized in that: The S9 is specifically: The electric eel will establish a hunting area before performing hunting behavior. The method to update the location of the electric eel individual is: x ∈ (t+1)=H′ prey (t+1)+η′×(H′prey(t+1)-round(rand)×x ∈ (t)) β′=λ′×β0×sin(2πrand) Among them, H′ prey (t+1) is the hunting position that the electric eel will obtain in the rest area before executing the hunting behavior, η′ is the curling factor, β′ is the size of the current hunting area; β0 represents the initial size of the hunting area.

9. The three-dimensional path planning method for low-altitude UAV based on the improved electric eel algorithm according to claim 8 is characterized in that: The S10 is specifically: The dynamic weight strategy coefficient is introduced into the electric eel algorithm. The specific expression is: ζ4=ζ1-ζ2+ζ3 Where c is a constant; ζ1, ζ2, ζ3 and ζ4 represent dynamic weight strategy factors; After optimization, the migration behavior is performed and the method for updating the position of the electric eel individuals is as follows: Among them, H′ r (t+1) is an arbitrary position in the hunting area, indicating that the electric eel individuals move to the hunting area through migration behavior. represents the Levy flight function, u, v represent randomly generated values ​​from the normal distribution N(0,1), Γ represents the standard Gamma function.

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