A three-dimensional path planning method for unmanned aerial vehicles based on a multi-gene optimized chimpanzee algorithm

Abstract

The present invention belongs to the technical field of three-dimensional UAV path planning, and in particular, is a three-dimensional UAV path planning method based on a multi-gene optimized chimpanzee algorithm, comprising the following steps: S1: initializing the information of the UAV and the target, obtaining the position and number of the initial UAVs, and the target point information of the UAVs before the allocation begins, and detecting the position of the target. The present invention optimizes the traditional chimpanzee search algorithm, takes minimizing the cost of UAV path planning as the optimization goal, and proposes a UAV path planning method based on an improved chimpanzee algorithm. The improved chimpanzee algorithm has a fast optimization speed, strong capabilities, and is not prone to local convergence, and can cope well with high-dimensional complex problems. By improving the chimpanzee algorithm, the cost of multi-UAV path planning is reduced, and an ideal path planning solution can be quickly found.

Description

Technical Field

[0001] The present invention relates to the technical field of three-dimensional unmanned aerial vehicle (UAV) path planning, and in particular to a three-dimensional UAV path planning method based on a polygene optimized chimpanzee algorithm. Background Art

[0002] Solar-powered drones, as aircraft powered by solar radiation, effectively utilize solar energy by converting solar energy into electricity through solar panels. These drones can adjust their flight altitude based on demand through a control system. Due to their flexible flight modes, solar-powered drones are increasingly being used in a variety of fields, including meteorological reconnaissance, search and rescue assistance, fire detection, and traffic control. Therefore, accurately planning the flight path of drones is crucial for practical operation. The essence of path planning lies in finding the optimal route from a starting point to a destination within diverse mission constraints. However, in complex environments, airspace restrictions often require drones to fly at low altitudes, and existing research has largely been limited to smaller-scale or simpler scenarios. Therefore, developing path planning methods applicable to large-scale and complex environments is crucial. In these complex scenarios, wind not only serves as a potential energy source, helping to increase drone flight range and speed and shorten arrival time, but its spatially varying uncertainty complicates effective path planning. In particular, in uniform and stable wind environments, variability in wind speed further complicates planning. The significant impact of wind on the aircraft and the vast state space make path planning a computationally intensive challenge. This study not only focuses on minimizing flight costs but also explores strategies that can be applied to other optimization criteria. In recent years, path planning has garnered widespread attention from researchers worldwide, with increasing exploration activity in related fields. Research has shown that both optimization and innovation in path planning are essential for challenging environments and complex mission requirements. By continuously improving and adapting new solution strategies and technologies, the accuracy and efficiency of path planning can be significantly improved. This is particularly true in multi-UAV systems, where the search for more stable and efficient path planning methods is crucial.

[0003] In order to improve the accuracy and efficiency of path planning and reduce costs, and to solve the problem of poor stability of the solution algorithm in the process of multi-UAV path planning, we proposed a UAV three-dimensional path planning method based on the polygene optimized chimpanzee algorithm to solve the above problems. Summary of the Invention

[0004] (1) Technical problems solved

[0005] In view of the shortcomings of the existing technology, the present invention provides a three-dimensional path planning method for unmanned aerial vehicles based on a multi-gene optimized chimpanzee algorithm, which solves the problems raised in the above background technology.

[0006] (2) Technical solution

[0007] In order to achieve the above-mentioned purpose, the present invention specifically adopts the following technical solutions:

[0008] A three-dimensional path planning method for unmanned aerial vehicles based on a polygene-optimized chimpanzee algorithm comprises the following steps:

[0009] S1: Initialize the information of the drone and the target. Before the allocation begins, obtain the initial drone's position, number, and target point information, and detect the target's position.

[0010] S2: Consider the impact of complex uniform wind fields on UAV flight speed in path planning scenarios; conduct a detailed analysis of the constraints affecting multiple UAVs in complex wind fields, and construct a multi-UAV path planning optimization function;

[0011] S3: Randomly generate multiple groups of initial UAV path planning solutions based on multi-gene segment encoding;

[0012] S4: Calculate the path planning cost of each solution based on the fitness function;

[0013] S5: When t=1, the initial optimal path planning scheme is calculated according to the improved IMG-CHOA algorithm, and the position of the individual with the minimum path planning cost is determined as the optimal position

[0014] S6: Generate an iterative path planning solution based on the improved IMG-CHOA algorithm to find the optimal path planning solution after the information changes;

[0015] S7: Perform reverse learning and Gauss-Cauchy mutation on the global optimal position, calculate the minimum path planning cost of the optimal solution after the updated position, compare it with the original position, and retain the better one; otherwise, discard the new path planning solution;

[0016] S8: Determine whether the current number of iterations reaches the preset number of iterations. If so, output the global optimal solution, that is, the minimum path planning cost and the corresponding path planning solution; otherwise, proceed to the next iteration.

[0017] Furthermore, in S1, it is assumed that U={U i ,i=1,2,…,N U} represents the set of multiple UAVs participating in the mission T = {T i ,i=1,2,…,N U} is the set of target points that these drones need to reach, and P = {P i ,i=1,2,…,N P} is the set of existing enemy threats. For a single UAV, when it moves from the starting position (starting point S i ) to the destination (target point M i ) during the flight, it will pass through a series of waypoints in sequence to form a complete flight path. These track segments are connected in series according to the established flight rules to form a complete track from the starting point to the destination point. Each track node (in W i-k (k=1,2,…,n-1) marks) are all key positions of the UAV in the mission execution, which requires precise planning to ensure safety and efficiency.

[0018] Furthermore, the construction of the multi-UAV path planning optimization function in S2 includes the following sub-steps:

[0019] Sub-step S2.1: Coordination constraints are a set of regulations that ensure that all members of the multi-UAV formation can complete the mission smoothly and in a coordinated manner while ensuring that individual UAVs comply with their individual path constraints. This constraint involves adjusting the spatiotemporal relationships between UAVs in the formation to avoid collisions, ensure mission efficiency, and optimize the flight path of the entire formation.

[0020] If the drone's flight altitude does not meet the specified minimum or maximum limits, its path planning can be adjusted by setting a penalty function to ensure that the drone maintains an appropriate flight altitude. The penalty functions are:

[0021]

[0022] Among them H max The maximum flight altitude allowed is H min To allow the minimum flight altitude, Q i is the scale factor;

[0023] Spatial coordination constraints, also known as anti-collision constraints, are designed to ensure that multiple drones operating together maintain a distance greater than a preset minimum safe flight interval. This constraint ensures that each drone can safely maintain sufficient spatial separation to avoid collisions when performing a mission. Specifically:

[0024] d i-j ≥d m (2)

[0025] Among them, marked as d i-j The variable represents the shortest distance between the track nodes of the i-th UAV and its subsequent j UAVs in the flight sequence; and d m It specifically refers to the minimum safe flight interval that any two drones must maintain;

[0026] Set the designated time for the drone to arrive at the destination as t uThe time synchronization of the UAVs during mission execution is ensured through time coordination constraints. Based on the maximum and minimum speed limits of the UAVs and the actual flight path length, the estimated time interval for the UAVs to reach the target location can be calculated. In this way, the actual arrival time of the UAVs needs to meet the following range:

[0027]

[0028] In this formula, the symbol v max With v min They represent the maximum and minimum flight speeds allowed, and L i It accurately reflects the total length of the actual navigation path of the i-th UAV;

[0029] In addition, the flight distance of the drone is limited by its energy reserves and flight time allocation. It has a maximum range parameter, which is set to L. Therefore, the distance of each flight segment must meet the following conditions: the length of each flight segment does not exceed L. This constraint ensures that the drone can effectively complete the planned route under limited energy supply. The distance of each flight segment should meet the following conditions:

[0030] ∑l i ≤L max (4)

[0031] According to the above conditions, the number of nodes in the drone's path planning is limited by its performance and cannot exceed a specific range. In addition, the cost of path planning also includes energy consumption. If the energy cost of a path is too high and exceeds the acceptable range, then this path will be considered infeasible. This setting ensures that the drone can complete its mission effectively within its energy limit.

[0032] The multi-UAV path planning evaluation function extends the basic path planning function to include the coordinated adjustment of multiple UAVs in time and space. In addition, it also includes consideration of the threat costs that may be encountered in specific environments such as uniform wind fields. Therefore, the evaluation formula for multi-UAV path planning integrates these key factors and is as follows:

[0033]

[0034] The f in the formula L-i , f H-i , f T-i , f m-i , f Z-i , f W-i represents the energy consumption of the i-th UAV under the path planning scheme, including flight altitude, time consumption, potential threats, collision risks, and additional threat costs brought by the wind field environment; parameter γ iThese correspond to the trade-off coefficients of the above-mentioned various costs, and G is the total number of UAVs participating in the mission;

[0035] Through the analysis of time coordination constraints, the time cost can be expressed as follows:

[0036]

[0037] Sub-step S2.2: Assuming the wind field the drone enters is uniform and stable, it is sufficient to use a kinematic model to describe its motion. The kinematics of steady-state straight-line flight include the effects of thrust. However, this is subsequently extended to stable turning flight. Specifically, the kinematics of the drone are described as follows:

[0038]

[0039] where v w is the air speed, ε is the path angle when the aircraft is in a stable position entering the wind field, and α is the heading angle of the UAV. Equating the forces parallel and perpendicular to the flight path, we obtain the following equation:

[0040]

[0041] Where β is the sideslip angle of the UAV entering the wind field, θ is the roll angle of the aircraft, and γ is the angle of incidence of the thrust vector with the flight path (note that if the thrust axis is aligned with the x-axis of the aircraft fuselage, then γ = 0, the angle of attack of the aircraft). Assuming γ = 0 (that is, the thrust is aligned with the track angle, so that the thrust perpendicular to the flight path can be ignored), the equation is as follows:

[0042]

[0043] The lift coefficient is defined as: According to the above formula:

[0044]

[0045] The drag coefficient can be expressed as a polynomial function of the lift coefficient. This relationship reflects the dependence between lift and drag and provides an important basis for the analysis and design of flight dynamics.

[0046]

[0047] And through the formula According to the above formula, the aircraft path angle is

[0048] By combining the drag coefficient and the horizontal component of the vertical force on the flight path, the turn rate can be calculated. Based on these factors, the aircraft's kinematic equations are adjusted accordingly. This approach effectively combines the dynamics of drag with the dynamics of turning, providing a more accurate model for flight control and performance analysis. The aircraft's kinematic equations become:

[0049]

[0050] Assume that V 0X 、V 0Y 、V 0Z is the velocity component of the UAV when it enters the wind field. The velocity change of the UAV entering the wind field is:

[0051]

[0052] Furthermore, the S3 effectively reduces the computational complexity of the path planning problem by adopting a multi-gene segment encoding method. This encoding method uses different gene segments to represent the paths of multiple drones, reducing the search computation and improving the optimization efficiency. In this model, if the formation consists of G drones, each gene segment will contain G gene segments. This strategy selects the gene segment with the lowest cost in each iteration of the algorithm, optimizes the processing speed of the algorithm by accumulating and storing track segments, and ensures the quality of understanding. In the gene segment encoding, not only the three-dimensional spatial positioning information of the track point is included, but also a state identifier p is specially added. i The key role of this identifier is to comprehensively record the various environmental constraints and state changes encountered by the drone during the execution of the track segment, especially the special constraints in complex operation scenarios. This coding method helps to systematically plan and optimize the path of multiple drone formations and ensure the efficiency and safety of coordinated flight.

[0053] Furthermore, the objective function of the model is used as the fitness function in S4:

[0054]

[0055] Furthermore, the improved IMG-CHOA algorithm in S5 includes the following sub-steps:

[0056] Sub-step S5.1: Develop a novel update strategy for the attacker, surround, and driver steps in the Chimpanzee algorithm. This strategy can achieve adaptive and nonlinear adjustment of the parameter w based on the algorithm's iterative process t, that is, the number of iterations, in order to achieve better optimization results. To prevent the algorithm from falling into a local optimal solution, iteration thresholds t1 and t2 are introduced. To ensure strong global exploration efficiency in the initial stage of the algorithm, the inertia weight needs to be maintained at a high level. For this purpose, the cosine function is selected as the strategy model for the dynamic adjustment of the inertia weight, and the weight value is finely controlled through nonlinear changes. Its specific mathematical expression is as follows:

[0057] In the above expression, w max Represent the upper limit of inertia weight, w min Symbolizes its lower limit, T max Indicates the maximum number of algorithm iterations. In addition, a quadratic polynomial function is designed. When t∈(t1, t2) meets the conditions, by increasing the value of w, the algorithm's global search potential can be significantly enhanced, effectively preventing it from converging to a suboptimal solution prematurely, ensuring the comprehensiveness and effectiveness of the search process. w(t)=2A1t 2 +A2t+2A3, where A is a constant and the w(t) function passes through the point (t1, w(t1)), ((t1+t2) / 2, w max ),(t2,w(t1)), so we can get the values ​​of A1, A2, and A3 respectively:

[0058]

[0059] The quadratic function is:

[0060]

[0061] In this expression, the inertia weight w(t1) is the value at a specific time point t1 and is calculated according to formula (15). The parameters t1 and t2 can be determined by human fine-tuning according to the specific instance. In order to prevent the algorithm from locking into the local minimum too early, we set the values ​​of t1 and t2 to 3·T respectively. max / 10 and 5·T max / 10, so for this situation, formula (19) is changed to:

[0062]

[0063] In summary, the adaptive inertia weight adjustment strategy with the addition of hyperbolic tangent function is:

[0064] The update formula for attackers, besiegers, and expellers becomes:

[0065] X1=w·X a -A1·|C1·X a -m1·X| (22)

[0066] X2=w·X b -A2·|C2·X b -m2·X| (23)

[0067] X3=w·X c -A3·|C3·X c -m3·X| (24)

[0068] Where: X a 、X b 、X c Represent the position vectors of attacker, besieger and expeller respectively, A is a random vector; m is the chaotic mapping vector, C is a random number between [0, 2];

[0069] Sub-step S5.2: To prevent the algorithm from falling into local optimality, the chaser search step in the chimpanzee algorithm is optimized, random particles are selected, and the particle positions are selected by applying fusion refraction and symbiotic mutualism. The strategy based on convex lens imaging can be obtained from formula (25):

[0070]

[0071] In the symbiotic search algorithm, the mutual benefit operation is one of the components of the symbiotic search algorithm. j is a randomly selected individual in the population, represented by X i and X j , mutually beneficial operations produce new individuals:

[0072]

[0073] Here, the chimpanzee chaser step is integrated into the refraction reverse learning symbiotic algorithm. According to the reverse position of the optimal position in the refraction reverse learning, the mutually beneficial operation in the symbiotic algorithm is integrated and the individuals are updated:

[0074]

[0075] The particle update formula of the Chimpanzee algorithm is:

[0076]

[0077] Furthermore, in S7, in order to enable individuals to better find the optimal solution, a reverse learning strategy is incorporated into the algorithm. The mathematical representation is as follows: In order to enable individuals to more efficiently approach the optimal solution, an innovative measure is taken to embed the reverse learning strategy into the chimpanzee social optimization algorithm. Its mathematical model can be expressed as:

[0078]

[0079]

[0080] X′ best (t) represents the inverse solution corresponding to the current optimal solution at the tth generation. Variables ub and lb respectively represent the upper and lower bounds of the solution space, while r is a random number matrix that follows the standard uniform distribution rule in the (0,1) interval. Parameter b1 is assigned the role of information exchange regulation factor:

[0081]

[0082] The Cauchy-Gaussian mutation mechanism is proposed, which can make good use of the advantages of the two distributions. The Cauchy mutation mechanism is used in the early stage of the algorithm iteration, and the Gaussian mutation mechanism is used in the later stage of the algorithm iteration. It can take into account the different mutation range requirements of different search stages of the algorithm. The mathematical definition of the Cauchy-Gaussian mutation mechanism is shown as follows:

[0083]

[0084] Indicates the position of the optimal individual after mutation; Cauchy (x0, γ) and Gauss (μ, σ 2 ) are two random variables that follow the Cauchy distribution and Gaussian distribution. To significantly enhance the optimization performance of the algorithm, a flexible dynamic decision-making mechanism is adopted to innovate target positioning. That is, under the control of the preset probability, the reverse learning strategy and the Cauchy mutation operator perturbation mechanism are periodically switched to dynamically optimize the target position. Specifically, the target position update strategy depends on the selection probability P. s The quantitative expression of this probability parameter follows the following formula:

[0085]

[0086] In the above expression, Σ is used as the adjustment factor, and its setting value is 0.05. The specific selection process is as follows: When the random number rand is less than P s When , the algorithm will enable the reverse learning mechanism to update the position; otherwise, if rand is greater than or equal to P s, then the Cauchy-Gaussian mixture mutation perturbation strategy is selected to update the target position. After the position undergoes perturbation mutation, the greedy criterion is further introduced. By comparing the fitness evaluation of the new and old positions, it is determined whether it is necessary to perform a position update. The implementation method of the greedy criterion follows the following formula:

[0087]

[0088] (3) Beneficial effects

[0089] Compared with the existing technology, the present invention provides a three-dimensional path planning method for UAV based on the multi-gene optimized chimpanzee algorithm, which has the following beneficial effects:

[0090] This paper proposes a UAV path planning method based on an improved Chimpanzee algorithm, optimizing the traditional Chimpanzee search algorithm with the goal of minimizing the cost of UAV path planning. The improved Chimpanzee algorithm offers fast optimization speed, robustness, and a high resistance to local convergence, making it well suited for complex, high-dimensional problems. By using the improved Chimpanzee algorithm, the cost of multi-UAV path planning can be reduced, enabling rapid identification of optimal path planning solutions. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] Figure 1 This is a flow chart of the UAV path planning algorithm of the present invention;

[0092] Figure 2 This is the coding map of the multi-gene segment of the present invention;

[0093] Figure 3 This is the UAV path planning diagram of the GWO algorithm of the present invention;

[0094] Figure 4 This is the drone path planning diagram of the CHOA algorithm of the present invention;

[0095] Figure 5 The UAV path planning diagram of the MCHOA algorithm of the present invention;

[0096] Figure 6 This is the UAV path planning diagram of the IMG-CHOA algorithm of the present invention;

[0097] Figure 7 This is a comparison chart of performance indicators of different algorithms of the present invention;

[0098] Figure 8 Comparison of energy cost and time cost of drones using different algorithms in this invention

[0099] Figure 9 is the fitness difference of the last 60 iterations of the present invention;

[0100] Figure 10 This is a force model diagram of the UAV wind field of the present invention. DETAILED DESCRIPTION

[0101] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0102] Example

[0103] like Figure 1-10 As shown, an embodiment of the present invention proposes a three-dimensional path planning method for a UAV based on a multi-gene optimized chimpanzee algorithm, comprising the following steps:

[0104] S1: Initialize the information of the drone and the target. Before the allocation begins, obtain the initial drone's position, number, and target point information, and detect the target's position.

[0105] S2: Consider the impact of complex uniform wind fields on UAV flight speed in path planning scenarios; conduct a detailed analysis of the constraints affecting multiple UAVs in complex wind fields, and construct a multi-UAV path planning optimization function;

[0106] S3: Randomly generate multiple groups of initial UAV path planning solutions based on multi-gene segment encoding;

[0107] S4: Calculate the path planning cost of each solution based on the fitness function;

[0108] S5: When t=1, the initial optimal path planning scheme is calculated according to the improved IMG-CHOA algorithm, and the position of the individual with the minimum path planning cost is determined as the optimal position

[0109] S6: Generate an iterative path planning solution based on the improved IMG-CHOA algorithm to find the optimal path planning solution after the information changes;

[0110] S7: Perform reverse learning and Gauss-Cauchy mutation on the global optimal position, calculate the minimum path planning cost of the optimal solution after the updated position, compare it with the original position, and retain the better one; otherwise, discard the new path planning solution;

[0111] S8: Determine whether the current number of iterations reaches the preset number of iterations. If so, output the global optimal solution, that is, the minimum path planning cost and the corresponding path planning solution; otherwise, proceed to the next iteration.

[0112] In this embodiment, it is assumed in S1 that U={Ui ,i=1,2,…,N U} represents the set of multiple UAVs participating in the mission T = {T i ,i=1,2,…,N U} is the set of target points that these drones need to reach, and P = {P i ,i=1,2,…,N P} is the set of existing enemy threats. For a single UAV, when it moves from the starting position (starting point S i ) to the destination (target point M i ) during its flight, it will successively pass through a series of waypoints to form a complete flight path. These track segments are connected in series according to the established flight rules to form a complete track from the starting point to the destination point. Each track node (in W i-k (k=1,2,…,n-1) marks) are all key positions of the UAV in the mission execution, which requires precise planning to ensure safety and efficiency.

[0113] In this embodiment, the construction of the multi-UAV path planning optimization function in S2 includes the following sub-steps:

[0114] Sub-step S2.1: Coordination constraints are a set of regulations that ensure that all members of the multi-UAV formation can complete the mission smoothly and in a coordinated manner while ensuring that individual UAVs comply with their individual path constraints. This constraint involves adjusting the spatiotemporal relationships between UAVs in the formation to avoid collisions, ensure mission efficiency, and optimize the flight path of the entire formation.

[0115] If the drone's flight altitude does not meet the specified minimum or maximum limits, its path planning can be adjusted by setting a penalty function to ensure that the drone maintains an appropriate flight altitude. The penalty functions are:

[0116]

[0117] Among them H max The maximum flight altitude allowed is H min To allow the minimum flight altitude, Q i is the scale factor;

[0118] Spatial coordination constraints, also known as anti-collision constraints, are designed to ensure that multiple drones operating together maintain a distance greater than a preset minimum safe flight interval. This constraint ensures that each drone can safely maintain sufficient spatial separation to avoid collisions when performing a mission. Specifically:

[0119] d i-j ≥d m (2)

[0120] Among them, marked as d i-j The variable represents the shortest distance between the track nodes of the i-th UAV and its subsequent j UAVs in the flight sequence; and d m It specifically refers to the minimum safe flight interval that any two drones must maintain;

[0121] Set the designated time for the drone to arrive at the destination as t u The time synchronization of the UAVs during mission execution is ensured by time coordination constraints. Based on the maximum and minimum speed limits of the UAVs and the actual flight path length, the estimated time interval for the UAVs to reach the target location can be calculated. In this way, the actual arrival time of the UAVs needs to meet the following range:

[0122]

[0123] In this formula, the symbol v max With v min They represent the maximum and minimum flight speeds allowed, and L i It accurately reflects the total length of the actual navigation path of the i-th UAV;

[0124] In addition, the flight distance of the drone is limited by its energy reserves and flight time allocation. It has a maximum range parameter, which is set to L. Therefore, the distance of each flight segment must meet the following conditions: the length of each flight segment does not exceed L. This constraint ensures that the drone can effectively complete the planned route under limited energy supply. The distance of each flight segment should meet the following conditions:

[0125] ∑l i ≤L max (4)

[0126] According to the above conditions, the number of nodes in the drone's path planning is limited by its performance and cannot exceed a specific range. In addition, the cost of path planning also includes energy consumption. If the energy cost of a path is too high and exceeds the acceptable range, then this path will be considered infeasible. This setting ensures that the drone can complete its mission effectively within its energy limit.

[0127] The multi-UAV path planning evaluation function extends the basic path planning function to include the coordinated adjustment of multiple UAVs in time and space. In addition, it also includes consideration of the threat costs that may be encountered in specific environments such as uniform wind fields. Therefore, the evaluation formula for multi-UAV path planning integrates these key factors, as follows:

[0128]

[0129] The f in the formula L-i , f H-i , fT-i , f m-i , f Z-i , f W-i represents the energy consumption of the i-th UAV under the path planning scheme, including flight altitude, time consumption, potential threats, collision risks, and additional threat costs brought by the wind field environment; parameter γ i These correspond to the trade-off coefficients of the above-mentioned various costs, and G is the total number of UAVs participating in the mission;

[0130] Through the analysis of time coordination constraints, the time cost can be expressed as follows:

[0131]

[0132] Sub-step S2.2: Assuming the wind field the drone enters is uniform and stable, it is sufficient to use a kinematic model to describe its motion. The kinematics of steady-state straight-line flight include the effects of thrust. However, this is subsequently extended to stable turning flight. Specifically, the kinematics of the drone are described as follows:

[0133]

[0134] where v w is the air speed, ε is the path angle when the aircraft is in a stable position entering the wind field, and α is the heading angle of the UAV. Equating the forces parallel and perpendicular to the flight path, we obtain the following equation:

[0135]

[0136] Where β is the sideslip angle of the UAV entering the wind field, θ is the roll angle of the aircraft, and γ is the angle of incidence of the thrust vector with the flight path (note that if the thrust axis is aligned with the x-axis of the aircraft fuselage, then γ = 0, the angle of attack of the aircraft). Assuming γ = 0 (that is, the thrust is aligned with the track angle, so that the thrust perpendicular to the flight path can be ignored), the equation is as follows:

[0137]

[0138] The lift coefficient is defined as: According to the above formula:

[0139]

[0140] The drag coefficient can be expressed as a polynomial function of the lift coefficient. This relationship reflects the dependence between lift and drag and provides an important basis for the analysis and design of flight dynamics.

[0141]

[0142] And through the formula According to the above formula, the aircraft path angle is

[0143] By combining the drag coefficient and the horizontal component of the vertical force on the flight path, the turn rate can be calculated. Based on these factors, the aircraft's kinematic equations are adjusted accordingly. This approach effectively combines the dynamics of drag with the dynamics of turning, providing a more accurate model for flight control and performance analysis. The aircraft's kinematic equations become:

[0144]

[0145] Assume that V 0X 、V 0Y 、V 0Z is the velocity component of the UAV when it enters the wind field. The velocity change of the UAV when entering the wind field is:

[0146]

[0147] In this embodiment, the S3 adopts a multi-gene segment encoding method to effectively reduce the computational complexity of the path planning problem. This encoding method uses different gene segments to represent the paths of multiple drones, reducing the search operation amount and improving the optimization efficiency. In this model, if the formation consists of G drones, each gene segment will contain G gene segments. This strategy selects the gene segment with the lowest cost in each iteration of the algorithm, optimizes the processing speed of the algorithm by accumulating and storing track segments, and ensures the quality of understanding. In the gene segment encoding, not only the three-dimensional spatial positioning information of the track point is included, but also a state identifier p is specially added. i The key role of this identifier is to comprehensively record the various environmental constraints and state changes encountered by the drone during the execution of the track segment, especially the special constraints in complex operation scenarios. This coding method helps to systematically plan and optimize the path of multiple drone formations and ensure the efficiency and safety of coordinated flight.

[0148] In this embodiment, the objective function of the model is used as the fitness function in S4:

[0149]

[0150] In this embodiment, the improved IMG-CHOA algorithm in S5 includes the following sub-steps:

[0151] Sub-step S5.1: Develop a novel update strategy for the attacker, surround, and driver steps in the Chimpanzee algorithm. This strategy can achieve adaptive and nonlinear adjustment of the parameter w based on the algorithm's iterative process t, that is, the number of iterations, in order to achieve better optimization results. To prevent the algorithm from falling into a local optimal solution, iteration thresholds t1 and t2 are introduced. To ensure strong global exploration efficiency in the initial stage of the algorithm, the inertia weight needs to be maintained at a high level. For this purpose, the cosine function is selected as the strategy model for the dynamic adjustment of the inertia weight, and the weight value is finely controlled through nonlinear changes. Its specific mathematical expression is as follows:

[0152] In the above expression, w max Represent the upper limit of inertia weight, w min Symbolizes its lower limit, T max Indicates the maximum number of algorithm iterations. In addition, a quadratic polynomial function is designed. When t∈(t1, t2) meets the conditions, by increasing the value of w, the algorithm's global search potential can be significantly enhanced, effectively preventing it from converging to a suboptimal solution prematurely, ensuring the comprehensiveness and effectiveness of the search process. w(t)=2A1t 2 +A2t+2A3, where A is a constant and the w(t) function passes through the point (t1, w(t1)), ((t1+t2) / 2, w max ),(t2,w(t1)), so we can get the values ​​of A1, A2, and A3 respectively:

[0153]

[0154] The quadratic function is:

[0155]

[0156] In this expression, the inertia weight w(t1) is the value at a specific time point t1 and is calculated according to formula (15). The parameters t1 and t2 allow their values ​​to be determined according to human fine-tuning of specific instances. Based on the in-depth analysis of a wide range of experimental data sets, the studied method achieves a stable convergence state when the number of iterations exceeds 240. In order to prevent the algorithm from locking into a local minimum prematurely, we set the values ​​of t1 and t2 to 3·T respectively. max / 10 and 5·T max / 10, so for this situation, formula (19) is changed to:

[0157]

[0158] In summary, the adaptive inertia weight adjustment strategy with the addition of hyperbolic tangent function is:

[0159] The update formula for attackers, besiegers, and expellers becomes:

[0160] X1=w·X a -A1·|C1·X a -m1·X| (22)

[0161] X2=w·X b -A2·|C2·X b -m2·X| (23)

[0162] X3=w·X c -A3·|C3·X c -m3·X| (24)

[0163] Where: X a 、X b 、X c Represent the position vectors of attacker, besieger and expeller respectively, A is a random vector; m is the chaotic mapping vector, C is a random number between [0, 2];

[0164] Sub-step S5.2: To prevent the algorithm from falling into local optimality, the chaser search step in the chimpanzee algorithm is optimized, random particles are selected, and the particle positions are selected by applying fusion refraction and symbiotic mutualism. The strategy based on convex lens imaging can be obtained from formula (25):

[0165]

[0166] In the symbiotic search algorithm, the mutual benefit operation is one of the components of the symbiotic search algorithm. j is a randomly selected individual in the population, represented by X i and X j , mutually beneficial operations produce new individuals:

[0167]

[0168] Here, the chimpanzee chaser step is integrated into the refraction reverse learning symbiotic algorithm. According to the reverse position of the optimal position in the refraction reverse learning, the mutually beneficial operation in the symbiotic algorithm is integrated and the individuals are updated:

[0169]

[0170] The particle update formula of the Chimpanzee algorithm is:

[0171]

[0172] In this embodiment, in S7, a reverse learning strategy is incorporated into the algorithm to enable individuals to better find the optimal solution. The mathematical representation is as follows: In order to enable individuals to more efficiently approach the optimal solution, an innovative measure is taken to embed the reverse learning strategy into the chimpanzee social optimization algorithm. Its mathematical model can be expressed as follows:

[0173]

[0174]

[0175] X′ best (t) represents the inverse solution corresponding to the current optimal solution at the tth generation. Variables ub and lb respectively represent the upper and lower bounds of the solution space, while r is a random number matrix that follows the standard uniform distribution rule in the (0,1) interval. Parameter b1 is assigned the role of information exchange regulation factor:

[0176]

[0177] This study proposes a Cauchy-Gaussian mutation mechanism that can make good use of the advantages of the two distributions. The Cauchy mutation mechanism is used in the early stage of the algorithm iteration, and the Gaussian mutation mechanism is used in the later stage of the algorithm iteration. It can take into account the different mutation range requirements of different search stages of the algorithm. The mathematical definition of the Cauchy-Gaussian mutation mechanism is shown as follows:

[0178]

[0179] Indicates the position of the optimal individual after mutation; Cauchy (x0, γ) and Gauss (μ, σ 2 ) are two random variables that follow the Cauchy distribution and Gaussian distribution. To significantly enhance the optimization performance of the algorithm, a flexible dynamic decision-making mechanism is adopted to innovate target positioning. That is, under the control of the preset probability, the reverse learning strategy and the Cauchy mutation operator perturbation mechanism are periodically switched to dynamically optimize the target position. Specifically, the target position update strategy depends on the selection probability P. s The quantitative expression of this probability parameter follows the following formula:

[0180]

[0181] In the above expression, Σ is used as the adjustment factor, and its recommended setting value is 0.05. The specific selection process is as follows: When the random number rand is less than P s When , the algorithm will enable the reverse learning mechanism to update the position; otherwise, if rand is greater than or equal to P s, then the Cauchy-Gaussian mixture mutation perturbation strategy is selected to update the target position. After the position undergoes perturbation mutation, the greedy criterion is further introduced. By comparing the fitness evaluation of the new and old positions, it is determined whether it is necessary to perform a position update. The implementation method of the greedy criterion follows the following formula:

[0182]

[0183] In the simulation experiment, an air formation consisting of four drones corresponds to four designated target objects distributed on the ground. This experiment stipulates that the maximum total path length of the drone shall not exceed 1.5 times the straight-line distance from the starting point to the target point, and the minimum path segment length is set to 2 kilometers. The maximum flight altitude of the drone is 100 kilometers, the maximum turning angle is 60 degrees, and the maximum climb / dive angle is also 60 degrees. The scheduled target arrival time of the drone is set to 6900 seconds. In addition, the population size of the algorithm is set to 60, and the number of iterations is 300. For the IMG-CHOA algorithm used in this study, considering that path planning requires the integration of six evaluation indicators, the number of cost indicators for storing gene segments is set to 6. As for the wind field threat area, clockwise and counterclockwise wind fields are used in the experiment to interfere with the flight of the drone.

[0184] Figures 3 to 6 This image shows the three-dimensional search process of four drones using different path planning algorithms in a complex wind environment. In the image, blue areas represent minefield threat zones, while black areas indicate areas of strong wind. Image analysis shows that the four drones guided by the improved algorithms IMG-CHOA and MCHOA successfully avoided the minefield threat zones and successfully reached their destination. In particular, the IMG-CHOA algorithm guided the drones to choose a path through a clockwise wind field. In contrast, the four drones controlled by the basic algorithms CHOA and GWO failed to effectively avoid the minefield threat zones.

[0185] Figure 7 The average performance indicators of different algorithms in the scene are compared, and it can be seen that the algorithm IMG-CHOA has the advantage in multi-UAV path planning. Figure 8The energy and time costs of path planning by different algorithms in a complex wind field environment are demonstrated. In particular, the IMG-CHOA algorithm selects a path that passes through a stable and unchanging clockwise wind field. Analysis shows that the path selection of the IMG-CHOA algorithm optimizes both the flight speed and arrival time of the UAV, thereby reducing the time coordination cost in path planning to zero without significantly increasing the fuel cost. Therefore, the total cost is significantly reduced. Compared with other algorithms, the IMG-CHOA algorithm shows significant advantages in both fuel cost and time cost. This shows that selecting a suitable wind field path is crucial for optimizing the trajectory planning of the UAV, which not only saves costs but also improves the efficiency of mission execution.

[0186] like Figure 9 As shown in , it shows an optimization trajectory that depicts the evolution of the evaluation function as the iteration progresses. From this curve, we can clearly observe a progressive optimization process: in regular iterations, the overall cost overhead shows a continuous downward trend with the accumulation of iteration rounds, and eventually converges to an equilibrium state. This dynamic transformation strongly proves the practical value and high efficiency of the IMG-CHOA algorithm in the field of path planning. It shows a comparison chart of the fitness difference of each algorithm relative to the basic algorithm GWO in the last 60 iterations. From Figure 9 The data shows that the IMG-CHOA algorithm reduces costs by 27% compared to the GWO algorithm, 20% compared to the CHOA algorithm, and 17% compared to the MCHOA algorithm when handling collaborative path planning for multiple UAVs in complex scenarios. These data highlight the significant advantages of the IMG-CHOA algorithm in reducing the total cost of multi-UAV path planning, especially in complex environments. This cost optimization not only improves the algorithm's economic efficiency but also enhances its practicality and feasibility.

[0187] Experiments have demonstrated that the IMG-CHOA optimization algorithm demonstrates significant advantages in addressing multimodal optimization challenges. Its flexibility is sufficient to adapt to route calculation requirements in a variety of environmental contexts, thereby achieving efficient and accurate path planning. Despite this, current research is limited in fully considering the complex influencing factors of multi-UAV collaborative operations. To further meet the requirements of real-world applications, subsequent work will focus on deepening model optimization and enhancing its applicability and robustness in practical scenarios.

[0188] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art will be able to modify the technical solutions described in the aforementioned embodiments or substitute equivalents for some of the technical features. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A three-dimensional path planning method for unmanned aerial vehicles based on a polygene-optimized chimpanzee algorithm, characterized by: The following steps are involved: S1: Initialize the information of the drone and the target. Before the allocation begins, obtain the initial drone's position, number, and target point information, and detect the target's position. S2: Consider the impact of complex uniform wind fields on UAV flight speed in path planning scenarios; conduct a detailed analysis of the constraints affecting multiple UAVs in complex wind fields, and construct a multi-UAV path planning optimization function; S3: Randomly generate multiple groups of initial UAV path planning solutions based on multi-gene segment encoding; S4: Calculate the path planning cost of each solution based on the fitness function; S5: When t=1, the initial optimal path planning scheme is calculated according to the improved IMG-CHOA algorithm, and the position of the individual with the minimum path planning cost is determined as the optimal position S6: Generate an iterative path planning solution based on the improved IMG-CHOA algorithm to find the optimal path planning solution after the information changes; S7: Perform reverse learning and Gauss-Cauchy mutation on the global optimal position, calculate the minimum path planning cost of the optimal solution after the updated position, compare it with the original position, and retain the best one; otherwise, discard the new path planning solution; S8: Determine whether the current number of iterations reaches the preset number of iterations. If so, output the global optimal solution, that is, the minimum path planning cost and the corresponding path planning solution; otherwise, proceed to the next iteration.

2. The method for three-dimensional path planning of an unmanned aerial vehicle based on a polygene-optimized chimpanzee algorithm according to claim 1, characterized in that: In S1, let U = {U i ,i=1,2,…,N U } represents the set of multiple drones participating in the mission, T = {T i ,i=1,2,…,N U } is the set of target points that the UAV needs to reach, and P = {P i ,i=1,2,…,N P } is the set of existing enemy threats. For a single UAV, when starting from the starting point S i To target point M i During the flight, the aircraft will pass through a series of waypoints in sequence to form a complete flight path. These track segments are connected in series according to the established flight rules to form a complete track from the starting point to the destination point. Each track node is represented by W i-k The (k=1,2,…,n-1) marks are all key positions of the drone in performing the mission.

3. The method for three-dimensional path planning of an unmanned aerial vehicle based on a polygene-optimized chimpanzee algorithm according to claim 2, characterized in that: The construction of the multi-UAV path planning optimization function in S2 includes the following sub-steps: Sub-step S2.1: If the UAV's flight altitude does not meet the specified minimum or maximum limits, adjust its path planning by using the set penalty function to ensure that the UAV maintains the appropriate flight altitude. The penalty function is: Among them H max The maximum flight altitude allowed is H min To allow the minimum flight altitude, Q i is the scale factor; Spatial coordination constraints ensure that each UAV can safely maintain sufficient spatial separation when performing a mission to avoid collisions, namely: d i-j ≥d m (2) Among them, marked as d i-j The variable represents the shortest distance between the track nodes of the i-th UAV and its subsequent j UAVs in the flight sequence; and d m It specifically refers to the minimum safe flight interval that any two drones must maintain; Set the designated time for the drone to arrive at the destination as t u The time synchronization of the UAVs during mission execution is ensured through time coordination constraints. The estimated time interval for the UAVs to reach the target location is calculated based on the maximum and minimum speed limits of the UAVs and the actual flight path length. The actual arrival time of the UAVs needs to meet the following range: In the formula, the symbol v max With v min They represent the maximum and minimum flight speeds allowed, and L i represents the total length of the actual navigation path of the i-th UAV; The flight distance of a drone is limited by its energy reserves and flight time allocation. It has a maximum range parameter. Set this maximum track length to L. The distance of each flight segment must meet the following conditions: the length of each segment does not exceed L. This constraint ensures that the drone can effectively complete the planned route under limited energy supply. The distance of each segment should meet the following conditions: ∑l i ≤L max (4) According to the above conditions, the number of nodes in the drone's path planning is limited by its performance and cannot exceed a specific range. The cost of path planning also includes energy consumption. If the energy cost of a path is too high and exceeds the acceptable range, the trajectory will be considered infeasible. This setting ensures that the drone can complete its mission effectively within its energy limit. The multi-UAV path planning evaluation function extends the basic path planning function to include the coordinated adjustment of multiple UAVs in time and space. It also includes consideration of the threat costs that may be encountered in specific environments such as uniform wind fields. The evaluation formula for multi-UAV path planning integrates these key factors and is as follows: f in the formula L-i , f H-i , f T-i , f m-i , f Z-i , f W-i represents the energy consumption of the i-th UAV under the path planning scheme, including flight altitude, time consumption, potential threats, collision risks, and additional threat costs brought by the wind field environment; parameter γ i These correspond to the trade-off coefficients of the above-mentioned various costs, and G is the total number of UAVs participating in the mission; Through the analysis of time coordination constraints, the time cost can be expressed as follows: Sub-step S2.2: Assuming the wind field the drone enters is uniform and stable, a kinematic model is sufficient to describe its motion. The kinematics of steady-state straight-line flight include the effects of thrust, which is subsequently extended to stable turning flight. Specifically, the kinematics of the drone are described as follows: where v w is the air speed, ε is the path angle of the aircraft when it enters the wind field in a stable manner, and α is the heading angle of the UAV. Equating the forces parallel to and perpendicular to the flight path, we obtain the following equation: Where β is the sideslip angle of the UAV entering the wind field, θ is the roll angle of the aircraft, and γ is the angle of incidence of the thrust vector with the flight path. Assuming γ = 0, that is, the thrust is aligned with the track angle, so that the thrust perpendicular to the flight path is negligible, the equation is as follows: The lift coefficient is defined as: According to the above formula, we can get: The drag coefficient is expressed as a polynomial function of the lift coefficient: And through the formula According to the above formula, the aircraft path angle is: The turn rate is calculated by combining the drag coefficient and the horizontal component of the vertical force along the flight path. Based on these factors, the aircraft's kinematic equations are adjusted accordingly and become: Assume that V 0X 、V 0Y 、V 0Z is the velocity component of the UAV when it enters the wind field. The velocity change of the UAV entering the wind field is:

4. The method for three-dimensional path planning of an unmanned aerial vehicle based on a polygene-optimized chimpanzee algorithm according to claim 3, characterized in that: In the S3, a multi-gene segment encoding method is adopted and different gene segments are used to represent the paths of multiple drones. If the formation consists of G drones, each gene segment will contain G gene segments. This strategy selects the gene segment with the lowest cost in each iteration of the algorithm, and optimizes the processing speed of the algorithm by accumulating and storing track segments, while ensuring the quality of the solution. The gene segment encoding includes the three-dimensional spatial positioning information of the track point, and an additional state identifier p is added. i .

5. The method for three-dimensional path planning of an unmanned aerial vehicle based on a polygene-optimized chimpanzee algorithm according to claim 4, characterized in that: The objective function of the model is used as the fitness function in S4. The objective function of the model is:

6. The method for three-dimensional path planning of an unmanned aerial vehicle based on a polygene-optimized chimpanzee algorithm according to claim 5, characterized in that: The improved IMG-CHOA algorithm in S5 includes the following sub-steps: Sub-step S5.1: Develop an update strategy for the attacker, surround, and driver steps in the Chimpanzee algorithm. This strategy can achieve adaptive and nonlinear adjustment of the parameter w based on the algorithm's iterative process t, that is, the number of iterations, in order to achieve better optimization results. To prevent the algorithm from falling into a local optimal solution, iteration thresholds t1 and t2 are introduced. The cosine function is selected as the strategy model for the dynamic adjustment of the inertia weight, and the weight value is finely controlled through nonlinear changes. The specific mathematical expression is as follows: In the above expression, w max Represents the upper limit of inertia weight, w min Represents the lower limit value, T max Indicates the maximum number of algorithm iterations. In addition, a quadratic polynomial function is designed. When t∈(t1, t2) meets the conditions, by increasing the value of w, the algorithm's global search potential can be enhanced, effectively preventing it from converging to a suboptimal solution prematurely, ensuring the comprehensiveness and effectiveness of the search process. w(t)=2A1t 2 +A2t+2A3, where A is a constant and the w(t) function passes through the point (t1, w(t1)), ((t1+t2) / 2, w max ),(t2,w(t1)), so the values ​​of A1, A2, and A3 are: The quadratic function is: In this expression, the inertia weight w(t1) is the value at a specific time point t1 and is calculated according to formula (15). The parameters t1 and t2 can be determined by human fine-tuning according to the specific instance. In order to prevent the algorithm from locking into the local minimum too early, the values ​​of t1 and t2 are set to 3·T respectively. max / 10 and 5·T max / 10, so for this situation, formula (19) is changed to: In summary, the adaptive inertia weight adjustment strategy with the addition of hyperbolic tangent function is: The update formula for attackers, besiegers, and expellers becomes: X1=w·X a -A1·|C1·X a -m1·X| (22) X2=w·X b -A2·|C2·X b -m2·X| (23) X3=w·X c -A3·|C3·X c -m3·X| (24) Where: X a 、X b 、X c Represent the position vectors of attacker, besieger and expeller respectively, A is a random vector; m is the chaotic mapping vector, C is a random number between [0, 2]; Sub-step S5.2: To prevent the algorithm from falling into local optimality, the chaser search step in the chimpanzee algorithm is optimized, random particles are selected, and the particle positions are selected by applying fusion refraction and symbiotic mutualism. The strategy based on convex lens imaging can be obtained from formula (25): In the symbiotic search algorithm, the mutual benefit operation is one of the components of the symbiotic search algorithm. j is a randomly selected individual in the population, represented by X i and X j , mutually beneficial operations produce new individuals: The chimpanzee chaser step is integrated into the refraction reverse learning symbiotic algorithm. The mutually beneficial operations in the symbiotic algorithm are integrated according to the reverse position of the optimal position in the refraction reverse learning, and then the individuals are updated: The particle update formula of the Chimpanzee algorithm is:

7. The method for three-dimensional path planning of an unmanned aerial vehicle based on a polygene-optimized chimpanzee algorithm according to claim 6, characterized in that: In order to encourage individuals to approach the optimal solution in S7, the reverse learning strategy is embedded in the chimpanzee social optimization algorithm, and its mathematical model can be expressed as: X′ best (t) represents the inverse solution corresponding to the current optimal solution when evolving to the tth generation. The variables ub and lb respectively represent the upper and lower bounds of the solution space, while r is a random number matrix that follows the standard uniform distribution law in the (0,1) interval. The parameter b1 represents the information exchange control factor: The Cauchy mutation mechanism is used in the early stage of algorithm iteration, and the Gaussian mutation mechanism is used in the later stage of algorithm iteration. This can take into account the different mutation range requirements of different search stages of the algorithm. The mathematical definition of the Cauchy-Gaussian mutation mechanism is shown in the formula: Indicates the position of the optimal individual after mutation; Cauchy (x0, γ) and Gauss (μ, σ 2 ) are two random variables that follow the Cauchy distribution and Gaussian distribution laws; and a dynamic decision-making mechanism is adopted to innovate target positioning, that is, under the control of the preset probability, periodically switching between the reverse learning strategy and the Cauchy mutation operator perturbation mechanism to dynamically optimize the target position. Specifically, the target position update strategy depends on the selection probability P s The quantitative expression of this probability parameter follows the following formula: In the above expression, Σ is used as the adjustment factor, and its setting value is 0.

05. The specific selection process is as follows: When the random number rand is less than P s When , the algorithm will enable the reverse learning mechanism to update the position; otherwise, if rand is greater than or equal to P s , then the Cauchy-Gaussian mixture mutation perturbation strategy is selected to update the target position. After the position undergoes perturbation mutation, the greedy criterion is further introduced. By comparing the fitness evaluation of the new and old positions, it is determined whether it is necessary to perform a position update. The implementation method of the greedy criterion follows the following formula:

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