Multi-unmanned aerial vehicle cooperative path planning method and system based on white egret search mechanism of entropy and hedgehog rule
By introducing the egret search mechanism based on entropy and the hedgehog rule, the problems of high computational complexity, slow convergence speed, and poor accuracy in multi-UAV cooperative path planning are solved, achieving efficient path planning that is applicable to multi-UAV systems.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HARBIN ENG UNIV
- Filing Date
- 2026-03-17
- Publication Date
- 2026-06-12
AI Technical Summary
Existing swarm intelligence-based optimization methods for multi-UAV cooperative path planning suffer from high computational complexity, slow convergence speed, poor convergence accuracy, and susceptibility to getting trapped in local maxima.
An egret search mechanism incorporating entropy and the hedgehog's rule is proposed. By measuring population diversity through information entropy, the step size and random walk amplitude are dynamically adjusted. Combined with the hedgehog's rule, the success rate of the strategy is periodically statistically analyzed, and resources are reallocated to accelerate convergence and improve convergence accuracy. A multi-UAV cooperative path planning method is designed.
Under obstacle avoidance requirements, efficient multi-UAV collaborative path planning was achieved, improving convergence speed and accuracy, and enabling the planning of reasonable routes.
Smart Images
Figure CN122192313A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of unmanned aerial vehicle (UAV) path planning technology, and more specifically, to a multi-UAV collaborative path planning method and system based on the egret search mechanism of entropy and the hedgehog's law. Background Technology
[0002] Multi-UAV cooperative path planning, as a core technology for multi-UAV cooperative operations, involves multiple aspects such as mutual coordination, obstacle avoidance, and task allocation among UAVs. Compared with single-UAV path planning methods, the path planned using multi-UAV cooperative path planning methods may not be the optimal path for each individual UAV, but it is the optimal planned path for the multiple UAV swarm.
[0003] A search of existing literature revealed that Li Jie et al. [1] To address the 3D path planning problem for unmanned aerial vehicles (UAVs), a Gaussian mutation strategy and a differential evolution strategy are introduced to improve the global search and local optimization capabilities of the existing Harris Eagle algorithm. Finally, the improved Harris Eagle algorithm is used to solve the problem. (Zhang Le et al.) [2] To address the problem of cooperative path planning among multiple UAVs, Pearson correlation coefficients are introduced to calculate the similarity among individuals in a dung beetle optimization algorithm population. This enhances information exchange between individuals, improves the global search capability of the existing dung beetle optimization algorithm, and ultimately enables the search for flyable routes within a 3D environment model. (Zhang Zitang et al.) [3] To address the UAV path planning problem in complex 3D terrain environments, an adaptive evolutionary direction selection strategy is introduced, and historical information and differential operators are utilized to improve the convergence speed and optimization capability of the Grey Wolf Optimization (GWO) algorithm. Existing research shows that multi-UAV cooperative path planning methods rarely consider the constraint of simultaneous UAV arrival, but in real-world scenarios, multiple UAVs are often required to arrive at a predetermined target location simultaneously to perform corresponding tasks. Furthermore, existing multi-UAV cooperative path planning methods based on swarm intelligence optimization algorithms still suffer from high computational complexity, slow convergence speed, poor convergence accuracy, and susceptibility to getting trapped in local optima. Summary of the Invention
[0004] The technical problem to be solved by this invention is:
[0005] Existing swarm intelligence-based optimization methods for multi-UAV cooperative path planning suffer from problems such as high computational complexity, slow convergence speed, poor convergence accuracy, and susceptibility to getting trapped in local extrema.
[0006] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:
[0007] This invention provides a multi-UAV cooperative path planning method, denoted as EEOA, based on entropy and the hedgehog's law of egret search mechanism, which additionally considers simultaneous arrival under obstacle avoidance requirements. EEOA addresses the premature convergence and local trapping problems of existing egret swarm algorithms caused by fixed step size decay and the parallel implementation of three strategies by introducing two enhancement mechanisms: entropy-driven adaptive step size and the hedgehog's law. This invention uses information entropy to measure population diversity and dynamically adjusts the step size and random walk amplitude to ensure that the designed method can flexibly explore according to the current disorder and achieve fine convergence in the later stages. By periodically calculating the actual success rate of the three strategies through the hedgehog's law and redistributing the strategy call probability after weighted smoothing, more resources are concentrated on the "most effective" search strategy, thereby accelerating convergence and reducing invalid attempts. This results in a fast convergence speed and high convergence accuracy, enabling efficient path planning solutions for UAVs in multi-UAV cooperative scenarios.
[0008] This invention provides a multi-UAV cooperative path planning method based on entropy and the hedgehog's law for egret search, characterized by the following steps:
[0009] Step 1: Establish a multi-UAV cooperative path planning model that considers simultaneous arrival and obstacle avoidance requirements;
[0010] Step 2: Construct a fitness function based on the cost function of multi-UAV cooperative path planning, and initialize the egret flock;
[0011] Step 3: Perform fitness calculations on the egret flock to determine its optimal location;
[0012] Step 4: Measure the dispersion of the population across various dimensions using population entropy;
[0013] Step 5: Adaptively adjust the step size and random walk amplitude based on population entropy;
[0014] Step 6: Update the individual egret positions based on gradient direction and the waiting, wandering, and encirclement strategies;
[0015] Step 7: Based on the hedgehog principle, redistribute the probability of calling the waiting strategy, the roaming strategy, and the encirclement strategy according to the success rate of the strategies;
[0016] Step 8: Calculate the fitness of each updated egret to determine the optimal position of the population;
[0017] Step 9: Repeat steps 4 through 8 until the maximum number of iterations is reached;
[0018] Step 10: Obtain the optimal multi-UAV cooperative path.
[0019] Furthermore, step one includes the following steps:
[0020] Assuming all drones are flying at the same altitude, the no-fly zone is... ,in Indicates the position of obstacle l. Let l represent the radius of the obstacle. A quasi-uniform B-spline curve is used to fit the UAV's flight path, defined as... ,in This indicates the trajectory position of the h-th UAV. Here, H represents the number of the drone, and H represents the total number of drones. It is a quasi-uniform B-spline basis function, where m is the order of the basis function. These are the control vertex coordinates of the h-th UAV. n is the number of control points minus one. The recursive formula is:
[0021] ,in, Defined as a non-decreasing sequence of node vectors, a quasi-uniform B-spline curve sequence has uniformly distributed nodes in the middle and repeatability m+1 at both ends. ;
[0022] The set of attributes for drone h is ,in, Let h be the initial position of the drone. Let h be the termination position of the drone. The discretization time parameter is S, which represents the number of discretization time points. Let h be the velocity matrix of the drone. Let h be the speed of the h-th drone at time s. For discretization time interval, Let h be the acceleration matrix of the UAV. Let h be the acceleration of the h-th UAV at time s. Let h be the position of the h-th drone at the s-th time point;
[0023] Let the cost function for multi-UAV cooperative path planning be... ,in, For multi-UAV flight path matrix, For the flight speed matrix of multiple drones, Let h be the path length of the h-th UAV. For the smoothness penalty of the h-th drone, Hard penalty for avoiding obstacles For the maximum flight time of the H-type UAV, For the minimum flight time of the H-type UAV, The weighting coefficients for the smoothness penalty. To avoid obstacles and impose heavy penalties, This refers to the minimum safe distance that the target point needs to maintain from the obstacle. To simultaneously reach the constraint penalty factor, Let the radius be the radius of the k-th obstacle. This represents the center position of the k-th obstacle.
[0024] Furthermore, step two includes the following steps:
[0025] Let the size of the egret flock be N, the maximum number of iterations be T, and the number of iterations be t. In the t-th iteration, what is the position of the k-th egret in the i-th egret flock? , ,in, Given an ordered J-dimensional vector space, A, B, and C represent waiting, roaming, and encircling, respectively, and a squad consists of 3 egrets.
[0026] Furthermore, step three includes the following steps:
[0027] No. In the next iteration, the fitness of the k-th egret in the i-th squad is calculated using the objective function. The optimal position in generation t is selected based on the optimal fitness. Its fitness value is ,in, For the t-th iteration The fitness value of the kth egret in the squad.
[0028] Furthermore, step four includes the following steps:
[0029] Calculate the coordinates of the egret in the j-th dimension. The frequency of the landing point, with a probability of . τ is an index variable, N is the total number of egrets, and M is the number of regions into which the spatial dimension of the data is divided, resulting in an M-term probability distribution. The Shannon entropy is then calculated from this probability distribution. Introducing normalization processing ,in, .
[0030] Furthermore, step five includes the following steps:
[0031] According to the normalized population entropy, when When the step size is increased, it encourages exploration over a wider area; when Decreasing the step size accelerates convergence; the initial step size... , ,in, To adjust the entropy intensity, It is a linear decay factor. Entropy threshold and The lower and upper boundaries are defined as follows: The diversity coefficient is a very small positive number. For egrets in a flock that tend to search for prey randomly, stronger shaking is used to escape local predators when diversity is insufficient, while shaking is appropriately reduced when diversity is high. Actual amplitude adjustment factor ,in, It is the basic amplitude constant.
[0032] Furthermore, step six includes the following steps:
[0033] No. In the next iteration, the i-th team randomly samples a vector that follows a multivariate normal distribution. Used to generate the direction of the simulated gradient and calculate the gradient estimation vector. Its unit vector ,in, (t) is the th The state vector of the i-th team at the next iteration. It is a very small positive number; let the egret using the wait-and-see strategy be named egret A, and its position coordinate update formula be: Where α is the decay rate constant and the fitness value is Egret B is an egret using a random walk strategy, and its behavior... fitness is Egret C employs a siege strategy to pursue its prey, and its position update method is as follows: fitness is ,in, A random number in the interval (-π / 2, π / 2). and They are respectively Random numbers in an interval The upper limit of the interval, , For the i-th egret squad up to the i-th The historical best position up to the next iteration. Let be the difference matrix between the current position of the i-th egret team and its historical best position at the t-th iteration. Let be the difference matrix between the current position of the i-th egret squad and the global optimal position of the population at the t-th iteration. Multiply the corresponding elements of the matrix.
[0034] Furthermore, step seven includes the following steps:
[0035] Maintain the probability of strategy s being invoked among the three strategies: wait-and-go, roam, and encirclement. Number of calls With the number of successes ,initialization When the number of iterations t is exactly the update period When the value is an integer multiple of the target value, calculate the success rate of each strategy. Reallocate call probability ,in, As a smoothing factor, the number of calls to strategy s in each generation is weighted and accumulated. , Let be the probability of policy s being invoked in the next cycle. If policy s improves the fitness of the individual, let . .
[0036] Furthermore, step eight includes the following steps:
[0037] The updated position of the i-th egret squad is Its fitness value is If the fitness of the current position of the egret squad is better than its historical best, then update its historical best to... If the fitness of the current egret squad is better than the global optimum, when ,but Otherwise, let .
[0038] This invention provides a multi-UAV cooperative path planning system based on the egret search mechanism of entropy and the hedgehog's law. The system has program modules corresponding to the steps of the method described in any of the above technical solutions, and executes the steps in the multi-UAV cooperative path planning method based on the egret search mechanism of entropy and the hedgehog's law when running.
[0039] Compared with the prior art, the beneficial effects of the present invention are:
[0040] This invention, considering simultaneous arrival constraints under obstacle avoidance requirements, designs a multi-UAV cooperative obstacle avoidance path planning method and establishes a multi-UAV cooperative path planning model and cost function considering simultaneous arrival constraints. To achieve efficient solution of the model, this invention designs an entropy and hedgehog rule-based egret search mechanism. By introducing information entropy-driven adaptive step size and random walk amplitude, and a strategy success rate focusing mechanism based on the hedgehog rule, the probability of calling three search strategies is passively adjusted, resulting in fast convergence speed and high convergence accuracy. The proposed method can plan a reasonable route for each UAV in a multi-UAV system. Simulation experiments demonstrate the effectiveness of the multi-UAV cooperative path planning method based on the entropy and hedgehog rule-based egret search mechanism considering simultaneous arrival constraints, broadening the application scenarios of existing methods. Attached Figure Description
[0041] Figure 1This is a schematic diagram illustrating the operation of the multi-UAV cooperative path planning method based on the egret search mechanism and the hedgehog rule in an embodiment of the present invention.
[0042] Figure 2 This is a path diagram of each drone in the multi-UAV system of this invention embodiment;
[0043] Figure 3 This is a curve showing the relationship between the cost function value of multi-UAV cooperative path planning and the number of mechanism evolutions in an embodiment of the present invention. Detailed Implementation
[0044] To enable those skilled in the art to better understand the present invention, exemplary embodiments or examples of the present invention will be described below in conjunction with the accompanying drawings. Obviously, the described embodiments or examples are merely some, not all, of the embodiments or examples of the present invention. All other embodiments or examples obtained by those skilled in the art based on the embodiments or examples of the present invention without inventive effort should fall within the scope of protection of the present invention.
[0045] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
[0046] Combination Figure 1 As shown, this invention provides a multi-UAV cooperative path planning method based on entropy and the hedgehog's law for egret search, comprising the following steps:
[0047] Step 1: Establish a multi-UAV cooperative path planning model that considers simultaneous arrival and obstacle avoidance requirements.
[0048] This invention makes the following assumptions regarding the multi-UAV cooperative path planning model: Considering that the actual area is very small relative to the maximum achievable altitude of multiple UAVs, in other words, the multiple UAVs operate at almost the same altitude, this invention assumes that the UAVs fly at the same altitude and solves the multi-UAV cooperative path planning problem in two-dimensional space. The area containing obstacles in this invention is collectively referred to as a no-fly zone, which is represented by a circle for ease of handling, specifically as follows: ,in Indicates the position of obstacle l. Let represent the radius of obstacle l. This invention uses a quasi-uniform B-spline curve to fit the UAV flight path, defined as... ,in This indicates the trajectory position of the h-th UAV. It is a quasi-uniform B-spline basis function, where m is the order of the basis function. The recursive formula is:
[0049] ,in Defined as a non-decreasing sequence of node vectors, a quasi-uniform B-spline curve sequence has uniformly distributed nodes in the middle and repeatability m+1 at both ends. n is the number of control points minus one, meaning there are n+1 control points. These are the control vertex coordinates of the h-th UAV.
[0050] In a multi-UAV system, the attribute set of UAV h is: ,in, Here, H represents the number of the drone, and H represents the total number of drones. Let h be the initial position of the drone. Let h be the termination position of the drone. For discretization time parameters, The discretization time interval is S, where S represents the number of discretization time points. Let h be the velocity matrix of the drone. Let h be the speed of the h-th drone at time s. Let h be the acceleration matrix of the UAV. Let h be the acceleration of the h-th UAV at time s. Let h be the position of the h-th drone at the s-th time point.
[0051] The cost function for multi-UAV cooperative path planning is set as follows: ,in, For multi-UAV flight path matrix, For the flight speed matrix of multiple drones, Let h be the path length of the h-th UAV. For the smoothness penalty of the h-th drone, Hard penalty for avoiding obstacles For the maximum flight time of the H-type UAV, For the minimum flight time of the H-type UAV, The weighting coefficients for the smoothness penalty. To avoid obstacles and impose heavy penalties, This refers to the minimum safe distance that the target point needs to maintain from the obstacle. To simultaneously reach the constraint penalty factor, Let the radius be the radius of the k-th obstacle. This represents the center position of the k-th obstacle.
[0052] Step 2: Construct a fitness function based on the cost function of multi-UAV cooperative path planning, and initialize the egret flock.
[0053] Let the size of the egret flock be N, the maximum number of iterations be T, and the iteration number be an integer t. In the t-th iteration, the position of the k-th egret in the i-th egret flock is... The t-th generation, the i-th squad, the k-th egret Dimensional position ,in, An ordered J-dimensional vector space, A, B, and C represent waiting, roaming, and encircling, respectively, and a squad consists of 3 egrets.
[0054] Step 3: Calculate the fitness of the egret flock to determine its optimal location.
[0055] No. In the next iteration, the fitness of the k-th egret in the i-th squad is calculated using the objective function. The optimal position in generation t is selected based on the optimal fitness. Its fitness value is ,in, For the t-th iteration The fitness value of the kth egret in the squad; For until the The globally optimal position up to the nth iteration. For the t-th iteration The position of the kth egret in the squad.
[0056] Step 4: Measure the degree of dispersion of the population across various dimensions using population entropy.
[0057] Calculate the coordinates of all egrets in the j-th dimension. The frequency of the landing point, with a probability of . We obtain an M-term probability distribution, reflecting the dispersion of the population along this dimension. τ is an index variable used to iterate through all elements in a set, taking values from 1 to M. N is the total number of egrets, and M is the number of regions into which the spatial dimension of the data is divided. The continuous numerical range is divided into M non-overlapping intervals, and the probability of a sample point falling into each interval is calculated, yielding M corresponding probability values. Shannon entropy is then calculated on the probability distribution. To eliminate the influence of the size of M on the absolute value of entropy, a normalization process is introduced. ,in, The closer to 0, the lower the population diversity; the closer to 1, the higher the diversity.
[0058] Step 5: Adaptively adjust the step size and random walk amplitude based on population entropy.
[0059] According to the normalized population entropy, when diversity is too low, i.e. At times, increasing the step size encourages broader exploration; when diversity is too high, that is... To accelerate convergence, appropriately reduce the step size; initial step size ,
[0060] ,in, To adjust the entropy intensity, It is a linear decay factor. Entropy threshold and The lower and upper boundaries are defined as follows: The step size is a very small positive number to ensure it doesn't decay to zero and preserves small perturbations. For egrets in a flock that tend to randomly search for prey, a stronger "jitter" is needed to escape localized situations when diversity is insufficient, while the jitter can be appropriately reduced when diversity is high. A diversity coefficient is defined. Actual amplitude adjustment factor ,in, It is the basic amplitude constant.
[0061] Step 6: Update the individual egret positions based on gradient direction and the waiting, wandering, and encirclement strategies.
[0062] No. In the next iteration, the i-th team randomly samples a vector that follows a multivariate normal distribution. Used to generate the direction of the simulated gradient and calculate the current predicted value. With reality The error between them is multiplied by the current position vector. This yields a gradient estimation vector. Its unit vector ,in, (t) is the th The state vector of the i-th team at the next iteration. It is a very small positive number. Of the three strategies, the egret using the wait-and-see strategy will be named Egret A, and its position coordinate update formula can be described as... Where α is the decay rate constant and the fitness value is Egret B is an egret using a random walk strategy, and its behavior is described as follows: fitness is Egret C employs a siege strategy to pursue its prey, and its position update method is as follows: , fitness is ,in, A random number in the interval (-π / 2, π / 2). For the i-th egret squad up to the i-th The historical best position up to the next iteration. and for Random numbers in an interval The upper limit of the interval, Let be the difference matrix between the current position of the i-th egret team and its historical best position at the t-th iteration. Let be the difference matrix between the current position of the i-th egret squad and the global optimal position of the population at the t-th iteration. Multiply the corresponding elements of the matrix.
[0063] Step 7: Based on the hedgehog principle, redistribute the probability of calling the waiting strategy, the roaming strategy, and the encirclement strategy according to the success rate of the strategies.
[0064] Maintain the invocation probability of the three strategies Number of calls With the number of successes ,initialization When the number of iterations t is exactly the update period When the value is an integer multiple of the target value, calculate the success rate of each strategy. Reallocate call probability ,in, As a smoothing factor, the number of calls to strategy s in each generation is weighted and accumulated. , Let be the probability of policy s being invoked in the next cycle. If policy s improves the fitness of the individual, let . .
[0065] This implementation adopts an adaptive strategy selection mechanism based on success rate, which implicitly incorporates the 'hedgehog principle' idea: initially exploring various strategies in a balanced manner, and later focusing on high-performance strategies (hedgehog behavior) through power-weighted selection, thereby achieving a dynamic balance between exploration and utilization.
[0066] Step 8: Calculate the fitness of each updated egret to determine the optimal position of the population.
[0067] The position of the i-th egret squad after the movement is Its fitness value is If the fitness of the current position of the egret squad is better than its historical best, then update its historical best to... If the fitness of the current egret squad is better than the global optimum, when ,but Otherwise, let .
[0068] Step Nine: Determine if the maximum number of iterations has been reached. If the maximum number of iterations has been reached, the algorithm terminates and proceeds to Step Ten; otherwise, let... Return to step four and continue.
[0069] Step 10: Output the optimal multi-UAV cooperative path.
[0070] The multi-UAV cooperative path planning method (algorithm) based on entropy and the hedgehog law search mechanism proposed in this invention is the underlying technical core of this invention, and various products can be derived based on the algorithm.
[0071] Based on the method proposed in this invention, a multi-UAV cooperative path planning system based on entropy and the hedgehog's law search mechanism for egrets is developed using a programming language. This system has program modules corresponding to the steps of the above-mentioned technical solution, and executes the steps in the multi-UAV cooperative path planning method based on entropy and the hedgehog's law search mechanism when running.
[0072] The developed system (software) computer program is stored on a computer-readable storage medium. This computer program is configured to implement the steps of the multi-UAV cooperative path planning method based on the entropy and hedgehog law search mechanism when invoked by a processor. In other words, the invention is materialized on a carrier, becoming a computer program product.
[0073] Various implementations of the systems and techniques described herein can be implemented in digital electronic circuit systems, integrated circuit systems, application-specific integrated circuits (ASICs), computer hardware, firmware, software, and / or combinations thereof. These various implementations may include: implementations in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transmitting data and instructions to the storage system, the at least one input device, and the at least one output device.
[0074] The computational programs (also referred to as programs, software, software applications, or code) of this invention include machine instructions of a programmable processor and can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. As used herein, the terms "machine-readable medium" and "computer-readable medium" refer to any computer program product, device, and / or apparatus (e.g., disk, optical disk, memory, programmable logic device PLD) for providing machine instructions and / or data to a programmable processor, including machine-readable media that receive machine instructions as machine-readable signals. The term "machine-readable signal" refers to any signal for providing machine instructions and / or data to a programmable processor.
[0075] The beneficial effects of the present invention will be described below with reference to specific embodiments.
[0076] Example 1
[0077] Population size is set in this invention Maximum number of iterations The location and radius of the obstacle are... , , , , , and .
[0078] exist Figure 3 In this invention, the multi-UAV cooperative path planning method based on entropy and the hedgehog's law search mechanism is denoted as EEOA; the multi-UAV cooperative path planning method based on the egret flock optimization algorithm is denoted as ESOA. In EEOA, the parameter is set to M=20. =0.5, =0.5, =0.2, =0.01, , , =10, =2, =0.5. Parameter settings in ESOA should refer to existing models. [4] .from Figures 2-3 Simulation results show that the multi-UAV cooperative path planning method based on entropy and the hedgehog rule proposed in this invention has fast convergence speed and high convergence accuracy, and is suitable for practical engineering problems.
[0079] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.
[0080] The documents cited in this invention include:
[0081] [1] Li Jie, Tao Wei, Zhang Juan, et al. 3D path planning for UAVs based on improved Harris Eagle algorithm [J]. Firepower and Command Control, 2024, 49(12):27-35+46.
[0082] [2] Zhang Le, Hu Yiwen, Yang Hong, et al. Cooperative path planning of UAVs based on decision learning dung beetle optimization algorithm [J]. Computer Applications Research, 2025, 42(01):196-204.
[0083] [3]Zhang Z, Li Y, Sun Q, et al. A novel waypoint guidance andadaptive evolution strategy for unmanned aerial vehicle 3D route planning[J].Journal of the Franklin Institute, 2023, 360(13): 9602-9636.
[0084] [4]Chen Z, Francis A, Li S, et al. Egret swarm optimizationalgorithm: an evolutionary computation approach for model free optimization[J]. Biomimetics, 2022, 7(4): 144.
Claims
1. A multi-UAV cooperative path planning method based on entropy and the hedgehog's law for egret search, characterized in that, Includes the following steps: Step 1: Establish a multi-UAV cooperative path planning model that considers simultaneous arrival and obstacle avoidance requirements; Step 2: Construct a fitness function based on the cost function of multi-UAV cooperative path planning, and initialize the egret flock; Step 3: Perform fitness calculations on the egret flock to determine its optimal location; Step 4: Measure the dispersion of the population across various dimensions using population entropy; Step 5: Adaptively adjust the step size and random walk amplitude based on population entropy; Step 6: Update the individual egret positions based on gradient direction and the waiting, wandering, and encirclement strategies; Step 7: Based on the hedgehog principle, redistribute the probability of calling the waiting strategy, the roaming strategy, and the encirclement strategy according to the success rate of the strategies; Step 8: Calculate the fitness of each updated egret to determine the optimal position of the population; Step 9: Repeat steps 4 through 8 until the maximum number of iterations is reached; Step 10: Obtain the optimal multi-UAV cooperative path.
2. The method according to claim 1, characterized in that, Step one includes the following steps: Assuming all drones are flying at the same altitude, the no-fly zone is... ,in Indicates the position of obstacle l. Let l represent the radius of the obstacle. A quasi-uniform B-spline curve is used to fit the UAV's flight path, defined as... ,in This indicates the trajectory position of the h-th UAV. Here, H represents the number of the drone, and H represents the total number of drones. It is a quasi-uniform B-spline basis function, where m is the order of the basis function. These are the control vertex coordinates of the h-th UAV. n is the number of control points minus one. The recursive formula is: ,in, Defined as a non-decreasing sequence of node vectors, a quasi-uniform B-spline curve sequence has uniformly distributed nodes in the middle and repeatability m+1 at both ends. ; The set of attributes for drone h is ,in, Let h be the initial position of the drone. Let h be the termination position of the drone. The discretization time parameter is S, which represents the number of discretization time points. Let h be the velocity matrix of the drone. Let h be the speed of the h-th drone at time s. For discretization time interval, Let h be the acceleration matrix of the UAV. Let h be the acceleration of the h-th UAV at time s. Let h be the position of the h-th drone at the s-th time point; Let the cost function for multi-UAV cooperative path planning be... ,in, For multi-UAV flight path matrix, For the flight speed matrix of multiple drones, Let h be the path length of the h-th UAV. For the smoothness penalty of the h-th drone, Hard penalty for avoiding obstacles For the maximum flight time of the H-type UAV, For the minimum flight time of the H-type UAV, The weighting coefficients for the smoothness penalty. To avoid obstacles and impose heavy penalties, This refers to the minimum safe distance that the target point needs to maintain from the obstacle. To simultaneously reach the constraint penalty factor, Let the radius be the radius of the k-th obstacle. This represents the center position of the k-th obstacle.
3. The method according to claim 1, characterized in that, Step two includes the following steps: Let the size of the egret flock be N, the maximum number of iterations be T, and the number of iterations be t. In the t-th iteration, what is the position of the k-th egret in the i-th egret flock? , ,in, Given an ordered J-dimensional vector space, A, B, and C represent waiting, roaming, and encircling, respectively, and a squad consists of 3 egrets.
4. The method according to claim 1, characterized in that, Step three includes the following steps: No. In the next iteration, the fitness of the k-th egret in the i-th squad is calculated using the objective function. The optimal position in generation t is selected based on the optimal fitness. Its fitness value is ,in, For the t-th iteration The fitness value of the kth egret in the squad.
5. The method according to claim 1, characterized in that, Step four includes the following steps: Calculate the coordinates of the egret in the j-th dimension. The frequency of the landing point, with a probability of . τ is an index variable, N is the total number of egrets, and M is the number of regions into which the spatial dimension of the data is divided, resulting in an M-term probability distribution. The Shannon entropy is then calculated from this probability distribution. Introducing normalization processing ,in, .
6. The method according to claim 1, characterized in that, Step five includes the following steps: According to the normalized population entropy, when When the step size is increased, it encourages exploration over a wider area; when Decreasing the step size accelerates convergence; the initial step size... , ,in, To adjust the entropy intensity, It is a linear decay factor. Entropy threshold and The lower and upper boundaries are defined as follows: The diversity coefficient is a very small positive number. For egrets in a flock that tend to search for prey randomly, stronger shaking is used to escape local predators when diversity is insufficient, while shaking is appropriately reduced when diversity is high. Actual amplitude adjustment factor ,in, It is the basic amplitude constant.
7. The method according to claim 1, characterized in that, Step six includes the following steps: No. In the next iteration, the i-th team randomly samples a vector that follows a multivariate normal distribution. Used to generate the direction of the simulated gradient and calculate the gradient estimation vector. Its unit vector ,in, (t) is the th The state vector of the i-th team at the next iteration. It is a very small positive number; let the egret using the wait-and-see strategy be named egret A, and its position coordinate update formula be: Where α is the decay rate constant and the fitness value is Egret B is an egret using a random walk strategy, and its behavior... fitness is Egret C employs a siege strategy to pursue its prey, and its position update method is as follows: fitness is ,in, A random number in the interval (-π / 2, π / 2). and They are respectively Random numbers in an interval The upper limit of the interval, , For the i-th egret squad up to the i-th The historical best position up to the next iteration. Let be the difference matrix between the current position of the i-th egret team and its historical best position at the t-th iteration. Let be the difference matrix between the current position of the i-th egret squad and the global optimal position of the population at the t-th iteration. Multiply the corresponding elements of the matrix.
8. The method according to claim 1, characterized in that, Step seven includes the following steps: Maintain the probability of strategy s being invoked among the three strategies: wait-and-go, roam, and encirclement. Number of calls With the number of successes ,initialization When the number of iterations t is exactly the update period When the value is an integer multiple of the target value, calculate the success rate of each strategy. Reallocate call probability ,in, As a smoothing factor, the number of calls to strategy s in each generation is weighted and accumulated. , Let be the probability of policy s being invoked in the next cycle. If policy s improves the fitness of the individual, let . .
9. The method according to claim 1, characterized in that, Step eight includes the following steps: The updated position of the i-th egret squad is Its fitness value is If the fitness of the current position of the egret squad is better than its historical best, then update its historical best to... If the fitness of the current egret squad is better than the global optimum, when ,but Otherwise, let .
10. A multi-UAV cooperative path planning system based on entropy and the hedgehog's law for egret search, characterized in that, The system has a program module corresponding to the steps of the method described in any one of claims 1 to 9, and executes the steps in the multi-UAV cooperative path planning method based on the egret search mechanism of entropy and hedgehog rule when it is run.