Multi-unmanned aerial vehicle cooperative three-dimensional trajectory planning method based on hybrid meta-heuristic algorithm

Abstract

The invention discloses a multi-unmanned aerial vehicle cooperative three-dimensional trajectory planning method based on a hybrid meta-heuristic algorithm, and the method comprises the steps: constructing an unmanned aerial vehicle cooperative trajectory planning model containing cooperative defense constraints, and constructing a three-dimensional geographic map containing a research region in the unmanned aerial vehicle cooperative trajectory planning model; an unmanned aerial vehicle cooperative system comprising N unmanned aerial vehicles is constructed, and an unmanned aerial vehicle cooperative trajectory planning model enables all the unmanned aerial vehicles of the unmanned aerial vehicle cooperative system to cooperatively search and simulate flight in a research area according to unmanned aerial vehicle flight tasks in a three-dimensional geographic map. And the unmanned aerial vehicle cooperative trajectory planning model constructs a population by taking the unmanned aerial vehicle flight trajectory as an individual, executes iterative optimization processing of a fusion cooperative defense strategy and ant lion optimization random walk based on a PHOENIX algorithm, and finally outputs an optimal unmanned aerial vehicle cooperative flight three-dimensional trajectory. According to the invention, efficient, safe and cooperative trajectory planning processing of multiple unmanned aerial vehicles in a complex three-dimensional environment is realized, and important technical support is provided for research and application of an intelligent autonomous system.

Description

Technical Field

[0001] This invention relates to a collaborative path planning method for unmanned aerial vehicles (UAVs) in a research area, and more particularly to a collaborative 3D trajectory planning method for multiple UAVs based on a hybrid meta-heuristic algorithm. Background Technology

[0002] With the rapid development of unmanned aerial vehicle (UAV) technology, multi-UAV systems are increasingly widely used in military reconnaissance, disaster response, smart city logistics, and environmental monitoring. Achieving collaborative trajectory planning for multiple UAVs in complex three-dimensional (3D) environments requires simultaneously satisfying multiple constraints, including obstacle avoidance, path optimization, energy consumption control, and communication maintenance, presenting unprecedented technical challenges. Traditional UAV path planning methods are mainly divided into four categories: graph search methods (such as A* and Dijkstra's algorithms), cell decomposition methods, potential field methods, and natural heuristic algorithms. However, these methods have significant limitations when dealing with collaborative planning for multiple UAVs in complex 3D environments. Traditional methods such as A* and RRT (Rapid Expanding Random Tree) cannot simultaneously optimize collision avoidance, energy efficiency, and trajectory smoothness under UAV kinematic constraints, resulting in an average infeasibility rate as high as 41.2% in cluttered environments. These methods often ignore the actual maneuverability limitations of UAVs when generating paths, resulting in paths that are theoretically feasible but practically unenforceable. Furthermore, simplified two-dimensional planning models ignore highly dependent risks, including terrain-induced signal blockage and aerodynamic turbulence, which account for 34% of real-world UAV failures. In complex 3D spatial domains, obstacle density can exceed 0.8 threats / km³. The computational complexity of traditional methods increases exponentially with dimensionality, making it difficult to meet real-time requirements. Existing hybrid algorithms (such as HGWODE and GDRRT*-PSO) can handle obstacle densities exceeding 0.8 threats / km³. 3 The performance degradation is mainly due to an insufficient exploration-exploitation balance. These algorithms lack effective adaptive mechanisms when facing dynamic obstacles and time-varying environments.

[0003] In recent years, emerging methods based on deep reinforcement learning (DRL) and neuromorphic computing have shown some potential, but also face serious limitations: DRL requires over 400 hours of GPU-accelerated training, and neuromorphic implementation requires dedicated hardware incompatible with UAV embedded systems. Meanwhile, bio-inspired meta-heuristics (PSO particle swarm optimization, GWO gray wolf optimization), while demonstrating inherent multi-objective optimization capabilities, converge too early in high-dimensional spaces, with a suboptimal solution rate as high as 45.3%. Existing technologies suffer from the following core problems: 1. Lack of standardized safety constraints: Existing methods lack effective integration with international aviation safety standards (such as RTCA DO-263), leading to planned trajectories that may not meet safety requirements in practical applications. Traditional circular or rectangular protected area models are overly simplified and cannot accurately reflect real collision risks. 2. Static multi-objective weights: Traditional methods use fixed weight coefficients to balance different optimization objectives (path length, threat avoidance, energy consumption, etc.), which cannot adapt to dynamically changing task requirements and environmental conditions, resulting in insufficient adaptability and robustness of the optimization results. 3. Poor adaptability to dynamic environments: Existing algorithms lack effective mechanisms for handling dynamic obstacles and managing population diversity, resulting in insufficient robustness in time-varying environments. When population diversity declines, there is a lack of diversity recovery schemes, leading to premature high convergence rates.

[0004] Therefore, there is an urgent need for a multi-UAV collaborative trajectory planning method that can comprehensively consider multi-level constraints, dynamically balance exploration and development, meet safety standards, and achieve rapid convergence. Summary of the Invention

[0005] The purpose of this invention is to provide a multi-UAV cooperative 3D trajectory planning method based on a hybrid meta-heuristic algorithm, which realizes efficient, safe and cooperative trajectory planning processing of multiple UAVs in complex 3D environments.

[0006] The objective of this invention is achieved through the following technical solution: A multi-UAV cooperative 3D trajectory planning method based on a hybrid meta-heuristic algorithm, the method comprising: S1. Construct a UAV cooperative trajectory planning model that includes cooperative defense constraints. The UAV cooperative trajectory planning model contains a three-dimensional geographic map of the study area. The starting point and ending point of the UAV flight mission in the study area are marked in the three-dimensional geographic map. S2. Construct a UAV collaborative system including N UAVs. The UAV collaborative trajectory planning model enables all UAVs in the joint system to collaboratively search and simulate flight in the study area according to the UAV flight mission on a 3D geographic map. The UAV collaborative trajectory planning model constructs a population based on the UAV flight trajectory as an individual and performs iterative optimization processing based on the PHOENIX algorithm to implement a fusion collaborative defense strategy and antlion optimization random walk. Finally, it outputs the optimal UAV collaborative flight 3D trajectory.

[0007] To better implement the present invention, in method S1, the cooperative defense constraint is constructed using a layered flight protection zone, the method of which includes: defining a two-layered cylindrical protection zone, a collision zone (CAZ) and a protection zone (PAZ), for each UAV.

[0008] Preferably, in method S2, the collaborative defense strategy includes a layered flight protection zone defense strategy and a two-layer collaborative optimization mechanism strategy. The layered flight protection zone defense strategy method includes: combining the two-layer cylindrical protection zone of the UAV with the four-layer defense mechanism of the Crowned Porcupine Optimizer (CPO) to form a three-layer compliance architecture verification. The first and second defense mechanisms of the Crowned Porcupine Optimizer (CPO) are associated with the collision area (CAZ), and the third and fourth defense mechanisms of the Crowned Porcupine Optimizer (CPO) are associated with the protection area (PAZ). The three-layer compliance architecture verification includes size compliance verification, operational verification, and adaptive improvement verification. Size compliance verification is used to verify the correspondence and size of each defense mechanism, collision area (CAZ), and protection area (PAZ). Operational verification is used to verify the separation of defense mechanisms or regions in the horizontal and vertical directions during each iteration of optimization. Adaptive improvement verification is used to increase the local sampling density to refine the judgment and increase the compliance margin when approaching the defense compliance boundary.

[0009] Preferably, the dual-layer collaborative optimization mechanism strategy includes an improved CPO defense mechanism and a fusion defense mechanism. The improved CPO defense mechanism includes a swarm defense strategy, a location defense strategy, a passive defense strategy, and an active defense strategy. The swarm defense strategy is the defense of all UAVs in the UAV joint system, and the location defense strategy is the defense of the UAVs themselves. The UAV collaborative trajectory planning model introduces an elite strategy and selects the individual with the best fitness in the population as the elite solution. Each individual performs an antlion-optimized random walk around the elite individual. The fusion defense mechanism combines the antlion-optimized random walk and the elite strategy to verify the improved CPO defense mechanism.

[0010] Preferably, a two-layer defense mechanism is constructed using an adaptive weight coefficient dynamic fusion optimization two-layer collaborative optimization mechanism strategy. The adaptive weight coefficients are dynamically adjusted with the iteration process using a non-linear decay method, as shown in the following expression: , , These are the maximum and minimum weights, respectively, and are set to the maximum weight in the initial stage of the iteration. In the later stages of iteration, the weight is set to the minimum value. , It is a non-linear adjustment factor. The maximum number of iterations, This represents the current iteration number.

[0011] Preferably, the UAV cooperative trajectory planning model is further configured with a multi-objective cost function that includes path length cost, threat avoidance cost, altitude constraint cost, path smoothing cost, energy consumption cost, and communication reliability cost. The multi-objective cost function imposes cost constraints on the flight of each UAV and calculates the total cost by weighting the costs. The UAV cooperative trajectory planning model constrains the total cost of all UAVs to be minimized.

[0012] Preferably, the UAV cooperative trajectory planning model uses a chaos enhancement strategy to initialize the population. The chaos enhancement strategy introduces interval-constrained Logistic chaotic mapping to generate chaotic mapping operators, and the iterative equations are as follows: , Represents the internal state values ​​of the iterative equation. is the chaos coefficient.

[0013] Preferably, the UAV cooperative trajectory planning model incorporates a dynamic diversity management mechanism to constrain population diversity, continuously monitoring population diversity throughout the iterative optimization process. This dynamic diversity management mechanism uses Shannon entropy as a quantitative diversity indicator, and the expression for population diversity is as follows: , Let be the population diversity at the t-th iteration. Let be the probability density of an individual in subspace k at the t-th iteration, determined by a grid-based adaptive solution space partitioning, where N is the total number of subspaces in the adaptive solution space; a critical threshold is set. When H(t) < H crit At that time, a diversity recovery method is initiated for processing.

[0014] Preferably, the 3D geographic map includes obstacle data and dynamic obstacle data for the study area, and the UAV cooperative trajectory planning model dynamically manages obstacles using the following method: A1. Predict the trajectory of dynamic obstacles using the Kalman filter algorithm and a constant acceleration model, with a prediction time window. Dynamically adjusted based on obstacle speed and drone maneuverability limitations; A2. Filter the affected drones and trigger local replanning to avoid obstacles.

[0015] Compared with the prior art, the present invention has the following advantages and beneficial effects: (1) This invention provides a safe and reliable multi-UAV collaborative three-dimensional trajectory planning method for multi-UAV collaborative trajectory planning in complex three-dimensional environments. It realizes efficient, safe and collaborative trajectory planning processing of multi-UAVs in complex three-dimensional environments, bridging the gap between theoretical optimization and actual deployment, and providing important technical support for the research and application of intelligent autonomous systems.

[0016] (2) The UAV cooperative trajectory planning model of the present invention integrates the cooperative defense strategy CPO and the antlion optimized random walk algorithm ALO, and utilizes their complementary optimization characteristics. The four-layer defense mechanism of the cooperative defense strategy CPO provides excellent local search optimization capabilities, while the random walk mechanism and elite preservation strategy of the antlion optimized random walk algorithm ALO perform well in global search. The fusion of the two creates a balanced search paradigm with fast convergence speed.

[0017] (3) The present invention uses interval-constrained Logistic chaotic mapping for population initialization. Compared with Gaussian randomization, the solution diversity is increased by 32.7% (through Shannon entropy quantization, p<0.05). The ergodicity of chaotic mapping ensures that the search space is fully covered by deterministic but non-repeating trajectories, and the uniform space coverage is increased by 28.3% (p<0.01), which significantly reduces the risk of getting trapped in local optima.

[0018] (4) This invention is based on the construction of a hierarchical flight protection zone according to the RTCA DO-263 standard. It directly embeds aviation safety regulations into the optimization process and verifies the generated trajectory through a three-layer compliance architecture to ensure that it meets international aviation safety requirements. It achieves a 100% collision-free success rate in AirSim simulation. Through an adaptive weight adjustment mechanism with nonlinear decay, it dynamically balances exploration and development. It focuses on global exploration in the early stage of optimization and strengthens local optimization in the later stage, which effectively solves the exploration-development dilemma. This mechanism enables the algorithm to automatically adjust the search strategy according to the optimization progress, which improves the adaptability and robustness of the algorithm.

[0019] (5) The present invention adopts a continuous population diversity monitoring and management mechanism, and prevents premature convergence through Shannon entropy measurement and a three-stage diversity recovery scheme. Compared with the static initialization method, dynamic diversity management reduces premature convergence and maintains effective exploration capability throughout the optimization process. The present invention maintains a computational efficiency of less than 50 milliseconds per planning cycle in all test scenarios. Even in complex environments with obstacle density as high as 2.0 threats / km³, the performance degradation is limited to within 28.3%.

[0020] (6) This invention has multi-objective optimization capabilities, comprehensively considering six optimization objectives: path length, threat avoidance, altitude constraint, path smoothing, energy consumption, and communication reliability. In the LANDSAT 9-derived scenario, the average path length and trajectory smoothness are greatly improved, achieving an effective balance among multiple objectives. This invention supports the swarm coordination of multiple UAVs and maintains stable performance under different terrain types (open terrain, hills, mountains, urban canyons) and obstacle densities. The dynamic obstacle handling capability enables the algorithm to adapt to time-varying environments and demonstrates excellent robustness in practical applications such as disaster response and smart city logistics. Attached Figure Description

[0021] Figure 1 This is a flowchart of the multi-UAV cooperative 3D trajectory planning method of the present invention; Figure 2 This is a schematic diagram illustrating the principle of the PHOENIX algorithm, a UAV cooperative trajectory planning model, in the embodiment. Figure 3 This is a schematic diagram illustrating the construction of a layered flight protection zone for unmanned aerial vehicles (UAVs) in the embodiment. Figure 4 This is a schematic diagram of the four-layer defense mechanism of the Crown Porcupine Optimizer (CPO) in the embodiment; Figure 5 This is a graph illustrating the effect of the chaos coefficient α on the initial entropy of the population in the example. Figure 6 The diagram shows a comparison between initialization using a chaotic enhancement strategy and random initialization for the UAV cooperative trajectory planning model in the embodiment. Figure 7 The following is a graph illustrating the variation of the nonlinear adjustment factor β in the examples; Figure 8 The illustration shows the dynamic management effect of population diversity in the example. Figure 9 The graph shows a comparison of the convergence curves of the PHOENIX algorithm in three scenarios. Figure 10 Examples of computational performance diagrams for the UAV cooperative trajectory planning model of this invention under different terrain complexities; Figure 11 The example provided illustrates a path planning view for multiple drones working collaboratively in an AirSim environment. Detailed Implementation

[0022] The present invention will be further described in detail below with reference to embodiments: Example like Figure 1 As shown, a multi-UAV cooperative 3D trajectory planning method based on a hybrid meta-heuristic algorithm is presented, the method comprising: S1. Construct a UAV cooperative trajectory planning model that includes cooperative defense constraints. The UAV cooperative trajectory planning model internally includes a 3D geographic map of the study area, and the start and end points of the UAV flight missions within the study area are delineated on the 3D geographic map. Preferably, as follows... Figure 3As shown, the collaborative defense constraint is constructed using the tiered flight protection zone based on the RTCA DO-263 aviation safety standard. The method involves defining a two-tiered cylindrical protection zone for each UAV: ​​a Collision Zone (CAZ) and a Protective Zone (PAZ). An example of the tiered flight protection zone construction is as follows: the CAZ has a radius of 100 feet (approximately 30.5 meters) and an HCAZ height of 100 feet, representing the core area where no other aircraft (including UAVs) are permitted to enter; the PAZ has a radius of 200 feet (approximately 61 meters) and an HCAZ height of 200 feet, representing a buffer zone where vigilance and preventative measures are required.

[0023] S2. Construct a drone cooperative system comprising N drones. A drone cooperative trajectory planning model allows all drones in the joint system to collaboratively search and simulate flight within the study area according to their flight missions on a 3D geographic map. Figure 2 As shown, the UAV cooperative trajectory planning model constructs a population based on the UAV flight trajectory as an individual. It executes the fusion cooperative defense strategy based on the PHOENIX algorithm and the iterative optimization process of antlion optimization random walk, and finally outputs the optimal UAV cooperative flight three-dimensional trajectory.

[0024] In some embodiments, the collaborative defense strategy includes a layered flight protection zone defense strategy and a two-layer collaborative optimization mechanism strategy. The layered flight protection zone defense strategy method includes combining and fusing the two-layer cylindrical protection zone of the UAV with the four-layer defense mechanism of the Crowned Porcupine Optimizer (CPO) to form a three-layer compliance architecture verification, such as... Figure 4 As shown, the first and second defense mechanisms of the Crowned Porcupine Optimizer (CPO) are constructed in association with the Collision Area Zone (CAZ), and the third and fourth defense mechanisms are constructed in association with the Protection Area Zone (PAZ). The three-layer compliance architecture verification includes size compliance verification, operational verification, and adaptive improvement verification. Size compliance verification verifies the correspondence and dimensions of each defense mechanism, CAZ, and PAZ. An example is shown below: The protection zone size is parameterized according to the DO-263 specification, with the CAZ radius set to 100 feet and the PAZ radius set to 200 feet. Based on the standard Time-of-Collapse (TTC) requirement, dynamic scaling is applied according to the aircraft speed. Operational verification verifies the horizontal and vertical defense mechanisms or zone separation during each optimization iteration. During each optimization iteration, explicit compliance checks are performed on candidate trajectories to verify the horizontal and vertical separation criteria, as expressed below: ; ; in, and These represent the positions of drones i and j at iteration time t, respectively. Set the drone speed (e.g., 15m / s). Set the minimum collision time threshold (e.g., 10 seconds). For the maximum climb / descent angle (e.g., set to 30°), non-standard trajectory segments are subject to excessively high cost penalties (e.g., set to 10). 6 This ensures that rejection is carried out during the optimization process. Adaptive improvement verification is used to increase the local sampling density for refined judgment and increase compliance margin when approaching the defense compliance boundary; when the trajectory segment approaches the DO-263 compliance boundary (within 10% of the minimum separation requirement), the algorithm dynamically increases the local sampling density (increases to 2 times the original) and applies targeted refinement operations to ensure robust compliance margin.

[0025] In some embodiments, the UAV cooperative trajectory planning model uses a chaos enhancement strategy to initialize the population. The chaos enhancement strategy introduces an interval-constrained Logistic chaotic mapping to generate a chaotic mapping operator, and the iterative equation is as follows: , This represents the internal state values ​​of the iterative equation (the states of all individuals in the population). The chaos coefficient is the coefficient used in this embodiment. The example is set to 3.8. The position initialization expression after chaotic mapping is as follows: ; in, and Let r be the upper and lower boundaries of the search space (which is the space of the study area), respectively. i This is a chaotic mapping operator. Shannon entropy is used to measure the diversity of population initialization. , Let be the population diversity at the t-th iteration. Let N be the probability density of an individual in subspace k at the t-th iteration, determined by an adaptive solution space partitioning based on a grid, where N is the total number of subspaces in the adaptive solution space (e.g., set to 10). Figure 5 As shown, when the chaos coefficient When the value is 3.8, the Shannon entropy reaches its peak (H≈2.87), verifying the promoting effect of the "marginal chaos" state on diversity in chaotic dynamics; the experimental entropy value is always higher than the theoretical lower bound, indicating that the constraint strategy avoids the chaotic sequence from falling into short-period oscillations while ensuring randomness. Figure 6A comparative analysis of chaotic initialization and stochastic initialization is presented. Across all test dimensions, chaotic initialization demonstrates superior distribution characteristics, improving search space coverage by 28.3% (p<0.01). Compared to uniform stochastic initialization in the baseline scenario, chaotic initialization reduces the average convergence time by 23.7% (p<0.01) and improves solution quality by 7.2% (p<0.05).

[0026] In some embodiments, the initial values ​​of the PHOENIX algorithm parameters in the UAV cooperative trajectory planning model are set as shown in Table 1. Table 1 Initial values ​​of PHOENIX algorithm parameters

[0027] In some embodiments, the two-layer collaborative optimization mechanism strategy includes an improved CPO defense mechanism and a fusion defense mechanism. The improved CPO defense mechanism includes a swarm defense strategy, a location defense strategy, a passive defense strategy, and an active defense strategy. The swarm defense strategy P group : Simulates the collective defensive behavior of a group of hogs (i.e., a population or group in a UAV cooperative trajectory planning model) when facing threats, for cooperative obstacle avoidance in collision areas; Positional defense strategy P position : Simulates the behavior of crested porcupines adjusting their position to achieve the optimal defensive posture, used for position optimization of protected areas; passive defense strategy P passive Simulates the defensive behavior of a crowned porcupine when it senses a potential threat but has not yet determined the direction of the threat; active defense strategy P active This study simulates the proactive defensive behavior of crowned porcupines after identifying a threat source. The group defense strategy involves all drones in the drone-based joint system, while the location-based defense strategy is also implemented. A drone cooperative trajectory planning model introduces an elite strategy, selecting the individual with the best fitness as the elite solution. Each individual then performs an antlion-optimized random walk around the elite individual. A fusion defense mechanism combining the antlion-optimized random walk and the elite strategy is used to improve the CPO defense mechanism for validation. The first layer of the two-layer collaborative optimization mechanism is an improved CPO defense mechanism, and the second layer is a fusion defense mechanism. ,in The location of an individual after the location update following the improved CPO defense mechanism. To integrate the updated defense mechanism, Let be the random walk position generated in the t-th iteration. The positions after the Antlion optimization random walk are normalized, and the normalized positions are shown in the following formula. ,in and Let be the minimum and maximum values ​​of the random walk of the i-th dimension variable, respectively. and Let be the minimum and maximum values ​​of the i-th dimension variable in the t-th iteration, respectively; the expression for the elite-policy-guided random walk is as follows: ,in The position an individual takes during a random walk around a fitness roulette wheel. The position of an individual after a random walk around an elite individual.

[0028] In some embodiments, a two-layer defense mechanism is constructed using an adaptive weight coefficient dynamic fusion optimization two-layer collaborative optimization strategy. The adaptive weight coefficients are dynamically adjusted with the iteration process using a non-linear decay method, as shown in the following expression: , , These are the maximum and minimum weights, respectively, and are set to the maximum weight in the initial stage of the iteration. (Example below:) =0.8 (in the initial stage, CPO is given a higher weight to achieve fast convergence), and in the later stage, the weight is set to the minimum value. (Example below:) =0.2, and later ALO weights were added to enhance global search. This is a non-linear adjustment factor (examples are shown below): =2.5, controlling the transition rate). This represents the maximum number of iterations (example value: T=1000). This represents the current iteration number. For example... Figure 7 As shown, the nonlinear adjustment factor The change curves demonstrate a smooth transition of weights from global exploration to local development; larger This allows the algorithm to maintain a relatively long exploration phase in the early stages and quickly shift to development in the later stages, making it suitable for incremental optimization in complex environments.

[0029] The convergence rate expression is as follows: ,in ( Example value is 0.15) and ( The example value is 0.102), which represents the Lipschitz constant for the improved CPO defense mechanism and the antlion-optimized random walk ALO, respectively.

[0030] In some embodiments, the UAV cooperative trajectory planning model incorporates a dynamic diversity management mechanism to constrain population diversity. This mechanism continuously monitors population diversity throughout the iterative optimization process. The dynamic diversity management mechanism uses Shannon entropy as a quantitative diversity indicator, and the expression for population diversity is as follows: , Let be the population diversity at the t-th iteration. Let be the probability density of an individual in subspace k at the t-th iteration, determined by an adaptive solution space partitioning based on a grid, where N is the total number of subspaces in the adaptive solution space. A critical threshold is set. When H(t) < H crit When this happens, a diversity recovery method is initiated. For example, a critical threshold H is set. crit =1.5, when H(t) < H crit When the time comes, the diversity restoration method is initiated. In this embodiment, the diversity restoration method adopts the following three-stage diversity restoration scheme: Phase 1 (Diversity Assessment): Identify convergence regions using density-based spatial clustering (DBSCAN algorithm, ε=0.1, MinPts=5) to determine whether the suboptimal solution region has premature convergence.

[0031] The second stage (targeted injection): Injecting new individuals into underdeveloped or low-density areas (i.e., underdeveloped or low-density areas of the study area), as expressed below: ,in Reference points for low-density regions (determined through K-means clustering). =0.3 is the adaptive step size parameter. The entropy gradient vector is calculated using the finite difference method, and the number of individuals injected is set to 10% of the population size (i.e., 20 individuals).

[0032] The third stage (adaptive search parameter adjustment): The search parameters controlling the exploration-development balance are dynamically adjusted based on the current diversity level, amplifying the exploration component during the diversity recovery phase; specifically, the step size of the random walk is increased to 1.5 times the original, and the influence range of elite individuals is increased. For example... Figure 8 As shown in the figure, the effect of dynamic population diversity management demonstrates how entropy-triggered intervention (vertical dashed line) prevents diversity collapse and maintains robust exploration throughout the optimization process. Statistical analysis confirms that dynamic diversity management reduces premature convergence by 37.8% compared to the static initialization method (p<0.01).

[0033] In some embodiments, the 3D geographic map includes obstacle data and dynamic obstacle data for the study area, and the UAV cooperative trajectory planning model dynamically manages obstacles using the following method: A1. Predict the trajectory of dynamic obstacles using the Kalman filter algorithm and a constant acceleration model, with a prediction time window. Dynamic adjustments are made based on obstacle speed and UAV maneuverability limitations. An example is shown below: The dynamic obstacle trajectory is predicted using a Kalman filter algorithm and a constant acceleration model, expressed as follows: , where the state vector Includes location and velocity information. Assuming the process noise follows a zero-mean Gaussian distribution with a covariance matrix Q = 0.01·I, the state transition matrix is ​​defined as follows: ; Prediction Time Window The speed of obstacles and the maneuverability limits of the drone are dynamically adjusted, as shown in the following formula. , For the safe obstacle avoidance distance of drones, The moving speed of the obstacle is constrained, with a maximum time window of 5 seconds.

[0034] A2. Select affected drones and trigger local replanning to avoid obstacles. Example: Trigger local replanning within a 5-meter radius of the affected drones, implementing a sliding window optimization method (window size of 5 waypoints). This method addresses the risk of direct collision while maintaining the optimal global path, ensuring rapid obstacle avoidance while preserving computational efficiency.

[0035] In some embodiments, the population sequence {X(t)} generated by the PHOENIX algorithm of the UAV cooperative trajectory planning model is a homogeneous Markov chain on a finite state space S, provided that it satisfies ergodicity (any state in state space S can reach any other state within a finite number of steps) and the elitist retention strategy (elite solutions X... * If the fitness of the algorithm is monotonically non-decreasing, then the algorithm converges to the global optimum with probability 1, as shown in the following formula. ;in, This is the set of globally optimal solutions.

[0036] Performance evaluation and validation of the PHOENIX algorithm for UAV cooperative trajectory planning model: Calculate the average path length reduction rate, threat exposure reduction rate, and trajectory smoothness improvement rate to evaluate the performance improvement compared to benchmark algorithms (PSO, GWO, CPO, ALO); statistically analyze the collision-free success rate to verify robustness in dynamic obstacle scenarios; measure the computation time for each planning cycle to ensure real-time performance (less than 50 milliseconds); evaluate the algorithm under different obstacle densities (0.2-2.0 threats / km). 3 Scalability under different terrain types (open terrain, hills, mountains, urban canyons).

[0037] In some embodiments, the UAV cooperative trajectory planning model further includes a multi-objective cost function comprising path length cost, threat avoidance cost, altitude constraint cost, path smoothing cost, energy consumption cost, and communication reliability cost. The path length cost F1 is obtained by calculating and summing the Euclidean distances between adjacent waypoints; the expression is as follows: ,in, Represents Euclidean distance. and Let (j, j+1) be the two adjacent waypoints of UAV i. UAV i has a total number of waypoints. The threat avoidance cost F2 is based on the distance d from the UAV to the obstacle. m With the radius R of the obstacle m The relationship between the drone diameter D and the safe distance S is calculated as follows: when the distance is less than the radius of the danger zone, the cost is infinitely high; when the distance is within the safe buffer zone, the cost increases as the distance decreases. The expression is as follows: Where M is the set of all threats in the search space, and each static threat is represented as a cylinder with a center coordinate O. m and radius R m Threat cost function f m Defined as: ; where d m Where D is the distance from the path segment to the center of the obstacle, D is the diameter of the drone, and S is the safe distance. This is the attenuation coefficient.

[0038] The altitude constraint cost F3 occurs when the drone's flight altitude exceeds the minimum altitude h. min and maximum height h max Apply a penalty when the range is exceeded; the expression is as follows: Among them, the height penalty function g h The definition is as follows: ; where h min and h max These are the minimum and maximum flight altitudes, respectively. This is the penalty coefficient.

[0039] Path smoothing cost F4, by evaluating turning angle and climbing angle Determine, including angle penalty coefficient and The expression is as follows: ;in, For the turning angle, For the climbing angle, and The penalty coefficient is used to calculate the turning angle using the following formula: ;in, and This is the projection vector of the path segment onto the horizontal plane. The formula for calculating the climb angle is: Energy consumption cost F5, taking into account the unit energy consumption P during level flight. motion Energy consumption per unit of ascent (P) climb and average flight speed v avg The expression is as follows: Among them, P motion For level flight unit energy consumption, P climb To increase the unit energy consumption, v avg The average flight speed is given. The communication reliability cost, F6, is calculated based on the distance from the UAV to the communication base station and the signal propagation rate, determining the communication delay; the expression is as follows: Where Cbase represents the coordinates of the communication base station, and c represents the signal propagation rate.

[0040] The multi-objective cost function applies cost constraints to each UAV flight and then weights them to obtain the total cost. The expression for the total cost function is as follows: ,in These are weighting coefficients used to balance the effects of different cost functions; This represents one of six costs: path length cost, threat avoidance cost, height constraint cost, path smoothing cost, energy consumption cost, and communication reliability cost. k represents the choice of one of these six costs. Let be the total cost of drone i. The drone cooperative trajectory planning model constrains all drones to minimize the total cost.

[0041] In some embodiments, the present invention further includes the following method: S3. Experimental verification and performance evaluation, the methods are as follows: Step 3.1 Baseline Scene Generation To verify the effectiveness of the method of this invention, experiments were conducted on real digital remote sensing image maps derived from publicly available LANDSAT 9 data. Regions with different topographical structures in the Tibet region of China were selected, and three baseline scenes were generated, such as... Figure 9 As shown.

[0042] Step 3.2 Convergence Characteristics Verification like Figure 9 As shown in the comparison of convergence curves of the PHOENIX algorithm in three scenarios, the method of this invention can reach the optimal solution with the fewest iterations, and its convergence speed is significantly better than benchmark algorithms such as CPO, ALO, PSO, and GWO. It achieves convergence in approximately 200 iterations in Map1, approximately 300 iterations in Map2, and approximately 400 iterations in Map3.

[0043] Step 3.3 Three-dimensional visualization trajectory planning The 3D path planning view generated by the PHOENIX algorithm shows that the algorithm can generate feasible paths that meet the preset cost function requirements, and no collisions occur during flight. The trajectories of the five drones are smooth and evenly distributed, effectively avoiding all static obstacles (yellow cylinders) while maintaining reasonable spacing between them.

[0044] Step 3.4 Computational Performance Evaluation like Figure 10 As shown, computational performance evaluations under different terrain complexities demonstrate that PHOENIX remains below the 50ms threshold in all test scenarios. In tests with obstacle densities ranging from 0.2 to 2.0 threats / km³, even in the most complex urban canyon scenario (obstacle density 2.0 threats / km³), the average planning cycle is only 47.2ms, less than 5.6% of the 50ms real-time threshold, with performance degradation limited to within 28.3%, exhibiting excellent scalability.

[0045] Step 3.5 AirSim Environment Verification To verify the applicability of the algorithm in real-world environments, hardware-in-the-loop testing was conducted in the AirSim environment. AirSim is a high-fidelity drone simulation platform based on Unreal Engine, providing accurate 3D environment simulation and collision detection capabilities. A city scene containing complex obstacles such as buildings and trees was constructed, and five drones were used as a joint drone system. The multi-drone cooperative 3D trajectory planning method of this invention was implemented, as follows: Figure 11 As shown, in the AirSim environment, collaborative 3D trajectory planning flight was performed. According to the "Collision Count" data recorded by the system, no collision events occurred during the entire flight, achieving a 100% collision-free success rate. This strongly demonstrates the robustness and applicability of the method of this invention in complex real-world environments. Experimental results show that the multi-UAV collaborative 3D trajectory planning method based on the hybrid metaheuristic algorithm of this invention outperforms existing methods in many aspects, including path length, threat avoidance, trajectory smoothness, and computational efficiency. It can generate safe, efficient, and coordinated flight trajectories while maintaining real-time performance, providing reliable technical support for multi-UAV systems in critical tasks such as disaster response and smart city logistics.

[0046] This embodiment combines a deep learning software platform with a high-fidelity simulation environment, enabling the method of this invention to flexibly adapt to different application scenarios. Technical personnel can customize and configure it according to specific needs to ensure that the multi-UAV trajectory planning system can meet the requirements of different industries. Through innovative technologies such as the collaborative use of hybrid optimization strategies, enhanced diversity of chaotic initialization, standardized security guarantees, adaptive weighting mechanisms, and dynamic diversity management, this method significantly improves the performance and reliability of multi-UAV collaborative trajectory planning, providing a clear technical path for those skilled in the art.

[0047] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for multi-unmanned aerial vehicle (UAV) cooperative three-dimensional trajectory planning based on a hybrid element heuristic algorithm, characterized in that: The method comprises: S1, constructing a UAV cooperative trajectory planning model containing cooperative defense constraints, a three-dimensional geographical map containing a study area is constructed inside the UAV cooperative trajectory planning model, and a starting point and an ending point of a UAV flight task in the study area are demarcated in the three-dimensional geographical map; S2, constructing a UAV cooperative system including N UAVs, the UAV cooperative trajectory planning model makes all UAVs in the UAV cooperative system search in the three-dimensional geographical map according to the UAV flight task in the study area, and finally outputs an optimal UAV cooperative flight three-dimensional trajectory through iterative optimization processing of the UAV flight trajectory as an individual, fusion of the cooperative defense strategy based on the PHOENIX algorithm, and ant lion optimization random walk.

2. The method of claim 1, wherein the method is based on a hybrid meta-heuristic algorithm. In method S1, the cooperative defense constraints are constructed by using layered flight protection zones, and the method comprises: demarcating a collision area CAZ and a protection area PAZ for each UAV.

3. The method of claim 2, wherein the method is based on a hybrid meta-heuristic algorithm. In method S2, the cooperative defense strategy comprises a layered flight protection zone defense strategy and a double-layer cooperative optimization mechanism strategy, the layered flight protection zone defense strategy comprises: combining and fusing the two-layer cylindrical protection zones of the UAVs with the four-layer defense mechanisms of the CPO to form a three-layer compliance architecture verification, the first and second defense mechanisms of the CPO are constructed in correspondence with the collision area CAZ, and the third and fourth defense mechanisms of the CPO are constructed in correspondence with the protection area PAZ; the three-layer compliance architecture verification comprises size compliance verification, operation verification and adaptive improvement verification, the size compliance verification is used for verifying the corresponding relationship and size of each defense mechanism, the collision area CAZ and the protection area PAZ, the operation verification is used for verifying the separation of the defense mechanisms or the areas in the horizontal and vertical directions during each iteration optimization, and the adaptive improvement verification is used for increasing the local sampling density for refined judgment and increasing the compliance margin when approaching the defense compliance boundary.

4. The method of claim 3, wherein the method is characterized in that: The double-layer cooperative optimization mechanism strategy comprises an improved CPO defense mechanism and a fusion defense mechanism, the improved CPO defense mechanism comprises a group defense strategy, a position defense strategy, a passive defense strategy and an active defense strategy, the group defense strategy is for the defense of all UAVs in the UAV cooperative system, and the position defense strategy is for the defense of the UAVs; the UAV cooperative trajectory planning model introduces an elite strategy and selects the individual with the best fitness in the population as an elite solution, and each individual performs ant lion optimization random walk around the elite individual, and the fusion defense mechanism combines the ant lion optimization random walk and the elite strategy to improve the CPO defense mechanism for defense verification.

5. The method of claim 4, wherein the method further comprises: The adaptive weight coefficient dynamic fusion optimization double-layer collaborative optimization mechanism strategy is constructed. The adaptive weight coefficient is adjusted dynamically with the iteration process in a nonlinear decay manner, and the expression is as follows: , , are the maximum and minimum values of the weight respectively, the maximum value of the weight is set in the initial stage of iteration , and the minimum value of the weight is set in the later stage of iteration , is a nonlinear adjustment factor, is the maximum number of iterations, is the current number of iterations.

6. The method of claim 1, wherein the method further comprises: The UAV cooperative trajectory planning model is also provided with a multi-objective cost function containing a path length cost, a threat avoidance cost, a height constraint cost, a path smoothing cost, an energy consumption cost and a communication reliability cost, the multi-objective cost function respectively performs cost constraints on the flight of each UAV and obtains a total cost through weighting, and the UAV cooperative trajectory planning model constrains all UAVs to have the lowest total cost.

7. The method of claim 1, wherein the method further comprises: The unmanned aerial vehicle cooperative trajectory planning model adopts a chaos enhancement strategy to initialize the population, and the chaos enhancement strategy introduces an interval constraint Logistic chaos mapping to generate a chaos mapping operator, and the iterative equation is as follows: , represents the internal state value of the iterative equation, is a chaos coefficient. 8.The method of claim 1, wherein: The drone cooperative trajectory planning model is constrained by a dynamic diversity management mechanism to manage population diversity. The dynamic diversity management mechanism uses Shannon entropy as a quantitative diversity index, and the expression of population diversity is as follows: , is the population diversity at the tth iteration, is the probability density of the individual in the subspace k at the tth iteration, determined by the grid-based adaptive solution space partitioning, N is the total number of subspace in the adaptive solution space; the critical threshold is set When H(t) < H crit , the diversity recovery method is started. 9.The method of claim 1, wherein: The three-dimensional geographic map contains obstacle data and dynamic obstacle data of the study area. The drone cooperative trajectory planning model dynamically manages obstacles using the following methods: A1, predict dynamic obstacle trajectory with Kalman filter algorithm and constant acceleration model, prediction time window Dynamic adjustment according to obstacle speed and UAV maneuverability A2, screen affected drones and trigger local re-planning to avoid obstacles.

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