A multi-unmanned aerial vehicle path planning method and system based on a quantum song hawk mechanism and a storage medium

Abstract

The application discloses a multi-unmanned aerial vehicle path planning method and system based on a quantum hawk mechanism and a storage medium, relates to the field of unmanned aerial vehicle path planning, and aims to solve the problem that the performance of the existing method is significantly reduced or even fails in a complex scene. The method comprises the following steps: step one, establishing a complex environment and threat source model; step two, setting a cost function in the process of unmanned aerial vehicle path planning; step three, initializing a quantum hawk algorithm; step four, calculating the fitness value and the optimal quantum position of each hawk; step five, an exploration stage, using a Cauchy inverse cumulative distribution mutation to enhance the population diversity and using a quantum rotation gate to evolve the quantum hawk position; step six, an exploitation stage, using a dynamic boundary strategy to avoid falling into a local optimal solution and using a quantum rotation gate to evolve the quantum hawk position; step seven, adopting a greedy selection strategy to determine the quantum hawk position of the next generation; and step eight, repeatedly executing steps five to seven, outputting the global optimal quantum hawk position, and obtaining a path planning result.

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 path planning method, system, and storage medium based on the quantum eagle mechanism. Background Technology

[0002] In the field of UAV path planning, intelligent path planning is receiving increasing attention as a core research direction, especially in areas such as complex environment adaptation, efficient task execution, and accurate target tracking. These aspects not only concern the autonomous flight capability of UAVs but also directly impact their practicality and effectiveness in various application scenarios. Compared to traditional path planning methods, swarm intelligence-based path planning methods offer high flexibility, dynamically adjusting to complex and changing environmental conditions, and achieving efficient task execution with limited resources. Individual members in the group explore and optimize paths through information sharing and collaboration, effectively avoiding errors that may arise from single navigation methods. Furthermore, this approach is applicable to more specific flight missions, improving the flexibility and success rate of UAVs and effectively avoiding the limitations of traditional methods that rely excessively on empirical rules. However, despite the significant achievements of swarm intelligence-based path planning methods, existing swarm intelligence algorithms still face challenges in complex environments such as mountainous and urban areas. These complex environments often contain numerous obstacles and irregular terrain, posing significant difficulties for UAV path planning. Therefore, how to further improve the performance of swarm intelligence algorithms in complex environments so that they can better adapt to these challenges has become a key issue that urgently needs to be addressed in the field of UAV path planning.

[0003] Significant progress has been made in path planning methods for swarm intelligence. Yao Xinyu et al., in their paper "Research on UAV 3D Path Planning Based on Improved Goal-bias RRT" published in *Flight Mechanics*, presented their research on UAV 3D path planning based on an improved Goal-bias RRT. By introducing the gravitational component and repulsive field constraint of the artificial potential field method during node expansion, the random tree expansion exhibits a directional bias towards the target point while avoiding obstacles. This algorithm significantly improves path planning performance in simple 3D environments with a single threat, but its ability to plan paths in complex environments requires further research. Hu Mingzhe et al., in their paper "UAV 3D Path Planning Based on A* Algorithm with Improved Heuristic Function" published in *Acta Armamentarii*, addressed the problems of low real-time performance, high computational cost, and severe memory consumption in traditional A* algorithms for 3D path planning. They optimized the heuristic function of the A* algorithm, adjusted its weight values, and used the heuristic function as the base for exponential operations, thereby improving search efficiency. The optimized heuristic function weight design depends on specific application scenarios and experimental data. This means that under different environmental conditions, the weight values ​​may need to be readjusted to achieve the best results, and it is prone to getting trapped in local optima. Peng Yi et al., in their paper "Improved PID Search Algorithm for UAV Path Planning in Mountainous Environments" published in the *Journal of System Simulation*, introduced a set of optimal points to make the population distribution more uniform, increasing population diversity and improving the algorithm's global search capability. They also used the Q-learning algorithm to map the action space to PID parameter adjustment strategies and designed an exploration rate factor to improve the algorithm's exploratory and solution capabilities for different strategies. This research significantly improved the path planning performance of single UAVs in mountainous environments, but further research is needed on collaborative planning for multiple UAVs. Lü Chao et al., in their paper "UAV Hybrid Path Planning Based on Hierarchical Deep Reinforcement Learning" published in the *Journal of Beijing University of Aeronautics and Astronautics*, organically combined the two sub-tasks required for autonomous UAV flight—autonomous obstacle avoidance and flight towards waypoints after global path planning—using a hierarchical model to achieve effective functional integration. This method can achieve the expected function in a two-dimensional environment. However, in a three-dimensional environment, the training workload increases significantly, especially in terms of training efficiency, model generalization ability, and computational resource consumption, which pose significant challenges.

[0004] Existing literature reviews indicate that multi-UAV path planning methods perform well in simple scenarios or environments with a single type of obstacle, but their performance degrades significantly or even fails in complex scenarios. Furthermore, existing path planning algorithms often face trade-offs between time efficiency and convergence speed, and convergence accuracy and real-time performance, and struggle to effectively avoid local optima, leading to noticeable inflection points in the path planning results. Summary of the Invention

[0005] The technical problem to be solved by this invention is:

[0006] Existing multi-UAV path planning methods perform well in simple scenarios or environments with a single type of obstacle, but their performance drops significantly or even fails in complex scenarios. At the same time, they face the trade-off between time efficiency and convergence speed, and convergence accuracy and real-time performance, and it is difficult to effectively avoid local optima, resulting in obvious inflection points in the path planning results.

[0007] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0008] This invention provides a multi-UAV path planning method based on the quantum eagle mechanism, comprising the following steps:

[0009] Step 1: Establish a model of complex environments and threat sources;

[0010] Step 2: Set the cost function in the UAV path planning process;

[0011] Step 3: Initialize the quantum hawk swarm and set parameters;

[0012] Step 4: Calculate the fitness value of each hawk in the quantum hawk swarm based on the cost function in the UAV path planning process, and initialize the optimal quantum position of the quantum hawk swarm;

[0013] Step 5: The quantum song eagle swarm performs the exploration phase, using Cauchy inverse cumulative distribution mutation to enhance population diversity and using quantum rotation gates to evolve the quantum position of the quantum song eagles;

[0014] Step Six: The quantum hawk swarm is executed in the development phase, using a dynamic boundary strategy to avoid getting trapped in local optima and using quantum rotation gates to evolve the quantum position of the quantum hawks;

[0015] Step 7: Use a greedy selection strategy to determine the quantum position of the next generation of quantum singing eagles, and update the quantum singing eagle positions and the optimal quantum position of the singing eagle swarm;

[0016] Step 8: Repeat steps 5 to 7 until the maximum number of iterations T is reached, output the globally optimal quantum eagle position, and map it to the path planning result.

[0017] Furthermore, step one includes the following steps:

[0018] Let the starting coordinates of the planning space be... The endpoint coordinates are Let the total number of threat sources be C, and the threat regions generated by these sources be represented by a cylindrical model, where the center of the c-th threat region is O. c (x c y c , z c ), with radius R cThe mountain peaks are simulated using an exponential function and treated as terrain obstacles. Let the total number of mountain peaks be N, and the ground clearance of the i-th drone be h. i Its mathematical model is:

[0019]

[0020] Where z is the height of the mountain peak, (x i y i (x) represents the center coordinates of the i-th mountain peak. ri and y ri These represent the extent of the expansion of the i-th mountain peak in the x and y directions, respectively.

[0021] Furthermore, step two includes the following steps:

[0022] Let P be the coordinates of the j-th node of the i-th UAV path. ij =(x ij y ij , z ij If the two adjacent nodes P are... ij To P i，j+1 The distance between them is ||P ij P i，j+1 ||2, then the total cost function of the i-th path of the UAV is F1(p i )for:

[0023]

[0024] Where n is the total number of nodes in the path, p i Let be the set of all nodes in the i-th flight path of the UAV;

[0025] Flight altitude cost function H ij for:

[0026]

[0027] Where h ij h is the height of the i-th UAV at the j-th flight node above the ground. min and h max These are the minimum and maximum permissible altitudes above the ground during flight;

[0028] Then the total cost of the drone's altitude is F2(p i )for:

[0029]

[0030] Assuming the drone's diameter is D, the safe distance between the drone and the threat source is S, and the drone flies from point P... ij To P i，j+1The flight path between the two nodes to the threat source center O c The vertical distance is d c Then for drones from P ij To P i,j+1 Security cost T c (P ij P i，j+1 )for:

[0031]

[0032] Then the total threat cost function F3(p) i )for:

[0033]

[0034] Suppose the drone starts from P ij To P i,j+1 Then to P i,j+2 The node's projection point on the XOY plane is P′. ij 、P′ i，j+1 and P′ i，j+2 Then line segment P′ ij P′ i，j+2 The extension of the line segment P′ i，j+1 P′ i，j+2 The angle formed is the turning angle. Let path node P i,j+2 On line segment P ij P i,j+1 The projection point on the plane is P″ i，j+2 Then line segment P i,j+1 P i,j+2 With line segment P i,j+1 P″ i，j+2 The angle formed is the climbing angle. The total turning cost of the UAV's flight path is F4(p i )for:

[0035]

[0036] Where a1 and a2 are the weights of the turning angle cost and the climb angle cost, and a1 + a2 = 1, then the cost function in the UAV path planning process is expressed as: b k Let be the weight coefficient of the k-th cost function, and

[0037] Furthermore, step three includes the following steps:

[0038] Let p be the starting point for the quantum eagle flock's flight. s =[x s y s zs ] T The flight destination is p e =[x e y e z e ] T The flight path of the eagle can be represented by the set of points from the starting point to the ending point as follows:

[0039]

[0040] Where M is the total number of path points, and satisfies M = I ndex (p e )-I ndex (p s )+1,I ndex (p s ) and I ndex (p e ) represent the labels of the starting point and the ending point, respectively. When m = 1, p m Describes the flight start point and satisfies p m =p s When m = M, p m Indicates the flight destination and satisfies p m =p e ;

[0041] Let the size of the quantum hawk population be H, the maximum number of iterations be T, and the iteration number be t, where t∈[1,T]; at the t-th iteration, the quantum position of the i-th hawk in the O-dimensional search space is... i = 1, 2, ..., H; when t = 1, initialize each dimension of the quantum position of the first-generation quantum eagle to a uniform random number between [0, 1].

[0042] Furthermore, step four includes the following steps:

[0043] In the t-th iteration, each dimension of all quantum hawk positions is mapped to the path solution space, resulting in the mapped state of the quantum hawk as follows:

[0044]

[0045] The mapping equation is:

[0046]

[0047] in Denotes the lower bound of the j-th dimension. Denotes the upper bound of the j-th dimension, j = 1, 2, ..., O. The node set of the UAV flight path constructed after mapping each dimension of the quantum position of the i-th quantum eagle in the t-th generation to the range of the path solution space. The corresponding quantum position of the t-th quantum hawk in the j-th dimension of the t-th generation is used to obtain its fitness value by substituting it into the comprehensive cost function. The optimal quantum position found by the quantum hawk swarm up to generation t is denoted as .

[0048] Furthermore, step five includes the following steps:

[0049] The quantum hawk swarm is in the exploration phase. The i-th quantum hawk of the (t+1)-th generation has the j-th quantum position. The update equation is:

[0050]

[0051] in The quantum rotation angle during the exploratory phase;

[0052] During the expanded exploration phase, the quantum eagle, by soaring vertically to increase its search range, obtained the following quantum rotation angle:

[0053]

[0054] in Let γ1 be the optimal quantum position up to the j-th dimension in the t-th generation, and let γ1 be a random number uniformly distributed in the interval [0, 1].

[0055] During the shrinking exploration phase, the quantum rotation angle in preparation for the landing and attack phase is:

[0056]

[0057] Where L evy For Levi's flight strategy:

[0058]

[0059]

[0060] Where s and β are constants, γ2 and γ3 are random numbers uniformly distributed in the interval [0, 1], and Γ is the gamma function;

[0061] The following results were obtained by performing Cauchy inverse cumulative distribution mutation on the quantum eagle population:

[0062]

[0063] Where γ4 and γ5 are random numbers uniformly distributed in the interval [0, 1];

[0064] The newly generated quantum eagle quantum position Each dimension is mapped to the path solution space to obtain the mapped state of the quantum eagle. And calculate the fitness value like Then the transient local optimal quantum position of the i-th quantum eagle up to generation t+1 is determined. otherwise The value remains unchanged; the globally optimal quantum position is set to [value] until generation t+1.

[0065] Furthermore, as described in step six, after completing the exploration phase, the quantum hawk swarm executes the development phase, using a dynamic boundary strategy to avoid getting trapped in local optima and using quantum rotation gates to evolve the quantum positions of the quantum hawks, including the following steps:

[0066] The quantum hawk swarm is in the development phase, and the j-th quantum position of the i-th quantum hawk in the (t+1)-th generation is... The update equation is:

[0067]

[0068] in Quantum rotation angle during the development phase;

[0069] First, the quantum rotation angle obtained by the Quantum Hawk through its expanded development strategy is:

[0070]

[0071] Where γ6 and γ7 are uniformly distributed random numbers in the interval [0, 1], and α and δ are development and adjustment parameters. Let i be the average quantum position of the i-th individual in the j-th dimension of the (t+1)-th generation. Let i be the optimal quantum position of the i-th individual in the j-th dimension of the (t+1)-th generation;

[0072] Then, the quantum eagle walks and grasps, and executes the quantum rotation angle for the shrinking development phase:

[0073]

[0074] Q F To balance the quality function value of the search strategy, G1 represents the movement of the prey being tracked, G = 2 × γ 11 -1, G2 represents the linearly decreasing flight slope value. Among them, γ8, γ9, γ 10 and γ 11 A random number uniformly distributed within the interval [0, 1].

[0075] Then, the quantum rotation angle is updated using a dynamic boundary strategy:

[0076]

[0077] in A is a constant. It is a random number between [0, 1].

[0078] Furthermore, step seven includes the following steps:

[0079] Quantum position of the quantum eagle Each dimension is mapped to the path solution space to obtain the mapped state of the quantum eagle. And calculate the fitness value A greedy strategy is used to determine the quantum position of the next-generation quantum eagle. Then the local optimal quantum position of the i-th quantum eagle up to generation t+1 is determined. otherwise The best quantum position among the locally optimal quantum positions up to generation t+1 is set as the globally optimal quantum position up to generation t+1, denoted as .

[0080] The present invention also provides a multi-UAV path planning system based on the quantum eagle mechanism. The system has a program module corresponding to the steps of the method described in any of the above technical solutions, and executes the steps in the multi-UAV path planning method based on the quantum eagle mechanism when running.

[0081] The present invention also provides a computer-readable storage medium storing a computer program configured to, when invoked by a processor, implement the steps of the multi-UAV path planning method based on the quantum eagle mechanism described in any of the above technical solutions.

[0082] Compared with the prior art, the beneficial effects of the present invention are:

[0083] (1) This invention focuses on the path planning problem in complex mountainous urban environments. By introducing Cauchy inverse cumulative distribution variation and dynamic boundary strategies, it effectively enhances the diversity of solutions and avoids the population from getting trapped in local optima when searching for paths. At the same time, this invention directly addresses the path planning problem in complex mountainous urban environments, which not only improves the performance of path planning, but also enables the Quantum Eagle algorithm to solve UAV flight paths with lower overall costs.

[0084] (2) The quantum eagle optimization algorithm proposed in this invention optimizes the update method of local and global optimal solutions by designing a quantum rotation gate evolution strategy based on quantum encoding. This not only improves the convergence accuracy of the algorithm, but also enhances its adaptability to complex environments and effectively improves the running efficiency of the algorithm in high-dimensional search; it provides a new solution to the UAV path planning problem and demonstrates stronger search capabilities and robustness. Attached Figure Description

[0085] Figure 1 This is a flowchart of the multi-UAV path planning method based on the quantum eagle mechanism in an embodiment of the present invention;

[0086] Figure 2 This is a convergence curve of the path cost function value versus the number of iterations in a simple environment according to an embodiment of the present invention;

[0087] Figure 3 This is a 3D simulation diagram of multi-UAV path planning in a simple environment according to an embodiment of the present invention;

[0088] Figure 4 A two-dimensional top view of multi-UAV path planning in a simple environment in this embodiment of the invention;

[0089] Figure 5 Convergence curves showing the relationship between path cost function value and iteration number in complex environments in this embodiment of the invention;

[0090] Figure 6 A 3D simulation diagram of multi-UAV path planning in a complex environment in an embodiment of the present invention;

[0091] Figure 7 A two-dimensional top view of multi-UAV path planning in a complex environment in an embodiment of the present invention. Detailed Implementation

[0092] 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.

[0093] 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.

[0094] Specific Implementation Plan 1: Combining Figure 1 As shown, this invention provides a multi-UAV path planning method based on the quantum eagle mechanism, comprising the following steps:

[0095] Step 1: Establish an environmental and threat model for mountainous cities;

[0096] Step 2: Set the cost function in the UAV path planning process;

[0097] Step 3: Initialize the quantum hawk swarm and set parameters;

[0098] Step 4: Calculate the fitness value of each hawk in the quantum hawk swarm based on the cost function in the UAV path planning process, and initialize the optimal quantum position of the quantum hawk swarm;

[0099] Step 5: The quantum song eagle swarm performs the exploration phase, using Cauchy inverse cumulative distribution mutation to enhance population diversity and using quantum rotation gates to evolve the quantum position of the quantum song eagles;

[0100] Step Six: The quantum hawk swarm is executed in the development phase, using a dynamic boundary strategy to avoid getting trapped in local optima and using quantum rotation gates to evolve the quantum position of the quantum hawks;

[0101] Step 7: Apply a greedy selection strategy to determine the quantum position of the next generation of quantum hawks, and update the quantum hawk position and the optimal quantum position of the hawk swarm;

[0102] Step 8: Determine if the iteration count t has reached the maximum iteration count T. If it has not reached the maximum iteration count T, let t = t + 1 and return to step 5. If it has reached the maximum iteration count T, terminate the evolution, output the globally optimal quantum eagle position, and map it to the path planning result.

[0103] Specific Implementation Plan Two: Step One includes the following steps:

[0104] In complex mountainous urban environments, drones may encounter terrain obstacles and other threats. Let the starting coordinates of the planning space be... The endpoint coordinates are Let the total number of threat sources be C, and the threat regions generated by these sources be represented by a cylindrical model, where the center of the c-th threat region is O. c (x c y c , z c ), with radius R c The mountain peaks are simulated using an exponential function and treated as terrain obstacles. Let the total number of mountain peaks be N, and the ground clearance of the i-th drone be h. i Its mathematical model is:

[0105]

[0106] Where z is the height of the mountain peak, (x i y i (x) represents the center coordinates of the i-th mountain peak. ri and y ri These represent the extent of the i-th mountain peak's expansion in the x and y directions, respectively. This implementation scheme is otherwise identical to Implementation Scheme 1.

[0107] Specific implementation plan three: Step two includes the following steps:

[0108] The path distance cost during drone flight is mainly related to the total flight path length from the starting point to the destination. During flight, Euclidean distance is used to calculate the distance between adjacent nodes. Let P be the coordinate of the j-th node in the i-th drone path. ij =(x ij y ij , z ij If the two adjacent nodes P are... ij To P i，j+1 The distance between them is ||P ij P i,j+1 ||2, then the total cost function of the i-th path of the UAV is F1(p i )for:

[0109]

[0110] Where n is the total number of nodes in the path, p i Let be the set of all nodes in the i-th flight path of the UAV;

[0111] Drones flying in the city need to stay within a set altitude range, so a flight altitude cost function needs to be set. When the altitude range is exceeded, the altitude cost is increased to correct the result.

[0112] The flight altitude cost function is the cost of the drone's altitude above the ground during flight; the higher the altitude, the greater the cost. The flight altitude cost function H... ij for:

[0113]

[0114] Where h ij h is the height of the i-th UAV at the j-th flight node above the ground. min and h max These are the minimum and maximum permissible altitudes above the ground during flight;

[0115] Total cost of drone altitude F2(p i )for:

[0116]

[0117] The threat source center that generates threat costs when a drone passes through a threat area is O. c Assuming the diameter of the drone is D, the safe distance between the drone and the threat source is S, and the drone flies from point P... ij To P i，j+1 The flight path between the two nodes to the threat source center O c The vertical distance is d c Then for drones from P ijTo P i，j+1 The security cost is:

[0118]

[0119] The total threat cost function is then:

[0120]

[0121] To make the flight path as smooth as possible, the turning angle φ during the drone's flight is introduced. ij and the angle of ascent θ ij Let's calculate the cornering cost. Assume the drone starts from point P... ij To P i，j+1 Then to P i，j+2 The node's projection point on the XOY plane is P′. ij 、P′ i，j+1 and P′ i，j+2 Then line segment P′ ij P′ i，j+2 The extension of the line segment P′ i，j+1 P′ i，j+2 The angle formed is the turning angle. Let path node P i，j+2 On line segment P ij P i,j+1 The projection point on the plane is P″ i，j+2 Then line segment P i,j+1 P i,j+2 With line segment P i,j+1 P″ i，j+2 The angle formed is the climbing angle. The total turning cost of the drone's flight path is:

[0122]

[0123] Where a1 and a2 are the weights of turning angle cost and climb angle cost, and a1+a2=1;

[0124] The cost function in the UAV path planning process is expressed as:

[0125]

[0126] Where b k Let be the weight coefficient of the k-th cost function, and This implementation plan is otherwise the same as Implementation Plan Two.

[0127] Specific implementation plan four: Step three includes the following steps:

[0128] Let p be the starting point for the quantum eagle flock's flight. s =[x s ys z s ] T The flight destination is p e =[x e y e z e ] T The flight path of the eagle can be represented by the set of points from the starting point to the ending point as follows:

[0129]

[0130] Where M is the total number of path points, and satisfies M = I ndex (p e )-I ndex (p s )+1,I ndex (p s ) and I ndex (p e ) represent the labels of the starting point and the ending point, respectively. When m = 1, p m Describes the flight start point and satisfies p m =p s When m = M, p m Indicates the flight destination and satisfies p m =p e ;

[0131] Let the size of the quantum hawk population be H, the maximum number of iterations be T, and the iteration number be t, where t∈[1,T]; at the t-th iteration, the quantum position of the i-th hawk in the O-dimensional search space is... i = 1, 2, ..., H; when t = 1, initialize each dimension of the quantum position of the first-generation quantum eagle to a uniform random number between [0, 1]. This implementation scheme is otherwise the same as specific implementation scheme three.

[0132] Specific implementation plan five: Step four includes the following steps:

[0133] In the t-th iteration, each dimension of all quantum hawk positions is mapped to the path solution space, resulting in the mapped state of the quantum hawk as follows:

[0134]

[0135] The mapping equation is:

[0136]

[0137] in Denotes the lower bound of the j-th dimension. Let H represent the upper bound of the j-th dimension, i = 1, 2, ..., H, j = 1, 2, ..., O. The node set of the UAV flight path constructed after mapping each dimension of the quantum position of the i-th quantum eagle in the t-th generation to the range of the path solution space. The corresponding quantum position of the i-th quantum hawk in the j-th dimension of the t-th generation is used to obtain its fitness value by substituting it into the comprehensive cost function. The optimal quantum position found by the quantum hawk swarm up to generation t is denoted as . This implementation plan is otherwise the same as Specific Implementation Plan Four.

[0138] Specific implementation plan six: Step five includes the following steps:

[0139] During the exploration phase of the quantum hawk swarm, the update equation for the j-th dimension quantum position of the i-th quantum hawk in the (t+1)-th generation is:

[0140]

[0141] Where i = 1, 2, ..., H, j = 1, 2, ..., O, The quantum rotation angle during the exploratory phase;

[0142] The exploration is divided into two phases: expanding the exploration and narrowing the exploration. In the expanding exploration phase, the quantum eagle expands its search range by soaring vertically to obtain the quantum rotation angle as follows:

[0143]

[0144] in Let γ1 be the optimal quantum position up to the j-th dimension in the t-th generation, and let γ1 be a random number uniformly distributed in the interval [0, 1].

[0145] Then, during the shrinking exploration phase, the quantum rotation angle for preparing for the landing and attack phase is:

[0146]

[0147] Where L evy For Levi's flight strategy:

[0148]

[0149]

[0150] Where s is a constant fixed at 0.01, β is a constant fixed at 1.5, γ2 and γ3 are random numbers uniformly distributed in the interval [0, 1], and Γ represents the gamma function;

[0151] The following results were obtained by performing Cauchy inverse cumulative distribution mutation on the quantum eagle population:

[0152]

[0153] Where γ4 and γ5 are random numbers uniformly distributed in the interval [0, 1];

[0154] The newly generated quantum eagle quantum position Each dimension is mapped to the path solution space to obtain the mapped state of the quantum eagle. And calculate the fitness value like Then the transient local optimal quantum position of the i-th quantum eagle up to generation t+1 is determined. otherwise The value remains unchanged; the globally optimal quantum position is set to [value] until generation t+1. This implementation plan is otherwise the same as Implementation Plan Five.

[0155] Specific Implementation Plan Seven: After completing the exploration phase as described in Step Six, the quantum hawk swarm executes the development phase, using a dynamic boundary strategy to avoid getting trapped in local optima and using quantum rotation gates to evolve the quantum position of the quantum hawks, including the following steps:

[0156] During the development phase of the quantum hawk swarm, the update equation for the j-th dimension quantum position of the i-th quantum hawk in the (t+1)-th generation is:

[0157]

[0158] in Quantum rotation angle during the development phase;

[0159] The development is divided into two phases: expansion and contraction. First, the quantum eagle executes the expansion strategy to obtain the quantum rotation angle:

[0160]

[0161] Where γ6 and γ7 are uniformly distributed random numbers in the interval [0, 1], and α and δ are development and adjustment parameters. Let i be the average quantum position of the i-th individual in the j-th dimension of the (t+1)-th generation. Let i be the optimal quantum position of the i-th individual in the j-th dimension of the (t+1)-th generation;

[0162] Then, the quantum eagle walks and grasps, and executes the quantum rotation angle for the shrinking development phase:

[0163]

[0164] Q F To balance the quality function value of the search strategy, G1 represents the movement of the prey being tracked, G1 = 2 × γ 11 -1, G2 represents the linearly decreasing flight slope value. Among them, γ8, γ9, γ 10 and γ 11 A random number uniformly distributed within the interval [0, 1].

[0165] Then, the quantum rotation angle is updated using a dynamic boundary strategy:

[0166]

[0167] in A is a constant. The result is a random number between [0, 1]. This implementation scheme is otherwise identical to specific implementation scheme six.

[0168] Specific implementation plan eight: Step seven includes the following steps:

[0169] The newly generated quantum eagle quantum position Each dimension is mapped to the path solution space to obtain the mapped state of the quantum eagle. And calculate the fitness value A greedy strategy is used to determine the quantum position of the next-generation quantum eagle. Then the local optimal quantum position of the i-th quantum eagle up to generation t+1 is determined. otherwise The best quantum position among the locally optimal quantum positions up to generation t+1 is set as the globally optimal quantum position up to generation t+1, denoted as . This implementation plan is otherwise the same as Specific Implementation Plan VII.

[0170] The multi-UAV path planning method (algorithm) based on the quantum eagle mechanism proposed in this invention is the underlying technical core of this invention, and various products can be derived based on the algorithm.

[0171] Based on the method proposed in this invention, a multi-UAV path planning system based on the quantum eagle mechanism 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 path planning method based on the quantum eagle mechanism when running.

[0172] 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 aforementioned multi-UAV path planning method based on the quantum eagle mechanism when invoked by a processor. In other words, the invention is materialized on a carrier, becoming a computer program product.

[0173] 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.

[0174] 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.

[0175] The beneficial effects of the present invention will be described below with reference to specific embodiments.

[0176] Example 1

[0177] Based on the actual scale of the local mountain city, the coordinate unit is set to meters (m), with the starting and ending coordinates being (150, 150, 50) and (900, 720, 50) respectively. The horizontal coordinate range of the planning space is set to [0, 1000], the vertical coordinate range to [0, 1000], and the altitude range to [0, 300]. The population size is set to H = 100, and the number of iterations is T = 600. Multi-UAV path planning in a simple environment is as follows: Figure 3 and 4 As shown in Table 1, the threat source parameter settings are as follows: numbers 1-4 represent the threat source parameter settings for simple environments; multi-UAV path planning in complex environments is as follows: Figure 6 and 7As shown, numbers 6-10 represent the parameter settings for threat sources in complex environments. To verify the effectiveness of the proposed QMAO algorithm in multi-UAV path planning, simulation experiments were conducted in mountainous environments with obstacles of varying complexity. Simultaneously, the Aquila Optimizer (AO), Polar Lights Optimization (PLO), Moss Growth Optimization (MGO), and Educational Competitive Optimization (ECO) algorithms were compared and analyzed with the Quantum Music Aquila Optimize (QMAO) algorithm of this invention under the same conditions. The path planning results in simple and complex environments are shown below. Figure 2 and Figure 5 As shown in the figure, the convergence curves of each algorithm demonstrate that the QMAO algorithm proposed in this invention can significantly reduce the overall cost of multi-UAV path planning results, yielding the shortest and smoothest paths. It not only exhibits excellent hazard avoidance capabilities in simple environments but also maintains good performance in complex environments, enhancing the algorithm's robustness, avoiding local optima in the path planning process, and overcoming the limitation of existing optimization algorithms that experience drastic performance degradation when facing path planning problems in complex environments.

[0178] Table 1 Threat Source Parameter Settings

[0179]

[0180]

[0181] 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.

Claims

1. A multi-UAV path planning method based on the quantum eagle mechanism, characterized in that, Includes the following steps: Step 1: Establish a model of complex environments and threat sources; Step 2: Set the cost function in the UAV path planning process; Step 3: Initialize the quantum hawk swarm and set parameters; Step 4: Calculate the fitness value of each hawk in the quantum hawk swarm based on the cost function in the UAV path planning process, and initialize the optimal quantum position of the quantum hawk swarm; Step 5: The quantum song eagle swarm performs the exploration phase, using Cauchy inverse cumulative distribution mutation to enhance population diversity and using quantum rotation gates to evolve the quantum position of the quantum song eagles; Step Six: The quantum hawk swarm is executed in the development phase, using a dynamic boundary strategy to avoid getting trapped in local optima and using quantum rotation gates to evolve the quantum position of the quantum hawks; Step 7: Use a greedy selection strategy to determine the quantum position of the next generation of quantum singing eagles, and update the quantum singing eagle positions and the optimal quantum position of the singing eagle swarm; Step 8: Repeat steps 5 through 7 until the maximum number of iterations is reached. Output the globally optimal quantum eagle position, which is then mapped to the path planning result; Step five includes the following steps: The quantum eagle swarm is in the exploratory phase, the first... The generation Quantum Eagle Quantum position The update equation is: in The quantum rotation angle during the exploratory phase; During the expanded exploration phase, the quantum eagle, by soaring vertically to increase its search range, obtained the following quantum rotation angle: in , As of the date The generation The optimal quantum position of dimensionality. for A random number uniformly distributed within the interval, where T is the maximum number of iterations; During the shrinking exploration phase, the quantum rotation angle in preparation for the landing and attack phase is: in For Levi's flight strategy: in and It is a constant. and for Uniformly distributed random numbers within an interval. It is a gamma function; The following results were obtained by performing Cauchy inverse cumulative distribution mutation on the quantum eagle population: in and for A random number that is uniformly distributed within an interval; The newly generated quantum eagle quantum position Each dimension is mapped to the path solution space to obtain the mapped state of the quantum eagle. And calculate the fitness value. ,like Then it is determined until up to the generation Transient Local Optimal Quantum Position of a Quantum Hawk ;otherwise The value remains unchanged; until The global optimal quantum position is set to ; Step Six: After completing the exploration phase, the quantum hawk swarm executes the development phase, using a dynamic boundary strategy to avoid getting trapped in local optima and using quantum rotation gates to evolve the quantum positions of the quantum hawks. This includes the following steps: The Quantum Eagle Swarm is in the development phase, the first... The generation Quantum Eagle Quantum position The update equation is: in Quantum rotation angle during the development phase; First, the quantum rotation angle obtained by the Quantum Hawk through its expanded development strategy is: in and for Uniformly distributed random numbers within an interval. and To adjust parameters for development, For the first The generation Vidi The average quantum position of each individual For the first The generation Vidi The optimal quantum position of each individual; Then, the quantum eagle walks and grasps, and executes the quantum rotation angle for the shrinking development phase: in To balance the quality function value of the search strategy, , This indicates the tracking of the prey's movement. , This represents a linearly decreasing flight slope value. ,in , , and for A random number that is uniformly distributed within an interval; Then, the quantum rotation angle is updated using a dynamic boundary strategy: in , It is a constant. for A random number between [a certain number of points].

2. The multi-UAV path planning method based on the quantum eagle mechanism according to claim 1, characterized in that, Step one includes the following steps: Let the starting coordinates of the planning space be... The endpoint coordinates are Let the total number of threat sources be The threat area generated by the threat source is represented by a cylindrical model, where the first... The center of each threat area is , radius is The mountain peaks are simulated using an exponential function and treated as terrain obstacles. Let the total number of mountain peaks be... , No. The drone's altitude above the ground is Its mathematical model is: in The height of the mountain peak Indicates the first The center coordinates of the mountain peak and They represent the first The mountain peak is and The degree of expansion in direction.

3. The multi-UAV path planning method based on the quantum eagle mechanism according to claim 2, characterized in that, Step two includes the following steps: Let the first The first drone path The coordinates of each node are Then two adjacent nodes arrive The distance between them is Then the total cost function of the i-th path of the UAV for: in This represents the total number of nodes in the path. For drones The set of all nodes in a flight path; Flight altitude cost function for: in It is the first The first drone The altitude of each flight node above the ground and These are the minimum and maximum permissible altitudes above the ground during flight; The total cost of drone altitude for: Assume the diameter of the drone is The safe distance between the drone and the threat source is During the flight of the drone arrive Flight line segment between two nodes to the center of the threat source The vertical distance is For drones from arrive security costs for: Then the total threat cost function for: ； Let the drone be from arrive Then The node, its projection point on the XOY plane is , and Then the line segment extensions and line segments The angle formed is the turning angle. Set path nodes Online segment The projection point on the plane is Then the line segment With line segment The angle formed is the climbing angle. The total turning cost of the drone's flight path for: in and The weights for turning angle cost and climb angle cost are given, and The cost function in the UAV path planning process is expressed as: , For the first The weighting coefficients of each cost function, and .

4. The multi-UAV path planning method based on the quantum eagle mechanism according to claim 3, characterized in that, Step three includes the following steps: The starting point for the quantum eagle flock's flight is set as The flight destination is The flight path of the eagle can be represented by the set of points from the starting point to the ending point as follows: in Let be the total number of path points, and satisfy . , and The labels represent the start and end points respectively. hour, Indicates the flight start point and satisfies ;when hour, Indicates the flight destination and satisfies ; The size of the Quantum Song Eagle population is set as follows: The maximum number of iterations is The iteration label is , ;No. During the nth iteration, the 1st A song eagle in The quantum position in the dimensional search space is , ;when At that time, each dimension of the quantum position of the first-generation quantum eagle is initialized as Uniformly distributed random numbers between [a certain range].

5. The multi-UAV path planning method based on the quantum eagle mechanism according to claim 4, characterized in that, Step four includes the following steps: No. In the next iteration, each dimension of all quantum hawk positions is mapped to the path solution space, resulting in the mapped state of the quantum hawk as follows: The mapping equation is: in , Indicates the first Lower limit, Indicates the first Dimensional upper limit, , Corresponding to the The generation The set of nodes for constructing the UAV flight path after mapping each dimension of the quantum position of the quantum eagle to the path solution space range. Corresponding to the The generation Vidi The quantum position of the eagle is determined and substituted into the comprehensive cost function to obtain its fitness value. Quantum Hawks group as of the [number]th The optimal quantum position found by the method is denoted as .

6. The multi-UAV path planning method based on the quantum eagle mechanism according to claim 5, characterized in that, Step seven includes the following steps: Quantum position of the quantum eagle Each dimension is mapped to the path solution space to obtain the mapped state of the quantum eagle. And calculate the fitness value A greedy strategy is used to determine the quantum position of the next-generation quantum eagle. Then it is determined until up to the generation Local optimal quantum position of a quantum hawk ;otherwise ; until The optimal quantum position in the local optimal quantum position is set to until The global optimal quantum position is denoted as . .

7. A multi-UAV path planning system based on the quantum eagle mechanism, characterized in that, The system has a program module corresponding to the steps of the method described in any one of claims 1 to 6, and executes the steps in the multi-UAV path planning method based on the quantum eagle mechanism described above when it is run.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program configured to, when invoked by a processor, implement the steps of the multi-UAV path planning method based on the quantum eagle mechanism as described in any one of claims 1 to 6.

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