A method for solving an unmanned aerial vehicle path planning based on a genetic algorithm and a quantum particle swarm

Abstract

This invention relates to a quantum particle swarm optimization method based on a genetic algorithm for UAV trajectory planning, comprising: initializing particle swarm parameters; calculating particle positions through Monte Carlo random simulation based on the probability density function of a particle appearing at a point in quantum space, obtaining multiple first particles; updating the current best position and the global best position of the particles using particle fitness values; performing a crossover operation on all first particles based on the current best position and the global best position, and updating the first particles using a strategy of retaining excellent individuals, obtaining multiple second particles; performing a mutation operation on the second particles, and updating the second particles using a strategy of retaining excellent individuals, obtaining multiple third particles; repeating the process until the maximum number of iterations is reached to obtain the global best position of the particles, thereby obtaining the optimal solution for UAV trajectory planning. This method has strong global search capability, fewer sensitive parameters, and higher convergence accuracy.

Description

Technical Field

[0001] This invention belongs to the field of UAV trajectory planning, specifically involving a method for solving UAV trajectory planning based on quantum particle swarm optimization using a genetic algorithm. Background Technology

[0002] Many researchers have proposed technical solutions for drone trajectory planning.

[0003] For example, patent application CN115903888A, entitled "An Autonomous Path Planning Method for Rotary-Wing UAVs Based on the Beetle Swarm Algorithm," discloses an autonomous path planning method for rotary-wing UAVs based on the beetle swarm algorithm. This method fuses the beetle swarm algorithm and particle swarm optimization (PSO) to obtain the beetle swarm algorithm, constructs a path obstacle model for the rotary-wing UAV, performs environmental modeling, designs UAV performance constraints and cost functions, and finally performs iterative search based on the beetle swarm algorithm. After reaching the maximum number of iterations, the UAV positions after each iteration are connected by a smooth curve to obtain the optimal path for the rotary-wing UAV. However, this algorithm has reduced applicability and does not consider the influence of parameters on the PSO algorithm. This method is prone to causing the algorithm to stagnate, exhibits premature convergence during iteration, and suffers from slow convergence speed, increasing the time cost of UAV path planning.

[0004] For example, patent application CN107065876A, entitled "A Path Planning Method for Mobile Robots Based on Improved Particle Swarm Optimization," discloses a path planning method for mobile robots based on improved particle swarm optimization. This method implements a perturbation-based global optimal update strategy within the particle swarm algorithm and uses an adaptive strategy to fine-tune the three control parameters of the particles, resulting in a stochastic perturbation adaptive particle swarm optimization algorithm to solve the path planning problem for unmanned aerial vehicles (UAVs). However, while this algorithm balances global and local search capabilities, it has too many sensitive parameters. Changes in any one parameter directly affect the direction and speed of the particle swarm's search for the optimal solution in the solution space. Furthermore, particle positions are still limited, meaning the search solution space is restricted, and it cannot guarantee that all positions in the solution space will be searched. This results in weak global search capability and low algorithm convergence.

[0005] Therefore, existing UAV trajectory planning methods have drawbacks such as poor convergence, imbalance between global and local search capabilities, and a tendency to prematurely fall into iterative stagnation, resulting in high time costs and long UAV trajectory planning paths. Summary of the Invention

[0006] To address the aforementioned problems in existing technologies, this invention provides a method for UAV trajectory planning based on quantum particle swarm optimization using a genetic algorithm. The technical problem to be solved by this invention is achieved through the following technical solution:

[0007] This invention provides a method for solving UAV trajectory planning based on quantum particle swarm optimization using a genetic algorithm, comprising the following steps:

[0008] S1. Initialize particle swarm parameters;

[0009] S2. For the current iteration number, based on the planning space model and the task constraints between the UAV and the target point, according to the probability density function of the particle appearing at a certain point in quantum space, the particle position is calculated by Monte Carlo random simulation to obtain multiple first particles;

[0010] S3. Calculate the particle fitness value according to the objective function, and update the current best position and global best position of the particle using the positions of the multiple first particles;

[0011] S4. Using a genetic algorithm, perform crossover operations on all first particles by combining the current best position and the global best position, and update the first particles by adopting a strategy of retaining excellent individuals to obtain multiple second particles.

[0012] S5. Perform a mutation operation on the second particle and update the second particle using a strategy of retaining excellent individuals to obtain multiple third particles;

[0013] S6. Return to step S2 and repeat until the maximum number of iterations is reached to obtain the global optimal position of the particle;

[0014] S7. Obtain the optimal solution for UAV trajectory planning based on the global best position of the particle.

[0015] In one embodiment of the present invention, the planning spatial model is:

[0016] {(x,y)∣0≤x≤maxX,0≤y≤maxY}

[0017] Where (x,y) are the coordinates of each target in the trajectory planning space, maxX is the maximum horizontal coordinate in space, and maxY is the maximum vertical coordinate in space;

[0018] The task constraints are: each task point needs to be traversed by the drone once, and each drone must be assigned to a target point at least once; the formula for the task constraints is expressed as:

[0019]

[0020]

[0021] Where i is the task starting node, v is the v-th drone, M is the number of drones, and N is the number of task points. For 0-1 decision variables, The value 1 indicates that the v-th drone performs a task from node i to node j. A value of 0 indicates that no task has been assigned.

[0022] The objective function is:

[0023] F=λ1f w +λ2f L

[0024] Where λ1 is the weighting coefficient of the fuel consumption constraint, λ2 is the weighting coefficient of the trajectory length constraint, and f w For fuel consumption constraints, f w =ε·L, where ε is the ratio of fuel consumption cost to flight path length L, and f L For track length constraints, n is the target quantity, L i The length of the two-dimensional track. (X i ,Y i (X) represents the coordinates of the previous target. i+1 ,Y i+1 () represents the coordinates of the next target.

[0025] In one embodiment of the present invention, step S1 includes:

[0026] The particle dimension is set as the number of task points, the number of particles in the swarm, the maximum number of iterations, the initial position of the particle swarm, the optimal position of an individual particle, and the global optimal position.

[0027] Define the fitness function as the objective function, and use the objective function to calculate the initial fitness values ​​of all particles.

[0028] In one embodiment of the present invention, step S2 includes:

[0029] Update the contraction-expansion factor β(t) for the current iteration number:

[0030]

[0031] Where, β max As the initial value of the contraction-expansion factor, β min The contraction-expansion factor is the final value, t is the iteration number, and T is the final value. max It is the maximum number of algorithm iterations;

[0032] Combining the updated contraction-expansion factor, and based on the probability density function of a particle appearing at a point in quantum space, the particle position for the current iteration is calculated using Monte Carlo random simulation, resulting in multiple first particles. The formula for calculating the particle position is as follows:

[0033]

[0034]

[0035]

[0036] Where mbest(t) is the average optimal position of all particles in the population at the t-th iteration, M is the number of potential solutions for the trajectory optimization, i.e., the number of particles in the population, and p i (t) represents the current optimal position of the i-th particle in the t-th iteration, d is the dimension of the particle, and p g (t) represents the global optimal position of the i-th particle in the t-th iteration, PP id (t) is p i (t) and p g Random points between (t), X id (t+1) represents the position of the i-th particle in the (t+1)-th iteration, and u is a random number that follows a uniform distribution on [0,1].

[0037] In one embodiment of the present invention, step S3 includes:

[0038] The first fitness of the first particle at the current iteration number is calculated based on the objective function, and the fitness of the same first particle at the current best position is used as the second fitness.

[0039] When the first fitness is less than the second fitness, the current best position of the first particle is updated to the position of the first particle in this iteration;

[0040] Compare the first fitness of each first particle with the third fitness of the global best position;

[0041] When the first fitness is less than the third fitness, the global best position is updated to the position of the first particle.

[0042] In one embodiment of the present invention, step S4 includes:

[0043] Using the integer crossover method, a first crossover position is randomly selected from the coordinates of each first particle in the current iteration number. The corresponding coordinate component of the current best position of the same particle is taken as the second crossover position. The first crossover position and the second crossover position are crossovered to obtain multiple first crossover particles.

[0044] For each first intersecting particle, delete the element that is the same as the intersecting position from the unintersecting position, and replace the deleted element with the element that was not included in the first intersecting particle to obtain multiple second intersecting particles;

[0045] The fourth fitness of the second cross particle is calculated using the objective function and compared with the first fitness of the corresponding first particle. When the fourth fitness is less than the first fitness, the first particle is updated to the second cross particle, resulting in multiple updated first particles.

[0046] Using the integer cross method, a third cross position is randomly selected from the coordinates of each updated first particle. The corresponding coordinate component of the global best position is taken as the fourth cross position. The third cross position and the fourth cross position are crossed to obtain multiple third cross particles.

[0047] For each third intersecting particle, remove the element that is the same as the intersecting position from the unintersecting position, and replace the removed element with the element that was not included in the third intersecting particle to obtain multiple fourth intersecting particles;

[0048] The objective function is used to calculate the fifth fitness of the fourth cross particle and the sixth fitness of the corresponding updated first particle. When the fifth fitness is less than the sixth fitness, the updated first particle is updated to the fourth cross particle, resulting in multiple second particles.

[0049] In one embodiment of the present invention, the formula for the crossover operation is:

[0050]

[0051] Where Φ and Ω are N-dimensional vectors containing 0-1 elements, Φ and Ω are... Ω and Elements are inverses. The position of the first intersecting particle. The position of the first particle. This is the best position at present. The position of the third intersecting particle. To update the position of the first particle, This is the optimal position globally.

[0052] In one embodiment of the present invention, step S5 includes:

[0053] Two mutation positions are randomly selected from the second particle and interchanged to obtain multiple mutated particles;

[0054] The seventh fitness of the mutated particle and the eighth fitness of the second particle are calculated using the objective function. When the seventh fitness is less than the eighth fitness, the second particle is updated to the corresponding mutated particle, resulting in multiple third particles.

[0055] In one embodiment of the present invention, step S7 includes:

[0056] The elements in the particles corresponding to the global best position are converted into the order in which the UAV arrives at each task point by ascending order of dimensions, thus forming the optimal scheme for UAV trajectory planning.

[0057] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0058] 1. The method of this invention calculates the particle position by Monte Carlo random simulation based on the probability density function of a particle appearing at a certain point in quantum space, and introduces quantum space into the particle swarm algorithm to obtain the quantum particle swarm algorithm. Compared with the existing improved particle swarm algorithm, it increases the search solution space, improves the global search capability of the algorithm, and has only one control parameter, reducing the number of sensitive parameters and effectively improving the optimization efficiency of the algorithm. Thus, this method improves the effect of UAV trajectory planning and reduces the time cost of trajectory planning.

[0059] 2. The method of this invention utilizes a genetic algorithm, combining the current best position and the global best position to perform crossover and mutation operations on all particles, thus integrating the genetic algorithm with the quantum particle swarm algorithm. Compared with existing particle swarm fusion algorithms, it improves population diversity by utilizing the crossover and mutation capabilities of the genetic algorithm, further enhancing the algorithm's global search capability, mitigating the drawback of premature convergence during algorithm iteration, improving convergence accuracy, providing a better solution for UAV trajectory planning, and enhancing the effectiveness of UAV trajectory planning. Attached Figure Description

[0060] Figure 1 This is a flowchart illustrating the method for solving UAV trajectory planning based on quantum particle swarm optimization using a genetic algorithm, as provided in an embodiment of the present invention.

[0061] Figure 2 This figure shows a comparison of the average fitness curves of the Sphere function simulation results between the method of this embodiment and the standard particle swarm optimization algorithm, quantum particle swarm optimization algorithm, and genetic-particle swarm optimization algorithm.

[0062] Figure 3 This figure shows a comparison of the average fitness curves of the Rosenbrock function simulation results between the method of this embodiment and the standard particle swarm optimization algorithm, quantum particle swarm optimization algorithm, and genetic-particle swarm optimization algorithm.

[0063] Figure 4 This is a comparison chart showing the average path length obtained by the method in this embodiment and the standard particle swarm optimization algorithm in UAV path planning.

[0064] Figure 5 This diagram shows a comparison of the shortest path lengths obtained by the method in this embodiment and the standard particle swarm optimization algorithm in UAV path planning. Detailed Implementation

[0065] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0066] Example 1

[0067] As a key technology for achieving UAV autonomy, mission planning is currently a major research focus in the UAV field. Path planning, as a crucial component of the mission planning system, is also a key technology for improving UAV autonomy. UAV path planning algorithms are the core of UAV mission systems, used to solve the problems of rational target allocation and flyable path planning among UAVs. Among these, particle swarm optimization (PSO) is widely used in UAV path planning research due to its simplicity and excellent optimization performance. However, due to varying actual mission requirements and objectives, and the unavoidable shortcomings of standard PSO algorithms, reasonable improvements are needed. These improvements can not only better meet the actual requirements and objectives of UAV missions but also enhance the efficiency and success rate of UAV path planning. This embodiment proposes a quantum particle swarm optimization method based on a genetic algorithm to solve UAV path planning problems, addressing shortcomings in existing path planning algorithms such as poor convergence, imbalance between global and local search capabilities, and premature iteration stagnation.

[0068] Please see Figure 1 , Figure 1 This is a flowchart illustrating the method for solving UAV trajectory planning based on quantum particle swarm optimization using a genetic algorithm, as provided in an embodiment of the present invention.

[0069] In this embodiment, the UAV trajectory planning method is based on a UAV trajectory planning model, which includes a planning space model, task constraints between the UAV and the target point, and an objective function. Its construction method includes the following steps:

[0070] a) Establish a spatial planning model.

[0071] To verify the feasibility of the algorithm, it is assumed that the starting position of the UAV and the target position are on the same horizontal plane, transforming the UAV trajectory planning problem into a two-dimensional trajectory planning problem. The UAV trajectory planning space is represented by a global coordinate system o-xy, with the UAV and target treated as point masses. The coordinates (x, y) of each target in the planning space are determined proportionally based on their relative distance and position to the target. The planning space model is described using sets:

[0072] {(x,y)∣0≤x≤maxX,0≤y≤maxY}

[0073] Where (x,y) are the coordinates of each target in the trajectory planning space, maxX is the maximum horizontal coordinate in space, and maxY is the maximum vertical coordinate in space.

[0074] b) Set task constraints.

[0075] The task constraints are that each task point must be traversed by the drone exactly once, and each drone must be assigned to a target point at least once, as expressed by the formula:

[0076]

[0077]

[0078] Where i is the task starting node, v is the v-th drone, M is the number of drones, and N is the number of task points (i.e., the number of target points). For 0-1 decision variables, The value 1 indicates that the v-th drone performs a task from node i to node j. A value of 0 indicates that no task has been assigned.

[0079] c) Define the objective function. The objective function comprehensively considers the fuel consumption constraint f w and track length constraint f L .

[0080] Assuming the drone's speed remains constant, the flight distance and fuel consumption are directly proportional, i.e.:

[0081] f w =ε·L

[0082] Among them, the ratio of fuel consumption cost to flight path length L coefficient, f L For track length constraints.

[0083] Let L i (i = 1, 2, ..., n) represents the trajectory length of the UAV, and the trajectory length constraint is:

[0084]

[0085] Among them, L i The length of the two-dimensional track. (X i ,Y i (X) represents the coordinates of the previous target. i+1 ,Y i+1 () represents the coordinates of the next target.

[0086] Therefore, the objective function for the UAV trajectory is:

[0087] F=λ1f w +λ2f L

[0088] Where λ1 is the weighting coefficient of the fuel consumption constraint, and λ2 is the weighting coefficient of the trajectory length constraint.

[0089] Based on the aforementioned UAV trajectory planning model, this embodiment first improves the particle swarm optimization algorithm by introducing particles into quantum space; then, it fuses the genetic algorithm with the quantum particle swarm optimization algorithm to obtain the GA-QPSO algorithm, and performs crossover mutation on the particles; finally, the crossover mutated particles provide a solution for UAV trajectory planning. The specific steps of this embodiment's method for solving UAV trajectory planning based on the genetic algorithm and quantum particle swarm optimization algorithm are as follows:

[0090] S1. Initialize particle swarm parameters.

[0091] Specifically, the particle dimension is set as the number of task points N, the number of particles in the swarm K, the maximum number of iterations genmax, the initial position of the particle swarm, the optimal position of an individual particle Pbest, and the global optimal position Gbest; the fitness function is defined as the objective function set in c), and the initial fitness value of all particles is calculated using the objective function.

[0092] S2. For the current iteration number, based on the planning space model and the task constraints between the UAV and the target point, according to the probability density function of the particle appearing at a certain point in quantum space, the particle position is calculated by Monte Carlo random simulation to obtain multiple first particles.

[0093] First, quantum computing is combined with particle swarm optimization (PSO) to obtain the Quantum Particle Swarm Optimization (QPSO) algorithm. Specifically, based on the planning space model and the probability density function of a particle appearing at a point in quantum space, the position equation of the particle is obtained through Monte Carlo random simulation:

[0094]

[0095] In the formula, u is a random number that follows a uniform distribution on [0,1], and L is determined by the following formula:

[0096] L(t+1)=2β∣mbest-X(t)∣

[0097] The final formula for calculating particle position is:

[0098]

[0099]

[0100]

[0101] in, Used to select a random number that follows a uniform distribution on [0,1].

[0102]

[0103] In the above formula, mbest(t) is the average optimal position of all particles in the population at the t-th iteration, K is the number of potential solutions for trajectory optimization, i.e., the number of particles in the population, and p i (t) represents the current best position (Pbest) of the i-th particle in the t-th iteration, where d is the dimension of the particle, and p g (t) represents the global best position (Gbest) of the i-th particle in the t-th iteration, PP. id (t) is p i (t) and p g A random point between (t), X id (t+1) represents the position of the i-th particle in the (t+1)-th iteration.

[0104] The above particle position calculation formula uses a wave function to describe the particle's position, and the Schrödinger equation determines the particle's changing state, increasing the search solution space and improving the algorithm's global search capability. Simultaneously, with only one control parameter, β(t), the number of sensitive parameters is reduced, effectively improving the algorithm's optimization efficiency.

[0105] β(t) is the contraction-expansion factor, and the update formula is:

[0106]

[0107] Where, β max As the initial value of the contraction-expansion factor, β min The contraction-expansion factor is the final value, t is the iteration number, and T is the final value. max It represents the maximum number of algorithm iterations.

[0108] Therefore, for each iteration of the calculation, the first step is to use the formula... Update the intermediate parameter contraction-expansion factor β(t); then, iterate the particle positions according to the particle position calculation formula to obtain multiple first particles.

[0109] S3. Calculate the particle fitness value based on the objective function, and update the current best position and global best position of the particle using the positions of multiple first particles.

[0110] The approach to updating the current best position Pbest and the global best position Gbest of a particle is as follows: Calculate the particle's fitness value, compare the fitness at the new position with the fitness of the particle's previous best position Pbest, and if the fitness of the new position is better than the fitness of the previous best position, update Pbest to the new position; then set the new position X for each particle. t+1 The fitness function is compared with the fitness function of the global best position Gbest. If the fitness of the new position is better than that of the global best position, Gbest is updated to the new position.

[0111] Step S3 specifically includes the following steps:

[0112] S31. Calculate the first fitness of the first particle in the current iteration number according to the objective function, and take the fitness of the current best position of the same first particle as the second fitness.

[0113] S32. When the first fitness is less than the second fitness, update the current best position of the first particle to the position of the first particle in this iteration; otherwise, keep the original current best position unchanged.

[0114] S33. Compare the first fitness of each first particle with the third fitness of the global best position.

[0115] S34. When the first fitness is less than the third fitness, update the global best position of the first particle in the previous iteration to the position of the first particle; otherwise, keep the original global best position unchanged.

[0116] S4. Using a genetic algorithm, perform crossover operations on all first particles by combining the current best position and the global best position, and update the first particles by adopting a strategy of retaining excellent individuals, to obtain multiple second particles.

[0117] The crossover operation works as follows: Each particle is treated as an individual particle, and an integer crossover method is used. Individual particles are updated by crossing their individual extreme values ​​and the population extreme values. First, crossover positions are selected from both individual particles and their extreme values, and these positions are used for the first crossover. Then, crossover positions are selected from both individual particles and their population values, and these positions are used for the second crossover. After the first and second crossovers, the resulting individual particles are processed as follows: elements identical to those in the crossover region are deleted, and elements not included in the original particle's fitness are replaced with duplicate elements. A strategy of retaining superior individuals is adopted for the new individual particles; the particle is only updated if its fitness value is better than that of the old individual particles.

[0118] Step S4 specifically includes:

[0119] S41. Using the integer crossover method, a first crossover position is randomly selected from the coordinates of each first particle in the current iteration. The corresponding coordinate component of the current best position of the same particle is taken as the second crossover position. The first crossover position and the second crossover position are crossovered to obtain multiple first crossover particles. The coordinates of the second crossover position correspond to the coordinates of the first crossover position, and the multiple first crossover particles correspond one-to-one with the multiple first particles.

[0120] S42. For each first intersecting particle, delete the element that is the same as the intersecting position from the unintersecting position, and replace the deleted element with the element that was not included in the first intersecting particle to obtain multiple second intersecting particles. Among them, the multiple second intersecting particles correspond one-to-one with the multiple first intersecting particles, therefore, the multiple second intersecting particles correspond one-to-one with the multiple first particles.

[0121] S43. Calculate the fourth fitness of the second cross particle using the objective function, and compare it with the first fitness of the corresponding first particle. If the fourth fitness is less than the first fitness, update the first particle to the second cross particle; otherwise, keep the original first particle unchanged, and obtain multiple updated first particles.

[0122] S44. Using the integer crossover method, a third crossover position is randomly selected from the coordinates of each updated first particle. The corresponding coordinate component of the globally optimal position is taken as the fourth crossover position. The third crossover position and the fourth crossover position are then crossovered to obtain multiple third crossover particles. The coordinates of the fourth crossover position correspond to the coordinates of the third crossover position, and each of the multiple third crossover particles corresponds one-to-one with a multiple updated first particle.

[0123] S45. For each third intersecting particle, delete the element that is the same as the intersecting position from the unintersecting position, and replace the deleted element with the element that was not included in the third intersecting particle to obtain multiple fourth intersecting particles. Among them, the multiple fourth intersecting particles correspond one-to-one with the multiple third intersecting particles.

[0124] S46. Calculate the fifth fitness of the fourth cross particle and the sixth fitness of the corresponding updated first particle using the objective function. When the fifth fitness is less than the sixth fitness, update the updated first particle to the fourth cross particle; otherwise, keep the original updated first particle unchanged to obtain multiple second particles.

[0125] Accordingly, the formulas for the crossover operations in steps S41 and S43 are as follows:

[0126]

[0127] Where Φ and Ω are N-dimensional vectors containing 0-1 elements, Φ and Ω are... Ω and Elements are inverses. The position of the first intersecting particle. The position of the first particle. This is the best position at present. The position of the third intersecting particle. To update the position of the first particle, This is the optimal position globally.

[0128] S5. Perform a mutation operation on the second particle and update the second particle using a strategy of retaining excellent individuals to obtain multiple third particles.

[0129] The mutation operation works as follows: two mutation positions are randomly selected from within a particle, and the two mutation positions within the particle are swapped; the resulting new particle adopts a strategy of retaining the best particles, and the particle is only updated when the fitness value of the new particle is better than that of the old particle.

[0130] Step S5 specifically includes:

[0131] S51. Randomly select two mutation positions from the second particle and swap them, that is... Multiple mutated particles were obtained.

[0132] S52. Calculate the seventh fitness of the mutated particle and the eighth fitness of the second particle using the objective function. When the seventh fitness is less than the eighth fitness, update the second particle to the corresponding mutated particle; otherwise, keep the second particle unchanged and obtain multiple third particles.

[0133] S6. Return to step S2 and loop until the maximum number of loops genmax is reached, to obtain the global optimal position Gbest of the particle.

[0134] S7. Obtain the optimal solution for UAV trajectory planning based on the global best position of the particles.

[0135] Specifically, the elements in the particles corresponding to the global best position are sorted in ascending order of dimension, and the global best position of the particles is converted into the order in which the UAV arrives at each task point, forming the optimal solution for UAV trajectory planning.

[0136] Furthermore, this embodiment also provides the following simulation results to verify the method of this embodiment.

[0137] Please see Figure 2 , Figure 2 This figure shows a comparison of the average fitness curves of the Sphere function simulation results between the method of this embodiment and the standard particle swarm optimization algorithm, quantum particle swarm optimization algorithm, and genetic-particle swarm optimization algorithm. Figure 2 This demonstrates that, compared to the traditional particle swarm optimization algorithm, the method in this embodiment achieves higher convergence accuracy and faster convergence speed for finding unimodal functions under the same population size and number of iterations.

[0138] Please see Figure 3 , Figure 3 This figure shows a comparison of the average fitness curves of the Rosenbrock function simulation results between the method of this embodiment and the standard particle swarm optimization algorithm, quantum particle swarm optimization algorithm, and genetic particle swarm optimization algorithm. Figure 3This demonstrates that, compared to the traditional particle swarm optimization algorithm, the method in this embodiment achieves higher convergence accuracy for finding multimodal functions under the same population size and number of iterations.

[0139] Please see Figure 4 , Figure 4 This figure shows a comparison of the average path length obtained by the method in this embodiment and the standard particle swarm optimization algorithm in UAV path planning. Figure 4 This demonstrates that, in UAV path planning, the method in this embodiment has higher convergence accuracy, faster convergence speed, and stronger optimization capability compared to the standard particle swarm optimization algorithm.

[0140] Please see Figure 5 , Figure 5 This diagram shows a comparison of the shortest path lengths obtained by the method in this embodiment and the standard particle swarm optimization algorithm in UAV path planning. Figure 5 This demonstrates that, in UAV path planning, the method in this embodiment has higher convergence accuracy and faster convergence speed compared to the standard particle swarm optimization algorithm, and can provide a better solution for UAV trajectory planning.

[0141] In summary, the method of this embodiment calculates the particle position through Monte Carlo random simulation based on the probability density function of a particle appearing at a certain point in quantum space, and introduces quantum space into the particle swarm algorithm to obtain the quantum particle swarm algorithm. Compared with the existing improved particle swarm algorithm, it increases the search solution space, improves the global search capability of the algorithm, and has only one control parameter, reducing the number of sensitive parameters and effectively improving the optimization efficiency of the algorithm. Thus, this method improves the effect of UAV trajectory planning and reduces the time cost of trajectory planning.

[0142] The method in this embodiment utilizes a genetic algorithm, combining the current best position and the global best position to perform crossover and mutation operations on all particles. That is, it introduces crossover and mutation operations from the genetic algorithm into the traditional particle swarm optimization (PSO) method of updating particle positions by tracking extreme values. The optimal solution is searched through crossover between particles and individual and group extreme values, as well as through particle mutation. This integrates the genetic algorithm with the quantum particle swarm optimization algorithm. Compared to existing PSO fusion algorithms, the crossover and mutation capabilities of the genetic algorithm improve population diversity, further enhance the algorithm's global search capability, mitigate the premature convergence problem during iteration, improve convergence accuracy, provide a better solution for UAV trajectory planning, and improve the effectiveness of UAV trajectory planning.

[0143] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for solving the unmanned aerial vehicle path planning based on the genetic algorithm and the quantum particle swarm, characterized in that, Including the following steps: S1. Initialize particle swarm parameters; S2. For the current iteration number, based on the planning spatial model and the task constraints between the UAV and the target point, and according to the probability density function of a particle appearing at a certain point in quantum space, the particle position is calculated through Monte Carlo random simulation to obtain multiple first particles; including: updating the shrinkage-expansion factor for the current iteration number : wherein, is an initial value of the shrinkage-expansion factor, is a final value of the shrinkage-expansion factor, is the number of iterations, is the maximum number of iterations of the algorithm; Combining the updated contraction-expansion factor, and based on the probability density function of a particle appearing at a point in quantum space, the particle position for the current iteration is calculated using Monte Carlo random simulation, resulting in multiple first particles. The formula for calculating the particle position is as follows: in, For all particles in the population The average optimal position at the next iteration The number of potential solutions for optimizing the trajectory is equivalent to the number of particles in the population. For the first During the nth iteration The current optimal position of each particle. Let be the dimension of the particle. For the first During the nth iteration The global optimal position of each particle for and random points between, , , For the first During the nth iteration The position of each particle. It is a random number that follows a uniform distribution on [0,1]. S3. Calculate the particle fitness value according to the objective function, and update the current best position and global best position of the particles using the positions of the multiple first particles; the objective function is: in, These are the weighting coefficients for fuel consumption constraints. These are the weighting coefficients for the track length constraint. To constrain fuel consumption, , For fuel consumption and flight path length Coefficient ratio, For track length constraints, , For the target quantity, The length of the two-dimensional track. , The coordinates of the previous target. The coordinates of the next target; S4. Using a genetic algorithm, perform crossover operations on all first particles by combining the current best position and the global best position, and update the first particles by adopting a strategy of retaining excellent individuals to obtain multiple second particles. S5. Perform a mutation operation on the second particle and update the second particle using a strategy of retaining excellent individuals to obtain multiple third particles; S6. Return to step S2 and repeat until the maximum number of iterations is reached to obtain the global optimal position of the particle; S7. Obtain the optimal solution for UAV trajectory planning based on the global best position of the particle.

2. The method for solving UAV trajectory planning based on quantum particle swarm optimization using a genetic algorithm according to claim 1, characterized in that, The planning spatial model is as follows: in, The coordinates of each target in the trajectory planning space. The maximum x-coordinate in space. The maximum ordinate in space; The task constraints are: each task point needs to be traversed by the drone once, and each drone must be assigned to a target point at least once; the formula for the task constraints is expressed as: in, This is the starting node for the task. For the first A drone, For the number of drones, For the number of task points, , For 0-1 decision variables, , 1 indicates the first A drone from Node to The node executes the task. , A value of 0 indicates that no task has been assigned.

3. The method for solving UAV trajectory planning based on quantum particle swarm optimization using genetic algorithms according to claim 1, characterized in that, Step S1 includes: The particle dimension is set as the number of task points, the number of particles in the swarm, the maximum number of iterations, the initial position of the particle swarm, the optimal position of an individual particle, and the global optimal position. Define the fitness function as the objective function, and use the objective function to calculate the initial fitness values ​​of all particles.

4. The method for solving UAV trajectory planning based on quantum particle swarm optimization using genetic algorithms according to claim 1, characterized in that, Step S3 includes: The first fitness of the first particle at the current iteration number is calculated based on the objective function, and the fitness of the same first particle at the current best position is used as the second fitness. When the first fitness is less than the second fitness, the current best position of the first particle is updated to the position of the first particle in this iteration; Compare the first fitness of each first particle with the third fitness of the global best position; When the first fitness is less than the third fitness, the global best position is updated to the position of the first particle.

5. The method for solving UAV trajectory planning based on quantum particle swarm optimization using a genetic algorithm according to claim 1, characterized in that, Step S4 includes: Using the integer crossover method, a first crossover position is randomly selected from the coordinates of each first particle in the current iteration number. The corresponding coordinate component of the current best position of the same particle is taken as the second crossover position. The first crossover position and the second crossover position are crossovered to obtain multiple first crossover particles. For each first intersecting particle, delete the element that is the same as the intersecting position from the unintersecting position, and replace the deleted element with the element that was not included in the first intersecting particle to obtain multiple second intersecting particles; The fourth fitness of the second cross particle is calculated using the objective function and compared with the first fitness of the corresponding first particle. When the fourth fitness is less than the first fitness, the first particle is updated to the second cross particle, resulting in multiple updated first particles. Using the integer cross method, a third cross position is randomly selected from the coordinates of each updated first particle. The corresponding coordinate component of the global best position is taken as the fourth cross position. The third cross position and the fourth cross position are crossed to obtain multiple third cross particles. For each third intersecting particle, remove the element that is the same as the intersecting position from the unintersecting position, and replace the removed element with the element that was not included in the third intersecting particle to obtain multiple fourth intersecting particles; The objective function is used to calculate the fifth fitness of the fourth cross particle and the sixth fitness of the corresponding updated first particle. When the fifth fitness is less than the sixth fitness, the updated first particle is updated to the fourth cross particle, resulting in multiple second particles.

6. The method for solving UAV trajectory planning based on quantum particle swarm optimization using a genetic algorithm according to claim 5, characterized in that, The formula for the crossover operation is: in, and Given an N-dimensional vector containing elements of 0 and 1, and , and Elements are inverses. The position of the first intersecting particle. The position of the first particle. This is the best position at present. The position of the third intersecting particle. To update the position of the first particle, This is the optimal position globally.

7. The method for solving UAV trajectory planning based on quantum particle swarm optimization using a genetic algorithm according to claim 1, characterized in that, Step S5 includes: Two mutation positions are randomly selected from the second particle and interchanged to obtain multiple mutated particles; The seventh fitness of the mutated particle and the eighth fitness of the second particle are calculated using the objective function. When the seventh fitness is less than the eighth fitness, the second particle is updated to the corresponding mutated particle, resulting in multiple third particles.

8. The method for solving UAV trajectory planning based on quantum particle swarm optimization using a genetic algorithm according to claim 1, characterized in that, Step S7 includes: The elements in the particles corresponding to the global best position are converted into the order in which the UAV arrives at each task point by ascending order of dimensions, thus forming the optimal scheme for UAV trajectory planning.

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