Rare earth mine path planning method based on particle swarm optimization algorithm for unmanned aerial vehicle

Abstract

The application discloses a rare earth mine path planning method based on a particle swarm optimization algorithm unmanned aerial vehicle, and comprises the following steps: establishing an unmanned aerial vehicle automatic path planning model under a rare earth mine three-dimensional map, establishing a cost function, establishing a main constraint model of the unmanned aerial vehicle path planning, establishing an unmanned aerial vehicle path planning mathematical model, solving the unmanned aerial vehicle automatic path planning by using a TLDEPSO algorithm, dividing each round of iteration in the evolution process into two stages, and respectively adopting respective learning mechanisms for different particles in the population in different stages. A particle modification method is used to correct the search direction of the particle and guide the population to explore the problem space; a top-level neighborhood exploration mechanism is proposed to guarantee the convergence performance of the algorithm. The application has the advantages that in a complex rare earth mine three-dimensional flight scene, the obstacle avoidance capability and the optimal obstacle avoidance route are best, all obstacle threats in the test scene can be perfectly avoided, and the obstacle avoidance efficiency is higher.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) path planning technology, and in particular to a UAV rare earth mine path planning method based on an improved particle swarm optimization algorithm with a top-level dual development mechanism. Background Technology

[0002] With the advancement of technology, optimization problems are ubiquitous and increasingly complex. Traditional mathematical methods, when dealing with these problems, require strict property requirements, such as continuity and differentiability, resulting in very low optimization efficiency. Evolutionary algorithms, due to their inherent parallelism and intelligence, have significant advantages in handling complex optimization problems. Particle Swarm Optimization (PSO) is an important member of evolutionary algorithms. Its simple parameter settings, easily implemented learning structure, and good optimization efficiency have led to its widespread application in solving various problems, such as workshop resource scheduling, recommendation systems, and wastewater treatment. However, as the scale and difficulty of problems increase, PSO has also revealed some problems: 1. Its learning strategy is singular, failing to effectively cope with different evolutionary environments; 2. Its solution accuracy is poor when dealing with indivisible problems and complex optimization problems with multiple local optima; 3. Diversity is easily lost during the search process, resulting in poor global search ability and a tendency to get trapped in local optima.

[0003] Therefore, researchers have worked on improving PSO from multiple aspects to further optimize its performance. These mainly include adjusting parameters, modifying the learning strategy, and employing a hybrid strategy.

[0004] Improving learning strategies and optimizing learning structures have become mainstream research directions in recent years, while designing reliable learning models to handle optimization problems under different fitness landscapes remains a key challenge. In the field of genetic engineering, gene editing (GE) is a technology that can relatively precisely modify specific target genes in an organism's genome. [1]With the continuous evolution of gene editing technology, it has been applied to multiple subfields of biology and clinical medicine. GE provides strong technical support for targeted modification of organisms and the cultivation of novel organisms. GE technology has also brought groundbreaking developments to the medical field. Researchers, using CRISPR / Cas9 gene editing technology, successfully inactivated the HIV-1 viral gene in cells infected with HIV-1 for the first time, exploring new clinical medical methods for HIV treatment. In the PSO algorithm, each particle contains two vectors: velocity and position. Each vector consists of several dimensions. However, during the search process, not every dimension is helpful for the population to explore the problem space. Modifying and enhancing specific dimensions helps optimize the search performance of the entire particle, which is consistent with the goal of enhancing the adaptability of the genome through GE technology.

[0005] Therefore, this embodiment proposes a particle modification method based on gene editing technology to optimize and adjust the direction of particle movement, thereby better helping the population to find the best.

[0006] Besides the above analysis, how to accelerate population convergence is another issue that needs to be considered. In the third aspect of PSO improvement work, the hybrid strategy, some scholars have used local search operators to improve the convergence speed of the population. [2] Inspired by this, the present invention proposes a top-level neighborhood exploration mechanism.

[0007] In summary, by combining the particle modification method based on gene editing technology and the top-level neighborhood exploration mechanism, this invention proposes an improved particle swarm optimization algorithm (TLDEPSO) with a top-level dual development mechanism to fully utilize the evolutionary information of the population and enhance the optimization ability of the PSO algorithm.

[0008] Unmanned aerial vehicles (UAVs) are a type of modern aviation weaponry characterized by high maneuverability, stealth, and the ability to perform dangerous tasks in place of humans. They are widely used in reconnaissance, rescue, and real-time monitoring of forest fires. Therefore, developing UAV flight technology has become a strategic policy for many countries. Automatic path planning and design is a crucial task in UAV research, aiming to obtain the safest and optimal path from the starting point to the destination under specific constraints.

[0009] With the increasing complexity of real-world mission environments, automatic path planning algorithms for unmanned aerial vehicles (UAVs) have become a major research hotspot. Researchers have conducted extensive applied research on UAVs in various environments across different scenarios. [12,13]In path planning problems, modeling complex flight scenarios is a key issue that needs to be explored. This problem requires considering a series of constraints, such as flight altitude, turning angle, flight path length, and pitch angle. The flight path, also known as the flight trajectory, needs to be accurately evaluated to ensure reasonable obstacle avoidance. In recent years, the PSO algorithm and its variants have been adopted to more effectively solve the automatic path planning problem for UAVs. For example, Hoang et al. proposed an angular-coded PSO algorithm that uses angular velocity and position to locate particles, aiming to minimize the UAV's flight distance while maintaining altitude constraints and UAV formation shape.

[14] Fu et al. proposed a phase angle-encoded quantum behavior (PSO) algorithm, based on which they solved the UAV path planning problem in flight scenarios with multiple different threats.

[15] As described above, various methods exist for solving UAV path planning using PSO, but these methods all have certain shortcomings. The UAV path planning model proposed by Hoang et al. does not consider additional constraints, while the path planning model in this invention comprehensively considers yaw and pitch angle constraints. The UAV path planning model proposed by Fu et al. does not effectively smooth the obtained path, while this invention uses cubic B-spline curves to smooth the flight path to make it more closely resemble the actual flight scenario.

[0010] Definitions of abbreviations and key terms

[0011] Particle Swarm Optimization (PSO) algorithm, an improved Particle Swarm Optimization algorithm with a top-level dual development mechanism (TLDEPSO), gene editing (GE), global historical best (gbest), neighborhood historical best (lbest), and individual historical best (pbest).

[0012] References

[0013] [1]Puchta H, Fauser F. Gene targeting in plants:25years later[J]. International Journal of Developmental Biology, 2013, 57(6-7-8): 629-637;

[0014] [2]Xia X,Xie C,Wei B,et al.Particle swarm optimization using multi-level adaptation and purposeful detection operators[J].Information Sciences,2017,385:174-195;

[0015] [3]Cheng R,Jin Y.A social learning particle swarm optimizationalgorithmfor scalable optimization[J].Information Sciences,2015,291:43-60;

[0016] [4]Xia X,Gui L,He G,et al.An expanded particle swarm optimizationbased on multi-exemplar and forgetting ability[J].Information Sciences,2020,508:105-120;

[0017] [5]Liu H,Zhang X W,Tu L P.A modified particle swarm optimizationusing adaptive strategy[J].Expert systems with applications,2020,152:113353;

[0018] [6]Li W,Meng X,Huang Y,et al.Multipopulation cooperative particleswarm optimization with a mixed mutation strategy[J].Information Sciences,2020,529:179-196;

[0019] [7]Xia X,Gui L,Yu F,et al.Triple archives particle swarm optimization[J].IEEE transactions on cybernetics,2019,50(12):4862-4875;

[0020] [8]Varna F T,Husbands P.AHPSO:Altruistic Heterogeneous Particle SwarmOptimisation Algorithm for Global Optimisation[C] / / 2021 IEEE SymposiumSerieson Computational Intelligence(SSCI).IEEE,2021:1-8;

[0021] [9]Li T,Shi J,Deng W,et al.Pyramid particle swarm optimizationwithnovel strategies of competition and cooperation[J].Applied SoftComputing,2022,121:108731;

[0022]

[10] Mirjalili S,Mirjalili S M,Lewis A.Grey wolf optimizer[J].Advancesin engineering software,2014,69:46-61;

[0023]

[11] Mendes R,Kennedy J,Neves J.The fully informed particle swarm:simpler,maybe better[J].IEEE transactions on evolutionary computation,2004,8(3):204-210。

[0024]

[12] Yu Z, Si Z, Li X, et al. A novel hybrid particle swarm optimization algorithm for path planning of UAVs[J]. IEEE Internet of Things Journal, 2022, 9(22): 22547-22558.

[0025]

[13] Phung M D, Ha Q P. Safety-enhanced UAV path planning with spherical vector-based particle swarm optimization[J]. Applied Soft Computing, 2021, 107: 107376.

[0026]

[14] Hoang V T, MD Phung, Dinh T H, et al. Angle-Encoded Swarm Optimization for UAV Formation Path Planning[C] / / 2018 IEEE / RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2018.

[0027]

[15] Fu Y, Ding M, Zhou C. Phase Angle-Encoded and Quantum-Behaved Particle Swarm Optimization Applied to Three-Dimensional Route Planning for UAV[J]. IEEE Transactions on Systems Man and Cybernetics-Part A Systems and Humans, 2012, 42(2): 511-526. Summary of the Invention

[0028] This invention addresses the problems of existing technologies, such as limited learning strategies, poor solution accuracy, and easy loss of diversity. It provides a UAV-based path planning method for rare earth mines using particle swarm optimization (PSO) algorithm. Each iteration in the evolutionary process is divided into two stages, with each stage employing its own learning mechanism for different particles in the population. The search direction of the particles is corrected to better guide the population in exploring the problem space. Furthermore, a top-level neighborhood exploration mechanism is proposed to ensure the algorithm's convergence performance.

[0029] To achieve the above-mentioned objectives, the technical solution adopted by the present invention is as follows:

[0030] A path planning method for rare earth mines based on particle swarm optimization algorithm for UAVs includes the following steps:

[0031] Step 1: Establish an automatic path planning model for drones based on a 3D map of the rare earth mine, as detailed below:

[0032] Step 1.1: Establish an obstacle threat model. Threats are represented by cylinders, and each flight scenario contains several obstacle threats. A drone colliding with a threat will incur a corresponding threat cost.

[0033] Step 1.2: Establish a 3D map of the rare earth mine within the UAV flight path planning space. Store the UAV flight space as data, setting the starting point as: S: (x0, y0, z0) and the ending point as: T: (x0, y0, z0). n y n , z n The goal of drone path planning is to obtain the optimal flight path from the starting point S to the destination T while satisfying all constraints and mission requirements. Connect the starting point S and the target point T, then divide the straight line ST into multiple parts using line segments. The set of line segments {L} k In the set of line segments L, k = 1, 2, ..., D, all line segments are perpendicular to the line ST. k In the diagram, a node set {(x) is formed by taking one point on each line segment. k y k , z k The given information is given by the equation (1): (where k = 1, 2, ..., D)

[0034]

[0035] Where x min x max y min and y max The z-axis represents the boundary values ​​of the horizontal x-axis and y-axis. min and z max This represents the boundary value of the vertical z-axis.

[0036] The path planning problem for UAVs is transformed into an optimization problem of obtaining the coordinates of the optimal flight path. The direction of line ST is taken as the x-axis, and the set of line segments L... k Using the direction as the y-axis, a new coordinate system is constructed. The coordinates of the nodes on the original flight path are transformed according to equation (2):

[0037]

[0038] Where θ represents the angle between line segment ST and the original x-axis. These are the path points after coordinate transformation.

[0039] Step 1.3, Path Smoothing. A cubic B-spline curve is introduced to ensure the flightability and smoothness of the path. It is derived from the Bézier curve and inherits its advantages such as convexity preservation, affine invariance, and geometric invariance. The definition of the B-spline curve is shown in formula (3):

[0040]

[0041] Let U=u0,u1,…,u n Let u be a monotonically non-decreasing sequence of real numbers, that is, for all i, i = 0, 1, 2, ..., n-1, we have u i ≤u i+1 Where x i Represents the control point, u i Let U represent a node, and U be the node vector, with the half-open interval [u i ,u i+1 ) represents the interval of the i-th node. i,k (u) is the i-th k-th B-spline basis function, defined by the following Cox-de Boor recursive formula (4):

[0042]

[0043] When a 0 / 0 condition occurs, set it to 0; the basis functions are determined by the monotonically non-decreasing sequence U of real numbers, and N i,k (u) has multiple segmented patterns in each interval, satisfying formula (5):

[0044]

[0045] B-spline curves are highly effective for smoothing flight paths. Compared to Betz curves, B-spline curves overcome the drawback that moving control nodes affects the entire curve, and they do not increase the degree of the polynomial even as the number of nodes increases.

[0046] Step 2: Establish the cost function: The cost function consists of fuel cost and obstacle threat cost, as shown in formula (6):

[0047]

[0048] Where μ is a weight parameter between 0 and 1, and L represents the set of road segments L on the entire flight path. k W fuel and W threat Let L represent the fuel cost and threat cost for each segment, respectively, and l represent the length of the entire flight path. Each segment L... k The cost of the threat is calculated using five points, including L. k The starting and ending points. If a road segment contains obstacles or threats, then W... threat The calculation method is shown in formula (7):

[0049]

[0050] Where m is the number of obstacles or threats. Let L be the distance from the center of the i-th obstacle threat to the road segment. k The distance at point 0.25, R i Let J be the radius of the i-th obstacle threat. Since the drone's flight speed is set to a constant, J can be... fuel It is considered the length of the flight path.

[0051] Step 3: Establish the main constraint model for UAV path planning. The yaw and pitch angle constraints of the UAV flight are selected as the constraints for path planning. Specifically, see formulas (5) and (6):

[0052]

[0053]

[0054] in, For the maximum yaw angle, θ max The maximum pitch angle, and θ k For path point (x) k y k , z k ) yaw angle and pitch angle.

[0055] Step 4: Establish a mathematical model for UAV path planning. This involves minimizing the cost of flight while satisfying all constraints.

[0056] Step 5: Use the TLDEPSO algorithm to solve the automatic path planning problem for the UAV. The specific steps are as follows:

[0057] Step 5.1: Based on the established UAV path planning model for the complex 3D rare earth mine scenario, select the decision variables for the TLDEPSO algorithm and determine the upper and lower bounds of the decision variables, such as the upper and lower bounds of the dimensions of the position vector and velocity vector. Use the cost function described above as the fitness function of the TLDEPSO algorithm.

[0058] Step 5.2: Set parameters such as population size, maximum number of function evaluations, acceleration coefficient, inertia weight, number of top-level particles, and mutation probability during the TLDEPSO algorithm iteration process.

[0059] Step 5.3: Under different flight scenarios and different initial environments, obtain the path planning results that meet the constraints using the TLDEPSO algorithm.

[0060] Furthermore, the steps of the improved particle swarm optimization algorithm are as follows:

[0061] Step 6.1: Randomly initialize the velocity and position of the population, evaluate the entire population and obtain pbest, lbest and gbest, then enter the main loop;

[0062] Step 6.2: Divide the population into top-level particles and ordinary particles according to fitness, and enter the first iteration stage. Use a particle modification method based on gene editing technology to update the top-level particles, and use the classic ring neighborhood topology learning strategy to update the ordinary particles.

[0063] Step 6.3: Update pbest, lbest, and gbest;

[0064] Step 6.4: Enter the second iteration stage, apply the top-level neighborhood exploration mechanism to the top-level particles, and complete the secondary development;

[0065] Step 6.5: Determine whether the number of function evaluations has reached the termination condition MaxFes. If so, the algorithm ends and outputs the optimal solution; otherwise, repeat steps 6.2 to 6.5.

[0066] Furthermore, the population is divided into top-level particles and ordinary particles based on fitness, as detailed below:

[0067] The particles are classified. Based on their fitness, particles are divided into top-level particles and ordinary particles. The number of top-level particles, TopK, is calculated using the following formula:

[0068]

[0069] Where floor is the floor function, and T is the current iteration number. max This represents the maximum number of iterations. TopK gradually increases during the evolutionary process, from 1 to 10.

[0070] Furthermore, the specific steps of the particle modification method are as follows:

[0071] Step 7.1: Locate the target dimension based on probability.

[0072] Anchoring target sites is mapped onto particles, and specific dimensions are labeled. To ensure that all dimensions have the potential for modification, sample probabilities are used to evaluate each dimension. Each dimension contains two values: a sample probability value generated by a Cauchy distribution and a random number between [0, 1]. When the random number is less than the sample probability pm, the dimension is positioned and labeled; otherwise, the dimension does not need to be modified.

[0073] Step 7.2: Construct homologous vectors.

[0074] Each dimension of the source vector is generated by the exploration and mining operators, defined as follows:

[0075]

[0076]

[0077] The exploration operator's "self-awareness" is achieved by randomly selecting pbest. t The mining operator's "self-awareness" is based on its own pbest. k Each dimension contains a random number rand within the range [0, 1]. When rand is less than pm, this dimension is generated by the exploration operator; otherwise, it is generated by the mining operator. By adjusting the size of pm, the proportion of dimensions generated by the two operators for the same source vectors is adjusted, thereby adjusting the attribute characteristics of the same source vectors.

[0078] Step 7.3: Modify the particles.

[0079] pbest k Copy once to obtain pbest_. For dimension components marked with the target dimension, replace the corresponding dimension component in pbest_ with the component in the same dimension as the source vector, while unmarked dimension components remain unchanged. After all marked dimensions have been replaced, a modified top-level particle pbest' will be generated.

[0080] Step 7.4: Perform a fitness evaluation on pbest'. If pbest' has a better fitness than the original pbest, replace the original pbest; otherwise, discard pbest'.

[0081] Furthermore, the learning strategy for the classic ring neighborhood topology is as follows:

[0082] In the first stage, ordinary particles use the classical ring neighborhood topology PSO learning strategy to update their velocity and position. The update strategy is as follows:

[0083]

[0084]

[0085] Where ω represents the inertia weight; c1 and c2 are acceleration coefficients that regulate the search bias of the algorithm at different evolutionary stages. r1 and r2 are random numbers in the interval [0, 1]. pbest i lbest represents the best historical experience of particle i. i This represents the best experience in the neighborhood history of particle i.

[0086] Furthermore, the top-level neighborhood exploration mechanism is as follows:

[0087] For each dimensional component of the top-level particle, a neighborhood exploration is performed in the component space, as shown in Equation (12):

[0088]

[0089] Where ri is the neighborhood radius, pm is the mutation probability, and s is a randomly generated dimension, ensuring that at least one dimension is available for neighborhood exploration.

[0090] The new value is the result of perturbing the original value's ri radius based on the Cauchy distribution. After performing probabilistic perturbations on all dimensions of a top-level particle, a new solution p will be generated. k , for p k Perform an evaluation; if the fitness of the new solution is better than the original solution, then replace the original solution with the new solution.

[0091] Compared with the prior art, the advantages of the present invention are as follows:

[0092] To better utilize population evolutionary information and enhance algorithm convergence performance, particles are divided into top-level particles and ordinary particles based on fitness. On one hand, a gene-editing particle modification method is designed for top-level particles to adjust their search direction, helping the population better explore the problem space. A top-level neighborhood exploration mechanism is also designed to accelerate population convergence. On the other hand, ordinary particles use the classic circular neighborhood topology (PSO) learning strategy to aid evolution and maintain population diversity. TLDEPSO achieved the best overall performance in solving test problems with different fitness landscapes, especially in complex mixture and combinatorial functions, where it demonstrated strong competitiveness in convergence accuracy. Furthermore, in a complex rare earth mine 3D flight scenario, TLDEPSO was applied to solve the automatic path planning problem for UAVs. From both top-down and 3D panoramic views, it is evident that TLDEPSO exhibits the best obstacle avoidance capability and route, perfectly avoiding all obstacles and threats in the test scenario. Statistical analysis shows that TLDEPSO has higher obstacle avoidance efficiency. Attached Figure Description

[0093] Figure 1 This is a flowchart of the TLDEPSO algorithm according to an embodiment of the present invention.

[0094] Figure 2 This is a schematic diagram of drone path planning according to an embodiment of the present invention.

[0095] Figure 3 This is a convergence graph of all comparison algorithms in all functions in the embodiments of the present invention. (a)f1, (b)f2, (c)f3, (d)f4, (e)f5, (f)f6, (g)f7, (h)f8, (i)f9, (j)f10, (k)f11, (l)f12;

[0096] Figure 4 This is a comparison result diagram of flight paths in an embodiment of the present invention; (a) is a three-dimensional perspective view, and (b) is a top view.

[0097] Figure 5 This is a convergence curve diagram of all comparison algorithms in the embodiments of the present invention. Detailed Implementation

[0098] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and examples.

[0099] In the classic PSO algorithm, the population consists of several particles, each containing a position and velocity vector. Each vector is composed of several dimensions. However, during the search process, not every dimension is beneficial for optimization. Modifying and enhancing specific dimensions can help optimize the search performance of the entire particle, which is similar to the goal of enhancing the adaptability of the genome through gene editing technology. Therefore, this embodiment proposes a particle modification method based on gene editing technology to optimize and adjust the motion direction of particles, thereby better assisting the population in finding the best.

[0100] In addition to the above analysis, how to accelerate population convergence is another issue that needs to be considered. In the third aspect of PSO improvement work, the hybrid strategy, some scholars have used local search operators to improve the convergence speed of the population. Inspired by this, this embodiment proposes a top-level neighborhood exploration mechanism.

[0101] Combining two novel learning mechanisms with the classic ring neighborhood topology PSO learning strategy, this invention proposes the TLDEPSO algorithm. In general, the TLDEPSO algorithm operates in several iterations, with each iteration consisting of two phases. The first phase updates all particles in the population. Based on fitness, particles are divided into top-level particles and ordinary particles. A particle modification method based on gene editing technology is designed for the top-level particles, while the ordinary particles employ the classic ring neighborhood topology PSO learning strategy. The second phase is executed only for the top-level particles, and a corresponding top-level neighborhood exploration mechanism is designed and applied to them.

[0102] Particle classification

[0103] The preceding discussion explained that different learning models are applied to different particles at different stages of each iteration. Therefore, this embodiment requires particle classification. Based on the degree of fitness, particles are divided into top-level particles and ordinary particles. The number of each type of particle is not fixed but changes continuously during the evolutionary process. The key parameter here is the number of top-level particles, TopK, which is calculated using the following formula:

[0104]

[0105] Where floor is the floor function, and T is the current iteration number. max The maximum number of iterations is denoted by TopK. TopK gradually increases during the evolution process, from 1 to 10. This indicates that in the early stages of evolution, the proportion of top-level particles in the total number of particles is very small. At this time, there is no need to adjust the optimization direction of the particles too much. Instead, it is to ensure that a wider problem space can be explored. In the later stages of evolution, more particles are invested in executing particle modification methods and top-level neighborhood exploration mechanisms, which can effectively ensure the convergence performance of the algorithm.

[0106] Particle modification methods based on gene editing technology

[0107] To minimize the risk of particles getting trapped in local optima within a complex search space, inspired by gene editing (GE) technology, optimizing the particle's trajectory helps in population optimization. Therefore, a particle modification method based on gene editing technology is proposed, with the following specific steps:

[0108] Step 1: Locating the Target Dimension Based on Probability. The first step in GE technology is to anchor the target site and map it onto the particle, which requires labeling specific dimensions. To ensure that all dimensions have the potential for modification, this embodiment uses sample probability to evaluate each dimension. Specifically, each dimension contains two values: one is the sample probability value generated by the Cauchy distribution, and the other is a random number between [0, 1]. When the random number is less than the sample probability pm, the dimension is located and labeled; otherwise, the dimension does not need to be modified.

[0109] Step 2: Constructing common source vectors. Similar to the second step of the GE technique, it is necessary to construct common source vectors.

[0110] Specifically, each dimension of the source vector is generated by the exploration and mining operators, defined as follows:

[0111]

[0112]

[0113] The exploration operator's "self-awareness" is achieved by randomly selecting pbest. t The mining operator's "self-awareness" is based on its own pbest. k Specifically, each dimension contains a random number rand within the range [0, 1]. When rand is less than pm, this dimension is generated by the exploration operator; otherwise, it is generated by the mining operator. By adjusting the size of pm, the proportion of dimensions of the same source vector generated by the two operators is adjusted, thereby adjusting the attribute characteristics of the same source vector. For example, increasing pm means that more dimensions of the same source vector are generated by the exploration operator to meet the need for diversity; otherwise, more dimensions are generated by the mining operator to ensure the convergence of the algorithm.

[0114] Step 3: Particle Refinement. At this stage, the particles need to be refined and improved. Specifically, pbest... k Copy once to obtain pbest_. For dimension components marked with the target dimension, replace the corresponding dimension component in pbest_ with the component in the same dimension as the source vector, while unmarked dimension components remain unchanged. After all marked dimensions have been replaced, a modified top-level particle pbest' will be generated.

[0115] After completing the above three steps, a fitness evaluation will be performed on pbest'. If pbest' has a better fitness than the original pbest, it will replace the original pbest; otherwise, pbest' will be discarded. Through the gene-edited top-level particles, each dimension can be modified with a probability, ensuring that different dimensions are on an equal footing in the evolutionary process. Evolutionary information is fully utilized, thereby better guiding the population to explore the problem space.

[0116] Top-level neighborhood exploration mechanism

[0117] The optimization direction of the population has been optimized and adjusted using a particle modification method based on gene editing technology. The next problem is how to accelerate population convergence. Inspired by local search operators, this invention proposes a top-level neighborhood exploration mechanism. As the name suggests, this mechanism is also executed for top-level particles. After completing the first stage of iteration, the second stage will be completed, that is, the mechanism will be executed. Specifically, for each dimension component of the top-level particle, a neighborhood exploration is performed in the component space, as shown in formula (6). The new value is the result of Cauchy distribution perturbation within the radius of the original value ri. After performing probability perturbation on all dimensions of a top-level particle, a new solution p will be generated. k In this embodiment, p k Perform an evaluation; if the fitness of the new solution is better than the original solution, replace the original solution with the new one.

[0118]

[0119] Where ri is the neighborhood radius, pm is the mutation probability, and s is a randomly generated dimension, ensuring that at least one dimension is available for neighborhood exploration.

[0120] Learning strategy of classic ring neighborhood topology PSO

[0121] In the first stage, ordinary particles use the classical ring neighborhood topology PSO learning strategy to update their velocity and position. The update strategy is as follows:

[0122]

[0123]

[0124] Where ω represents the inertia weight; c1 and c2 are acceleration coefficients that regulate the search bias of the algorithm at different evolutionary stages. r1 and r2 are random numbers in the interval [0, 1]. pbest i lbest represents the best historical experience of particle i. i This represents the best experience in the neighborhood history of particle i.

[0125] The above describes two proposed learning mechanisms and the learning strategy of the classic ring neighborhood topology PSO. Figure 1 A flowchart of the present invention is provided.

[0126] The specific steps of the algorithm are as follows:

[0127] Step 1: Randomly initialize the velocity and position of the population, evaluate the entire population and obtain pbest, lbest and gbest, then enter the main loop;

[0128] Step 2: Divide the population into top-level particles and ordinary particles according to fitness, and enter the first iteration stage. Use a particle modification method based on gene editing technology to update the top-level particles, and use a classic circular neighborhood topology learning strategy to update the ordinary particles.

[0129] Step 3: Update pbest, lbest, and gbest;

[0130] Step 4: Enter the second iteration stage, apply the top-level neighborhood exploration mechanism to the top-level particles, and complete the secondary development;

[0131] Step 5: Determine if the number of function evaluations has reached the termination condition MaxFes. If so, the algorithm ends and outputs the optimal solution; otherwise, repeat steps 2 to 5.

[0132] Mathematical model for path planning of unmanned aerial vehicles

[0133] To test the practical application and solution capability of the TLDEPSO algorithm, this embodiment designs a UAV path planning model that is affected by factors such as obstacle threat, altitude, and yaw angle.

[0134] Threat Resource Model in Drone Path Planning

[0135] In this model, the starting point is S: (x0, y0, z0), and the ending point is T: (x n y n , z n Two-dimensional flight panoramic image, such as Figure 2 As shown. The goal of UAV path planning is to obtain the optimal flight path from the starting point S to the destination T while satisfying all constraints and mission requirements.

[0136] First, connect the starting point S and the target point T. Then, use line segments to divide the straight line ST into multiple parts. Figure 2 For example, this embodiment uses the line segment set {L} k The sequence L, k = 1, 2, ..., D, divides ST into seven segments. It's important to note that these segments are all perpendicular to the line ST. In the set of line segments L... k In the diagram, a node set {(x) is formed by taking one point on each line segment.k y k , z k ), k = 1, 2, ..., D}, that is Figure 2 The light-colored square points in the equation satisfy the constraints of formula (9).

[0137]

[0138] Where x min x max y min and y max The z represents the boundary values ​​of the horizontal x-axis and y-axis. min and z max This represents the boundary value of the vertical z-axis. Connecting these square points forms a feasible path from point S to point T. Therefore, the path planning problem for a UAV can be transformed into an optimization problem of obtaining the coordinates on the optimal flight path. To accelerate the optimization process, this embodiment uses the direction of the straight line ST as the x-axis, and the set of line segments L... k Using the direction of ST as the y-axis (i.e., the direction perpendicular to ST), a new coordinate system is constructed. The coordinates of the nodes on the original flight path are transformed according to formula (10):

[0139]

[0140] Where θ represents the angle between line segment ST and the original x-axis. These are the path points after coordinate transformation.

[0141] Cost function and performance constraints

[0142] The performance evaluation indicators of UAV flight paths mainly consist of fuel costs and obstacle threat costs, as shown in formula (11):

[0143]

[0144] Where μ is a weight parameter between 0 and 1, and L represents the set of road segments L on the entire flight path. k W fuel and W threat Let L represent the fuel cost and threat cost for each segment, respectively, and l represent the length of the entire flight path. Each segment L... k The cost of the threat is calculated using five points (including L). k (The starting point and the destination). If a road segment contains obstacles or threats, then W threat The calculation method is shown in formula (12):

[0145]

[0146] Where m is the number of obstacles or threats. Let L be the distance from the center of the i-th obstacle threat to the road segment. k The distance at point 0.25, R i Let J be the radius of the i-th obstacle threat. Since the drone's flight speed is set to a constant, J can be... fuel It is considered the length of the flight path.

[0147] To generate a suitable flight path for the UAV, this invention also introduces yaw and pitch angle constraints, as shown in formulas (13) and (14):

[0148]

[0149]

[0150] in, For the maximum yaw angle, θ max The maximum pitch angle, and θ k For path point (x) k y k , z k ) yaw angle and pitch angle.

[0151] Simulation Experiments and Result Analysis

[0152] To verify the effectiveness of the TLDEPSO algorithm, this invention selects the newly proposed CEC2022 test function set for comparison. This test set includes 12 benchmark functions, divided into four parts: unimodal functions (f1), basic functions (f2-f5), mixed functions (f6–f8), and combined functions (f9–f9). 12 The specific information of the test set is shown in Table 1. Based on the experimental settings of the CEC2022 test set, the test dimension was chosen to be 10, the maximum number of function evaluations was 200,000, and each function was run independently 30 times. The final result is the average. The comparison between algorithms involves TLDEPSO and seven other advanced PSO variants, namely SLPSO... [3] XPSO [4] MPSO [5] MPCPSO [6] TAPSO [7] AHPSO [8] PPSO [9] The specific parameter settings for the algorithm are shown in Table 2. Table 3 presents the comparative results of the experiment, which records the mean, standard deviation, and ranking of the function.

[0153] Table 1. Detailed information on the CEC2022 test set.

[0154]

[0155] Table 2 Parameter settings for TLDEPSO and seven advanced PSO variants

[0156]

[0157] Table 3 Optimization results of TLDEPSO and 7 advanced PSO variants on the 10-dimensional CEC2022 test function.

[0158]

[0159]

[0160] To comprehensively verify the effectiveness of TLDEPSO, this embodiment compares TLDEPSO with seven PSO variants. Table 3 shows that TLDEPSO performs well in f1–f3 and f5–f... 12 It achieved best performance on 11 test problems, with an average ranking of 1.08, ranking first among the eight algorithms and significantly exceeding the second-place algorithm's 3.17. For MPSO and TAPSO, both achieved theoretically optimal solutions on f1 and f3. For AHPSO, it only achieved optimal results on f1. PPSO showed good competitiveness compared to the other six advanced variants, achieving optimal results on four functions: f1, f3, f4, and f5, and was the only algorithm to achieve optimal results on f4, but it was still significantly worse than the TLDEPSO proposed in this embodiment. Furthermore, for SL PSO, XPSO, and MPCPSO, these three could not achieve optimal performance on any test problem, demonstrating the superior performance of TLDEPSO.

[0161] To study the algorithm's performance at different evolutionary stages, convergence plots were used for further verification and analysis. Figure 3 Convergence plots for eight algorithms on all functions are provided. The upper right corner of the convergence plots is annotated with the color of the curve segment representing each algorithm. Figure 3It can be seen that TLDEPSO only finds a worse solution than PPSO on function f4, while finding better or approximate solutions on the other eleven functions. This demonstrates that TLDEPSO possesses a stronger ability to explore the problem space than other algorithms, thus finding a better solution. In functions such as f7, f8, and f9, other algorithms stop converging early and fall into local optima, while TLDEPSO, with its particle modification method based on gene editing technology, can fully utilize the evolutionary information of top-level particles to effectively adjust the search direction of particles, making the population less prone to falling into local optima. The top-level neighborhood exploration mechanism ensures the convergence performance of the algorithm. Therefore, this embodiment can conclude that TLDEPSO's competitiveness in algorithmic convergence is far stronger than other advanced variants of PSO.

[0162] To further verify the solution capability of TLDEPSO in practical applications, this embodiment applies it to solving the automatic path planning problem of unmanned aerial vehicles (UAVs). A complex three-dimensional scene is designed to evaluate the feasibility and effectiveness of the TLDEPSO algorithm. In the three-dimensional field, the UAV's flyable space is 1000m * 1000m * 1000m, with the starting point at (0m, 0m, 0m) and the destination point at (1000m, 1000m, 1000m). Each scene contains eight obstacles, represented by cylinders. The relevant information of the obstacles is shown in Table 4, and the weight parameter μ is 0.4.

[0163] Table 4. Detailed information on threatening obstacles

[0164]

[0165] The maximum number of iterations for all algorithms is 500, with a dimension of 10, meaning the data is divided into 11 route segments. The population size N for all algorithms is 50. The statistical results of the experiments consist of four indicators: mean (average result after thirty runs), standard deviation, best value, and worst value. The two algorithms proposed in this paper are compared with GWO...

[10] LPSO

[11] and MPSO [5] For comparison, Table 5 records the statistical results of these five algorithms in three flight scenarios.

[0166] Table 5 Comparison results of various algorithms in 3D scenes

[0167]

[0168] according to Figure 4The comparison of flight paths leads to the conclusion that there are significant differences in the flight paths generated by the four algorithms. The TLDEPSO algorithm is the only one that satisfies the given constraints and the complex flight environment, while GWO, LPSO, and MPSO collide with three, four, and two threatening obstacles, respectively. The convergence curves of the four algorithms are shown below. Figure 5 As shown in the figure, the TLDEPSO algorithm has a significantly better convergence performance than the other three algorithms. The GWO algorithm reaches its optimal value after about 150 iterations, the LPSO algorithm reaches its optimal value after about 105 iterations, and the MPSO algorithm has a convergence speed close to TLDEPSO, reaching its optimal value after about 70 iterations, but its convergence accuracy is far inferior to that of TLDEPSO.

[0169] The statistical results are shown in Table 4. LPSO has the worst results in terms of mean, standard deviation, best value and worst value. MPSO is better than GWO and LPSO in all four indicators, but still worse than TLDEPSO. The TLDEPSO algorithm proposed in this invention ranks first, and its lower standard deviation also shows that TLDEPSO can obtain the optimal flight path relatively stably.

[0170] The methods described above according to the invention can be implemented in hardware, firmware, or as software or computer code that can be stored in a recording medium (such as CD-ROM, RAM, floppy disk, hard disk, or magneto-optical disk), or as computer code originally stored on a remote recording medium or a non-transitory machine-readable medium and subsequently stored on a local recording medium, downloaded via a network. Thus, the methods described herein can be stored as software processing on a recording medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware (such as an ASIC or FPGA). It is understood that the computer, processor, microprocessor controller, or programmable hardware includes storage components (e.g., RAM, ROM, flash memory, etc.) capable of storing or receiving software or computer code. When said software or computer code is accessed and executed by the computer, processor, or hardware, it implements the path planning method for a UAV based on the improved particle swarm optimization algorithm described herein. Furthermore, when a general-purpose computer accesses the code used to implement the processing shown herein, the execution of the code transforms the general-purpose computer into a dedicated computer for performing the processing shown herein.

[0171] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the implementation methods of the present invention, and should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of the present invention.

Claims

1. A path planning method for rare earth mines using unmanned aerial vehicles (UAVs) based on particle swarm optimization algorithm, characterized in that, Includes the following steps: Step 1: Establish an automatic path planning model for drones based on a 3D map of the rare earth mine, as detailed below: Step 1.1: Establish an obstacle threat model; the threat is a cylinder, and each flight scenario contains several obstacle threats; the drone will incur corresponding threat costs when it collides with a threat. Step 1.2: Establish a 3D map of the rare earth mine in the UAV flight path planning space; store the UAV flight space in data form, and set the starting point as: The destination is: The goal of setting up UAV path planning is to obtain the optimal flight path from the starting point S to the destination T while satisfying all constraints and mission requirements. Connect the starting point S and the target point T, then divide the straight line ST into multiple parts using line segments; the set of line segments... The line segments are all perpendicular to the straight line ST; Set of line segments In this context, a node set is formed by taking one point on each line segment. And satisfy the constraints; the constraints are as shown in equation (1): （1） in , , and Represents the boundary values ​​of the horizontal x-axis and y-axis. and Represents the boundary values ​​along the vertical z-axis; The path planning problem for UAVs is transformed into an optimization problem of obtaining the coordinates on the optimal flight path; the direction of the straight line ST is taken as the x-axis, and the set of line segments is... Using the direction as the y-axis, construct a new coordinate system; perform coordinate transformation on the nodes on the original flight path according to equation (2): （2） in This represents the angle between line segment ST and the original x-axis. These are the path points after coordinate transformation; Step 1.3, Path Smoothing; A cubic B-spline curve is introduced to ensure the flightability and smoothness of the path. It is derived from the Bézier curve and inherits the advantages of the Bézier curve in terms of convexity preservation, affine invariance and geometric invariance. The definition of the B-spline curve is shown in formula (3): (3) make Let be a monotonically non-decreasing sequence of real numbers, that is, for all . They all ;in Indicates control points, Represents a node. For node vectors, half-open intervals It is the interval of the i-th node; It is the i-th k-th B-spline basis function, defined by the following Cox-de Boor recursive formula (4): （4） When a 0 / 0 condition occurs, set it to 0; the basis functions are determined by the monotonically non-decreasing sequence U of real numbers, and For each interval, there are multiple segmentation patterns that satisfy formula (5): （5） B-spline curves are very effective for smoothing flight paths; compared with Betz curves, B-spline curves overcome the disadvantage that moving control nodes will affect the entire curve, and the degree of the polynomial will not increase even when the number of nodes is continuously increased. Step 2: Establish the cost function: The cost function consists of fuel cost and obstacle threat cost, as shown in formula (6): （6） in The weight parameter is between 0 and 1. Represents the set of segments along the entire flight path. , and These represent the fuel cost and threat cost for each road segment, respectively. Indicates the length of the entire flight path; each segment The cost of the threat is calculated in five points, including The starting point and the target point; If a road segment contains obstacles or threats, then The calculation method is shown in formula (7): （7） in The number of obstacles or threats. For the first The center of the obstacle threat to the road segment The distance at 0.25 points, For the first The radius of the obstacle threat; since the drone's flight speed is set to a constant, it can be... The length of the flight path is considered as the flight path length; Step 3: Establish the main constraint model for UAV path planning; select the yaw angle and pitch angle constraints of UAV flight as the constraints for path planning; as shown in formulas (8) and (9): （8） （9） in, For the maximum yaw angle, The maximum pitch angle, and path point yaw and pitch angles; Step 4: Establish a mathematical model for UAV path planning; that is, minimize the cost of flight while satisfying all constraints. Step 5: Use an improved particle swarm optimization algorithm to solve the automatic path planning problem for the UAV; the specific steps are as follows: Step 5.1: Based on the UAV path planning model, select the decision variables for the improved particle swarm optimization algorithm and determine the upper and lower bounds of the decision variables, including the upper and lower bounds of the dimensions of the position vector and velocity vector; use the cost function described above as the fitness function of the improved particle swarm optimization algorithm. Step 5.2: Set the population size, maximum number of function evaluations, acceleration coefficient, inertia weight, number of top-level particles, and mutation probability parameters during the iterative process of the improved particle swarm optimization algorithm; Step 5.3: Under different flight scenarios and different initial environments, obtain path planning results that meet the constraints by improving the particle swarm optimization algorithm; The steps of the improved particle swarm optimization algorithm are as follows: Step 6.1: Randomly initialize the velocity and position of the population, evaluate the entire population and obtain... , and Enter the main loop; Step 6.2: Divide the population into top-level particles and ordinary particles according to fitness, and enter the first iteration stage. Use a particle modification method based on gene editing technology to update the top-level particles, and use the classic ring neighborhood topology learning strategy to update the ordinary particles. Step 6.3: Update , and ; Step 6.4: Enter the second iteration stage, apply the top-level neighborhood exploration mechanism to the top-level particles, and complete the secondary development; Step 6.5: Determine if the function evaluation count has reached the termination condition. If so, the algorithm terminates and outputs the optimal solution; otherwise, steps 6.2 to 6.5 are repeated. The specific steps of the particle modification method are as follows: Step 7.1: Locate the target dimension based on probability; Anchoring target sites and mapping them onto particles marks specific dimensions. To ensure that all dimensions have the potential to be modified, sample probabilities are used to evaluate each dimension. Each dimension contains two values: one is the sample probability value generated by the Cauchy distribution, and the other is an interval... A random number between the given and the specified values; if the random number is less than the sample probability p, then this dimension is marked; otherwise, this dimension does not need to be modified. Step 7.2: Construct homologous vectors; Each dimension of the source vector is generated by the exploration and mining operators, defined as follows: (10) or （11） The "self-awareness" of the exploration operator is randomly selected. The mining operator's "self-awareness" is based on its own... Each dimension contains a range in random numbers ,when When the value of p is less than p, this dimension is generated by the exploration operator; otherwise, it is generated by the mining operator. By adjusting the value of p, the proportion of the dimensions of the same source vector generated by the two operators can be adjusted, thereby adjusting the attribute characteristics of the same source vector. Step 7.3: Modify the particles; Will Copy once, get For dimension components marked with the target dimension, replace and modify them with the components of the corresponding dimension from the same source vector. The components in the corresponding dimensions are replaced, while the unlabeled dimension components remain unchanged; after all labeled dimensions have been replaced, a modified top-level particle will be generated. ; Step 7.4: For Perform an fitness assessment; if Its adaptability is better than the original. Then it replaces the original Otherwise, discard directly. .

2. The rare earth mine path planning method for UAVs based on particle swarm optimization algorithm according to claim 1, wherein the population is divided into top-level particles and ordinary particles according to fitness, as follows: The particles are classified; based on their fitness level, they are divided into top-tier particles and ordinary particles, with the number of top-tier particles... The calculation formula is as follows: （12） in For the floor function, This is the current iteration number. The maximum number of iterations; It gradually increases with the process of evolution, from 1 to 10.

3. The rare earth mine path planning method for UAVs based on particle swarm optimization algorithm according to claim 2, wherein the learning strategy for the classic ring neighborhood topology is as follows: In the first stage, ordinary particles use the classical ring neighborhood topology PSO learning strategy to update their velocity and position. The update strategy is as follows: （13） （14） in, Indicates inertia weight; and It is the acceleration coefficient that controls the search bias of the algorithm at different evolutionary stages; and It is an interval Random numbers between; This represents the individual best experience of particle i. This represents the best experience in the neighborhood history of particle i.

4. The rare earth mine path planning method for UAVs based on particle swarm optimization algorithm according to claim 3, wherein the top-level neighborhood exploration mechanism is as follows: For each dimensional component of the top-level particle, a neighborhood exploration is performed in the component space, as shown in equation (15): （15） in The neighborhood radius, This represents the mutation probability. The dimensions are randomly generated, ensuring that at least one dimension allows for neighborhood exploration. The new value is the original value. Results within the radius based on Cauchy distribution perturbation; a new solution is generated after performing probabilistic perturbations on all dimensions of a top-level particle. ,right Perform an evaluation; if the fitness of the new solution is better than the original solution, then replace the original solution with the new solution.

Images