Unmanned aerial vehicle path planning method based on multi-objective optimization and improved particle swarm optimization

Abstract

The invention discloses an unmanned aerial vehicle path planning method based on multi-objective optimization and improved particle swarm optimization. The method comprises the steps of 1, constructing a three-dimensional space map model; 2, introducing a multi-objective optimization strategy, and designing an objective function by adopting a weighted objective optimization method for evaluating the advantages and disadvantages of each path; 3, initializing particles by adopting an improved RRT algorithm in combination with a Sobol low-difference sequence, calculating a fitness value of each unmanned aerial vehicle path, and recording an optimal solution; 4, introducing a dynamic inertia weight adjustment strategy, and dynamically adjusting the inertia weight according to the number of iterations; a dive search mechanism in an eagle search algorithm is fused, and a particle restart mechanism is introduced to avoid falling into local optimum; 5, judging whether the set number of iterations is reached or not; if yes, iteration is stopped, and the optimal route of the unmanned aerial vehicle is returned to the environment model; if not, iteration is continued, and the optimal air route is searched. The invention aims to improve the path planning efficiency and robustness of the unmanned aerial vehicle in a complex environment.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of unmanned aerial vehicle path planning and intelligent optimization algorithm, and particularly relates to an unmanned aerial vehicle path planning method based on multi-objective optimization and improved particle swarm optimization algorithm. BACKGROUND

[0002] As an efficient and flexible aerial platform, unmanned aerial vehicles (UAVs) have been widely used in fields such as logistics distribution, agricultural inspection, disaster rescue, and environmental monitoring in recent years. With the complexity and diversification of UAV application scenarios, path planning, as one of the core technologies for autonomous flight of UAVs, has become a hot research topic. Path planning aims to find an optimal flight path for a UAV from the starting point to the destination under the constraints of safety, energy consumption, and time. However, in complex environments, UAV path planning faces challenges such as dynamic obstacle avoidance, multi-objective optimization, and real-time requirements, and traditional path planning methods often fail to meet actual needs.

[0003] Traditional path planning algorithms mainly include graph search-based algorithms (such as A* algorithm and Dijkstra algorithm) and sampling-based algorithms (such as Rapidly-exploring Random Tree, RRT). These methods perform well in simple environments, but have high computational complexity, poor real-time performance, and difficulty in handling dynamic obstacles in complex environments. In recent years, swarm intelligence optimization algorithms have gradually become a hot topic in the field of UAV path planning due to their strong global search ability and adaptability.

[0004] Particle swarm optimization (PSO) is an optimization algorithm based on swarm intelligence, which simulates the group behavior of birds or fish to find the optimal solution to a problem. It has the advantages of simple principle, few parameters, and fast convergence speed, and has been widely applied in fields such as path planning and parameter optimization. However, the traditional PSO algorithm has the following problems in UAV path planning: easy to fall into local optimum, slow convergence speed, and poor environmental adaptability.

[0005] To address the above problems, domestic and foreign scholars have proposed various methods to improve the PSO algorithm. For example, dynamic inertia weight, adaptive parameter adjustment, and falcon optimization algorithm are introduced to improve the global search ability and convergence speed of the algorithm. In addition, combining multi-objective optimization technology can optimize multiple objectives (such as path length, energy consumption, and safety) in path planning, further improving the comprehensive performance of path planning. However, existing improved methods still have certain limitations in UAV path planning in complex environments, especially in complex environment obstacle avoidance and real-time adjustment, which still need further research. SUMMARY

[0006] In order to overcome the deficiencies of the prior art, the purpose of the present application is to provide a kind of unmanned aerial vehicle path planning method based on multi-objective optimization and improved particle swarm algorithm, by the combination of environment modeling, multi-objective fitness function, RRT-Sobol hybrid initialization, dynamic adjustment, fish hawk dive and restart mechanism, the present application aims at improving the efficiency and robustness of unmanned aerial vehicle path planning in complex environment, and provides technical support for the application of unmanned aerial vehicle in logistics distribution, agricultural inspection, disaster relief field.

[0007] In order to achieve the above purpose, the technical scheme adopted by the present application is:

[0008] A kind of unmanned aerial vehicle path planning method based on multi-objective optimization and improved particle swarm algorithm, comprising the following steps:

[0009] Step 1: build environment model:

[0010] According to the working environment of unmanned aerial vehicle, build three-dimensional space map model;Three-dimensional space map model includes the information of starting point, end point, obstacle, no-fly zone and terrain;

[0011] Step 2: build algorithm fitness function:

[0012] Introduce multi-objective optimization strategy, comprehensively consider the multiple factors of path length, flight height, obstacle avoidance ability and safety under the working environment of step 1 mountain, adopt weighted objective optimization method to design objective function, for evaluating the pros and cons of each path;

[0013] Step 3: use RRT-Sobol hybrid sampling initialization:

[0014] Improved RRT algorithm is used to initialize particles combined with Sobol low difference sequence, and the basic parameters of particle swarm algorithm are set;Including particle number, maximum iteration number, inertia weight, learning factor, randomly generating initial path, and calculating the fitness value of each unmanned aerial vehicle path according to the objective function designed in step 2, and recording the optimal solution;

[0015] Step 4: improve particle swarm algorithm and update track:

[0016] Introduce dynamic inertia weight adjustment strategy, dynamically adjust inertia weight according to iteration number;Fusion dive search mechanism in fish hawk search algorithm, introduce particle restart mechanism, avoid falling into local optimum;

[0017] Step 5: output optimal path: judge whether the set iteration number has been reached;If yes, stop iteration and return the optimal flight path of unmanned aerial vehicle in the environment model set in step 1;If not, continue iteration to find the optimal flight path.

[0018] The specific process of step 1 is to build an environment model:

[0019] Step 1.1: The information required for the UAV path planning process needs to be extracted from the terrain model, and the reference terrain model is:

[0020]

[0021] In the formula, x and y are the point coordinates of the model projected on the horizontal plane; z is the elevation value corresponding to the horizontal plane point; a, b, c, d, e, f, g are constant coefficients, which control the reference terrain undulation in the digital map;

[0022] The high natural mountains in the flight environment are described by an exponential function, and the mathematical model is represented as:

[0023]

[0024] In the formula, N is the total number of mountains, x and y are the point coordinates of the model projected on the horizontal plane; z is the elevation value corresponding to the horizontal plane point; h i is the height of the ith peak; (c x,i ,c y,i ) is the center position of the ith peak; is the diffusion control parameter of the ith peak, which determines the gentleness or steepness of the peak; z is the terrain height value;

[0025] According to the characteristics of natural terrain obstacles threatening the region, a spherical dangerous region is constructed in space:

[0026] (x-c x,j ) 2 +(y-c y,j ) 2 +(z-c z,j ) 2 ≤r j 2 ,j=1,2,…,M (3)

[0027] Where j is the threat zone number, which is used to represent the center position coordinates of the jth threat region, (c x,j ,c y,j ,c z,j ) is the center coordinates of the jth sphere, r j is the radius of the jth sphere; M is the total number of spheres;

[0028] Step 1.2: Set the three-dimensional representation of the UAV takeoff point and termination point S=(x0,y0,z0), G=(x n ,y n ,z n ), where S and G represent the starting point and end point of the UAV, respectively.

[0029] The specific process of the step 2 defines the objective function as:

[0030] Step 2.1: Based on the three-dimensional environment model constructed in step 1, the path length of the unmanned aerial vehicle, the flight height, the threat level, the terrain threat, and the smoothness of the path are taken as the objective function; the overall objective function is as follows:

[0031] f = b1f L +b2f H +b3f T +b4f M +b5f S (4)

[0032] In the formula, f L , f H , f T , f M , f S respectively represent the cost functions of path length, height, threat level, terrain, and path smoothness, b i (i = 1, 2, 3, 4, 5) is a relative weight factor, and b1 + b2 + b3 + b4 + b5 = 1, since the importance of each loss function in overall path evaluation is different, the value of b i should be different in different scenarios;

[0033] Step 2.2: The path length is the total length of the unmanned aerial vehicle flight path, each path is determined by D intermediate nodes, the path is divided into D+1 segments, (x i , y i , z i ) is taken from the spatial coordinate system of the three-dimensional environment model constructed in step 1, the coordinates of each node are p i = (x i , y i , z i ), and the cost function f L related to path length is as follows:

[0034]

[0035] In the formula, l i represents the length of the i-th segment of the path, s punk is the penalty coefficient of path length, S is the starting point of the unmanned aerial vehicle flight path, and G is the end point of the unmanned aerial vehicle flight path;

[0036] Step 2.3: Combined with the terrain elevation set in step 1 and the task scenario, the cost function f H related to flight height is formulated as follows:

[0037]

[0038] where n is the total number of waypoints in the UAV flight path, h c is the height cost coefficient, g i represents the height cost in the UAV flight process, h i is the height of waypoint i, h min is the height constraint; max

[0039] Step 2.4: Cost function f T related to the threat degree

[0040]

[0041] where n is the total number of path nodes, m is the total number of threats in the space, f e (i,j) represents the threat cost received by the i-th leg from the j-th threat source, which is calculated as follows:

[0042]

[0043] where d ij is the three-dimensional distance from the i-th path point (x i ,y i ,z i ) to the center of the j-th sphere, where the coordinates of the center of the j-th sphere (c x,j ,c y,j ,c z,j ), and the radius r j of the j-th sphere are all from the threat region data of the three-dimensional environment model constructed in Step 1;

[0044] Step 2.5: Calculate the interaction threat of the path and the terrain, which is calculated as follows:

[0045] For the i-th point (x i ,y i ,z i ) in the path, define the collision indicator function δ i :

[0046]

[0047] where when δ i = 1, it indicates that the point collides with the terrain, and the path is not feasible;

[0048] Based on the collision indicator function, define the terrain threat cost function f M :

[0049]

[0050] Step 2.6: Set​ and For two consecutive segments in the flight process of the UAV, the deflection angle and the pitch angle are defined as:

[0051]

[0052] where the deflection angle of the UAV is θ ij , and the pitch angle is β ij , and the cost function formula related to path smoothness is:

[0053]

[0054] The step 3 uses RRT-Sobol hybrid sampling to initialize the particle position, and the specific process is as follows:

[0055] Step 3.1: initialize parameters: particle population size n, maximum iteration number T max , inertia weight w, and learning factors c1 and c2; wherein one particle is a candidate path;

[0056] Step 3.2: hybrid sampling is used to randomly initialize the position of each particle: α×n particles are initialized in the RRT path number mode, a path branch is randomly grown from the starting point S of the model in step 1 in the three-dimensional space map, the feasible region between terrain obstacles is quickly covered, and the particle (candidate path) is prevented from falling into dangerous terrain areas such as mountains and no-fly zones, thereby ensuring the effectiveness of the initial path; the remaining (1-α)×n particles are initialized by Sobol low-discrepancy sequence sampling;

[0057] Step 3.3: the initial position of the particle is generated using the RRT algorithm; the RRT algorithm grows in a random direction from the starting point S in the three-dimensional environment constructed in step 1, and the random tree nodes constructed are intermediate waypoints of the UAV path; when the random tree is constructed using RRT, it is necessary to check in real time whether the path conflicts with the obstacles and no-fly zones of the model in step 1;

[0058] Step 3.4: the initial position of the particle is generated using the Sobol sequence; the Sobol sequence is mapped to the search boundary range, and Gaussian disturbance is added to increase diversity, and the actual space position is converted through the coordinate system of the environment model in step 1, thereby ensuring that the particle is initialized in the effective environment;

[0059] Step 3.5: the particle positions generated by the two methods in steps 3.4 and 3.5 are integrated.

[0060] In step 3.3, a node q rand is randomly sampled from the state space:

[0061]

[0062] where p g is the target bias probability; q goal represents the target point, i.e. the position where the path is ultimately to arrive at;

[0063] Find the nearest node in the expanded node set:

[0064]

[0065] Expand a fixed step size from the heading direction to obtain a new node:

[0066]

[0067] where δ = 0.05·‖q max -q min ‖ is the expansion step size;

[0068] If the distance between the new node and the existing node is greater than δ / 2, then the new node is retained and added to the tree:

[0069]

[0070] Extract the particle path points in order from the generated RRT nodes to form an initial particle position matrix

[0071] In step 3.4, let s i ∈[0,1] 3n be the i-th point generated by Sobol:

[0072] s i ∈[0,1] 3n , i = 1, 2, …, M Sobol (19)

[0073] Map it to the search space boundary [x min , x max ] and add Gaussian perturbation:

[0074] P i = x min + s i ·(x max - x min ) + N(0, σ 2 ) (20)

[0075] And perform boundary clipping to ensure that the particle position is legal;

[0076] Combine the positions of all particles into a Sobol initialized particle position matrix

[0077] In step 3.5, construct a complete initial particle population matrix P:

[0078]

[0079] The step 4 improves the particle swarm algorithm and updates the track specific process:

[0080] Step 4.1: According to the environmental model and flight strategy, the method of dynamically adjusting the inertia weight coefficient is used, and the specific improvement formula is:

[0081]

[0082] In the formula, w(t) is the inertia weight coefficient of the tth iteration; w max is the maximum value of the inertia weight; k is the parameter controlling the decay speed; N is the maximum number of iterations;

[0083] Step 4.2: Introduce the diving mechanism in the fish-eagle optimization algorithm; design the "periodic diving to approach global optimum" mechanism; the position update formula of the diving strategy is:

[0084]

[0085] Where x * represents the current global optimal solution, that is, the best UAV track in the current iteration; λ is the diving step size coefficient, which satisfies the exponential decay form:

[0086]

[0087] δ t is the disturbance factor, which is used to simulate the inaccuracy of the fish-eagle in the diving process, that is, the inaccuracy of the UAV flight, to avoid the track falling into local optimum, and it is set as a slight Gaussian noise with exponential weakening with the number of generations; N(0,1) represents the standard normal distribution noise;

[0088] Step 4.3: Introduce the restart mechanism; when the global optimal fitness has no significant improvement for several generations in a row, or the population diversity converges too quickly, it means that the search is stagnant, at which time some particles are randomly restarted to try new paths on the other side of the mountain.

[0089] The triggering conditions of step 4.3 are as follows:

[0090] (1) The optimal fitness has no significant improvement for several generations in a row

[0091]

[0092] Where ò is a small threshold value; s is the observation number;

[0093] (2) The current generation fitness variance is lower than the set threshold

[0094]

[0095] wherein, delta is a variance threshold value; is the average fitness of the current generation.

[0096] The step 5 constructs the output optimal path specific process is:

[0097] Step 5.1: judge whether the maximum iteration number T is reached max ; if yes, stop iteration and return the optimal route; if not, return to step 4 to continue iteration to find the optimal route;

[0098] Step 5.2: after reaching the maximum iteration number, output the global optimal position g in the three-dimensional environment built in step 1 as the optimal path; at the same time, record the fitness value (objective function value) of the optimal path and other related information in the iteration process.

[0099] The beneficial effects of the application are:

[0100] 1、In the application, by introducing the reference terrain model and the peak model, the complex terrain environment can be accurately described, including natural obstacles such as mountains and hills; and a spherical model is used to model the radar detection area, no-fly area and other threat areas, providing comprehensive information for path planning.

[0101] 2、The path length, flight height, threat degree, terrain threat and path smoothing are included in the objective function in the application, realizing multi-objective optimization, so that a more efficient, safe and stable flight path is planned.

[0102] 3、Algorithm improvement and path planning

[0103] (1) The application uses RRT-Sobol hybrid sampling to solve the initial path feasibility problem: RRT algorithm uses the random growth tree feature to quickly explore the feasible area under the constraint of terrain and threat source, and generates an initial flight path; Sobol low difference sequence uniformly scatters points in the space boundary of the environment model, which makes up for the defect that RRT sampling is easy to cause flight path aggregation. The hybrid sampling method effectively improves the population diversity and provides sufficient path samples for subsequent optimization.

[0104] (2) The application balances global exploration and local optimization by adjusting the inertia weight number: simulates the logic of combining exploration and optimization in unmanned aerial vehicle path planning, and adapts to the needs of different iteration stages. In the early stage of iteration, the particle is given the ability to move greatly, avoiding the algorithm from falling into local optimum too early; in the later stage of iteration, the weight decays exponentially with the number of iterations, and the fine flight point is used to reduce the cost. Through dynamic adjustment, the algorithm adapts to the actual needs of path planning.

[0105] (3) The present application adopts the diving mechanism in the fish eagle optimization algorithm to accelerate the convergence of the optimal path: the global optimal solution x * is found by analogy with the prey found by the fish eagle, i.e., the best path in the current iteration; the diving step size λ is designed as an exponential decay form with a large step size in the early stage and a small step size in the later stage, so that the other paths are quickly converged to x * in the early stage, and the path points are finely adjusted in the later stage; the disturbance factor δ t is used to simulate the inaccuracy of the fish eagle in the diving process, avoid excessive aggregation of all paths to the same local optimum, accelerate the convergence of the algorithm to the global optimal path, and improve the convergence efficiency of the algorithm.

[0106] (4) The present application uses the particle restart mechanism to enhance the robustness of path planning in complex environments: when the global optimal fitness does not significantly improve for several consecutive generations, it indicates that the current search path has fallen into a local optimum, and the particle restart can force the algorithm to try a new area to adapt to the multi-solution demand of complex terrain; if the fitness variance of the current generation is lower than the set threshold, it represents that all candidate paths are excessively concentrated, and the restarted particle can explore other flight strategies to ensure that the unmanned aerial vehicle can still find a feasible path in the threatened environment, so that the algorithm has stronger environmental adaptability.

[0107] In summary, the present application proposes an unmanned aerial vehicle path planning method based on an improved particle swarm optimization (PSO) algorithm, which significantly improves the efficiency and performance of unmanned aerial vehicle path planning through environment modeling, multi-objective optimization function, chaotic mapping initialization, dynamic inertia weight adjustment, and the introduction of fish eagle search algorithm and particle restart mechanism. BRIEF DESCRIPTION OF DRAWINGS

[0108] Figure 1 The present application is applied to the overall flowchart of the unmanned aerial vehicle path planning task.

[0109] Figure 2 The present application is an improved particle swarm optimization algorithm diagram.

[0110] Figure 3 The present application is an environment modeling diagram.

[0111] Figure 4 The present application is a RRT-Sobol hybrid sampling initialization scatter plot.

[0112] Figure 5 The present application is an algorithm fitness iteration diagram.

[0113] Figure 6 The present application is an optimal path output diagram. DETAILED DESCRIPTION

[0114] The present application will be further described in detail below with reference to the accompanying drawings.

[0115] Reference Figure 1The application is applied to the overall flowchart of the unmanned aerial vehicle path planning task, and includes the following steps:

[0116] Step 1: constructing an environment model

[0117] According to the working environment of the unmanned aerial vehicle, a three-dimensional space map model is constructed; the three-dimensional space map model includes the information of a starting point, an ending point, an obstacle, a no-fly zone and a terrain; the model provides core environment data support for subsequent steps and provides a simulation basis for the path planning algorithm;

[0118] Step 2: constructing an algorithm fitness function

[0119] A target function is designed for evaluating the advantages and disadvantages of each path; a multi-objective optimization strategy is introduced to comprehensively consider multiple factors such as path length, flight height, obstacle avoidance ability and safety under the mountain working environment in step 1, and a weighted objective optimization method is adopted to improve the comprehensive quality of the unmanned aerial vehicle path;

[0120] Step 3: using RRT-Sobol hybrid sampling initialization

[0121] The improved RRT algorithm is combined with Sobol low-discrepancy sequence to initialize the particles to enhance the space coverage ability of the initial solution, and the basic parameters of the particle swarm algorithm are set; including the number of particles, the maximum number of iterations, the inertia weight, the learning factor, the initial path is randomly generated, and the fitness value of each unmanned aerial vehicle path is calculated according to the target function designed in step 2, and the optimal solution is recorded;

[0122] Step 4: improving the particle swarm algorithm and updating the track

[0123] A dynamic inertia weight adjustment strategy is introduced to dynamically adjust the inertia weight according to the number of iterations; a diving search mechanism in the fish eagle search algorithm is fused to improve the convergence efficiency; a particle restart mechanism is introduced to avoid falling into local optimum, and the stability and robustness of the algorithm are enhanced;

[0124] Step 5: outputting the optimal path: judging whether the set number of iterations has been reached; if yes, stopping iteration and returning the optimal track of the unmanned aerial vehicle in the environment model set in step 1; if not, continuing iteration to find the optimal track. The specific process of step 1 of constructing the environment model is:

[0125] Step 1.1: the information required in the process of unmanned aerial vehicle path planning needs to be extracted from the terrain model, and good terrain modeling can effectively improve the path planning efficiency; the original terrain, obstacle area and other factors are considered for environment modeling, and the benchmark terrain model is:

[0126]

[0127] In the formula, x and y are the point coordinates of the model projected on the horizontal plane; z is the elevation value corresponding to the horizontal plane point; a, b, c, d, e, f, and g are constant coefficients, which control the reference terrain undulation in the digital map;

[0128] For higher natural mountains in the flight environment, an exponential function is used for description, and the mathematical model is expressed as:

[0129]

[0130] In the formula, N is the total number of mountains, x and y are the point coordinates of the model projected on the horizontal plane; z is the elevation value corresponding to the horizontal plane point; h i is the height of the ith peak; (c x,i ,c y,i ) is the center position of the ith peak; is the diffusion control parameter of the ith peak, which determines the gentleness or steepness of the peak; z is the terrain height value;

[0131] In addition, when performing tasks, the unmanned aerial vehicle will be affected by natural terrain obstacles such as mountains and hills, and will be disturbed by radar detection and military no-fly zones. Therefore, according to the characteristics of the threat area of natural terrain obstacles, a spherical dangerous area is constructed in space:

[0132]

[0133] Wherein, j is the threat area number, which is used to represent the center position coordinates of the jth threat area, (c x,j ,c y,j ,c z,j ) is the center coordinates of the jth sphere, r j is the radius of the jth sphere; M is the total number of spheres;

[0134] Step 1.2: Set the three-dimensional representation of the take-off point and the termination point of the unmanned aerial vehicle S=(x0,y0,z0), G=(x n ,y n ,z n ), wherein S and G represent the starting point and the end point of the unmanned aerial vehicle respectively.

[0135] The specific process of defining the objective function in the step 2 is as follows:

[0136] Step 2.1: Based on the three-dimensional environment model constructed in step 1, the path length, flight height, threat degree, terrain threat, and path smoothness of the unmanned aerial vehicle are taken as the objective function; the minimization of the path length helps to reduce the flight time and energy consumption; the consideration of the flight height ensures the safety and adaptability of the unmanned aerial vehicle; at the same time, the consideration of the threat degree suffered by the unmanned aerial vehicle helps to plan a safer flight path; the path smoothness ensures that the flight trajectory of the unmanned aerial vehicle is more stable and continuous, and the overall objective function is as follows:

[0137] f = b1f L +b2f H +b3f T +b4f M +b5f S (4)

[0138] where f L , f H , f T , f M , f S represent the cost functions of path length, height, threat level, terrain and path smoothness respectively, b i (i = 1, 2, 3, 4, 5) are relative weight factors, satisfying b1+b2+b3+b4+b5 = 1, since the importance of each loss function to the overall path evaluation is different, the value of b i should be different in different scenarios;

[0139] Step 2.2: Path length is the total length of the UAV flight path, its minimization helps to reduce flight time and energy consumption; each path is determined by D intermediate nodes, and then the path is divided into D+1 segments, (x i , y i , z i ) are taken from the spatial coordinate system of the three-dimensional environment model constructed in step 1, the coordinates of each node are p i = (x i , y i , z i ), and the cost function f L related to path length is:

[0140]

[0141] where l i represents the length of the i-th segment of the path, s punk is the penalty coefficient of path length, S is the starting point of the UAV flight path, and G is the end point of the UAV flight path;

[0142] Step 2.3: When the height of the UAV approaches the ground height, the risk of the UAV hitting the ground will increase; when the path height is too high, the enemy radar is easy to detect the UAV in special tasks; combined with the terrain elevation set in step 1 and the task scene, the cost function f H related to flight height is formulated as:

[0143]

[0144] where n is the total number of waypoints in the UAV flight path involved in the height cost calculation, h cis the height cost coefficient, g i represents the height cost in the flight process of the UAV, h i is the height at which waypoint i is located, h min is the height at which waypoint i is located, h max is the height constraint;

[0145] Step 2.4: The threat degree is used to quantify the risk of the UAV being threatened in the flight process, in addition to the threat of terrain obstacles in the environment, factors such as radar and no-fly zones are also considered, and the threat cost is strongly related to the distance between the UAV segment and the sphere center; the cost function f related to the threat degree T The formula is:

[0146]

[0147] In the formula, n is the total number of path nodes, m is the total number of threats in space, f e (i,j) represents the threat cost received by the i-th segment from the j-th threat source, which is calculated as follows:

[0148]

[0149] In the formula, d ij is the three-dimensional distance from the i-th path point (x i , y i , z i ) to the j-th sphere center, where The j-th sphere center coordinates (c x,j , c y,j , c z,j ), the radius r j of the j-th sphere are all from the threat area data of the three-dimensional environment model constructed in step 1;

[0150] Step 2.5: The terrain threat is the risk brought by the terrain undulation (such as mountains, valleys, steep terrain, etc.) when the UAV flies, by extracting key features of the terrain model (such as the reference terrain, mountain distribution), the interactive threat of the path and the terrain is calculated, which is calculated as follows:

[0151] For the i-th point (x i , y i , z i ) in the path, the collision indicator function δ i is defined:

[0152]

[0153] In the formula, when δ i = 1, it means that the point collides with the terrain, and the path is not feasible;

[0154] Based on the collision indicator function, a terrain threat cost function f is defined M :

[0155]

[0156] Step 2.6: Since the UAV is subject to its own yaw angle and climb angle constraints, it is necessary to consider the smoothness quality of the path in the path planning process. The smoothness cost of the path is used to evaluate the cost of turning and climbing in the UAV path, assuming and are two consecutive segments in the UAV flight process, then the deflection angle and the pitch angle are defined as:

[0157]

[0158] where the UAV deflection angle is θ ij , the pitch angle is β ij , and the cost function formula related to the smoothness of the path is:

[0159]

[0160] The step 3 uses RRT-Sobol hybrid sampling to initialize the particle position, and the specific process is as follows:

[0161] Step 3.1: Initialize parameters: particle population size n, maximum iteration number T max , inertia weight w, and learning factors c1 and c2;

[0162] Step 3.2: Hybrid sampling randomly initializes the position of each particle: use RRT path number to initialize α×n particles, start from the starting point S of the step 1 model, randomly grow path branches in the three-dimensional space map, quickly cover the feasible area between terrain obstacles, avoid particles (candidate paths) from falling into dangerous terrain areas such as mountains and no-fly zones, and ensure the effectiveness of the initial path; the remaining (1-α)×n particles are initialized by Sobol low-discrepancy sequence sampling, which uniformly distributes candidate waypoints within the spatial boundary of the step 1 model, enhances the global exploration of the UAV path, avoids the aggregation of the flight path caused by RRT sampling, and covers more potential optimal paths.

[0163] Step 3.3: Generate initial positions of particles using RRT algorithm. RRT has good spatial expansion and path connectivity, and can quickly cover the feasible region in high-dimensional space. In the initialization stage, the RRT algorithm grows from the starting point S to a random direction in the three-dimensional environment constructed in step 1, and the random tree nodes constructed are the intermediate waypoints of the UAV path. By preferentially exploring the path feasibility region, the initial particles are prevented from falling in the obstacle-dense region, thereby improving the path feasibility and the quality of the initial solution, and accelerating the convergence speed of global optimization; when using RRT to construct a random tree, it is necessary to check in real time whether the path conflicts with the obstacles and no-fly zones of the model in step 1.

[0164] Step 3.4: Generate initial positions of particles using Sobol sequence; Sobol sequence is a low-discrepancy quasi-random sequence with good uniformity and coverage, which can uniformly distribute particles in the search space and avoid the aggregation or omission phenomenon caused by the initialization of the RRT algorithm. By mapping the Sobol sequence to the search boundary range and adding Gaussian perturbation to increase diversity, the diversity and global search ability of the initial population can be effectively improved. The particle positions generated by Sobol sequence need to be converted to actual space positions through the coordinate system of the environment model in step 1 to ensure that the particles are initialized in the effective environment;

[0165] Step 3.5: Integrate the particle positions generated in steps 3.4 and 3.5.

[0166] In step 3.3, a node q rand is randomly sampled from the state space

[0167]

[0168] where p g is the target bias probability; q goal represents the target point, i.e., the position that the path finally reaches;

[0169] Find the nearest node in the expanded node set:

[0170]

[0171] Get a new node by expanding a fixed step length in the direction:

[0172]

[0173] where δ = 0.05·‖q max -q min ‖ is the expansion step length;

[0174] If the distance between the new node and the existing node is greater than δ / 2, the new node is retained and added to the tree:

[0175]

[0176] Extract the particle path points in order from the generated RRT nodes to form the initial particle position matrix

[0177] In step 3.4, let s i ∈[0,1] 3n The i-th point generated by Sobol:

[0178] s i ∈[0,1] 3n ,i=1,2,...,M Sobol (19)

[0179] Map it to the search space boundary [x min ,x max ] and add Gaussian disturbance:

[0180] P i =x min +s i ·(x max -x min )+N(0,σ 2 ) (20)

[0181] And boundary clipping to ensure that the particle position is legal;

[0182] Combine the positions of all particles into the Sobol initialization particle position matrix

[0183] In step 3.5, the complete initial particle population matrix P is constructed:

[0184]

[0185] The specific process of step 4 is to improve the particle swarm algorithm and update the flight path:

[0186] Step 4.1: The traditional particle swarm algorithm usually uses a fixed inertia weight coefficient, which may cause the algorithm to be unable to effectively balance global exploration and local development during the search process; In order to solve this problem, the present application proposes a method of dynamically adjusting the inertia weight coefficient according to the environmental model and flight strategy, so that it changes adaptively according to the search state during the iteration process, thereby controlling the exploration strategy of the unmanned aerial vehicle path; The specific improvement formula is:

[0187]

[0188] In the formula, w(t) is the inertia weight coefficient of the t-th iteration; w max is the maximum value of the inertia weight; k is a parameter that controls the decay rate; N is the maximum number of iterations;

[0189] Step 4.2: To further improve the convergence efficiency of the algorithm, a dive mechanism from the Osprey optimization algorithm is introduced. This mechanism simulates the behavior of an Osprey suddenly approaching the optimal region after spotting prey, enabling the particle (i.e., the UAV) path to converge quickly when it approaches the global optimum. To enhance the particle's "surprise attack capability" on the global optimum, this algorithm borrows from the Osprey's dive-foraging behavior and designs a "periodic dive approaching the global optimum" mechanism. The dive strategy position update formula is:

[0190]

[0191] Where, x * This represents the current globally optimal solution, i.e., the best-performing UAV trajectory in the current iteration; λ is the dive step size coefficient, which satisfies the exponential decay form:

[0192]

[0193] δ t The perturbation factor is used to simulate the imprecision of the Osprey during its dive, i.e., the imprecise perturbation in the flight of the UAV, to avoid the trajectory from getting trapped in a local optimum, and is set as a slight Gaussian noise that decreases exponentially with algebra; N(0,1) represents standard normal distribution noise;

[0194] Step 4.3: To avoid the particle swarm getting stuck in local optima and unable to further optimize the path, this algorithm introduces a restart mechanism. When the global optimal fitness does not improve significantly for several consecutive generations, or when the population diversity converges too quickly, it indicates that the search has stalled. At this time, some particles are randomly restarted to try new paths on the other side of the mountain, thereby enhancing the global search capability and improving the robustness of the algorithm.

[0195] The triggering conditions for step 4.3 are as follows:

[0196] (3) The optimal fitness has not significantly improved over several generations.

[0197]

[0198] Where ò is the minute threshold; s is the observation algebra;

[0199] (4) The current generation's fitness variance is lower than the set threshold.

[0200]

[0201] Where δ is the variance threshold; This represents the average fitness of the current generation.

[0202] The specific process of constructing the optimal path in step 5 is as follows:

[0203] Step 5.1: Determine whether the maximum number of iterations T is reached max ; if yes, stop iteration and return the optimal path; if no, return to step 4 to continue iteration to find the optimal path;

[0204] Step 5.2: After reaching the maximum number of iterations, output the global optimal position g in the three-dimensional environment built in step 1 as the optimal path; at the same time, record the fitness value (objective function value) of the optimal path and other related information in the iteration process.

[0205] Referring to Figure 2 , the flowchart of the improved particle swarm algorithm is shown; step 1: initialize the particle swarm and parameters: set the particle swarm (corresponding to the unmanned aerial vehicle path) and algorithm parameters, such as the number of particles, the maximum number of iterations, the inertia weight, the learning factor, etc., to prepare for path optimization.

[0206] Step 2: Calculate the fitness value of each particle: evaluate the pros and cons of each candidate path according to the set multi-objective constraint function.

[0207] Step 3: Update the global optimum and individual optimum: compare the historical optimum of the particle with the global optimum, and record the optimal path of the current iteration.

[0208] Step 4: Particle iteration: adjust the position and flight parameters of the path through the improved particle swarm algorithm.

[0209] Step 5: Iteration judgment: if the algorithm iteration reaches the maximum number of iterations or the fitness converges, output the optimal path; otherwise, return to step 2.

[0210] Referring to Figure 3 , the environment modeling process in the path planning of the unmanned aerial vehicle is shown; as can be seen from the accompanying Figure 3 , the environment modeling is realized by combining the terrain surface and the threat source sphere: the color surface represents the reference terrain model, covering the elevation changes of mountains and hills; the transparent sphere represents the threat area model, and the threat range is defined by the sphere center coordinates and radius.

[0211] Referring to Figure 4 , the scatter plot generated by the RRT-Sobol hybrid sampling to generate the initial particles is shown; as can be seen from the accompanying Figure 4 , the hybrid sampling realizes the initial particle distribution of RRT directional search + Sobol uniform coverage: the particle swarm densely gathered along the central axis corresponds to the feasibility branch explored quickly by the RRT algorithm from the starting point in the environment model, thereby ensuring the basic obstacle avoidance of the initial aircraft; the scattered isolated particles correspond to the global exploration points generated by the Sobol low-discrepancy sequence, which makes up for the local aggregation defect of RRT and improves the diversity of the initial population. This distribution effectively improves the diversity of the initial population of the algorithm, providing sufficient samples for subsequent optimization.

[0212] Referring to Figure 5 , a diagram of the algorithm fitness iteration relationship is shown; as can be seen from the attached Figure 5 , the fitness presents a trend of rapid decline to gradual convergence with the number of iterations: in the early stage (0-20 iterations), the fitness decreases sharply, corresponding to the algorithm eliminating high-cost trajectories quickly through dynamic weights and the diving mechanism of the fish-eagle algorithm, focusing on optimizing better trajectories. In the later stage (after 20 iterations), the fitness tends to be stable, corresponding to the algorithm entering the local fine adjustment stage, fine-tuning the trajectory parameters to approach the global optimum. This curve verifies the effectiveness of the algorithm in quickly converging in the early stage and fine-tuning in the later stage in the path planning of the unmanned aerial vehicle.

[0213] Referring to Figure 6 , a diagram of the optimal path output is shown; as can be seen from the attached Figure 6 , the optimal path (red line segment) embodies the planning goals of obstacle avoidance and minimum fitness: in the three-dimensional view, the path starts from the starting point, avoids the mountain uplift and threat spheres of the terrain surface, and reaches the end point, verifying the realization of terrain obstacle avoidance and threat avoidance. In the two-dimensional view, the path avoids threat spheres and high-cost areas, intuitively displaying the multi-objective optimization result. This diagram is the final output of the algorithm flow, verifying the complete flow from environment modeling to algorithm optimization to the final output of the optimal path.

Claims

1. A method for unmanned aerial vehicle path planning based on multi-objective optimization and improved particle swarm optimization, characterized in that, Comprising the following steps; Step 1: according to the working environment of the unmanned aerial vehicle, a three-dimensional space map model is constructed; the three-dimensional space map model includes the information of the starting point, the ending point, the obstacle, the no-fly zone and the terrain; Step 2: a multi-objective optimization strategy is introduced, and multiple factors such as path length, flight height, obstacle avoidance ability and safety in the mountainous working environment in step 1 are comprehensively considered, a weighted objective optimization method is used to design the objective function for evaluating the pros and cons of each path; Step 3: the improved RRT algorithm is used to initialize the particles combined with Sobol low-discrepancy sequence, and the basic parameters of the particle swarm algorithm are set; including the number of particles, the maximum number of iterations, the inertia weight, the learning factor, the initial path is randomly generated, and the fitness value of each unmanned aerial vehicle path is calculated according to the objective function designed in step 2, and the optimal solution is recorded; Step 4: a dynamic inertia weight adjustment strategy is introduced, and the inertia weight is dynamically adjusted according to the number of iterations; the diving search mechanism in the fish eagle search algorithm is fused, and the particle restart mechanism is introduced to avoid falling into local optimum; Step 5: it is judged whether the set number of iterations has been reached; if yes, the iteration is stopped and the optimal route of the unmanned aerial vehicle is returned in the environment model set in step 1; if not, the iteration is continued to find the optimal route.

2. The unmanned aerial vehicle path planning method based on multi-objective optimization and improved particle swarm optimization algorithm according to claim 1, characterized in that, The specific process of constructing the environment model in step 1 is: Step 1.1: the information required in the process of unmanned aerial vehicle path planning is extracted from the terrain model, and the reference terrain model is: In the formula, x and y are the point coordinates of the model projected on the horizontal plane; z is the elevation value corresponding to the point on the horizontal plane; a, b, c, d, e, f and g are constant coefficients, which control the reference terrain undulation in the digital map; The high natural mountains in the flight environment are described by an exponential function, which is expressed as: where N is the total number of mountains, x and y are the coordinates of the points on the horizontal plane, z is the elevation value corresponding to the points on the horizontal plane, h i is the height of the ith mountain peak; (c x,i y,i ) is the central position of the ith mountain peak; is the diffusion control parameter of the ith mountain peak, which determines the gentleness or steepness of the mountain peak, and z is the terrain height value.​ According to the characteristics of the threat area of natural terrain obstacles, a spherical dangerous area is constructed in space: wherein j is the threat zone number, used to represent the jth threat zone center position coordinate, (c x,j ,c y,j ,c z,j ) is the center coordinate of the jth sphere, r j is the jth sphere radius; M is the total number of spheres; Step 1.2: Set the three-dimensional representation of the UAV takeoff point and termination point S = (x0, y0, z0), G = (x n ,y n ,z n ), wherein S and G represent the starting point and the end point of the UAV, respectively.

3. The method of claim 2, wherein, The specific process of defining the objective function in step 2 is: Step 2.1: based on the three-dimensional environment model constructed in step 1, the path length, flight height, threat degree, terrain threat and path smoothness of the unmanned aerial vehicle are taken as the objective function; the overall objective function is as follows: f = b1f L + b2f H + b3f T + b4f M + b5f S (4) where f L , f H , f T , f M , and f S represent the cost functions of path length, height, threat level, terrain, and path smoothness, respectively, b i (i = 1, 2, 3, 4, 5) are relative weight factors, satisfying b1+b2+b3+b4+b5=1, and the values of b i should be different in different scenarios, because the importance of each loss function to the overall path evaluation is different. Step 2.2: Path length is the total length of the UAV flight path, each path is determined by D intermediate nodes, and the path is divided into D+1 segments, (x i ,y i ,z i ) are taken from the spatial coordinate system of the three-dimensional environment model constructed in step 1, the coordinates of each node are p i =(x i ,y i ,z i ), and the cost function f L related to the path length is as follows: p0 = S, p D+1 = G (7) In the formula, l i represents the length of the i-th segment of the path, s punk is the penalty coefficient of the path length, S is the starting point of the UAV flight path, and G is the end point of the UAV flight path. Step 2.3: Combine the terrain elevation set in step 1 with the mission scenario, and formulate the cost function f related to the flight height H The formula is: In the formula, n is the total number of waypoints participating in the height cost calculation in the UAV flight path, h c is a height cost coefficient, g i represents the height cost in the UAV flight process, h i is the height of the waypoint i, h min is the height of the waypoint i, h max is the height constraint; Step 2.4: Cost function f related to threat level T The formula is: where n is the total number of path nodes, m is the total number of threats in the space, f e (i,j) represents the threat cost of the ith flight segment receiving the jth threat source, and is calculated as follows: where d ij is the three-dimensional distance from the ith waypoint (x i , y i , z i ) to the jth sphere center, where the jth sphere center coordinates (c x,j , c y,j , c z,j ) and the jth sphere radius r j are derived from the threat zone data of the three-dimensional environment model constructed in step 1. Step 2.5: the interaction threat of the path and the terrain is calculated as follows: For the i-th point (x i ,y i ,z i ) in the path, define a collision indicator function δ i : In the formula, when δ i = 1, it indicates that the point collides with the terrain and the path is not feasible. Based on the collision indicator function, a terrain threat cost function f is defined M : Step 2.6: Set and for two consecutive segments in the flight of the UAV, the deflection angle and the pitch angle are defined as: In the formula, the deflection angle of the UAV is θ ij , the pitch angle is β ij , and a cost function formula related to path smoothness is:

4. The unmanned aerial vehicle path planning method based on multi-objective optimization and improved particle swarm optimization algorithm according to claim 3, characterized in that, The specific process of using RRT-Sobol hybrid sampling to initialize the particle position in step 3 is: Step 3.1: Initialize parameters: population size n, maximum number of iterations T max , inertia weight w and learning factors c1, c2; where one particle is a candidate path; Step 3.2: randomly initialize the position of each particle by hybrid sampling: use RRT path number to initialize a proportion of particles, that is, alpha x n particles, start from the starting point S of the model in step 1, randomly grow the path branch in the three-dimensional space map, quickly cover the feasible area between the terrain obstacles, avoid the particles falling into dangerous terrain areas such as mountains and no-fly zones, and ensure the effectiveness of the initial path; the rest of the particles (1-alpha) x n are initialized by Sobol low-discrepancy sequence sampling; Step 3.3: the initial position of the particle is generated by using the RRT algorithm; the RRT algorithm grows in a random direction from the starting point S in the three-dimensional environment constructed in step 1, and the random tree nodes constructed are the intermediate waypoints of the unmanned aerial vehicle path; when using RRT to construct the random tree, it is necessary to check whether the path conflicts with the obstacles and no-fly zones of the model in step 1 in real time; Step 3.4: generate initial position of particles using Sobol sequence; convert to actual space position through coordinate system of step 1 environment model by mapping Sobol sequence to search boundary range and adding Gaussian disturbance to increase diversity, ensuring that particles are initialized within the effective environment; Step 3.5: integrate particle positions generated in step 3.4 and step 3.

5.

5. The method of claim 4, wherein, The step 3.3, randomly sample a node q from the state space rand : where p g is the target bias probability; q goal represents the target point, i.e. the position where the path is to end up. Find the nearest node in the expanded node set: Expand a fixed step length in the direction to get a new node: where δ = 0.05 · ‖q max -q min ‖ is the step size of the expansion. If the distance between the new node and the existing node is greater than δ / 2, keep and add the tree: Extracting the construction particle path points from the generated RRT nodes in order, and composing the initial particle position matrix 6. The method of claim 5, wherein, In step 3.4, let s i ∈ [0,1] 3n be the i-th point generated by Sobol. s i ∈[0,1] 3n ,i=1,2,…,M Sobol (19) Mapping it to the search space boundary [x min ,x max ] and adding a Gaussian perturbation: P i = x min + s i · (x max - x min ) + N(0, σ 2 ) (20) And perform boundary clipping to ensure that the particle position is legal; combining the positions of all particles into a Sobol initialized particle position matrix 7. The method of claim 6, wherein the method further comprises: In step 3.5, construct a complete initial particle population matrix P:

8. The method of claim 7, wherein, The specific process of step 4 is to improve the particle swarm algorithm and update the track: Step 4.1: use the method of dynamically adjusting the inertia weight coefficient according to the environment model and flight strategy, and the specific improvement formula is: where w(t) is the inertial weight coefficient at the tth iteration; w max is the maximum value of the inertial weight; k is a parameter that controls the speed of attenuation; and N is the maximum number of iterations. Step 4.2: introduce the diving mechanism in the fish eagle optimization algorithm; design the "periodic diving to approach global optimum" mechanism; the position update formula of the diving strategy is: where x * represents the current global optimal solution, i.e., the best UAV trajectory in the current iteration; λ is the step size coefficient, which satisfies the exponential decay form: δ t is the disturbance factor, used to simulate the inaccuracy of the fish eagle in the process of diving, that is, the inaccuracy of the disturbance in the flight of the unmanned aerial vehicle, to avoid the flight path from falling into local optimization, and set it as a slight Gaussian noise with an exponential weakening of the generation number; N(0, 1) represents the standard normal distribution noise; Step 4.3: introduce the restart mechanism; when the global optimal fitness has no significant improvement for a certain number of generations, or the population diversity converges too quickly, it means that the search is stagnant, at this time, randomly restart part of the particles to try a new path on the other side of the mountain.

9. The method of claim 8, wherein, The triggering conditions of step 4.3 are as follows: The optimal fitness has no significant improvement for a certain number of generations Wherein, ò is a small threshold value; s is the observation number of generations; The current generation fitness variance is lower than the set threshold wherein δ is a variance threshold value; is the average fitness of the current generation.

10. The unmanned aerial vehicle path planning method based on multi-objective optimization and improved particle swarm optimization algorithm according to claim 9, characterized in that, The specific process of step 5 is to output the optimal path: Step 5.1: Determine if the maximum number of iterations T is reached max ; if yes, stop the iteration and return the optimal route; if no, return to step 4 to continue the iteration to find the optimal route; Step 5.2: after reaching the maximum number of iterations, output the global optimal position g as the optimal path in the three-dimensional environment built in step 1; at the same time, record the fitness value of the optimal path and other related information in the iteration process.

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