An unmanned swarm route planning method and system based on improved particle swarm algorithm

Abstract

The present invention belongs to the technical field of unmanned swarm route planning, and discloses an unmanned swarm route planning method and system based on an improved particle swarm algorithm. The present invention adopts an unmanned swarm collaborative flight route planning method based on the improved particle swarm algorithm. First, the principle and process of the particle swarm algorithm are explained; secondly, the particle swarm algorithm is improved, and the search ability of the algorithm is improved by optimizing the inertia weight coefficient, learning factor and speed update strategy, and the extreme value variation method is used to avoid algorithm blocking; finally, route planning simulation is carried out based on two application modes: unmanned swarm formation flight and multi-aircraft collaborative flight; it is verified that the improved particle swarm algorithm is suitable for unmanned swarm route planning, and routes that do not conflict with each other and effectively avoid threats can be obtained. From the perspective of weighted objective function and range, the weighted objective function value of the route obtained based on the improved particle swarm algorithm is smaller, the range is smaller, that is, the obtained route is better.

Description

Technical Field

[0001] The invention belongs to the technical field of route planning, and in particular relates to an unmanned cluster route planning method based on an improved particle swarm algorithm. Background Art

[0002] In principle, UAV route planning is to calculate the flight route of the UAV through various algorithms. In actual operation, it is based on the flight performance of the selected UAV, inputting information such as the geographical environment information of the flight sea area and the existing air defense no-fly zones, calculating multiple UAV flight routes while meeting all constraints, and selecting the most suitable route based on route evaluation indicators; on the other hand, targets at sea are highly maneuverable, so route planning must also be completed in the shortest possible time, so UAV route planning is essentially a comprehensive optimal solution selection problem with multiple constraints.

[0003] Nowadays, the maritime air defense system is becoming more and more complete. A single unmanned aerial vehicle often cannot meet the requirements. Only by requiring unmanned aerial vehicles in numbers exceeding the air defense system's anti-attack capability can the target be hit. That is, through the unmanned cluster route planning method, multiple unmanned aerial vehicles can fly to the target at the agreed time and angle without interfering with each other, thereby effectively increasing the probability of penetration.

[0004] Through the above analysis, the problems and defects of the prior art are as follows:

[0005] Among the route planning methods, the advantages of particle swarm algorithm over other intelligent algorithms are mainly reflected in two aspects: 1. The performance advantage of particle swarm algorithm; 2. Good adaptability to route planning problems. However, it also has the disadvantages of insufficient search capability balance and easy to fall into iteration stagnation too early, and is rarely used in unmanned swarms. Summary of the invention

[0006] In view of the problems existing in the prior art, the present invention provides an unmanned cluster route planning method based on an improved particle swarm algorithm.

[0007] The present invention is implemented as follows: an unmanned cluster route planning system based on an improved particle swarm algorithm, the system comprising:

[0008] Route generation module: This module uses the piecewise cubic Hermite interpolation method to generate the route of the UAV, ensuring that the generated route is continuous and the convexity does not change when approaching the route control point, thereby avoiding oscillation and making the route more in line with actual flight needs.

[0009] Waypoint optimization module: This module optimizes waypoints based on the improved particle swarm algorithm. It uses the global search capability of the particle swarm algorithm to find the optimal waypoint set by continuously updating the particle swarm, ensuring that the UAV cluster can fly collaboratively and reach the optimal route.

[0010] Further, the system comprises:

[0011] Particle swarm initialization module: This module generates a specified number of particle swarms under the constraints to ensure the existence of the historical optimal solution for all particles, thereby ensuring the existence of a feasible solution, that is, the existence of a feasible route.

[0012] Improved particle swarm optimization module: Under the constraints, this module continuously updates the particle swarm to find the minimum objective function value, and outputs the global optimal solution, that is, the optimal waypoint set, after reaching the update end condition. Subsequently, the system uses the piecewise cubic Hermite interpolation method to convert the optimal waypoint set into the optimal route.

[0013] An unmanned swarm route planning method based on improved particle swarm algorithm includes:

[0014] Step 1, route generation based on piecewise cubic Hermite interpolation method;

[0015] The piecewise cubic Hermite interpolation method is used for route generation, which can obtain a curve that is 1st order continuous and does not change the concavity near the route control point. Compared with interpolation methods such as Lagrange interpolation and Newton interpolation, the piecewise cubic Hermite interpolation method does not have oscillation between the route points, which is more in line with the actual route.

[0016] The j-th waypoint vector of the ith route is T ij :

[0017] T ij =|x T,ij ,y T,ij ,z T,ij | T (1)

[0018] Set the number of waypoints to n c Considering that the piecewise cubic Hermite interpolation method requires at least 4 waypoints, and the route starting point and the target point have provided 2 points, so the number of waypoints n c Greater than or equal to 2;

[0019] Based on the position of the waypoints, the actual route is generated by the piecewise cubic Hermite interpolation method; the piecewise cubic Hermite interpolation operator is λ, and for the control point T in the actual coordinate system ij , we can get the actual route curve L i for

[0020] L i =[x ij ,y ij ,z ij ] T =λ(T ij ) (2)

[0021] Where j is the sequence number of the waypoints in the actual route curve, and n is the number of waypoints in the actual route curve. c Set according to tactical requirements;

[0022] Step 2: Waypoint optimization based on improved particle swarm algorithm;

[0023] The route of the UAV is generated by the waypoints based on the piecewise cubic Hermite interpolation method. Therefore, the optimization of the UAV cluster collaborative route is equivalent to the optimization of the waypoint positions of each route. The optimization process based on the improved particle swarm algorithm is as follows:

[0024]

[0025] x t+1 =x t +v t+1

[0026] Among them, x is the optimization parameter, ω is the inertia weight coefficient, c1 and c2 are learning factors, and rand() is a random number between (0,1); represents the historical optimal solution of a single particle, represents the global historical optimal solution; the optimization parameter is the vector composed of all waypoint parameters, that is, x = [T1,...,T nc ];

[0027] The optimization process can be divided into two parts: particle swarm initialization and improved particle swarm optimization; among them, particle swarm initialization is to generate a specified number of particle swarms under the constraints. The role of particle swarm initialization is to ensure the existence of historical optimal solutions for all particles and the existence of feasible solutions, that is, the existence of feasible routes; improved particle swarm optimization is to continuously update the particle swarm under the constraints to find the minimum objective function value, meet the update end conditions and output the global optimal solution, that is, the optimal waypoint set, and then obtain the optimal route based on the piecewise cubic Hermite interpolation method.

[0028] Furthermore, the particle swarm algorithm:

[0029] For a D-dimensional problem, during the optimization process, the calculation formula for each particle i at the t+1th iteration is as follows:

[0030]

[0031] Among them, ω is the inertia weight coefficient, which is used to adjust the global and local search capabilities of the algorithm; c1 and c2 are learning factors, whose sizes affect the self-learning and social learning capabilities of particles; rand() is a random number between (0,1); and represent the historical optimal position of the ith particle and the global optimal position of the particle respectively; Formula (4) shows the particle speed in the t+1th iteration period It is affected by three parts: the speed of the previous generation of particles, the individual historical optimal position and the global particle historical optimal position.

[0032] Furthermore, the improved particle swarm algorithm:

[0033] (1) Optimization of inertia weight coefficient;

[0034] (2) Learning factor optimization;

[0035] (3) Extreme value variation;

[0036] (4) Speed ​​update strategy optimization;

[0037] (5) Improve the particle swarm algorithm process.

[0038] Furthermore, the inertia weight coefficient is optimized:

[0039] The problem of balancing global and local search capabilities and the problem of being easily trapped in local optimality is solved by improving the particle swarm algorithm from three major directions: adaptive parameter adjustment, extreme value variation, and optimization of speed update strategy. The adaptive parameter adjustment includes the inertia weight coefficient ω, learning factors c1 and c2, and the optimization of speed update strategy includes adding time-varying terms and adding speed terms.

[0040] The global and local search capabilities of particles are affected by the size of the inertia weight coefficient ω. The larger ω is, the stronger the global search capability of the particle is, and the weaker the local search capability is. As far as the route planning of unmanned aerial vehicles is concerned, in the early stage of planning, it is necessary to quickly approach the optimal route, that is, a stronger global exploration capability is required, and ω should be larger; in the later stage of planning, in order to avoid missing the global optimal route, a stronger local search capability is required, and ω should be smaller.

[0041] In order to meet the above requirements for the change of the inertia weight coefficient ω, a concave function decreasing strategy is adopted to dynamically reduce the inertia factor ω; the concave function is defined as follows:

[0042]

[0043] Among them, b (b ≥ 0) is a random variable, a γ >0 is the resolution parameter;

[0044] Among them, t is the current iteration number, maxt is the maximum iteration number, ω max and ω min are the maximum and minimum values ​​of ω respectively. Here we take ω max =0.9,ω min =0.4; When b value is different, the time-varying law of ω(t) is different. Here, when b=0.05, the changing curve of ω(t) is max =0.9,ω min =0.4, and meets the time-varying requirements of ω(t), ω(t) variation curve.

[0045] Further, the learning factor is optimized:

[0046] In the optimization process of route planning, the requirements for particle self-learning ability and social learning ability change with the optimization time; in general, it can be expressed as follows: in the early stage of planning, in order to enhance the diversity of particle optimization, particles should have strong self-learning ability and weak social learning ability, that is, c1 should be larger and c2 should be smaller; in the later stage of planning, in order to accelerate convergence to obtain the optimal route, particles should have strong social learning ability and weak self-learning ability, that is, c1 should be smaller and c2 should be larger; c1 and c2 should be time-varying, and here the values ​​of c1 and c2 are changed in a time-varying way, as shown in the following formula:

[0047]

[0048] Among them, c 1,s 、c 2,s Represent the initial values ​​of c1 and c2 respectively, c 1,f 、c 2,f Represents the final value of c1 and c2; here c is set 1,s =c 2,f =2.5, c 1,f =c 2,s =0.5.

[0049] Furthermore, the extreme value variation:

[0050] In the later stage of route planning, particles fall into local optimal values. At this time, Gbest is the same as Poets, and the global optimal solution cannot be obtained. At this time, extreme value mutation is needed to avoid algorithm blockage; when it is detected that the objective function value does not reach the preset value, the global optimal objective function value of this iteration is compared with that of the previous k iterations. If the difference is within the set range and occurs continuously for a preset number of times, that is, k+1 times, extreme value mutation is triggered:

[0051] Gbest=[1+α×rand()]Gbest (9)

[0052] Where rand() is a random variable between (0,1), α is a constant, α=0.8.

[0053] Furthermore, the speed update strategy is optimized:

[0054] On the basis of avoiding algorithm blockage by extreme value mutation, in order to prevent the algorithm from falling into local optimum, it is necessary to add an acceleration term to the speed update strategy. The acceleration term is as follows:

[0055]

[0056] Wherein, B is the acceleration range coefficient, which is related to the size of the route planning map, and here B = 2; is the objective function value of the ith particle at the tth iteration, is the optimal objective function value of the tth iteration, is the average objective function value of the tth iteration; analysis shows that the greater the difference between the objective function value of the next generation of particles and the optimal objective function value of the previous generation of particles, the faster the particle update speed is, the larger the search area is, and it can effectively avoid falling into the local optimum;

[0057] In order to balance the global search capability and the local search capability, a time-varying term δ needs to be added to the speed update strategy. i (t):

[0058]

[0059] Among them, rand() is a random number in the interval (0,1); δ i The value of (t) is affected by the size of a, giving (1-t / maxt) a Time-varying curves under different values ​​of a; it can be seen that its value is larger in the early stage of planning, so δ i (t) is larger, making Approaching the average value of its own optimal particle This helps the global search; as the planning time increases, δ i (t) decreases, which helps local search and find the optimal route; according to the time-varying curve, a=5 is taken here to update the speed;

[0060] To sum up, the following speed update strategy is adopted:

[0061]

[0062] Further, the improved particle swarm algorithm process is as follows:

[0063] Step 1. Initialization: Particle swarm initialization, including particle swarm size, iteration limit, initial particle position and velocity, etc.

[0064] Step 2. Objective function calculation: determine the objective function, obtain the objective function value of the particle in the search area according to the objective function, and save and update the individual optimal value and the global optimal value;

[0065] Step 3. Adaptive parameter update, time-varying term δ i (t) and acceleration term update; time-varying update of inertia weight coefficient and learning factor, time-varying term δ i (t) update, acceleration term update, etc.

[0066] Step 4. Extreme value mutation: compare the global optimal objective function value of this iteration with the previous k iterations. If the difference is within the set range and occurs continuously for a preset number of times, i.e. k+1 times, it can be judged that the particle is trapped in the local optimum and extreme value mutation is performed;

[0067] Step 5. Particle swarm update: Use the updated adaptive parameters and extreme values ​​to update the speed and position of each particle under the new particle speed update strategy; if the speed and position of the particle exceed the limit value, use the limit value for calculation;

[0068] Step 6. Check the algorithm end condition; determine whether the algorithm end condition is met based on the objective function value or the maximum number of iterations. If the condition is met, the algorithm ends; otherwise, go to Step 2 to continue the next cycle.

[0069] In combination with the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solutions to be protected by the present invention are as follows:

[0070] First, the continuous expansion of flight space has put forward higher requirements for the route planning of unmanned aerial vehicles. This patent focuses on the route planning of unmanned aerial vehicle clusters, comprehensively considers the flight mode of unmanned aerial vehicles, and discusses the collaborative route planning of multiple unmanned aerial vehicles based on the particle swarm algorithm. The research mainly includes the following aspects:

[0071] Mathematical model of UAV route planning. First, the mathematical problems involved in UAV route planning are described, and the evaluation indicators and constraints of UAV route planning are determined; then, the digital map model of the planning space is constructed based on the vector model and the grid model, combining the influence of terrain and tactical constraints on UAVs; finally, based on the two application modes of formation flying and multi-UAV cooperative flight, the route optimization models are constructed respectively, laying the foundation for the improvement of route planning methods in the following text.

[0072] Unmanned swarm collaborative flight route planning method based on improved particle swarm algorithm. Firstly, the principle and process of particle swarm algorithm are explained; secondly, the particle swarm algorithm is improved by optimizing the inertia weight coefficient, learning factor and speed update strategy to improve the algorithm's search ability, and the extreme value variation method is used to avoid algorithm blocking; finally, route planning simulation is carried out based on two application modes: unmanned swarm formation flight and collaborative flight.

[0073] It is verified that the improved particle swarm algorithm is suitable for unmanned cluster route planning, and can obtain routes that do not conflict with each other and effectively avoid threats. From the perspective of weighted objective function and range, the weighted objective function value of the route obtained based on the improved particle swarm algorithm is smaller, and the range is smaller, that is, the obtained route is better; from the perspective of the objective function value change curve, the route planning method based on the improved particle swarm converges faster, obtains the optimal route faster, and can avoid falling into the local optimum.

[0074] Second, the continuous expansion of flight space has put forward higher requirements for the route planning of unmanned aerial vehicles. This patent focuses on the route planning of unmanned aerial vehicle clusters, comprehensively considers the flight mode of unmanned aerial vehicles, and discusses the collaborative route planning of multiple unmanned aerial vehicles based on the particle swarm algorithm. The research mainly includes the following aspects:

[0075] Mathematical model of UAV route planning. First, the mathematical problems involved in UAV route planning are described, and the evaluation indicators and constraints of UAV route planning are determined; then, the digital map model of the planning space is constructed based on the vector model and the grid model, combining the influence of terrain and tactical constraints on UAVs; finally, based on the two application modes of formation flying and multi-UAV cooperative flight, the route optimization models are constructed respectively, laying the foundation for the improvement of route planning methods in the following text.

[0076] Unmanned swarm collaborative flight route planning method based on improved particle swarm algorithm. Firstly, the principle and process of particle swarm algorithm are explained; secondly, the particle swarm algorithm is improved by optimizing the inertia weight coefficient, learning factor and speed update strategy to improve the algorithm's search ability, and the extreme value variation method is used to avoid algorithm blocking; finally, route planning simulation is carried out based on two application modes: unmanned swarm formation flight and multi-aircraft collaborative flight; it is verified that the improved particle swarm algorithm is suitable for unmanned swarm route planning, and routes that do not conflict with each other and effectively avoid threats can be obtained. From the perspective of weighted objective function and range, the route weighted objective function value obtained by the improved particle swarm algorithm is smaller, the range is smaller, that is, the route is better; from the perspective of the objective function value change curve, the route planning method based on the improved particle swarm converges faster, obtains the optimal route faster, and can avoid falling into the local optimum.

[0077] Third, the technical solution of the present invention solves the technical problems that people have been eager to solve but have never been able to solve successfully:

[0078] In the route planning method, the advantages of the particle swarm algorithm over other intelligent algorithms are mainly reflected in two aspects: 1. The performance advantage of the particle swarm algorithm; 2. Good adaptability to route planning problems. But at the same time, there are disadvantages such as insufficient balance of search capabilities and easy to fall into iterative stagnation too early. Therefore, this patent improves the particle swarm algorithm and verifies that the improved particle swarm algorithm is suitable for unmanned cluster route planning, and can obtain routes that do not conflict with each other and effectively avoid threats. From the perspective of weighted objective function and range, the weighted objective function value of the route obtained based on the improved particle swarm algorithm is smaller, and the range is smaller, that is, the obtained route is better; from the perspective of the objective function value change curve, the route planning method based on the improved particle swarm converges faster, obtains the optimal route faster, and can avoid falling into the local optimum.

[0079] Third, the significant technical progress of the unmanned swarm route planning method based on the improved particle swarm algorithm of the present invention is mainly reflected in the following aspects:

[0080] 1. Improve the accuracy and reliability of route generation: By using the piecewise cubic Hermite interpolation method to generate routes, compared with traditional interpolation methods such as Lagrange interpolation and Newton interpolation, this method can effectively avoid the oscillation phenomenon between waypoints. The generated route is smoother and more suitable for UAV flight, thereby improving the accuracy and reliability of route generation.

[0081] 2. Optimize the efficiency and accuracy of waypoint positions: The positions of waypoints are optimized by improving the particle swarm algorithm, and parameters such as inertia weight coefficient and learning factor are introduced, so that the algorithm can better balance between global search and local search, accelerate the convergence speed, and improve the efficiency and accuracy of finding the optimal waypoint set.

[0082] 3. Improve the performance of unmanned swarm collaborative flight: This method is not only suitable for the route planning of a single unmanned aerial vehicle, but also can perform collaborative route planning for unmanned aerial vehicle clusters, optimize the route layout of the entire cluster, and improve the overall performance and efficiency of unmanned swarm collaborative flight.

[0083] 2. Adaptability to complex environments: By improving the particle swarm algorithm, the adaptability and robustness of the algorithm in complex environments are enhanced. It can effectively cope with various complex flight environments and mission requirements, and improve the flexibility and practicality of route planning.

[0084] 5. Innovation and advancement of technology: This method combines piecewise cubic Hermite interpolation and improved particle swarm algorithm. This combination is not only innovative in technology, but also shows advancement and effectiveness in practical applications, promoting technological progress in the field of unmanned aerial vehicle path planning.

[0085] The unmanned swarm path planning method based on the improved particle swarm algorithm of the present invention embodies significant technological progress by improving the accuracy of route generation, optimizing the efficiency of waypoint positions, enhancing the performance of unmanned swarm collaborative flight, adaptability to complex environments, and the innovation and advancement of technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 It is a flow chart of an unmanned cluster route planning method based on an improved particle swarm algorithm provided by an embodiment of the present invention.

[0087] Figure 2 Schematic diagram of a digital elevation model provided by an embodiment of the present invention.

[0088] Figure 3 This is a digital nautical chart model diagram provided by an embodiment of the present invention.

[0089] Figure 4 This is an air defense threat model diagram provided by an embodiment of the present invention.

[0090] Figure 5 This is a model diagram of a designated no-fly zone provided by an embodiment of the present invention.

[0091] Figure 6 This is a flight environment model diagram provided by an embodiment of the present invention.

[0092] Figure 7 It is an unmanned cluster formation diagram provided by an embodiment of the present invention.

[0093] Figure 8 It is a side view of the climbing process of the unmanned aerial vehicle provided by an embodiment of the present invention.

[0094] Fig. 9 It is a terrain comparison map before and after threat amplification provided by an embodiment of the present invention.

[0095] Fig.10 It is a comparison diagram of air defense threat areas before and after threat amplification provided by an embodiment of the present invention.

[0096] Fig.11 It is a comparison diagram of the designated no-fly zone before and after threat amplification provided by an embodiment of the present invention.

[0097] Fig.12 This is a model diagram of the marine environment before threat amplification provided by an embodiment of the present invention.

[0098] Fig.13 This is a model diagram of the marine environment after threat amplification provided by an embodiment of the present invention.

[0099] Fig.14 It is a flow chart of a particle swarm algorithm provided by an embodiment of the present invention.

[0100] Fig.15 It is an inertia weight change curve diagram provided by an embodiment of the present invention.

[0101] Fig.16 It is a time-varying curve diagram under different values ​​of a provided by an embodiment of the present invention.

[0102] Fig.17 It is a flow chart of an improved particle swarm algorithm provided by an embodiment of the present invention.

[0103] Fig.18 4 is a comparison chart of various interpolation methods provided in the embodiments of the present invention.

[0104] Fig.19 It is a flow chart of particle swarm initialization provided by an embodiment of the present invention.

[0105] Fig. 20 It is a flow chart of improved particle swarm optimization provided by an embodiment of the present invention.

[0106] Fig.21 It is a comparison diagram of the actual marine environment model and the marine environment model after threat amplification provided by an embodiment of the present invention.

[0107] Fig. 22 It is a comparison diagram of objective function value changes provided by an embodiment of the present invention.

[0108] Fig.23 It is a comparison diagram of route planning simulation provided by an embodiment of the present invention.

[0109] Fig.24 It is a comparison diagram of objective function value changes provided by an embodiment of the present invention.

[0110] Fig.25 It is a comparison diagram of route planning simulation provided by an embodiment of the present invention.

[0111] Fig.26 It is a graph showing changes in the objective function value corresponding to the improved particle swarm algorithm for solving the route planning problem provided by an embodiment of the present invention.

[0112] Fig. 27 This is a simulation result diagram of unmanned cluster collaborative flight route planning based on the improved particle swarm algorithm provided by an embodiment of the present invention.

[0113] Fig.28 This is a simulation result diagram of unmanned cluster collaborative flight route planning based on particle swarm algorithm provided by an embodiment of the present invention.

[0114] Fig.29 It is a graph showing changes in the objective function value corresponding to the improved particle swarm algorithm for solving the route planning problem provided by an embodiment of the present invention.

[0115] Fig.30 This is a simulation result diagram of unmanned cluster collaborative flight route planning based on the improved particle swarm algorithm provided by an embodiment of the present invention.

[0116] Fig.31 This is a simulation result diagram of unmanned cluster collaborative flight route planning based on particle swarm algorithm provided by an embodiment of the present invention.

[0117] Fig.32 It is a graph showing changes in the objective function value corresponding to the improved particle swarm algorithm for solving the route planning problem provided by an embodiment of the present invention.

[0118] Fig.33 This is a simulation result diagram of unmanned cluster collaborative flight route planning based on the improved particle swarm algorithm provided by an embodiment of the present invention.

[0119] Fig.34 This is a simulation result diagram of unmanned cluster collaborative flight route planning based on particle swarm algorithm provided by an embodiment of the present invention.

[0120] Fig.35 It is a graph showing changes in the objective function value corresponding to the improved particle swarm algorithm for solving the route planning problem provided by an embodiment of the present invention.

[0121] Fig.36 This is a simulation result diagram of unmanned cluster collaborative flight route planning based on the improved particle swarm algorithm provided by an embodiment of the present invention.

[0122] Fig.37 This is a simulation result diagram of unmanned cluster collaborative flight route planning based on particle swarm algorithm provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0123] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0124] like Figure 1 As shown, the present invention provides an unmanned cluster route planning method based on an improved particle swarm algorithm, comprising the following steps:

[0125] S101, route generation based on piecewise cubic Hermite interpolation method;

[0126] The piecewise cubic Hermite interpolation method is used for route generation, which can obtain a curve that is 1st order continuous and does not change the concavity near the route control point. Compared with interpolation methods such as Lagrange interpolation and Newton interpolation, the piecewise cubic Hermite interpolation method does not have oscillation between the route points, which is more in line with the actual route.

[0127] The j-th waypoint vector of the ith route is T ij :

[0128] T ij =|x T,ij ,y T,ij ,z T,ij |T (1)

[0129] Set the number of waypoints to n c Considering that the piecewise cubic Hermite interpolation method requires at least 4 waypoints, and the route starting point and the target point have provided 2 points, so the number of waypoints n c Greater than or equal to 2;

[0130] Based on the position of the waypoints, the actual route is generated by the piecewise cubic Hermite interpolation method; the piecewise cubic Hermite interpolation operator is λ, and for the control point T in the actual coordinate system ij , we can get the actual route curve L i for

[0131] L i =[x ij ,y ij ,z ij ] T =λ(T ij ) (2)

[0132] Where j is the sequence number of the waypoints in the actual route curve, and n is the number of waypoints in the actual route curve. c Set according to tactical requirements;

[0133] S102, waypoint optimization based on improved particle swarm algorithm;

[0134] The route of the UAV is generated by the waypoints based on the piecewise cubic Hermite interpolation method. Therefore, the optimization of the UAV cluster collaborative route is equivalent to the optimization of the waypoint positions of each route. The optimization process based on the improved particle swarm algorithm is as follows:

[0135]

[0136] x t+1 =x t +v t+1

[0137] Among them, x is the optimization parameter, ω is the inertia weight coefficient, c1 and c2 are learning factors, and rand() is a random number between (0,1); represents the historical optimal solution of a single particle, represents the global historical optimal solution; the optimization parameter is the vector composed of all waypoint parameters, that is, x = [T1,...,T nc ];

[0138] The optimization process can be divided into two parts: particle swarm initialization and improved particle swarm optimization; among them, particle swarm initialization is to generate a specified number of particle swarms under the constraints. The role of particle swarm initialization is to ensure the existence of historical optimal solutions for all particles and the existence of feasible solutions, that is, the existence of feasible routes; improved particle swarm optimization is to continuously update the particle swarm under the constraints to find the minimum objective function value, meet the update end conditions and output the global optimal solution, that is, the optimal waypoint set, and then obtain the optimal route based on the piecewise cubic Hermite interpolation method.

[0139] The particle swarm algorithm provided by the present invention:

[0140] For a D-dimensional problem, during the optimization process, the calculation formula for each particle i at the t+1th iteration is as follows:

[0141]

[0142]

[0143] Among them, ω is the inertia weight coefficient, which is used to adjust the global and local search capabilities of the algorithm; c1 and c2 are learning factors, whose sizes affect the self-learning and social learning capabilities of particles; rand() is a random number between (0,1); and represent the historical optimal position of the ith particle and the global optimal position of the particle respectively; Formula (4) shows the particle speed in the t+1th iteration period It is affected by three parts: the speed of the previous generation of particles, the individual historical optimal position and the global particle historical optimal position.

[0144] The improved particle swarm algorithm provided by the present invention:

[0145] (1) Optimization of inertia weight coefficient;

[0146] (2) Learning factor optimization;

[0147] (3) Extreme value variation;

[0148] (4) Speed ​​update strategy optimization;

[0149] (5) Improve the particle swarm algorithm process.

[0150] The inertia weight coefficient optimization provided by the present invention is:

[0151] The problem of balancing global and local search capabilities and the problem of being easily trapped in local optimality is solved by improving the particle swarm algorithm from three major directions: adaptive parameter adjustment, extreme value variation, and optimization of speed update strategy. The adaptive parameter adjustment includes the inertia weight coefficient ω, learning factors c1 and c2, and the optimization of speed update strategy includes adding time-varying terms and adding speed terms.

[0152] The global and local search capabilities of particles are affected by the size of the inertia weight coefficient ω. The larger ω is, the stronger the global search capability of the particle is, and the weaker the local search capability is. As far as the route planning of unmanned aerial vehicles is concerned, in the early stage of planning, it is necessary to quickly approach the optimal route, that is, a stronger global exploration capability is required, and ω should be larger; in the later stage of planning, in order to avoid missing the global optimal route, a stronger local search capability is required, and ω should be smaller.

[0153] In order to meet the above requirements for the change of the inertia weight coefficient ω, a concave function decreasing strategy is adopted to dynamically reduce the inertia factor ω; the concave function is defined as follows:

[0154]

[0155] Among them, b (b ≥ 0) is a random variable, a γ >0 is the resolution parameter;

[0156] Among them, t is the current iteration number, maxt is the maximum iteration number, ω max and ω min are the maximum and minimum values ​​of ω respectively. Here we take ω max =0.9,ω min =0.4; When b value is different, the time-varying law of ω(t) is different. Here, when b=0.05, the changing curve of ω(t) is max =0.9,ω min =0.4, and meets the time-varying requirements of ω(t), ω(t) variation curve.

[0157] The learning factor optimization provided by the present invention:

[0158] In the optimization process of route planning, the requirements for particle self-learning ability and social learning ability change with the optimization time; in general, it can be expressed as follows: in the early stage of planning, in order to enhance the diversity of particle optimization, particles should have strong self-learning ability and weak social learning ability, that is, c1 should be larger and c2 should be smaller; in the later stage of planning, in order to accelerate convergence to obtain the optimal route, particles should have strong social learning ability and weak self-learning ability, that is, c1 should be smaller and c2 should be larger; c1 and c2 should be time-varying, and here the values ​​of c1 and c2 are changed in a time-varying way, as shown in the following formula:

[0159]

[0160] Among them, c 1,s 、c 2,s Represent the initial values ​​of c1 and c2 respectively, c 1,f 、c 2,f Represents the final value of c1 and c2; here we set c 1,s =c 2,f =2.5, c 1,f =c 2,s =0.5.

[0161] The extreme value variation provided by the present invention is:

[0162] In the later stage of route planning, particles fall into local optimal values. At this time, Gbest and Pbest are the same, and the global optimal solution cannot be obtained. At this time, extreme value mutation is needed to avoid algorithm blockage; when it is detected that the objective function value does not reach the preset value, the global optimal objective function value of this iteration is compared with that of the previous k iterations. If the difference is within the set range and occurs continuously for a preset number of times, that is, k+1 times, extreme value mutation is triggered:

[0163] Gbest=[1+α×rand()]Gbest (9)

[0164] Where rand() is a random variable between (0,1), α is a constant, α=0.8.

[0165] The speed update strategy optimization provided by the present invention:

[0166] On the basis of avoiding algorithm blockage by extreme value mutation, in order to prevent the algorithm from falling into local optimum, it is necessary to add an acceleration term to the speed update strategy. The acceleration term is as follows:

[0167]

[0168] Wherein, B is the acceleration range coefficient, which is related to the size of the route planning map, and here B = 2; is the objective function value of the ith particle at the tth iteration, is the optimal objective function value of the tth iteration, is the average objective function value of the tth iteration; analysis shows that the greater the difference between the objective function value of the next generation of particles and the optimal objective function value of the previous generation of particles, the faster the particle update speed is, the larger the search area is, and it can effectively avoid falling into the local optimum;

[0169] In order to balance the global search capability and the local search capability, a time-varying term δ needs to be added to the speed update strategy. i (t):

[0170]

[0171] Among them, rand() is a random number in the interval (0,1); δ i The value of (t) is affected by the size of a, giving (1-t / max t) a Time-varying curves under different values ​​of a; it can be seen that its value is larger in the early stage of planning, so δ i (t) is larger, making Approaching the average value of its own optimal particle This helps the global search; as the planning time increases, δ i (t) decreases, which helps local search and find the optimal route; according to the time-varying curve, a=5 is taken here to update the speed;

[0172] To sum up, the following speed update strategy is adopted:

[0173]

[0174] The improved particle swarm algorithm process provided by the present invention is specifically as follows:

[0175] Step 1. Initialization: Particle swarm initialization, including particle swarm size, iteration limit, initial particle position and velocity, etc.

[0176] Step 2. Objective function calculation: determine the objective function, obtain the objective function value of the particle in the search area according to the objective function, and save and update the individual optimal value and the global optimal value;

[0177] Step 3. Adaptive parameter update, time-varying term δ i (t) and acceleration term update; time-varying update of inertia weight coefficient and learning factor, time-varying term δ i (t) update, acceleration term update, etc.

[0178] Step 2. Extreme value mutation: compare the global optimal objective function value of this iteration with that of the previous k iterations. If the difference is within the set range and occurs continuously for a preset number of times, i.e. k+1 times, it can be judged that the particle is trapped in the local optimum and extreme value mutation is performed;

[0179] Step 5. Particle swarm update: Use the updated adaptive parameters and extreme values ​​to update the speed and position of each particle under the new particle speed update strategy; if the speed and position of the particle exceed the limit value, use the limit value for calculation;

[0180] Step 6. Check the algorithm end condition; determine whether the algorithm end condition is met based on the objective function value or the maximum number of iterations. If the condition is met, the algorithm ends; otherwise, go to Step 2 to continue the next cycle.

[0181] In order to prove the creativity and technical value of the technical solution of the present invention, this section provides application examples of the claimed technical solution on specific products or related technologies.

[0182] 1. Mathematical model for route planning of unmanned swarm collaborative flight

[0183] The establishment of digital nautical charts is completed using digital grid maps, which mainly includes two aspects of processing: the establishment of digital elevation models and the setting of grid division accuracy.

[0184] Rasterize the map and assign different elevations to different grids. Set the elevation of points on sea level to 0, and express the elevation H1(x,y) at the point (x,y) on the mountain island as:

[0185] H1(x,y)=h×h0(x,y,l x ,l y ,x1,y1) (13)

[0186]

[0187] Among them, x , l y are the spans of the high mountain island on the x-axis and y-axis respectively, (x1, y1) is the projection of the center point of the high mountain island on the sea level, and h is the elevation of the point.

[0188] The elevation can be expressed in two-dimensional form using an elevation matrix, such as Figure 2 As shown:

[0189] For route planning problems, different grid division accuracies have a certain impact on the generation of route planning. The more precise the grid division, the more optimal the route obtained. However, due to the increase in the number of grids, the algorithm search space becomes larger, the optimization speed becomes slower, and the efficiency of route planning results generation also becomes lower; when the grid accuracy is reduced, the algorithm optimization speed becomes faster, but it cannot effectively find the optimal route.

[0190] When establishing a grid map, the present invention sets the map size to 200×200 and the map accuracy to 1×1, that is, the span of each grid in the x-axis and y-axis directions is 1. Figure 3 shown.

[0191] In addition to considering the impact of natural terrain, the use of unmanned aerial vehicles also needs to consider the limitations of the air defense threat zone. According to the characteristics of the air defense threat zone, it is equivalent to a hemispherical model. The treatment of air defense threats is similar to the treatment of island terrain, that is, the map is rasterized, and different elevations are assigned to different grids. The elevation of the point on the sea level is set to 0, and the elevation H2(x,y) at the point (x,y) on the air defense threat zone is expressed as:

[0192]

[0193] Among them, (x1, y1) is the projection of the center point of the air defense threat zone on the sea level, and r is the radius of the air defense threat zone. The air defense threat model is as follows Figure 4 shown.

[0194] In order to avoid affecting civilian facilities or threatening friendly forces during the use of unmanned aerial vehicles, the impact of designated no-fly zones must also be considered. The no-fly zone is equivalent to a cylinder of sufficient height, and the elevation H3(x,y) at the point (x,y) on the designated no-fly zone is expressed as:

[0195] H3(x,y)=j(x1,y1,r)=C (16)

[0196] Where C is a constant value, C = 20, and the specified no-fly zone model is as follows: Figure 5 shown.

[0197] Based on the comprehensive digital chart model, air defense threat model and designated no-fly zone model of the present invention, a flight environment model can be obtained, such as Figure 6 As shown, the elevation value at the point (x, y) is:

[0198] H(x,y)=Max[H1(x,y),H2(x,y),H3(x,y)] (17)

[0199] The navigator model is a common unmanned swarm formation model, which can be divided into two categories: navigator and follower. The navigator has the best performance and is responsible for integrating the information collected by the followers and external and internal communications. The followers mainly collect target information, receive information transmitted by the navigator, and complete the flight operation. Usually, the formations of unmanned swarms can be divided into: column, horizontal column, diamond column, wedge column, such as Figure 7 shown.

[0200] The objective function of the unmanned swarm formation route planning is a weighted objective function, which takes into account two optimization directions, namely, the range and the amount of interception.

[0201] The shorter the range of the UAV, the shorter the flight time, the lower the probability of being discovered and the better the safety. Therefore, the shorter the range of the UAV, the better. The range of the unmanned swarm formation E(L) is the sum of multiple routes, and the expression is as follows:

[0202]

[0203] Among them l i It is the distance between the two waypoints before and after the unmanned cluster formation.

[0204] In the unmanned swarm formation flight route planning space, each position has a corresponding threat level, which constitutes the threat function W(x, y, z). The interception volume is defined as the integral of the threat function on the unmanned swarm formation route curve. The smaller the interception volume, the greater the probability of survival of the unmanned aerial vehicle.

[0205] The present invention simplifies the air defense threat zone, and regards the threat functions of all positions in the threat zone as 1, that is, the threat zone is regarded as terrain; similarly, the designated no-fly zone is also regarded as terrain, and the route planning space threat function W(x, y, z) is as follows:

[0206]

[0207] The intercepted quantity P is expressed as follows:

[0208]

[0209] where [x i ,y i ,z i ] T is the i-th waypoint, and W(x,y,z) is the spatial threat index function.

[0210] Assume the weighted objective function is J, then we have

[0211] j=aE(L)+bP (21)

[0212] Among them, E(L) is the range, P is the interception volume. λ=(a,b) is the weighting coefficient, and the weighting coefficient is related to the priority of each indicator. The priority can be reasonably set according to the actual flight needs and the performance of the unmanned aerial vehicle. The higher the relative priority, the greater the weighting coefficient.

[0213] The constraints that need to be considered in the route planning of unmanned swarm formation flight are: range constraint, minimum turning radius constraint, maximum pitch angle constraint, terrain obstacles and air defense threat zone constraint.

[0214] The range constraint of the UAV swarm formation mainly depends on the maximum range of the UAV, which is denoted as L. max , then the range constraint is:

[0215] L≤L max (twenty two)

[0216] Where: L is the distance of the route.

[0217] In the route planning of formation flight, the UAV needs to perform attitude control near the waypoint to change the flight direction. The formation is constrained by the flight performance of the UAVs in the formation during the turn. The waypoints [x i ,y i ] T The radius of curvature ρ i ,have

[0218]

[0219] Assume that the minimum turning radius of the UAV formation is r min , if i satisfy

[0220] ρ i ≥r min (twenty four)

[0221] Then the route meets the minimum turning radius constraint of the unmanned swarm formation.

[0222] In the route planning of unmanned swarm formation flight, the unmanned aerial vehicles climb or descend through attitude control. The formation climbing or descending process is constrained by the flight performance of the unmanned aerial vehicles in the formation. Assume that the maximum pitch angle and elevation angle of the unmanned aerial vehicle formation are α u and α d , T1 and T2 represent the starting and ending points of the UAV when it is climbing or descending, respectively, and Δd represents the vertical distance that the UAV deflects at T2 from the distance it flew at T1. Figure 8 As shown, to meet the maximum pitch angle limit, it is necessary to ensure that:

[0223]

[0224] Among them, |T1T2| is the flight distance of the UAV during the maneuvering process.

[0225] In the route planning of unmanned swarm collaborative flight, terrain constraints, air defense threat zone constraints and designated no-fly zone constraints are generally combined into one type of threat constraints. In the set nautical chart, add the actual terrain constraint R T0 , the actual air defense threat constraint R F0 , the actual designated no-fly zone constraint R J0 The combined threat area is expressed as (R T0 ∪R F0 ∪R J0 ). Let the UAV route curve be f(x,y,z,t), (x,y) is the coordinates of any point in the route projected on the sea level, z is the height of the point in the route, and t is the flight time of the UAV. Then the terrain, air defense threat and designated no-fly zone constraints can be expressed as

[0226]

[0227] Where H(x,y) is the elevation of the threat zone at point (x,y).

[0228] However, in order to ensure the flight safety of the UAV and avoid the influence of uncontrollable factors such as errors on the UAV, a safety distance s0 is often required. The present invention adopts a threat amplification method: that is, when constructing the environmental model, the terrain, air defense threat area and the designated no-fly zone are enlarged by λ times, and the elevation H(x, y) at the point (x, y) on the terrain is expressed as:

[0229] H1(x,y)=(h×λ)×h0(x,y,l x ×λ,l y ×λ,x1,y1) (27)

[0230] The elevation H2(x,y) at the point (x,y) in the air defense threat zone is expressed as:

[0231] H2(x,y)=w(x,y,x1,y1,r×λ) (28)

[0232] The height H3(x,y) at the point (x,y) on the designated no-fly zone is expressed as:

[0233] H3(x,y)=j(x1,y1,r×λ) (29)

[0234] Among them, for UAV formation flight, the λ value should be appropriately increased to ensure the safety of the formation. T , air defense threat constraint R F , specify the no-fly zone constraint R F, then the combined threat area is expressed as (R T ∪R F ∪R J ), then for a point (x, y, z) on the route, the terrain, air defense threat, and designated no-fly zone constraints can be expressed as:

[0235] z(x,y)>H(x,y)=Max[H1(x,y),H2(x,y),H3(x,y)] (30)

[0236] Comparison of terrain, air defense threat zones, and designated no-fly zones before and after threat amplification Figure 9-11 As shown:

[0237] The objective function of unmanned swarm collaborative flight route planning is a weighted multi-objective function, which takes into account three optimization directions, namely, average range, range standard deviation, and comprehensive interception amount.

[0238] The shorter the range of the UAV, the better it can guarantee the terminal maneuverability requirements of the UAV, and the more it can compress the target reaction time. Therefore, the shorter the range of the UAV, the better. For the coordinated flight of unmanned swarms, the shorter the average range, the better. The average range E(L i ) is the average value of the range of all unmanned aerial vehicles in the unmanned swarm collaborative flight, E(L i ) is expressed as follows:

[0239]

[0240] Where l(L i ) is the length of the i-th route.

[0241] In order to ensure that the time difference of the UAVs arriving at the target point is as small as possible, that is, the time window of all UAVs arriving at the target point is as small as possible, the standard deviation of the range σ(L i ) is used as an indicator to measure the time window size to reach the target point, σ(L i ) is the standard deviation of the range of each UAV, expressed as follows:

[0242]

[0243] Where n p is the route number, E(L i ) is the average flight distance, l(L i ) is the length of the i-th route.

[0244] In the coordinated flight of unmanned aerial vehicles, each unmanned aerial vehicle is subject to the constraints of terrain, air defense threat zones and designated no-fly zones. In the route planning space, each position has a corresponding threat level, which constitutes the threat function W(x, y, z). The interception volume is defined as the integral of the threat function on the route curve of the unmanned aerial vehicle formation, and the comprehensive interception volume is defined as the sum of the interception volumes of all routes. The smaller the comprehensive interception volume, the better.

[0245] Then the cumulative threat of the ith route in discrete form is:

[0246]

[0247] where [x ij ,y ij ,z ij ] T is the j-th waypoint of the i-th UAV.

[0248] Then the comprehensive interception amount of the unmanned swarm cooperative flight route is

[0249]

[0250] Assume the weighted objective function is J, then we have

[0251] J = aE(L i )+bσ(L i )+cP (35)

[0252] Among them, E(L i ) is the average flight distance, σ(L i ) is the standard deviation of the flight range, P is the comprehensive interception amount, λ=(a,b,c) is the weighting coefficient, and the weighting coefficient is related to the priority of each indicator. The priority can be reasonably set according to the actual flight needs and the performance of the unmanned aerial vehicle itself. The higher the relative priority of the indicator, the larger the corresponding weighting coefficient. For the route planning of unmanned swarm collaborative flight, the smaller the weighted objective function value, the better, and relative to the above three indicators, it has the highest priority, that is, the J value should be minimized first.

[0253] In the unmanned swarm collaborative flight route planning problem, in addition to satisfying the constraints of a single unmanned aerial vehicle: range constraint, minimum turning radius constraint, maximum pitch angle constraint, terrain constraint, air defense threat zone and designated no-fly zone constraint, the following constraints must also be met: terminal attack angle constraint and route intersection constraint. Among them, the range constraint, minimum turning radius constraint and maximum pitch angle constraint are the same as those when the unmanned aerial vehicles fly in formation, so they will not be repeated here.

[0254] In the unmanned swarm cooperative flight, the terrain constraints, air defense threat zone constraints and designated no-fly zone constraints are handled in the same way as the unmanned aerial vehicle formation flight. However, in the unmanned swarm cooperative flight, the λ value should not be too large to avoid the route not meeting the requirements. Then for the i-th route point (x i ,y i ,z i ),Require:

[0255] z i (x i ,y i )>H(x i ,y i )=max[H1(x i ,y i ),H2(x i ,y i ),H3(x i ,y i )] (36)

[0256] Comparison of maritime environment models before and after threat amplification Fig.12 , 13 As shown:

[0257] In order to achieve saturation attack, increase the effectiveness of coordinated attack of UAV clusters, and effectively improve the probability of penetration, it is necessary to ensure that the UAVs attack the target from different directions. To meet this requirement, the terminal attack angle constraint is introduced, which is defined as the angle of the UAV relative to the target ship after the UAV reaches the last waypoint, that is, the terminal radar power-on point, that is,

[0258] |A i (X f ,Y f ,X t ,Y t )|=D Ai (37)

[0259] Where: (X f ,Y f ) is the terminal radar start-up point of the ith route; (X t ,Y t ) is the target point on the digital map; A i (X f ,Y f ,X t ,Y t ) is the angle of the UAV relative to the target ship after it reaches the terminal radar start-up point, D Ai is the designated terminal attack angle of the i-th UAV.

[0260] In order to ensure that the interference between missiles is minimal during the coordinated flight of unmanned swarms, there will be no collision between missiles, and to reduce the non-penetration losses during the coordinated flight of unmanned swarms, it is necessary to ensure that the routes of the missiles will not intersect. For this purpose, a route intersection constraint is introduced, that is, any two routes in all unmanned swarm coordinated flight routes cannot intersect. For the ath route L ia and route L ib , it can be determined whether the line segments between adjacent waypoints intersect.

[0261] Assume that the ath route L ia The line segment in [x ia,j1 ,y ia,j1 ,z ia,j1 ] T →[x ia,j1+1 ,y ia,j1+1 ,z ia,j1+1 ] T , route L ib The line segment in [x ib,j2 ,y ib,j2 ,z ib,j2 ] T →[x ib,j2+1 ,y ib,j2+1 z ib,j2+1 ] T , for the convenience of representation, let vector X oa , X ob , X da , X db , X ab :

[0262] X oa =[x ia,j1 ,y ia,j1 ,z ia,j1 ] T

[0263] X ob =[x ib,j2 ,y ib,j2 ,z ib,j2 ] T

[0264] X da =[x ia,j1 ,y ia,j1 ,z ia,j1 ] T -[x ia,j1+1 ,y ia,j1+1 ,z ia,j1+1 ] T

[0265] X db =[x ib,j2 ,y ib,j2 ,zib,j2 ] T -[x ib,j2+1 ,y ib,j2+1 z ib,j2+1 ] T

[0266] X ab =[x ia,j1 ,y ia,j1 ,z ia,j1 ] T -[x ib,j2 ,y ib,j2 ,z ib,j2 ] T

[0267] If satisfied:

[0268]

[0269] Then the two line segments are in the same plane, and solving the following linear equation can obtain the intersection of the two line segments

[0270]

[0271] If both exist:

[0272]

[0273] If the two line segments have an intersection, the route does not satisfy the route intersection constraint; if all line segments between the routes do not intersect, the route intersection constraint is satisfied.

[0274] 2. Unmanned swarm collaborative flight path planning method based on improved particle swarm algorithm

[0275] In solving the problem of unmanned aerial vehicle route planning, the advantages of particle swarm algorithm over other intelligent algorithms are mainly reflected in two aspects: 1. The performance advantage of particle swarm algorithm; 2. Good adaptability to route planning problems. However, it also has the disadvantages of insufficient search ability balance and easy to fall into iteration stagnation too early. Therefore, this chapter intends to improve the particle swarm algorithm and conduct research on the collaborative route planning method of unmanned aerial vehicle clusters based on the improved particle swarm algorithm.

[0276] For a D-dimensional problem, during the optimization process, the calculation formula for each particle i at the t+1th iteration is as follows:

[0277]

[0278] Among them, ω is the inertia weight coefficient, which is used to adjust the global and local search capabilities of the algorithm; c1 and c2 are learning factors, whose sizes affect the self-learning and social learning capabilities of particles; rand() is a random number between (0,1). and They represent the historical optimal position of the ith particle and the historical optimal position of the global particle respectively. Formula (41) shows the particle velocity in the t+1th iteration period It is affected by three parts: the speed of the previous generation of particles, the individual historical optimal position and the global particle historical optimal position. The flowchart of the particle swarm algorithm is as follows: Fig.14 shown.

[0279] Aiming at the two problems of particle swarm algorithm: the balance problem between global and local search capabilities and the problem of being easily trapped in local optimality, the particle swarm algorithm is improved from three major directions: adaptive parameter adjustment, extreme value variation, and optimization of speed update strategy. The adaptive parameter adjustment includes the inertia weight coefficient ω, learning factors c1 and c2, and the optimization of speed update strategy includes adding time-varying terms and adding speed terms.

[0280] The global and local search capabilities of particles are affected by the size of the inertia weight coefficient ω. The larger ω is, the stronger the global search capability of the particle is, and the weaker the local search capability is. As far as the route planning of unmanned aerial vehicles is concerned, in the early stage of planning, it is necessary to quickly approach the optimal route, that is, a strong global exploration capability is required, and ω should be larger; in the later stage of planning, in order to avoid missing the global optimal route, a strong local search capability is required, and ω should be smaller.

[0281] In order to meet the above requirements for the change of the inertia weight coefficient ω, a concave function decreasing strategy is adopted to dynamically reduce the inertia factor ω. The concave function is defined as follows:

[0282]

[0283] Among them, b (b ≥ 0) is a random variable and a>0 is a resolution parameter.

[0284] Among them, t is the current iteration number, maxt is the maximum iteration number, ω max and ω min are the maximum and minimum values ​​of ω respectively. Here we take ω max =0.9,ω min =0.4. When b value is different, the time variation law of ω(t) is different. When b=0.05, the variation curve of ω(t) is max =0.9,ω min =0.4, and meets the time-varying requirements of ω(t). The ω(t) variation curve is as follows: Fig.15 shown.

[0285] In the optimization process of route planning problems, the requirements for particle self-learning ability and social learning ability change with the optimization time. In general, it can be expressed as follows: in the early stage of planning, in order to enhance the diversity of particle optimization, particles should have strong self-learning ability and weak social learning ability, that is, c1 should be larger and c2 should be smaller; in the later stage of planning, in order to accelerate convergence to obtain the optimal route, particles should have strong social learning ability and weak self-learning ability, that is, c1 should be smaller and c2 should be larger. c1 and c2 should be time-varying. Here, the values ​​of c1 and c2 are changed in a time-varying manner, as shown in the following formula:

[0286]

[0287] Among them, c 1,s 、c 2,s Represent the initial values ​​of c1 and c2 respectively, c 1,f 、c 2,f Represents the final value of c1 and c2. Here we set c 1,s =c 2,f =2.5, c 1,f =c 2,s =0.5.

[0288] In the later stage of route planning, particles fall into local optimal values. At this time, Gbest and Pbest are the same, and the global optimal solution cannot be obtained. At this time, extreme value mutation is needed to avoid algorithm blockage. When it is detected that the objective function value does not reach the preset value, the global optimal objective function value of this iteration is compared with that of the previous k iterations. If the difference is within the set range and occurs continuously for the preset number of times, that is, k+1 times, extreme value mutation is triggered:

[0289] Gbest=[1+α×rand()]Gbest (46)

[0290] Where rand() is a random variable between (0,1), α is a constant, α=0.8.

[0291] On the basis of avoiding algorithm blockage by extreme value mutation, in order to prevent the algorithm from falling into local optimum, it is necessary to add an acceleration term to the speed update strategy. The acceleration term is as follows:

[0292]

[0293] Wherein, B is the acceleration range coefficient, which is related to the size of the route planning map, and here B=2. is the objective function value of the ith particle at the tth iteration, is the optimal objective function value of the tth iteration, is the average objective function value of the tth iteration. From the analysis, it is known that the greater the difference between the objective function value of the next generation of particles and the optimal objective function value of the previous generation of particle swarm, the faster the particle update speed is, the larger the search area is, and it can effectively avoid falling into the local optimum.

[0294] In order to balance the global search capability and the local search capability, a time-varying term δ needs to be added to the speed update strategy. i (t):

[0295]

[0296] Among them, rand() is a random number in the interval (0,1); δ i The value of (t) is affected by the size of a. Fig.16 Given (1-t / maxt) a Time-varying curves under different values ​​of a. It can be seen that its value is larger in the early stage of planning, so δ i (t) is larger, making Approaching the average value of its own optimal particle This helps the global search; as the planning time increases, δ i (t) is reduced, which helps local search and find the optimal route. Fig.16 Time-varying curve, where a=5 is taken to update the speed.

[0297] In summary, the present invention adopts the following speed update strategy:

[0298]

[0299] Improved particle swarm algorithm process used in the present invention Fig.17 The improved particle swarm algorithm process is as follows:

[0300] Step 1. Initialization. Particle swarm initialization, including particle swarm size, iteration limit, initial particle position and velocity, etc.

[0301] Step 2. Objective function calculation. Determine the objective function, obtain the objective function value of the particle in the search area based on the objective function, and save and update the individual optimal value and the global optimal value.

[0302] Step 3. Adaptive parameter update, time-varying term δ i (t) and acceleration term update. Time-varying update of inertia weight coefficient and learning factor, time-varying term δ i (t), update of acceleration term, etc.

[0303] Step 2. Extreme value mutation. Compare the global optimal objective function value of this iteration with that of the previous k iterations. If the difference is within the set range and occurs continuously for a preset number of times, i.e. k+1 times, it can be determined that the particle is trapped in the local optimum and extreme value mutation is performed.

[0304] Step 5. Particle swarm update. Use the updated adaptive parameters and extreme values ​​to update the speed and position of each particle under the new particle speed update strategy; if the speed and position of the particle exceed the limit value, use the limit value for calculation.

[0305] Step 6. Check the algorithm end condition. Determine whether the algorithm end condition is met based on the objective function value or the maximum number of iterations. If the condition is met, the algorithm ends. Otherwise, go to Step 2 to continue the next cycle.

[0306] The movement of the UAV is uninterrupted, that is, the route is a continuous curve. It is labor-intensive to directly describe and optimize the route, which does not meet the actual flight needs. Therefore, the actual route is obtained by first solving the UAV route control points and then using the piecewise cubic Hermite interpolation method to generate the route. In this way, the route optimization process is actually the optimization of the waypoints.

[0307] The segmented cubic Hermite interpolation method is used for route generation, which can obtain a curve that is continuous to the first order and does not change the concavity near the route control point. Compared with interpolation methods such as Lagrange interpolation and Newton interpolation, the segmented cubic Hermite interpolation method does not have oscillation between the route points, which is more in line with the actual route. The segmented cubic Hermite interpolation method pchip, cubic spline interpolation spline, and modified Akima segmented cubic Hermite interpolation method makima are compared as follows Fig.18 :

[0308] The j-th waypoint vector of the ith route is T ij :

[0309] T ij =|x T,ij ,y T,ij ,z T,ij | T (50)

[0310] Set the number of waypoints to n c Considering that the piecewise cubic Hermite interpolation method requires at least 4 waypoints, and the route starting point and the target point have provided 2 points, so the number of waypoints n c Greater than or equal to 2.

[0311] Based on the position of the waypoints, the actual route is generated by the piecewise cubic Hermite interpolation method. The piecewise cubic Hermite interpolation operator is λ. For the control point T in the actual coordinate system ij , we can get the actual route curve L i for

[0312] L i =[x ij ,y ij z ij ] T =λ(T ij ) (51)

[0313] Where j is the sequence number of the waypoints in the actual route curve, and n is the number of waypoints in the actual route curve. c Set according to tactical requirements.

[0314] The route of the UAV is generated by the waypoints based on the piecewise cubic Hermite interpolation method. Therefore, the optimization of the coordinated route of the UAV cluster is equivalent to the optimization of the position of the waypoints of each route. The optimization process based on the improved particle swarm algorithm is as follows:

[0315]

[0316] x t+1 =x t +v t+1 (53)

[0317] Among them, x is the optimization parameter, ω is the inertia weight coefficient, c1 and c2 are learning factors, and rand() is a random number between (0,1). represents the historical optimal solution of a single particle, represents the global historical optimal solution. The optimization parameter is a vector composed of all waypoint parameters, that is, x = [T1,...,T nc ].

[0318] The optimization process can be divided into two parts: particle swarm initialization and improved particle swarm optimization. Particle swarm initialization is to generate a specified number of particle swarms under the constraints, such as Fig.19 As shown in ; the role of particle swarm initialization is to ensure the existence of historical optimal solutions for all particles, to ensure the existence of feasible solutions, that is, the existence of feasible routes. The improved particle swarm optimization is to continuously update the particle swarm to find the minimum objective function value under the constraints, to meet the update end conditions and output the global optimal solution, that is, the optimal waypoint set, and then obtain the optimal route based on the piecewise cubic Hermite interpolation method; as shown in Fig. 20 shown.

[0319] The embodiments of the present invention have achieved some positive effects during the development or use process, and indeed have great advantages over the prior art. The following content is described in conjunction with data, charts, etc. of the test process.

[0320] Considering the actual needs of different environments and application backgrounds, based on two typical tactical applications of unmanned swarm collaborative flight, a simulation analysis of the unmanned swarm collaborative flight path planning method based on the improved particle swarm algorithm was carried out to verify the practicality and effectiveness of the improved particle swarm algorithm.

[0321] During the route planning of unmanned swarm formation flight, it is assumed that the formation is a fixed formation, and simulation analysis is performed according to different environmental models:

[0322] (1) 2 terrain obstacles, 1 air defense threat zone, and 1 designated no-fly zone;

[0323] Since the formation of the unmanned swarm is fixed, considering the constraints of the coordinated flight of the unmanned swarm, it can be equivalent to increasing the safe distance of a certain unmanned aerial vehicle in the swarm, and then the constraint can be imposed in the form of threat zone amplification. The marine environment model before and after threat amplification is as follows, which will not be repeated in the following text:

[0324] Fig.21 Comparison of the actual marine environment model and the marine environment model after threat amplification

[0325] The comparison of the simulation results of UAV formation flight route planning based on particle swarm algorithm and improved particle swarm algorithm is shown in the figure below. Fig. 22 , Fig.23 As shown:

[0326] Table 2.1 Particle swarm algorithm and improved particle swarm algorithm performance comparison table

[0327]

[0328] (2) Four terrain obstacles, two air defense threat zones, and one designated no-fly zone.

[0329] The comparison of the simulation results of unmanned swarm formation flight route planning based on particle swarm algorithm and improved particle swarm algorithm is shown in the figure below. Fig.24 , Fig.25 As shown:

[0330] Table 2.2 Comparison of the performance of particle swarm algorithm and improved particle swarm algorithm

[0331]

[0332] Simulation results analysis: Figure 22-Figure 25The results in Tables 2.1 and 2.2 verify that the improved particle swarm algorithm is suitable for route planning of unmanned cluster formation flight, and can obtain routes that do not conflict with each other and effectively avoid threats; from the perspective of weighted objective function and range, the weighted objective function value of the route obtained based on the improved particle swarm algorithm is smaller, and the range is smaller, that is, the obtained route is better; from the perspective of the objective function value change curve, the route planning method based on the improved particle swarm converges faster, obtains the optimal route faster, and can avoid falling into the local optimum.

[0333] In the application of unmanned swarm cooperative flight, according to the different launch platforms and targets of the unmanned aerial vehicles, there are generally the following application backgrounds: (1) single platform vs. single target, (2) multiple platforms vs. single target, (3) single platform vs. multiple targets. Combining different application environments, the following simulation analysis is performed:

[0334] (1) 2 terrain obstacles, 1 air defense threat zone, and 1 designated no-fly zone;

[0335] Table 2.3 Comparison of the performance of particle swarm algorithm and improved particle swarm algorithm

[0336]

[0337] (2) Four terrain obstacles, two air defense threat zones, and one designated no-fly zone.

[0338] Table 2.4 Particle swarm algorithm and improved particle swarm algorithm performance comparison table

[0339]

[0340] Simulation results analysis: Figure 26-Figure 32 The results in Tables 2.3 and 2.4 verify that the improved particle swarm algorithm is suitable for unmanned cluster collaborative flight route planning, and can obtain routes that do not conflict with each other and effectively avoid threats; from the objective function value change curve, the route planning method based on the improved particle swarm converges faster, obtains the optimal route faster, and can avoid falling into the local optimum.

[0341] (1) 2 terrain obstacles, 1 air defense threat zone, and 1 designated no-fly zone;

[0342] Table 2.5 Particle swarm algorithm and improved particle swarm algorithm performance comparison table

[0343]

[0344] (2) Four terrain obstacles, two air defense threat zones, and one designated no-fly zone.

[0345] Table 2.6 Particle swarm algorithm and improved particle swarm algorithm performance comparison table

[0346]

[0347] Simulation results analysis: Figure 32-Figure 37 The results in Tables 2.5 and 2.6 verify that the improved particle swarm algorithm is suitable for unmanned cluster collaborative flight route planning, and can obtain routes that do not conflict with each other and effectively avoid threats; from the perspective of weighted objective function, average range and range standard deviation, the weighted objective function value of the route obtained based on the improved particle swarm algorithm is smaller, the average range is not much different, and the range standard deviation is smaller, that is, the obtained route is better; from the perspective of the objective function value change curve, the route planning method based on the improved particle swarm converges faster, obtains the optimal route faster, and can avoid falling into the local optimum.

[0348] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed by the present invention and within the spirit and principle of the present invention should be covered by the protection scope of the present invention.

Claims

1. An unmanned swarm route planning method based on improved particle swarm algorithm, characterized in that: The unmanned swarm route planning method based on the improved particle swarm algorithm comprises the following steps: Step 1, route generation based on piecewise cubic Hermite interpolation method; The piecewise cubic Hermite interpolation method is used for route generation, which can obtain a curve that is 1st order continuous and does not change the concavity near the route control point; compared with the Lagrange interpolation and Newton interpolation methods, the piecewise cubic Hermite interpolation method does not have oscillation between the route points, which is more in line with the actual route; The j-th waypoint vector of the ith route is T ij : T ij =|x T,ij ,y T,ij ,z T,ij | T (1) Set the number of waypoints to n c Considering that the piecewise cubic Hermite interpolation method requires at least 4 waypoints, and the route starting point and the target point have provided 2 points, so the number of waypoints n c Greater than or equal to 2; Based on the position of the waypoints, the actual route is generated by the piecewise cubic Hermite interpolation method; the piecewise cubic Hermite interpolation operator is λ, and for the control point T in the actual coordinate system ij , we can get the actual route curve L i for L i [x ij ,y ij ,z ij ] T =λ(T ij )(2) Where j is the sequence number of the waypoints in the actual route curve, and n is the number of waypoints in the actual route curve. c Set according to tactical requirements; Step 2: Waypoint optimization based on improved particle swarm algorithm; The route of the UAV is generated by the waypoints based on the piecewise cubic Hermite interpolation method. Therefore, the optimization of the UAV cluster collaborative route is equivalent to the optimization of the waypoint positions of each route. The optimization process based on the improved particle swarm algorithm is as follows: x t+1 =x t +v t+1 Among them, x is the optimization parameter, ω is the inertia weight coefficient, c1 and c2 are learning factors, and rand() is a random number between (0,1); represents the historical optimal solution of a single particle, represents the global historical optimal solution; the optimization parameter is the vector composed of all waypoint parameters, that is, x = [T1,...,T nc ]; The optimization process can be divided into two parts: particle swarm initialization and improved particle swarm optimization; particle swarm initialization is to generate a specified number of particle swarms under the constraints. The role of particle swarm initialization is to ensure the existence of the historical optimal solution of all particles and the existence of feasible solutions, that is, the existence of feasible routes; improved particle swarm optimization is to continuously update the particle swarm under the constraints to find the minimum objective function value, meet the update end conditions and output the global optimal solution, that is, the optimal waypoint set, and then obtain the optimal route based on the piecewise cubic Hermite interpolation method; The improved particle swarm algorithm: For a D-dimensional problem, during the optimization process, the calculation formula for each particle i at the t+1th iteration is as follows: Among them, ω is the inertia weight coefficient, which is used to adjust the global and local search capabilities of the algorithm; c1 and c2 are learning factors, whose sizes affect the self-learning and social learning capabilities of particles; rand() is a random number between (0,1); and represent the historical optimal position of the ith particle and the global optimal position of the particle respectively; Formula (4) shows the particle speed in the t+1th iteration period It is affected by three parts: the speed of the previous generation of particles, the individual historical optimal position and the global particle historical optimal position. The improved particle swarm algorithm: (1) Optimization of inertia weight coefficient; (2) Learning factor optimization; (3) Extreme value variation; (4) Speed ​​update strategy optimization; (5) Improve the particle swarm algorithm process; The speed update strategy is optimized: On the basis of avoiding algorithm blockage by extreme value mutation, in order to prevent the algorithm from falling into local optimum, it is necessary to add an acceleration term to the speed update strategy. The acceleration term is as follows: Wherein, B is the acceleration range coefficient, which is related to the size of the route planning map, and here B = 2; is the objective function value of the ith particle at the tth iteration, is the optimal objective function value of the tth iteration, is the average objective function value of the tth iteration; analysis shows that the greater the difference between the objective function value of the next generation of particles and the optimal objective function value of the previous generation of particles, the faster the particle update speed is, the larger the search area is, and it can effectively avoid falling into the local optimum; In order to balance the global search capability and the local search capability, a time-varying term δ needs to be added to the speed update strategy. i (t): Among them, rand() is a random number in the interval (0,1); δ i The value of (t) is affected by the size of a, giving (1-t / maxt) a Time-varying curves under different values ​​of a; it can be seen that its value is larger in the early stage of planning, so δ i (t) is larger, making Approaching the average value of its own optimal particle This helps the global search; as the planning time increases, δ i (t) decreases, which helps local search and find the optimal route; according to the time-varying curve, a=5 is taken here to update the speed; To sum up, the following speed update strategy is adopted: The improved particle swarm algorithm process is as follows: Step 1. Initialization: Particle swarm initialization, including particle swarm size, iteration limit, initial particle position and velocity; Step 2. Objective function calculation: determine the objective function, obtain the objective function value of the particle in the search area according to the objective function, and save and update the individual optimal value and the global optimal value; Step 3. Adaptive parameter update, time-varying term δ i (t) and acceleration term update; time-varying update of inertia weight coefficient and learning factor, time-varying term δ i Update of (t), update of acceleration term; Step 4. Extreme value mutation: compare the global optimal objective function value of this iteration with the previous k iterations. If the difference is within the set range and occurs continuously for a preset number of times, i.e. k+1 times, it can be judged that the particle is trapped in the local optimum and extreme value mutation is performed; Step 5. Particle swarm update: Use the updated adaptive parameters and extreme values ​​to update the speed and position of each particle under the new particle speed update strategy; if the speed and position of the particle exceed the limit value, use the limit value for calculation; Step 6. Check the algorithm end condition; determine whether the algorithm end condition is met based on the objective function value or the maximum number of iterations. If the condition is met, the algorithm ends; otherwise, go to Step 2 to continue the next cycle.

2. The unmanned cluster route planning method based on the improved particle swarm algorithm as claimed in claim 1, characterized in that: The inertia weight coefficient optimization: The problem of balancing global and local search capabilities and the problem of being easily trapped in local optimality is solved by improving the particle swarm algorithm from three major directions: adaptive parameter adjustment, extreme value variation, and optimization of speed update strategy. The adaptive parameter adjustment includes the inertia weight coefficient ω, learning factors c1 and c2, and the optimization of speed update strategy includes adding time-varying terms and adding speed terms. The global and local search capabilities of particles are affected by the size of the inertia weight coefficient ω. The larger ω is, the stronger the global search capability of the particle is, and the weaker the local search capability is. As far as the route planning of unmanned aerial vehicles is concerned, in the early stage of planning, it is necessary to quickly approach the optimal route, that is, a stronger global exploration capability is required, and ω is larger; in the later stage of planning, in order to avoid missing the global optimal route, a stronger local search capability is required, and ω is smaller. In order to meet the above requirements for the change of the inertia weight coefficient ω, a concave function decreasing strategy is adopted to dynamically reduce the inertia factor ω; the concave function is defined as follows: Among them, b≥0 is a random variable, a γ >0 is the resolution parameter; Among them, t is the current iteration number, maxt is the maximum iteration number, ω max and ω min are the maximum and minimum values ​​of ω respectively. Here we take ω max =0.9,ω min =0.4; When b value is different, the time-varying law of ω(t) is different. Here, when b=0.05, the changing curve of ω(t) is max =0.9,ω min =0.4 and meets the time-varying requirement of ω(t).

3. The unmanned cluster route planning method based on improved particle swarm algorithm as claimed in claim 1, characterized in that: The learning factor optimizes: In the optimization process of route planning, the requirements for particle self-learning ability and social learning ability change with the optimization time; in general, it can be expressed as follows: in the early stage of planning, in order to enhance the diversity of particle optimization, particles have stronger self-learning ability and weaker social learning ability, that is, c1 is larger and c2 is smaller; in the later stage of planning, in order to accelerate convergence to obtain the optimal route, particles have stronger social learning ability and weaker self-learning ability, that is, c1 is smaller and c2 is larger; c1 and c2 are time-varying, and the values ​​of c1 and c2 are changed in a time-varying way here, as shown in the following formula: Among them, c 1,s 、c 2,s Represent the initial values ​​of c1 and c2 respectively, c 1,f 、c 2,f Represents the final value of c1 and c2; here we set c 1,s =c 2,f =2.5, c 1,f =c 2,s =0.

5.

4. The unmanned cluster route planning method based on improved particle swarm algorithm as claimed in claim 1, characterized in that: The extreme value variation: In the later stage of route planning, particles fall into local optimal values. At this time, Gbest and Pbest are the same, and the global optimal solution cannot be obtained. At this time, extreme value mutation is needed to avoid algorithm blockage; when it is detected that the objective function value does not reach the preset value, the global optimal objective function value of this iteration is compared with that of the previous k iterations. If the difference is within the set range and occurs continuously for a preset number of times, that is, k+1 times, extreme value mutation is triggered: Gbest=[1+α×rand()]Gbest (9) Where rand() is a random variable between (0,1), α is a constant, α=0.

8.

5. An unmanned swarm routing planning system based on an improved particle swarm algorithm that implements the unmanned swarm routing planning method based on an improved particle swarm algorithm as described in any one of claims 1 to 4, characterized in that: The system includes: Route generation module: This module uses the piecewise cubic Hermite interpolation method to generate the route of the UAV, ensuring that the generated route is continuous and the convexity does not change when approaching the route control point, thereby avoiding oscillation and making the route more in line with actual flight requirements; Waypoint optimization module: This module optimizes waypoints based on the improved particle swarm algorithm. It uses the global search capability of the particle swarm algorithm to find the optimal waypoint set by continuously updating the particle swarm, ensuring that the UAV cluster can fly collaboratively and reach the optimal route.

6. The unmanned swarm route planning system based on improved particle swarm algorithm as claimed in claim 5, characterized in that: The system includes: Particle swarm initialization module: This module generates a specified number of particle swarms under the constraints to ensure the existence of the historical optimal solution of all particles, thereby ensuring the existence of a feasible solution, that is, the existence of a feasible route; Improved particle swarm optimization module: Under constraints, this module continuously updates the particle swarm to find the minimum objective function value, and outputs the global optimal solution, that is, the optimal waypoint set, after reaching the update end condition; then, the system uses the piecewise cubic Hermite interpolation method to convert the optimal waypoint set into the optimal route.

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