A multi-UAV autonomous collaborative trajectory planning method based on improved FGO algorithm

Abstract

The present invention discloses a multi-UAV autonomous collaborative trajectory planning method based on an improved FGO algorithm, comprising the following steps: constructing a multi-UAV collaborative system model; constructing a trajectory planning model for autonomous collaborative tracking of multiple targets by multiple UAVs, the trajectory planning model being constructed based on a target model and corresponding constraints, the target model including a target detection range model and a collision threat model; allocating targets and planning trajectories for multiple UAV models in the multi-UAV collaborative system model based on an improved Fungus Generation Optimization algorithm and the trajectory planning model until the targets are tracked; and analyzing the UAV trajectory results. The present invention not only takes into account the collaborative allocation of multiple targets, but also implements collaborative tasks in complex and changing environments through constraints, thus having high universality.

Description

Technical Field

[0001] The present invention belongs to the technical field of unmanned aerial vehicle (UAV) trajectory planning, and in particular relates to a multi-UAV autonomous collaborative trajectory planning method based on an improved FGO algorithm. Background Art

[0002] As mission environments become increasingly complex and mission types become increasingly diverse, single unmanned combat air vehicles (UCAVs) face limitations in mission application scenarios due to limited payload capacity, weak computing power, and low flight energy, making them unable to adapt to new mission environments. To address these issues faced by single UCAVs during unmanned missions, improve UCAV mission efficiency, expand mission capabilities, and meet future mission requirements, multi-UCAV autonomous collaborative mission technology has been proposed. Multi-UCAV collaborative trajectory planning is a key component of multi-UCAV autonomous collaborative mission systems. Taking into account inter-aircraft coordination, mission objectives, environmental factors, and aircraft performance limitations, the multi-UCAV collaborative trajectory planning problem coordinates and optimizes the flight trajectories of each aircraft to achieve efficient and safe missions. The multi-UCAV collaborative trajectory planning problem is essentially a multi-constraint and multi-objective optimization problem. By considering UCAV trajectory constraints and inter-UCAV coordination constraints, a multi-UCAV collaborative trajectory planning model is constructed with objective functions such as minimizing trajectory, minimizing threats, and minimizing mission execution time.

[0003] The collaborative trajectory planning problem for multiple UCAVs is a typical non-deterministic polynomial problem. As the planning space and constraints increase, the computational complexity rapidly increases, and the performance requirements for the algorithm also become increasingly stringent. Therefore, optimization methods are generally used to solve it. Currently, commonly used collaborative trajectory planning algorithms for multiple UCAVs can be divided into the following categories:

[0004] (1) Graph search-based methods. When using a graph search-based planning algorithm, the task space must first be divided using a landmark graph method or a grid method. After obtaining the state space graph, an appropriate graph search algorithm is selected for solution. Common graph search algorithms include the A* algorithm, the Dijkstra algorithm, and the Rapidly Exploring Random Trees (RRT). Although graph search-based algorithms are highly efficient, their performance depends on the way the task space is divided. In addition, they do not consider the performance constraints of the aircraft, and when performing multi-aircraft planning, it is difficult to coordinate the collaborative constraints of each UCAV.

[0005] (2) Potential field-based trajectory planning method. This type of method was first proposed by Khita in the 1980s. It regards the target point as a gravitational field and the obstacle as a repulsive field, and establishes a potential energy function based on the mission space. The UCAV solves the trajectory based on the direction of the resultant force and various constraints. It does not require complex optimization and search methods, so the computational complexity is low. However, when performing trajectory planning, the potential field method is prone to finding a local optimal point where the gravitational force and repulsive force are the same, resulting in planning failure.

[0006] (3) Trajectory planning methods based on numerical optimization. This type of method uses inequalities to represent the terrain constraints, threat constraints, and self-performance constraints of the UAV during the mission, and combines them with objective functions such as shortest trajectory and minimum threat to form a constrained optimization problem. Numerical optimization methods usually include mixed integer linear programming, nonlinear programming, and dynamic programming. As the dimension continues to increase, the difficulty of solving the problem increases exponentially, and traditional optimization algorithms are difficult to guarantee the optimization effect. Swarm intelligence optimization algorithms have the characteristics of simple structure, high optimization accuracy, fast convergence speed, and strong robustness. They have been widely used to solve trajectory planning problems, such as genetic algorithm (GA), differential evolution algorithm (DE), whale optimization algorithm (WOA), ant lion optimization algorithm (ALO), and grey wolf optimization algorithm (GWO).

[0007] Although the current multi-UCAV collaborative trajectory planning model has achieved considerable results, it still has the following limitations: 1) Real-time trajectory planning does not consider the real-time multi-target collaborative allocation problem; 2) Global track planning cannot meet the current complex and changing collaborative mission environment; 3) The collaborative trajectory planning solution algorithm is not universal enough, and it is necessary to propose a suitable collaborative trajectory planning method for specific problems. Summary of the Invention

[0008] In order to solve the problems of the existing methods, the present invention provides a multi-UAV autonomous collaborative trajectory planning method based on the improved FGO algorithm.

[0009] The purpose of the present invention is achieved through the following technical solutions:

[0010] The present invention discloses a multi-UAV autonomous collaborative trajectory planning method based on an improved FGO algorithm, comprising the following steps:

[0011] Constructing a multi-UAV collaborative system model, wherein the multi-UAV collaborative system model includes multiple UAV models built into the same formation on a two-dimensional plane, a sensor detection coverage model with self-balancing capabilities, and a line of sight occlusion judgment model;

[0012] Constructing a trajectory planning model for autonomous collaborative tracking of multiple targets by multiple UAVs. The trajectory planning model is constructed based on a target model and corresponding constraints. The target model includes a target detection distance model and a collision threat model. The constraints include that the distance between UAVs is greater than the anti-collision safety distance of the wingspan length, the maximum communication distance between UAVs is less than the maximum communication radius, the distance between UAVs and obstacles is greater than the safety distance, and each target is detected by at least one UAV.

[0013] Based on the fungus generation optimization algorithm and the trajectory planning model, targets of multiple UAV models in the multi-UAV cooperative system model are allocated and trajectory planning is performed until the target is tracked;

[0014] Analyze the UAV trajectory results.

[0015] Compared with the prior art, the present invention has at least the following advantages and beneficial effects:

[0016] 1. The present invention constructs a multi-UAV collaborative system model and a trajectory planning model, and uses the target model and corresponding constraints and an improved FGO algorithm to update the position of the fungal population, thereby obtaining a multi-UAV collaborative trajectory planning control sequence. It not only takes into account the collaborative allocation of multiple targets, but also realizes collaborative tasks in complex and changing environments through constraints, and has high universality.

[0017] 2. This scheme uses the improved FGO algorithm to update the position of the fungal population, effectively avoiding the trajectory planning process from falling into local optimality. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0019] Figure 1 A schematic diagram showing the field of view of the self-balancing sensor;

[0020] Figure 2 Showing a horizontal projection view between the UCAV, the target, and obstacles;

[0021] Figure 3Shows a vertical projection view between the UCAV, the target, and the obstacle;

[0022] Figure 4 The flowchart of the improved FGO algorithm of this scheme is shown;

[0023] Figure 5 Shows the Iterative Chaotic Sequence Diagram;

[0024] Figure 6 The schematic diagram of the hypha tip growth behavior strategy of the FGO algorithm is shown;

[0025] Figure 7 Shows a schematic diagram of the adaptive step size of Cauchy distribution and Gaussian distribution;

[0026] Figure 8 Showing two search state schematics in the development phase;

[0027] Figure 9 The schematic diagram of the hypha tip growth behavior strategy of the FGO algorithm is shown;

[0028] Figure 10 Shows the principle diagram of the refraction mirror learning strategy;

[0029] Figure 11 The flowchart of the multi-UAV autonomous collaborative trajectory planning method based on the improved fungus generation optimization algorithm is shown;

[0030] Figure 12 Shows the initial state of the UCAV;

[0031] Figure 13 Show obstacle parameters;

[0032] Figure 14 Shows a schematic diagram of decision variable coding;

[0033] Figure 15 A schematic diagram of tracking target allocation is shown. DETAILED DESCRIPTION

[0034] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0035] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort are also within the scope of protection of the present invention.

[0036] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments of the present invention can be combined with each other.

[0037] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.

[0038] In the description of the present invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," "outer," etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings, or are the orientations or positional relationships in which the inventive product is typically placed when in use, or are the orientations or positional relationships commonly understood by those skilled in the art. These terms are intended only to facilitate the description of the present invention and to simplify the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, be constructed, or operate in a specific orientation. Therefore, they should not be construed as limiting the present invention. Furthermore, the terms "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0039] In the description of the present invention, it should also be noted that, unless otherwise expressly specified or limited, the terms "disposed," "installed," "connected," and "connected" should be understood in a broad sense. For example, they may refer to fixed connections, detachable connections, or integral connections; they may refer to mechanical connections or electrical connections; they may refer to direct connections or indirect connections through an intermediate medium; and they may refer to internal communication between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on the specific circumstances.

[0040] The primary task of multi-UCAV collaborative tracking trajectory planning in urban environments is to detect and track moving targets through multi-UCAV collaboration under complex environmental conditions, thereby completing the task of destroying the targets. UCAV collaborative mission execution enables information sharing among different members. Even if some UCAVs lose their targets during tracking, effective information sharing can effectively prevent the entire formation from losing their targets. While tracking multiple moving targets, formation members use appropriate maneuvers and target allocation to avoid loss of sight due to buildings. They also avoid collisions with buildings or with other members during flight, preventing damage or crashes of the UCAVs.

[0041] Based on this, this solution discloses a multi-UAV autonomous collaborative trajectory planning method based on an improved FGO algorithm. This method is implemented based on an improved fungus generation optimization algorithm. Specifically, the method includes steps S1 to S4. It should be noted that the step identifiers in this solution are only for the purpose of illustrative purposes and do not constitute a sequential order. The order of the steps shall prevail based on their verbal descriptions and the sequential connection of the signals.

[0042] The method in this solution is not only suitable for UCAV trajectory planning, but also for other cargo-carrying UAVs. It should be noted that for ease of explanation, the UAVs in the figures of this solution are all UCAVs as examples, but this does not constitute a limitation on the type of UAVs to which this solution method can be applied.

[0043] Step S1: construct a multi-UAV collaborative system model, wherein the multi-UAV collaborative system model includes multiple UAV models built into the same formation on a two-dimensional plane, a sensor detection coverage model with self-balancing capability, and a line of sight occlusion judgment model.

[0044] Specifically, this step requires the construction of each sub-model in the multi-UAV collaborative system model, namely, the construction of the UAV model, sensor detection coverage model, line of sight occlusion judgment model, target allocation model and anti-collision model.

[0045] Among them, the drone model is:

[0046] ,

[0047] Where, For the The coordinate position of the UAV in the horizontal plane, is the number of drones; For the The speed of the drone; For the The acceleration of the drone; is the acceleration due to gravity, For the The yaw angle of the drone; For the The roll angle of the UAV; The state variables of the UAV are , the control variable is , Represents the coordinate position, velocity, and first-order differential of the drone in the horizontal plane. Due to the performance limitations of the drone, the drone should meet the following constraints during the entire flight process:

[0048]

[0049] Where, and are the minimum and maximum speeds of the drone respectively; is the maximum acceleration of the UAV; is the maximum roll angle of the drone.

[0050] For sensor detection coverage model:

[0051] The present invention adopts a detection sensor model with self-balancing ability, such as Figure 1 It can automatically compensate for the impact of UCAV posture changes and maintain the stability of the detection area.

[0052] When the drone is flying horizontally, the central axis of the sensor's field of view is perpendicular to the horizontal plane; when the drone's roll angle φ is not 0°, the sensor can compensate for the drone's roll angle to maintain the stability of the field of view coverage area. The maximum coverage radius of the sensor on the ground for:

[0053]

[0054] Where, is the UCAV flight altitude; is the maximum field of view of the sensor; the horizontal distance between the i-th UAV and the target for:

[0055]

[0056] Where, (x T ,y T ) is the horizontal position coordinate of the target. TU Less than When the target is within the detection coverage of the drone sensor.

[0057] Establishing a sensor detection coverage model with self-balancing capabilities can automatically compensate for the impact of UCAV posture changes and maintain the stability of the detection area.

[0058] For the line of sight occlusion judgment model:

[0059] The main challenge of tracking in urban environments is the obstruction of the UAV's line of sight to the target by urban buildings. Members need to collaborate to reduce or eliminate the time when the line of sight is blocked by obstacles. Based on a simplified urban obstacle model, the present invention determines whether the line of sight is blocked based on the spatial relative positions of the UAV, target, and obstacle. Urban buildings are usually cubic structures. In order to reduce the computational complexity of the occlusion model, a circumscribed cylinder is used instead of a cube to represent urban obstacles. The spatial relationship between the UAV, target, and obstacle is projected in the horizontal and vertical planes as follows: Figure 2 and Figure 3 shown.

[0060] Step S2: Construct a trajectory planning model. The trajectory planning model is used for multiple UAVs to autonomously and collaboratively track multiple targets. The trajectory planning model is constructed based on a target model and corresponding constraints. The target model includes a target detection distance model and a collision threat model. The constraints include that the distance between UAVs is greater than the anti-collision safety distance of the wingspan length, the relative distance between two adjacent UAVs is less than the maximum communication radius, the distance between the UAV and the obstacle is greater than the safety distance, and each target is detected by at least one UAV.

[0061] Building a trajectory planning model requires two considerations: the objective function and the constraints. A reasonable objective function helps the algorithm plan a collaborative trajectory that continuously tracks the target while satisfying various constraints. Previous research has treated this problem as an unconstrained one, with the objective function derived from the weighted sum of multiple sub-objectives. However, conflicts between these sub-objectives weaken the objective function's constraining power.

[0062] The target model is implemented based on the objective function, which mainly includes two parts: target detection distance model and collision threat model.

[0063] Multi-UAV collaborative tracking requires that the moving target is always within the coverage area of ​​the sensor. In addition, the closer the target is to the center of the sensor coverage area, the less likely it is to be lost. During the tracking process, the UAV should try to keep the center point of the detection coverage area as close to the target as possible. As the first sub-objective function, its calculation formula is as follows:

[0064]

[0065] Where, Represents the distance between the i-th UAV and its assigned tracking target, N U Indicates the total number of drones. The smaller the value, the closer the drone is to the target.

[0066] If the angle between the UAV's velocity vector and the UAV's target vector Greater than the angle between the drone's target vector and the tangent direction , or the distance between the i-th UAV and the k-th obstacle Greater than the safety distance , at this time the drone can avoid collision with obstacles. Collision Threat Model J C The collision threat objective function is established as follows:

[0067]

[0068]

[0069] in, Indicates the number of tall obstacles the UCAV needs to avoid.

[0070] The overall objective function takes the form of two weighted sub-objectives, which are calculated as follows:

[0071] ,

[0072] in, and is the weight coefficient.

[0073] Larger Can make the drone closer to the target, larger It can make the drone give priority to avoid collision. Here, anti-collision is regarded as a prerequisite for the drone to complete the task. and The possible values ​​are 1 and 5 respectively.

[0074] Regarding constraints:

[0075] Safe distance between drones in formation.

[0076] To avoid blocking the line of sight between drones, all drones fly at the same altitude. During the tracking process, the drone formation members must avoid collisions, so the relative distance between different members must be greater than the safe flight distance:

[0077]

[0078] Where, 、 Respectively represent the horizontal coordinates of the i-th and j-th UAVs in the horizontal plane, 、 Respectively represent the vertical coordinates of the i-th and j-th UAVs in the horizontal plane, represents the relative distance between the adjacent i-th UAV and j-th UAV. The anti-collision safety distance is the wingspan length, that is, the safe flight distance.

[0079] The minimum distance constraint between drones is established as:

[0080]

[0081] Maximum communication distance between drones:

[0082] UAV collaboration under centralized control can achieve target information sharing. The relative distance between two adjacent UAVs must be less than the maximum communication radius. , establish the communication distance constraint as:

[0083]

[0084] The distance between the drone and the obstacle:

[0085] Avoiding collisions with high obstacles is a prerequisite for drones to complete collaborative tracking tasks. Since the flight altitude of the drone is fixed, it can only bypass high obstacles by turning. Since this method only analyzes the state of the sampling point, the continuous state within the sampling interval is not considered. If the drone is inside the obstacle at the sampling moment, it is easy to determine that the drone has collided with the obstacle. However, if the drone is in the state at the sampling moment, the drone is outside the obstacle at the sampling point, but the flight track within the sampling interval interferes with the obstacle; in this case, the state of the current sampling point cannot be used to determine whether a collision has occurred. Therefore, the present invention determines whether a collision is likely to occur based on the motion state of the drone when it approaches the obstacle. At each sampling moment, when the drone state relative to the obstacle is greater than the safety distance required to prevent collision between the drone and the obstacle, it is considered that a collision with the obstacle can be avoided.

[0086] Since the drone is at a fixed altitude, only obstacles higher than the drone are considered to affect the flight path. The collision constraints are set as follows:

[0087]

[0088] in, represents the distance between the i-th UAV and the k-th obstacle, Indicates the number of high obstacles that the UCAV needs to avoid, that is, the number of obstacles that are higher than the drone. represents the radius of the obstacle circumscribed cylinder, Indicates the wingspan margin of the drone.

[0089] Target detected by drone:

[0090] Because a drone's line of sight to a target can be obstructed by obstacles, a single drone may not be able to track all targets at a given moment. Therefore, a formation needs to allocate targets appropriately based on their detectability. Assuming each target is detected by at least one drone, formation members can communicate and share target information. If a single drone can simultaneously detect multiple moving targets within its sensor coverage, it can only select one target for tracking.

[0091] Through target allocation, the dynamic target node selection problem of multi-target trajectory planning is solved.

[0092] To prevent the target from being lost during the tracking process, it is necessary to ensure that each target is detected by at least one drone, that is,

[0093]

[0094] Where N T is the target number, represents the line of sight of the i-th UAV to the j-th target, if , UAV i tracks the target, otherwise, UAV i’s sight of the target is blocked. Therefore, the constraint to prevent target loss is:

[0095]

[0096] Based on the above, the trajectory planning model is:

[0097] .

[0098] The trajectory planning model uses the detection distance and collision cost as the objective function and is constructed using the ϵ constraint method.

[0099] The ϵ constraint method is used to transform the multi-constrained optimization problem into an unconstrained optimization problem.

[0100] Step S3: Based on the improved fungus generation optimization algorithm and the trajectory planning model, targets of multiple UAV models in the multi-UAV collaborative system model are allocated and trajectory planning is performed until the target is tracked.

[0101] In order to search for a cooperative trajectory planning scheme that meets the conditions, the present invention proposes a multi-UAV autonomous cooperative trajectory planning method based on an improved fungus generation optimization algorithm. The key points of the multi-UAV autonomous cooperative trajectory planning method mainly include decision variable design and fitness function construction. The specific process of the multi-UAV autonomous cooperative trajectory planning method based on the improved fungus generation optimization algorithm is as follows: Figure 11 As shown, specifically, this step includes steps S31 to S35.

[0102] Step S31: Establish the mapping relationship between individual fungus positions and decision variables of collaborative trajectory planning based on rolling horizon by using a real number vector-based encoding method.

[0103] For example, the multi-UAV cooperative system model is designed to have five UAVs tracking two ground moving targets, namely , .

[0104] The initial positions of the two moving targets are (0, 0, 0) and (-100, 100, 0). The motion equation of the first target is: , ; The motion equation of the second target is: , , where t represents time, 、 Represent the horizontal coordinates of the first and second target positions respectively, 、 Represents the vertical coordinates of the first and second target positions respectively.

[0105] The flight altitude of the UAV is fixed at 300m. The initial state of each UAV is as follows: Figure 12 As shown. Minimum speed of drone , maximum speed , maximum acceleration , maximum roll angle , the sensor's field of view axis remains perpendicular to the ground, the sensor rotation compensation angle is equal to the maximum roll angle, and the sensor field of view angle , anti-collision distance between UCAVs , maximum communication distance , safe distance .

[0106] Number of obstacles in urban environments is 7, and the specific parameters are as follows Figure 13 As shown, the heights of the first four buildings are higher than the flying height of the drone, so .

[0107] In order to conveniently describe the mapping relationship, in each decision time, the individual fungus position corresponds to its control quantity in the process of multiple drones tracking multiple targets. The definition of , the encoding method uses real number encoding, and the corresponding relationship between individual position and problem decision variable, that is, control variable, is established. The mapping relationship is as follows Figure 14 shown.

[0108] Step S32: Determine the number of fungal mycelium populations and the maximum number of iterations of the fungal generation optimization algorithm.

[0109] Initialize the fungus hyphae population according to the encoding method based on real vectors. The fungus hyphae search space, that is, the search space of the collaborative trajectory planning control variable scheme, is abstracted into a Euclidean space. The Iterative chaotic mapping strategy is used in A uniformly distributed chaotic sequence is generated within the interval. The chaotic sequence generated by the iterative chaotic mapping strategy is used to search and initialize the mycelium population.

[0110] Iterative chaotic mapping strategy is used to initialize the fungal population and increase the diversity and ergodicity of the initial fungal population.

[0111] Step S33: Calculate the fitness value of the fungus individual.

[0112] First, the position information of the individual mycelium population is decoded into a collaborative trajectory planning control mapping relationship, which is the UAV control variable used to calculate the objective function of the multi-UCAV tracking multi-target collaborative trajectory planning model. Then, based on the multi-UCAV tracking multi-target collaborative trajectory planning objective function established in step S2, the penalty function method is used to transform the multi-constrained multi-UCAV tracking multi-target collaborative trajectory planning problem into an unconstrained optimization problem:

[0113]

[0114] in, represents the fitness value, Represents the objective function value of the collaborative trajectory planning model for multiple UCAVs tracking multiple targets. The collaborative trajectory planning problem for multiple UCAVs tracking multiple targets is a maximization problem. The smaller the objective function value of the model, the smaller the fitness value of the individual swarm members, and the better the solution to the collaborative trajectory planning control variable.

[0115] Step S34: Generate a random number, the random number including a first random number , the second random number and the third random number , and determine the corresponding FGO algorithm fungal population position update strategy according to the random number, wherein the FGO algorithm fungal population position update strategy includes a hypha branching mechanism and a spore germination mechanism.

[0116] Specifically, in response to the first random number Less than the second random number , the FGO algorithm fungus population position update strategy adopts the hyphae tip growth behavior strategy, and the selection probability Less than the exploration probability When the hypha tip growth behavior strategy is selected in the exploration phase, the Cauchy distribution adaptive step size is used, and the probability is selected Greater than or equal to exploration probability When the mycelial tip growth behavior strategy is selected in the development stage, the Gaussian distribution adaptive step size is adopted.

[0117] In response to the first random number Greater than or equal to the second random number ,The fungal population position update strategy of the FGO algorithm adopts the branching and spore germination behavior strategies, and when the third random number is less than 0.5, the hyphae branching mechanism is selected; when the third random number is greater than or equal to 0.5, the spore germination mechanism is selected.

[0118] The Cauchy distribution and Gaussian distribution adaptive step size are used to improve the mycelium tip growth behavior strategy, balance the development and exploration capabilities of the algorithm, and enhance the algorithm convergence speed.

[0119] The mirror learning strategy was used to improve the branching and spore germination behavior strategies, which would increase the convergence speed in the early iteration and the diversity of mycelial population in the later iteration.

[0120] The fungal growth optimizer (FGO) is a new type of nature-inspired metaheuristic algorithm, which is inspired by the growth behavior of fungi in nature. The algorithm provides a series of exploration and development operators to solve complex optimization problems by simulating the growth of hyphae tips, branching and spore germination of fungi. The FGO algorithm has shown good performance in many fields, especially in solving high-dimensional problems and avoiding falling into local optimality. The FGO algorithm converges quickly and maintains good diversity, but for high-dimensional complex problems, FGO's diversity maintenance ability is insufficient, which makes the algorithm easily fall into local optimality during the exploration process. However, the traditional FGO algorithm is prone to the defect of falling into local optimality. To this end, the present invention preferentially adopts the above-mentioned optimized adaptive growth FGO algorithm to realize trajectory optimization, so as to improve the solution accuracy of the trajectory planning problem of multi-UAV collaborative tracking in urban environments and accelerate the convergence efficiency of the optimization process.

[0121] The two different modes mentioned above simulate lateral branching, allowing fungi to explore in all directions. These two modes are powerful exploration operators, which enable the FGO algorithm to escape from local optimality and achieve outstanding solutions for complex optimization problems. The branching and spore germination behavior strategies will lead to low convergence speed in the early stage of iteration, and the mycelium population diversity will decrease in the later stage of iteration, causing the FGO algorithm to fall into local optimality. In order to prevent the algorithm from jumping out of the local optimality and enhance the diversity of the algorithm, the present invention proposes a mirror learning strategy to improve the mycelium population update method of the FGO algorithm. The branching and spore germination behavior strategies of the FGO algorithm mainly include mycelium branching mechanism and spore germination mechanism, and the specific selection timing is determined by a random number. Decision. When When , the hyphal branching mechanism is selected; when When , the spore germination mechanism is selected. The hyphae branching mechanism and the spore germination mechanism use the mirror learning strategy to further update the hyphae position information.

[0122] In order to understand the improved FGO algorithm of this solution, its method is now specifically explained. Specifically, the adaptive growth FGO algorithm combines the Iterative chaos mapping strategy, the mirror learning strategy and the adaptive growth step strategy. The flow chart is as follows Figure 4 As shown, the specific steps include Step 1 to Step 3.

[0123] Step 1: Initialize the fungal population using the Iterative Chaotic Mapping strategy. The FGO algorithm uses a random distribution to initialize the population, which will affect the algorithm's solution optimization speed. The Iterative Chaotic Mapping formula is as follows:

[0124]

[0125] in, is the chaotic map sequence value, and its specific value changes are as follows Figure 5 shown.

[0126] In order to improve the population search speed, this paper proposes an iterative chaotic mapping strategy to improve the initialization method of the FGO algorithm, as follows:

[0127]

[0128] Where, represents the i-th fungus individual, represents the upper bound of the problem, represents the lower bound of the problem, represents the number of fungal populations, Indicates the value generated by the iterative chaotic map.

[0129] Step 2: Calculate the fitness value of the fungus individual of the FGO algorithm. The specific calculation formula is as follows:

[0130]

[0131] Where, Indicates the The fitness value of each fungus individual, Represents fungal individuals Objective function for multi-UAV task allocation.

[0132] Step 3: Use the FGO algorithm to update the fungal population position. In order to balance the exploration and development operation strategies, the FGO algorithm generates two random numbers. and By comparing the sizes, the position update strategy of the FGO algorithm fungus population is determined. The position update strategy of the FGO algorithm fungus population includes the hypha tip growth behavior, branching and spore germination behavior. When , the FGO algorithm adopts the hypha tip growth behavior strategy for the fungal population position update strategy; when When , the fungal population position update strategy of the FGO algorithm adopts the branching and spore germination behavior strategy.

[0133] (1) When the FGO algorithm hyphae tip growth behavior strategy is running, random numbers are used, which is not conducive to speeding up the optimization process of the algorithm. In order to balance the development and exploration capabilities of the algorithm and enhance the convergence speed of the algorithm, an adaptive step size update formula is proposed for the control parameters of the position update strategy. The FGO algorithm hyphae tip growth behavior strategy mainly includes the exploration phase and the development phase. The specific selection timing is determined by the hyphae tip growth behavior strategy selection probability. and exploration rate When When , the hypha tip growth behavior strategy selects the exploration stage and adopts the Cauchy distribution adaptive step size; when When the hyphae tip growth behavior strategy is selected in the development stage, the Gaussian distribution adaptive step size is used. The specific operation of the hyphae tip growth behavior strategy of the FGO algorithm is as follows: Figure 6 As shown. The adaptive step size of Cauchy distribution and Gaussian distribution is as follows Figure 7 shown.

[0134] Phase 1: Exploration phase. When the hypha tip growth behavior strategy is reached, the exploration phase simulates the growth rate and direction of a large number of hyphae to properly explore the search space. This phase uses an exponential function related to the current fitness value to simulate the growth rate of FGO to represent eutrophic and oligotrophic areas. Solutions with high fitness values ​​represent eutrophic areas, while solutions with low fitness values ​​represent oligotrophic areas. The specific calculation formula for FGO growth rate is as follows:

[0135]

[0136] Where, is the growth rate. represents the fitness value of the i-th fungus individual. Represents the base of the exponential function, approximately equal to 2.71828.

[0137] The growth direction of hyphae is affected by environmental and chemical cues that may occur suddenly. In order to improve the convergence efficiency of the exploration phase, the present invention adopts an adaptive step size update method to improve the random growth method of the FGO algorithm. The specific calculation formula is as follows:

[0138]

[0139]

[0140]

[0141]

[0142] in, Indicates the growth direction of the FGO algorithm. and represents the position of a randomly selected fungus individual at the tth iteration. represents the candidate fungus individual at the tth iteration. Indicates that the random numbers are distributed using Cauchy distribution. Indicates the optimal fungal individual position. represents the i-th fungus candidate individual at the t+1th iteration, Represents the j-th dimension information of the i-th fungus candidate individual at the t-th iteration.

[0143] Represents the j-th dimension position information of the i-th fungus individual at the t+1-th iteration. Represents the j-th dimension randomly distributed value, whose value ranges from 0 to 1. Represents a random number. Represents the dimension of decision variables in the problem.

[0144] Phase 2: Development phase. During the development phase of the hyphae tip growth behavior strategy, we simulate the process of fungal hyphae growing towards nutrient-rich areas. This process is achieved through chemical signals, which help the hyphae quickly find nutrient-rich areas, thereby accelerating convergence. To simulate the ability of hyphae to produce chemical signals indicating nutrient availability, we define the direction of hyphae growth towards a randomly selected solution in the existing population, calculated as follows:

[0145]

[0146] in, represents the growth direction of the i-th solution based on the chemical signal. Represents a random number. represents the position of a randomly selected fungus individual at the tth iteration. represents the candidate fungus individual at the tth iteration.

[0147] Mycelium in the above state may migrate to the current best solution, as this is the most nutritious location, thereby increasing the convergence speed. However, moving directly to the best solution may lead to premature convergence, reducing the performance of FGO in solving various complex optimization problems. To solve this problem, the growth direction of mycelium is based on a preset probability to grow towards the most nutritious area. Finally, the mathematical model of the growth direction of the i-th mycelium is The calculation is as follows:

[0148]

[0149]

[0150] in, and Represents a random number. Indicates that Gaussian distributed random numbers are used. Represents a preset parameter between 0 and 1. Represents a Gaussian random generated number.

[0151] To simulate the increased growth rate of fungal hyphae in the presence of nutrients, a growth rate adjustment mechanism based on nutrient allocation is introduced. This mechanism encourages increased exploration of the current best solution or randomly selected solutions in the first half of the optimization process. The nutrient allocation is initially defined randomly and then adjusted based on the fitness value of each solution to associate the development operator with the fitness value of each solution. The higher the fitness value, the faster the convergence to the desired solution, and vice versa. The specific calculation of the nutrient allocation control parameters is as follows:

[0152]

[0153] in, represents the nutrient allocation control parameter; Represents a random number between 0 and 1; represents the fitness value of the i-th fungus individual; and Represents the current iteration number and the maximum iteration number respectively. The fitness value of the fungus individual may be very high, which will cause the updated solution to jump out of the search range. For this reason, the FGO algorithm uses a normalization method, which is calculated as follows:

[0154]

[0155] in, represents a random number, represents the kth nutrient allocation control parameter. Finally, the development phase searches for nutrient-rich areas (the development phase searches for the first state) and the update formula is as follows:

[0156]

[0157]

[0158]

[0159] in, represents the nutrient allocation control parameter; represents the growth direction of the i-th solution based on the chemical signal; represents the random exploration step length; 、 and Represents a random number; Represents the exploration step probability, which ranges from 0 to 1. It is mainly used in the development phase to search for the first state of random exploration step enable judgment.

[0160] During the development phase, search in the opposite direction of the eutrophic zone (search the second state during the development phase). The specific update formula is as follows:

[0161]

[0162]

[0163]

[0164] in, It indicates that the i-th solution of the second state is searched in the development phase based on the j-th dimension information of the growth direction of the chemical signal; It represents the growth direction of the i-th solution in the development phase searching for the second state based on the chemical signal; Indicates that the j-th dimension of the Cauchy distribution random number is used, which mainly improves the random step size of the standard FGO algorithm; Represents the j-th dimension information of the i-th fungus individual in the current iteration; represents the j-th dimension information of the optimal fungus individual; Represents the random distribution value of the jth dimension, whose range is 0 to 1; Represents a random number; Represents the decision variable dimension of the problem; represents the random exploration step length; and Represents a random number; and Represents a random number.

[0165] The two development phase search states above adopt a random execution method, and the specific calculation is as follows:

[0166]

[0167] in, and Represents a random number, when When , the development phase search adopts the second state to update the population individuals; when When , the development phase search uses the first state to update the population individuals. The specific operation of the two development phase search states is as follows Figure 8 shown.

[0168] (2) When the FGO algorithm's branching and spore germination behavior strategy is running, two different modes are used to simulate lateral branches, allowing the fungus to explore in all directions. These two modes are relatively powerful exploration operators, enabling FGO to escape local optimality and achieve outstanding solutions for complex optimization problems. The branching and spore germination behavior strategy will lead to a low convergence rate in the early stage of iteration, and the mycelium population diversity will decrease in the later stage of iteration, causing the FGO algorithm to fall into the local optimality. In order to prevent the algorithm from jumping out of the local optimality and enhance the algorithm diversity, the present invention proposes a mirror learning strategy to improve the mycelium population update method of the FGO algorithm. The branching and spore germination behavior strategy of the FGO algorithm mainly includes the mycelium branching mechanism and the spore germination mechanism, and the specific selection timing is determined by a random number. Decision. When When , the hyphal branching mechanism is selected; when When , the spore germination mechanism is selected. The specific operation of the FGO algorithm hyphae tip growth behavior strategy is as follows Figure 9 shown.

[0169] Mechanism 1: Mycelium branching mechanism. This mechanism determines the direction based on two solutions randomly selected from the current population. The specific data is defined as follows:

[0170]

[0171] in, Represents the j-th dimension information of the i-th fungus individual at the t+1-th iteration; Used to simulate the behavior that lateral hyphae branches may inherit some characteristics from the original hyphae, Represents a random number, Represents a preset threshold, usually between 0 and 1. If If true, the lateral hyphae branches are affected by the original hyphae in their growth direction and the position information of the original hyphae is used. Otherwise, the growth direction of the lateral hyphae branches is completely random. Represents the j-th dimension information of the i-th fungus individual in the current iteration; Represents a random number, usually between 0 and 1; represents the growth rate of lateral branches; Indicates random mode 1; Indicates random mode 2.

[0172]

[0173]

[0174]

[0175] in, 、 and Represents the fungus individual randomly selected at the current iteration; Indicates the optimal fungal individual at the current iteration; and represents a random number, represents the i-th direction of random pattern 1, represents the i-th direction of random pattern 2.

[0176] Mechanism 2: Spore germination mechanism. This mechanism mainly simulates spore reproduction and determines the direction based on the absolute difference between the best solution in the current population and the average position of two random solutions, and the average of three randomly selected solutions and the current solution. The specific data definitions are as follows:

[0177]

[0178]

[0179]

[0180] in, Indicates the direction determined by the best solution in the current population and the average position of the two random solutions; Indicates the direction determined by the absolute difference between the average of three randomly selected solutions and the current solution. and Represent the current number of iterations and the maximum number of iterations respectively; represents the j-th dimension information of the optimal fungus individual; 、 and Indicates that the j-th dimension information of fungal individuals is randomly selected at the current iteration number; represents a random factor containing −1 or 1 to determine whether the hyphae continues in the current direction or changes it to reach a safer position; Represents a random number; represents the growth rate of FGO. If If true, the spore reproduction is affected by the original hyphae in the growth direction, and the position information of the original hyphae is used. Otherwise, the growth direction of the spore reproduction is affected by the random solution and the optimal value.

[0181] In order to prevent the algorithm from jumping out of the local optimum and enhance algorithm diversity, the above-mentioned mycelium branching mechanism and spore germination mechanism adopt a mirror learning strategy. The specific calculation is as follows:

[0182]

[0183]

[0184] in, Represents a random number, when When , the hyphae branching mechanism based on the mirror learning strategy is adopted; when When the spores are germinating, a spore germination mechanism based on the mirror learning strategy is adopted. and They represent the position of the i-th hyphae individual obtained by the fungal individual branching mechanism and spore germination mechanism before improvement; Indicates the upper bound of the problem; Indicates the lower bound of the problem; represents the refraction angle ratio; represents the refractive index; and Represent the angle of incidence and the angle of refraction respectively. The specific principle is as follows Figure 10 As shown, Figure 10 Here, lb and ub represent the lower boundary and upper boundary respectively.

[0185] Step S35: After the termination condition is reached, the optimal collaborative trajectory planning control quantity solution based on the rolling time domain is output.

[0186] Determine whether the iteration end condition is met. If the number of iterations Reached the maximum number of iterations , then the iteration ends, the fitness value is calculated, the greedy strategy is adopted, the optimal value is output, and it is decoded into a multi-UAV collaborative trajectory planning control quantity solution within the unit decision execution time; otherwise, continue with step S34 of this step.

[0187] Step S4: Analyze the UAV track results.

[0188] According to the complexity of multi-UAV collaborative trajectory planning, the present invention analyzes the overall trajectory, UAV constraints, UAV control quantity, relative distance between UAV members, obstacle avoidance, relative distance between UAV and target, target detection, target allocation and other aspects. Figure 15 shown.

[0189] Furthermore, the simulation analysis can be expanded to the scale of UAVs. To verify the robustness of the improved FGO algorithm in solving the multi-UAV collaborative trajectory planning problem, the present invention uses the improved FGO algorithm to solve the multi-UAV collaborative trajectory planning problem of different scales multiple times, and statistically analyzes the planning success rate, planning time interval, average planning time, collision avoidance success rate, and average objective function value, and compares and analyzes the optimal collaborative trajectory planning solutions for different UAV scales.

[0190] Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments, or to make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A multi-UAV autonomous collaborative trajectory planning method based on an improved FGO algorithm, characterized in that: The following steps are involved: Constructing a multi-UAV collaborative system model, wherein the multi-UAV collaborative system model includes multiple UAV models built into the same formation on a two-dimensional plane, a sensor detection coverage model with self-balancing capabilities, and a line of sight occlusion judgment model; Construct a trajectory planning model, which is used for multi-UAV autonomous collaborative tracking of multiple targets. The trajectory planning model is constructed based on the target model and corresponding constraints. The target model includes a target detection distance model and a collision threat model. The constraints include that the distance between UAVs is greater than the anti-collision safety distance of the wingspan length, the relative distance between two adjacent UAVs is less than the maximum communication radius, the distance between UAVs and obstacles is greater than the safety distance, and each target is detected by at least one UAV. The target detection distance model for: ， Where, Represents the distance between the i-th UAV and its assigned tracking target, N U Indicates the total number of drones; The collision threat model J C for: ， ， Where, Indicates the number of high obstacles that the UCAV needs to avoid, represents the angle between the UAV velocity vector and the UAV target vector, Indicates the angle between the drone's target vector and the tangent direction; Indicates the distance between the drone and the obstacle. Indicates safe distance; The target model J p for: ， Where, and is the weight coefficient; The mapping relationship between individual fungus positions and decision variables of collaborative trajectory planning based on rolling horizon is established by using a real vector-based encoding method. Adopting the Iterative Chaotic Mapping Strategy generating a uniformly distributed chaotic sequence within the interval, and searching for and initializing the hyphae population of the fungus based on the chaotic sequence; Calculate the fitness value of fungal individuals; Generate a random number, the random number including a first random number , the second random number and the third random number , In response to the first random number Less than the second random number , the FGO algorithm fungus population position update strategy adopts the hypha tip growth behavior strategy, and the selection probability Less than the exploration probability When the hypha tip growth behavior strategy is selected in the exploration phase, the Cauchy distribution adaptive step size is used, and the probability is selected Greater than or equal to exploration probability When the mycelium tip growth behavior strategy is selected in the development stage, the Gaussian distribution adaptive step size is used. In response to the first random number Greater than or equal to the second random number ,The fungal population position update strategy of the FGO algorithm adopts the branching and spore germination behavior strategies, and when the third random number is less than 0.5, the hyphae branching mechanism is selected; when the third random number is greater than or equal to 0.5, the spore germination mechanism is selected; After reaching the termination condition, the optimal collaborative trajectory planning control solution based on the rolling horizon is output; Analyze the UAV trajectory results.

2. The multi-UAV autonomous collaborative trajectory planning method based on the improved FGO algorithm according to claim 1 is characterized by: The anti-collision safety distance between the drones is greater than the wingspan length: ， Where, 、 Respectively represent the horizontal coordinates of the i-th and j-th UAVs in the horizontal plane, 、 Respectively represent the vertical coordinates of the i-th and j-th UAVs in the horizontal plane, represents the relative distance between the adjacent i-th UAV and j-th UAV, The anti-collision safety distance is the wingspan length.

3. The multi-UAV autonomous collaborative trajectory planning method based on the improved FGO algorithm according to claim 2 is characterized by: The relative distance between the two adjacent drones is less than the maximum communication radius: ， Where, is the maximum communication radius.

4. The method for autonomous collaborative trajectory planning of multiple UAVs based on the improved FGO algorithm according to claim 2, characterized in that: The distance between the drone and the obstacle is greater than the safety distance: ， Where, represents the radius of the obstacle circumscribed cylinder, Indicates the wingspan margin of the drone, Indicates the number of obstacles higher than the drone. represents the distance between the i-th UAV and the k-th obstacle.

5. The method for autonomous collaborative trajectory planning of multiple UAVs based on the improved FGO algorithm according to claim 2, characterized in that: Each target is detected by at least one drone as follows: Where, represents the line of sight of the i-th UAV to the j-th target, if , UAV i tracks the target, otherwise, UAV i’s sight of tracking the target is blocked; N T is the target number.

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