Multi-unmanned aerial vehicle four-dimensional space-time cooperative distributed path planning method

Abstract

The invention relates to a multi-unmanned aerial vehicle four-dimensional space-time cooperative distributed path planning method, and belongs to the technical field of path planning. Comprising the following steps: collecting flight area information of an unmanned aerial vehicle cluster, starting point and terminal point position information of each unmanned aerial vehicle, threats in the area and an operation model of the unmanned aerial vehicle for modeling; using a DCOP model to decompose the cluster flight target function into target functions for path planning of each unmanned aerial vehicle individual; the individual objective function comprises external threats, dynamics and four-dimensional space-time cooperative constraints determined according to the modeling information; a distributed computing architecture is adopted, a moon motion optimizer is utilized, and the flight path of each unmanned aerial vehicle is solved through parallel iteration in combination with an elitist strategy and a self-adaptive population scale adjustment mechanism; in the moon motion optimizer, the positions of the moon, the earth and the sun respectively correspond to an unmanned aerial vehicle path, an optimal planning path and a suboptimal planning path. According to the invention, three-dimensional space collision avoidance and space-time collaborative optimization are realized, so that the expandability and robustness of the system are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicle (UAV) path planning, and in particular to a four-dimensional spatiotemporal collaborative distributed path planning method for multiple UAVs. Background Art

[0002] Drones, with their high flexibility, maneuverability, and ease of deployment, are widely used in various fields, including area search, target tracking, emergency rescue, and disaster monitoring. However, due to limitations in functionality and payload, a single drone cannot handle complex and diverse missions. Collaboration among multiple drones significantly expands the capabilities and scope of mission execution, gradually replacing single-drone operations and playing a vital role in various complex missions. Path planning, a core technology for drone swarm applications, involves the coordination and cooperation of multiple drones during mission execution, directly impacting mission efficiency and drone safety.

[0003] Multi-UAV path planning is a challenging problem due to its high dimensionality, multiple constraints, and spatiotemporal coordination requirements. An excellent path planning solution must comprehensively consider multiple factors, including inter-UAV collisions, environmental factors, and mission requirements, to ensure that the UAVs can complete their missions with minimal time and space consumption while maintaining their own safety. Current multi-UAV path planning methods primarily focus on spatial collision avoidance while ignoring temporal coordination optimization. They often adopt centralized architectures, resulting in exponential computational complexity as the number of UAVs increases, limiting their application in scalable multi-UAV systems and rapid decision-making. Summary of the Invention

[0004] In view of the above analysis, the present invention aims to disclose a four-dimensional spatiotemporal collaborative distributed path planning method for multiple UAVs. By decomposing the multi-UAV system into multiple subsystems, each subsystem can make independent decisions based on its own information and the information of neighboring UAVs, and simultaneously achieve three-dimensional spatial collision avoidance and spatiotemporal collaborative optimization, thereby improving the scalability and robustness of the system.

[0005] The present invention discloses a four-dimensional spatiotemporal collaborative distributed path planning method for multiple UAVs, comprising:

[0006] Step S1: collect information about the flight area of ​​the drone cluster, the starting and ending location information of each drone, the threats in the area, and the operation model of the drones to build a model;

[0007] Step S2: Using the DCOP model, the swarm flight objective function is decomposed into the objective function of each UAV's individual path planning; the individual objective function includes external threats, dynamics, and four-dimensional space-time coordination constraints determined based on the modeling information;

[0008] Step S3: Using a distributed computing architecture, utilizing the lunar motion optimizer, combining the elite strategy with the adaptive population size adjustment mechanism, and iteratively solving the flight paths of each UAV in parallel; outputting the four-dimensional space-time flight paths of the multiple UAVs;

[0009] In the lunar motion optimizer, the positions of the moon, earth, and sun correspond to the drone path, the optimal planning path, and the suboptimal planning path, respectively.

[0010] Furthermore, the dynamic constraints in the individual objective function include energy consumption constraints, angle constraints, and height constraints; among them,

[0011] In the energy consumption constraint, the path length of the drone flying at a constant speed through a series of waypoints is used as the energy consumption cost;

[0012] In the angle constraint, the angle penalty is the angle penalty when the yaw angle and pitch angle of the drone exceeds the maximum turning angle and maximum pitch angle of the drone during the flight through a series of waypoints;

[0013] In the altitude constraint, the altitude penalty for each waypoint that exceeds the altitude limit while the drone flies through a series of waypoints is used as the altitude cost.

[0014] Furthermore, the external threat constraints in the individual objective function include static obstacle constraints and dynamic obstacle constraints; among them,

[0015] In the static obstacle constraint, the penalty for avoiding static obstacles is the degree of intersection between the path segment in the obstacle area and the static obstacle when the UAV flies through a series of waypoints.

[0016] The dynamic obstacle constraints include the threat cost of air defense radar and the threat cost of countering UAVs;

[0017] The threat cost of the air defense radar is a penalty imposed on the degree of intersection between the drone and the air defense radar's detection area when the drone passes through a series of waypoints.

[0018] The threat cost of countering drones includes the cost of inter-drone collisions and the cost of airborne radar threats. The inter-drone collision cost is the penalty for a drone flying through a series of waypoints and its distance from the counterdrone is less than the safe distance. The threat cost of airborne radar is the penalty for a drone entering the detection area of ​​the counterdrone's airborne radar while flying through a series of waypoints.

[0019] Furthermore, the four-dimensional spatiotemporal coordination constraints in the individual objective function include time coordination constraints and space coordination constraints;

[0020] Among them, in the time coordination constraint, the maximum value of the minimum arrival time calculated by each drone based on the path length and maximum speed is used as the cluster estimated arrival time. By coordinating the flight speed of each drone, all drones can reach their respective target locations at the same preset time;

[0021] In spatial coordination constraints, the relative distance between each drone is monitored in real time, and penalties are imposed on route sections that are less than the safe distance to ensure that a safe distance is always maintained between drones.

[0022] Furthermore, the path planning objective function is expressed as:

[0023]

[0024] Where, ω n Represents the cost weight coefficient of the nth constraint, f n represents the nth constraint; among them, f1 represents the energy consumption cost, f2 represents the angle cost, f3 represents the height cost, f4 represents the cost of avoiding static obstacles, f5 represents the threat cost of air defense radar, f6 represents the cost of collision with the counter UAV, f7 represents the threat cost of the airborne radar of the counter UAV, and f8 represents the cost of spatiotemporal coordination of UAVs.

[0025] Furthermore, the steps of the lunar motion optimizer to solve the UAV flight path include:

[0026] 1) Initialization: Initialize a population consisting of multiple paths, where each initial path is a random path within the upper and lower bounds of the search space;

[0027] 2) Iterative optimization: The algorithm's iterative updates are characterized by changes in the net force acting on the moon. The net force acting on the moon includes the gravitational term due to the Earth, whose magnitude and direction change periodically with its position, and the gravitational term due to the Sun. To help the algorithm escape local optimal solutions, corresponding random variables are added to both the Earth's gravitational term and the Moon's gravitational term.

[0028] 3) Elite strategy: Capture and retain the optimal configuration in the iterative optimization process through the elite strategy.

[0029] Furthermore, in iterative optimization, the iterative update formula is:

[0030]

[0031] in, is the path of UAV i at the tth iteration, which represents the position of the moon at time t in the algorithm;

[0032] G e is the gravitational force exerted on the moon by the earth, whose size and direction change periodically with its position, Gs is the gravitational term of the moon exerted by the sun, whose size and direction change periodically with its position; r1 is a random number based on normal distribution, and α is a constant;

[0033] Levy(d) is:

[0034]

[0035] Where γ is a constant and d is the data dimension of the solution.

[0036] Furthermore, the moon, whose size and direction change periodically with its position, is subject to the gravitational force G of the earth. e for:

[0037]

[0038] Among them, X best represents the position of the Earth, T max Indicates the maximum number of iterations; the periodic function sin is used to simulate the periodic changes in the magnitude of the Earth's gravitational pull on the moon;

[0039]

[0040] The periodic function sin multiplied by U1 is used to simultaneously reflect the periodic changes in the magnitude and direction of gravity, thereby more comprehensively simulating the dynamic characteristics of the moon under the influence of the earth's gravity;

[0041] The moon, whose size and direction change periodically with its position, is subject to the gravitational force G of the sun. s for:

[0042]

[0043] Among them, X better represents the position of the sun, r2 is a random number based on normal distribution; the periodic function cos is used to simulate the periodic changes in the magnitude of the moon's gravitational pull on the sun;

[0044]

[0045] The periodic function cos multiplied by U2 is used to simultaneously reflect the periodic changes in the magnitude and direction of gravity, thereby more comprehensively simulating the dynamic characteristics of the moon under the influence of the sun's gravity.

[0046] Furthermore, in the elite strategy, the selection mechanism is:

[0047]

[0048] in, Represents the position of individual i after the elite strategy processing at iteration t+1.

[0049] Furthermore, the adaptive population size adjustment mechanism activates the population attenuation mechanism by setting corresponding thresholds, and adaptively adjusts the population size according to the population's evolutionary state;

[0050] The population size is adjusted as follows:

[0051]

[0052] Among them, N p is the size of the population, N′ p is the size of the adjusted population, represents the upper limit function; N min is the lower limit of the population size; β is the coefficient that controls the decay rate; R f is the current feasible solution ratio, which is the ratio of the number of feasible solutions to the total population; is the preset feasible solution threshold;

[0053] R f Expressed as:

[0054]

[0055] in, represents the Euclidean distance from the starting point to the end point, is the scaling factor.

[0056] The present invention can achieve the following beneficial effects:

[0057] The four-dimensional spatiotemporal collaborative distributed path planning method for multiple UAVs disclosed in the present invention addresses the challenging issues of high dimensionality, multiple constraints, and spatiotemporal collaboration in multi-UAV path planning. By establishing a distributed constraint optimization model and designing a lunar motion optimizer solution algorithm, it not only achieves collision avoidance in the spatial dimension, but also innovatively introduces a time coordination mechanism to ensure the precise synchronization of the UAV formation flight sequence. Compared with existing centralized methods, the distributed architecture of the present invention significantly reduces the computational complexity, making the system highly scalable and adaptable to the real-time decision-making needs of large-scale UAV clusters. At the same time, the proposed adaptive population size adjustment mechanism effectively improves the optimization solution efficiency, minimizes the time and space consumption of task execution while ensuring path safety, and provides an efficient and reliable solution for multi-UAV collaborative operations in complex environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] The accompanying drawings are only used for the purpose of illustrating specific embodiments and are not to be considered as limiting the present invention. Throughout the drawings, the same reference symbols denote the same components.

[0059] Figure 1This is a flow chart of a method for four-dimensional spatiotemporal collaborative distributed path planning for multiple UAVs according to an embodiment of the present invention;

[0060] Figure 2 This is a constraint diagram of the four-dimensional spatiotemporal collaborative distributed path planning for multiple UAVs in an embodiment of the present invention;

[0061] Figure 3 This is a schematic diagram of the coordination principle of arrival time of multiple UAVs in an embodiment of the present invention;

[0062] Figure 4 This is a flow chart of distributed path planning for multi-UAV four-dimensional spatiotemporal collaboration using a distributed computing architecture in an embodiment of the present invention;

[0063] Figure 5 A three-dimensional view of the flight paths of multiple UAVs in an embodiment of the present invention (scene S1);

[0064] Figure 6 A top view of the flight paths of multiple UAVs in an embodiment of the present invention (scene S1);

[0065] Figure 7 A three-dimensional view of the flight paths of multiple UAVs in an embodiment of the present invention (scene S2);

[0066] Figure 8 A top view of the flight paths of multiple UAVs in an embodiment of the present invention (scene S2);

[0067] Figure 9 : is a curve diagram of the change in the distance between UAV formations in scenario S2 in an embodiment of the present invention;

[0068] Figure 10 4 is a curve diagram of the change in the distance between drone formations in scene S2 in an embodiment of the present invention. DETAILED DESCRIPTION

[0069] The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, which constitute a part of this application and are used to illustrate the principles of the present invention together with the embodiments of the present invention.

[0070] In one embodiment of the present invention, a method for four-dimensional spatiotemporal collaborative distributed path planning for multiple UAVs is disclosed. Figure 1 Shown, including:

[0071] Step S1: collect information about the flight area of ​​the drone cluster, the starting and ending location information of each drone, the threats in the area, and the operation model of the drones to build a model;

[0072] Step S2: Using the DCOP model, the swarm flight objective function is decomposed into the objective function of each UAV's individual path planning; the individual objective function includes external threats, dynamics, and four-dimensional space-time coordination constraints determined based on the modeling information;

[0073] Step S3: Using a distributed computing architecture, utilizing the lunar motion optimizer, combining the elite strategy with the adaptive population size adjustment mechanism, and iteratively solving the flight paths of each UAV in parallel; outputting the four-dimensional space-time flight paths of the multiple UAVs;

[0074] In the lunar motion optimizer, the positions of the moon, earth, and sun correspond to the drone path, the optimal planning path, and the suboptimal planning path, respectively.

[0075] In step S1, the UAV flight area is constructed using a Cartesian coordinate system, whose boundaries in the x, y and z dimensions are [x min ,x max ]、[y min ,y max ] and [z min ,z max ]; Terrain height is determined by the function Represents that the threats in the flight area are composed of static obstacles and dynamic obstacles. Among them, the static obstacles include K cylinders of different sizes and M air defense radars; the dynamic obstacles include L counter-UAVs equipped with airborne radars.

[0076] The static obstacles include K cylinders of different sizes (usually used to represent buildings such as houses and base stations) and M air defense radars.

[0077] Each cylinder can be represented as:

[0078]

[0079] Where, Indicates the center of the projection of the cylinder on the xoy plane The coordinates of represents the radius, Indicates height;

[0080] The air defense radar can be modeled as a hemisphere, expressed as:

[0081]

[0082] Where, Indicates the center of the sphere The coordinates of Indicates the radius.

[0083] In this embodiment, among the L opposing UAVs included in the dynamic obstacle, each opposing UAV can be modeled as a sphere, and is equipped with a detection radius of The detection angle is The sector radar can be expressed as follows:

[0084]

[0085] Where, Indicates the center of the drone 's coordinates.

[0086] Each opposing drone is at a constant altitude Taking counterclockwise elliptical motion as an example, the equation of the ellipse can be expressed as:

[0087]

[0088] Where (m,n) represents the center of the ellipse, α represents the angle of rotation of the ellipse around the center, a and b represent the lengths of the major and minor axes of the ellipse respectively; the time required for the countermeasure drone to make one circle is T e ; After t e ∈[0,T e ], the position of the opposing drone is updated to

[0089]

[0090] Where,

[0091] At the same time, against UAVs l The angle between the direction of motion and the positive direction of the x-axis It can be expressed as:

[0092]

[0093]

[0094] Where,

[0095] The drone cluster consists of Q heterogeneous drones with different maneuverability. Each drone maintains a constant speed during flight. Constant speed, where For UAV U q The minimum and maximum flight speeds. q From P ij At speed v q Fly to P i,j+1 The time spent is Then after t∈[0,T j,j+1 ] moment, U q The location is updated to in,

[0096]

[0097] Specifically, in step S2, the DCOP (distributed constraint optimization problem, DCOP, distributed constraint optimization problem) model consists of tuples Composition, of which Represents a set of drones, drone a i Responsible for controlling its own path planning decisions. represents a set of finite variables, X i =[P i1 ,P i2 ,...,P ij ,...,P iN ] indicates drone a i The path, Indicates each There is only one a i ∈A; Is a variable collection The corresponding set of finite value spaces; F = {f1,...,f l ,...,f8} is a set of constraint functions.

[0098] The goal of DCOP is to find a solution that minimizes the total cost of the flight, where the total cost is the sum of all constraint functions:

[0099]

[0100] Since DCOP is solved in a distributed manner, the objective function can be decomposed into the individual objective function of each UAV, that is, the former is the sum of all individual objective functions,

[0101]

[0102] Where N u represents the number of drones, F(X i ) is the flight path cost of each UAV.

[0103] Specifically, the individual objective function of each UAV includes external threats, dynamics, and four-dimensional space-time coordination constraints determined based on modeling information; e.g. Figure 2 shown.

[0104] Among them, the dynamic constraints in the individual objective function include energy consumption constraints, angle constraints and height constraints;

[0105] In the energy consumption constraint, the path length of the UAV flying at a constant speed through a series of waypoints is used as the energy consumption cost; the flight path X of the i-th UAV is i It can be represented as a list X of N waypoints that the drone flies through i =[P i1 ,P i2 ,...,P ij ,…,P iN ];

[0106] In the angle constraint, the angle penalty is the angle penalty when the yaw angle and pitch angle of the drone exceeds the maximum turning angle and maximum pitch angle of the drone during the flight through a series of waypoints;

[0107] In the altitude constraint, the altitude penalty for each waypoint that exceeds the altitude limit while the drone flies through a series of waypoints is used as the altitude cost.

[0108] Specifically, the cost f1 associated with the path length in the energy consumption constraint can be calculated as:

[0109]

[0110] Where, P i1 and P iN are the starting point and the target point respectively, and ||·|| represents the Euclidean distance of the vector.

[0111] Specifically, in the angle constraint, according to the design limitations of the UAV, its maneuverability is determined to be subject to the maximum turning angle ψ max and the maximum pitch angle θ max The limit of the drone's yaw angle ψ ij Can be represented as a line segment and Projection on the xoy surface and The yaw angle ψ can be calculated according to the following formula ij :

[0112]

[0113] In the formula, “·” represents the inner product operation.

[0114] The pitch angle θ of the drone ij Can be represented as a line segment and its projection on the xoy plane The angle between them is expressed as:

[0115]

[0116] When the turning amplitude exceeds ψ max , the pitch angle exceeds θ max When , there will be corresponding penalties. The angle cost in the angle constraint is:

[0117]

[0118] Specifically, in the altitude constraint, in order to meet the requirements of flight safety and stealth, the flight altitude cannot be too low or too high, and is usually limited between two given extreme values, namely the minimum altitude h min and maximum height h max The drone will be penalized at each waypoint where it exceeds the altitude limit. The corresponding flight altitude cost f3 can be expressed as:

[0119]

[0120] Where h ij Indicates the flying height of the drone relative to the ground. h ij ≤0 means the drone crashes, and the flight altitude cost is infinite.

[0121] Among them, the external threat constraints in the individual objective function include static obstacle constraints and dynamic obstacle constraints;

[0122] In the static obstacle constraint, the penalty for avoiding static obstacles is the degree of intersection between the path segment in the obstacle area and the static obstacle when the UAV flies through a series of waypoints.

[0123] The dynamic obstacle constraints include the threat cost of air defense radar and the threat cost of countering UAVs;

[0124] The threat cost of the air defense radar is a penalty imposed on the degree of intersection between the drone and the air defense radar's detection area when the drone passes through a series of waypoints.

[0125] The threat cost of countering drones includes the cost of inter-drone collisions and the cost of airborne radar threats. The inter-drone collision cost is the penalty for a drone flying through a series of waypoints and its distance from the counterdrone is less than the safe distance. The threat cost of airborne radar is the penalty for a drone entering the detection area of ​​the counterdrone's airborne radar while flying through a series of waypoints.

[0126] Specifically, obstacle avoidance is a key constraint in UAV trajectory planning. All waypoints on the candidate path within the obstacle area will be penalized. The static obstacle avoidance cost f4 in the static obstacle constraint is given by the following formula:

[0127]

[0128] Where, Represents a path segment and the kth obstacle C k The intersection length of with C k∈K When tangent or separated,

[0129] Specifically, all waypoints on the candidate path within the radar detection area will be penalized. The threat cost f5 of the air defense radar is expressed as:

[0130]

[0131] Where, Represents a path segment With the mth air defense radar S m The intersection length of With S m When tangent or separated,

[0132] Specifically, the collision cost f6 with the adversarial drone is expressed as:

[0133]

[0134] Where, Represents the path segment for the drone to fly over The time required. represents the distance to the lth opposing drone at time t. The positions of both drones at time t can be obtained based on the operation model.

[0135] Specifically, the threat cost f7 of the airborne radar can be expressed as:

[0136]

[0137] Where, p u represents the penalty constant of the airborne radar; represents the radar detection surface of the lth UAV at time t, S i,j,t Represents the drone sphere and plane The intersecting surface.

[0138] Among them, the four-dimensional space-time coordination constraint in the individual objective function includes time coordination constraint and space coordination constraint;

[0139] In the time coordination constraint, the maximum value of the minimum arrival time calculated by each drone based on the path length and maximum speed is used as the cluster's estimated arrival time. By coordinating the flight speeds of each drone, all drones can reach their respective target locations at the same preset time.

[0140] In spatial coordination constraints, the relative distance between each drone is monitored in real time, and penalties are imposed on route sections that are less than the safe distance to ensure that a safe distance is always maintained between drones.

[0141] Specifically, the spatiotemporal coordination of UAVs requires that each UAV arrive at the designated target location at the same time while ensuring the safety of the flight process, that is, the distance between the UAVs must always be no less than D safe To ensure the same arrival time, the path length and the flight speed of the drone must be considered at the same time. The speed constraint of each drone is The time t at which UAV q arrives at the target location q , which can be expressed as:

[0142]

[0143] Where, d q represents the flight path length of UAV q.

[0144] like Figure 3 As shown in Figure 2, the expected arrival time (EAT) of the entire drone group can be expressed as:

[0145]

[0146] Here, assuming It is always true, that is, the speed of each UAV can meet the needs of time coordination. The cost f8 of UAV spatiotemporal coordination can be expressed as:

[0147]

[0148] Where, represents the distance to the qth ally UAV at time t. First, we need to determine the track segment of each UAV at time t, and then determine the position of each UAV according to formula (10).

[0149] According to the above specific constraints, the path planning objective function in step S2 of this embodiment can be expressed as:

[0150]

[0151] Where, ω n Represents the cost weight coefficient of the nth constraint, f n represents the nth constraint; among them, f1 represents the energy consumption cost, f2 represents the angle cost, f3 represents the height cost, f4 represents the cost of avoiding static obstacles, f5 represents the threat cost of air defense radar, f6 represents the cost of collision with the counter UAV, f7 represents the threat cost of the airborne radar of the counter UAV, and f8 represents the cost of spatiotemporal coordination of UAVs.

[0152] Specifically, in step S3, the Moon Motion Optimizer (MMO) algorithm is inspired by the periodic motion of the moon under the gravitational pull of the earth and the sun. It uses periodic functions to model the changes in the gravitational pull of the earth and the sun during the moon's motion and introduces an elite strategy to achieve iterative optimization of the population. The MMO algorithm uses the flight path cost F(X i ) is the optimization target, the predicted path X i is a variable. Through continuous information exchange, each drone can collaboratively optimize path selection in a distributed manner. The steps of the MMO algorithm to solve the drone flight path are as follows:

[0153] 1) Initialization: Initialize a population consisting of multiple paths, where each initial path is a random path within the upper and lower bounds of the search space;

[0154] 2) Iterative optimization: The algorithm's iterative updates are characterized by changes in the net force acting on the moon. The net force acting on the moon includes the gravitational term due to the Earth, whose magnitude and direction change periodically with its position, and the gravitational term due to the Sun. To help the algorithm escape local optimal solutions, corresponding random variables are added to both the Earth's gravitational term and the Moon's gravitational term.

[0155] 3) Elite strategy: Capture and retain the optimal configuration in the iterative optimization process through the elite strategy.

[0156] Specifically, during initialization, N is randomly selected p Path N p represents the size of the population,

[0157] X j =LB+r×(UB-LB),j=1,2,...,N p

[0158] Where, X i represents the i-th candidate solution of the UAV, UB and LB represent the upper and lower bounds of the search space, respectively, and r is a vector randomly initialized between 0 and 1.

[0159] Specifically, in iterative optimization, the iterative update formula is:

[0160]

[0161] in, is the path of UAV i at the tth iteration, which represents the position of the moon at time t in the algorithm;

[0162] G eis the gravitational force exerted on the moon by the earth, whose size and direction change periodically with its position, G s is the gravitational term of the moon exerted by the sun, whose size and direction change periodically with its position; r1 is a random number based on normal distribution, and α is a constant;

[0163] Levy(d) is:

[0164]

[0165] Where γ is a constant and d is the data dimension of the solution.

[0166] The moon, whose size and direction change periodically with its position, is subject to the gravitational force G of the earth. e for:

[0167]

[0168] Among them, X best represents the position of the Earth, T max Indicates the maximum number of iterations; the periodic function sin is used to simulate the periodic changes in the magnitude of the Earth's gravitational pull on the moon; further considering that when the moon is at different positions in the orbit, the angle between the Earth's gravitational direction and the direction of the orbit's major axis can be divided into two cases ( and ), introduce the symbol U1 to represent these two situations,

[0169]

[0170] The periodic function sin multiplied by U1 is used to simultaneously reflect the periodic changes in the magnitude and direction of gravity, thereby more comprehensively simulating the dynamic characteristics of the moon under the influence of the earth's gravity;

[0171] The moon, whose size and direction change periodically with its position, is subject to the gravitational force G of the sun. s for:

[0172]

[0173] Among them, X better represents the position of the sun, r2 is a random number based on a normal distribution; the periodic function cos is used to simulate the periodic changes in the magnitude of the sun's gravitational pull on the moon; the same symbol U2 is also introduced to represent two cases of the angle between the direction of the sun's gravitational pull and the direction of the orbit's major axis. This invention considers the Earth and the moon as a whole, so the orbit's major axis is the major axis of the Earth's orbit.

[0174]

[0175] The periodic function cos multiplied by U2 is used to simultaneously reflect the periodic changes in the magnitude and direction of gravity, thereby more comprehensively simulating the dynamic characteristics of the moon under the influence of the sun's gravity.

[0176] Specifically, in the elite strategy, the selection mechanism is:

[0177]

[0178] in, Represents the position of individual i after the elite strategy processing at iteration t+1.

[0179] This strategy ensures that in each iteration, individual positions are updated with the preference for positions with better fitness (smaller evaluation function values), thus preserving the optimal situation in the current search process. In this way, the algorithm can fully utilize existing excellent solution information, avoid deviations from the optimal direction due to random search factors, and more effectively converge towards the global optimal solution in the search space.

[0180] Specifically, the adaptive population size adjustment mechanism in step S3 activates the population attenuation mechanism by setting a corresponding threshold, and adaptively adjusts the population size according to the evolutionary state of the population;

[0181] The population size is adjusted as follows:

[0182]

[0183] in, represents the upper limit function (ceil); N p is the size of the population, N min is the lower limit of the population size; β = 5 is the coefficient that controls the decay rate; R f is the current feasible solution ratio, that is, the ratio of the number of feasible solutions to the total population; is the preset feasible solution threshold; the purpose of path planning is to avoid all dangers during flight while making the flight route as short as possible. Therefore, the final path cost is only composed of the energy cost (path length);

[0184] R f Expressed as:

[0185]

[0186] in, represents the Euclidean distance from the starting point to the end point, is the scaling factor. The introduction of the scaling factor is because the actual flight path cannot be a straight line in order to meet the actual needs of obstacle avoidance. Set to 1.2.

[0187] The distributed computing architecture is used to carry out distributed path planning for multiple UAVs in four-dimensional space-time collaboration, as shown in the following figure: Figure 4 shown.

[0188] In summary, the four-dimensional spatiotemporal collaborative distributed path planning method for multiple UAVs disclosed in this embodiment addresses the challenging issues of high dimension, multiple constraints and spatiotemporal collaboration in multi-UAV path planning, and proposes a four-dimensional spatiotemporal collaborative distributed path planning method for multiple UAVs. By establishing a distributed constraint optimization model and designing a lunar motion optimizer solution algorithm, not only collision avoidance in the spatial dimension is achieved, but also an innovative time coordination mechanism is introduced to ensure the precise synchronization of the UAV formation flight sequence. Compared with the existing centralized method, the distributed architecture of the present invention significantly reduces the computational complexity, so that the system has good scalability and can adapt to the real-time decision-making needs of large-scale UAV clusters. At the same time, the proposed adaptive population size adjustment mechanism effectively improves the optimization solution efficiency, minimizes the time and space consumption of task execution while ensuring path safety, and provides an efficient and reliable solution for multi-UAV collaborative operations in complex environments.

[0189] To verify the effectiveness of the solution, this embodiment conducts simulation verification of the method; the simulation verification scenarios involve two experimental scenarios S1 and S2, which are tested using 3 and 5 drones respectively. The results of drone path planning are as follows: Figure 5-8 As shown in Figure 2. Each drone departed simultaneously from different starting points and successfully reached the shared destination, avoiding all threats and obstacles in the map. The generated flight path was smooth enough without any sharp turns or slopes for the drones to follow. No collisions occurred between any drone pairs during the flight. Figure 9 and 10 As shown, the distance between any two drones is always greater than the safety value D safe . Each group of drones can reach the destination at the same time, meeting the requirements of spatiotemporal coordination between drones. In addition, by setting different activation thresholds for the decay mechanism of the population, the performance of the population decay mechanism in reducing time overhead was verified. As shown in Table 1, compared with a fixed population size, using three different activation thresholds of low, medium, and high (30%-50%-80%), the time overhead of the MMO algorithm was shortened by 23.15% and 24.43% in the two scenarios, respectively.

[0190] Table 1 Effects of different activation thresholds on time overhead and algorithm performance

[0191]

[0192]

[0193] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by the scope of protection of the present invention.

Claims

1. A four-dimensional spatiotemporal collaborative distributed path planning method for multiple UAVs, characterized by: include: Step S1: collect information about the flight area of ​​the drone cluster, the starting and ending location information of each drone, the threats in the area, and the operation model of the drones to build a model; Step S2: Using the DCOP model, the swarm flight objective function is decomposed into the objective function of each UAV's individual path planning; the individual objective function includes external threats, dynamics, and four-dimensional space-time coordination constraints determined based on the modeling information; Step S3: Using a distributed computing architecture, utilizing the lunar motion optimizer, combining the elite strategy with the adaptive population size adjustment mechanism, and iteratively solving the flight paths of each UAV in parallel; outputting the four-dimensional space-time flight paths of the multiple UAVs; In the lunar motion optimizer, the positions of the moon, earth, and sun correspond to the drone path, the optimal planning path, and the suboptimal planning path, respectively.

2. The multi-UAV four-dimensional spatiotemporal collaborative distributed path planning method according to claim 1 is characterized in that: The dynamic constraints in the individual objective function include energy consumption constraints, angle constraints, and height constraints; among them, In the energy consumption constraint, the path length of the drone flying at a constant speed through a series of waypoints is used as the energy consumption cost; In the angle constraint, the angle penalty is the angle penalty when the yaw angle and pitch angle of the drone exceeds the maximum turning angle and maximum pitch angle of the drone during the flight through a series of waypoints; In the altitude constraint, the altitude penalty for each waypoint that exceeds the altitude limit while the drone flies through a series of waypoints is used as the altitude cost.

3. The multi-UAV four-dimensional spatiotemporal collaborative distributed path planning method according to claim 2 is characterized in that: The external threat constraints in the individual objective function include static obstacle constraints and dynamic obstacle constraints; among them, In the static obstacle constraint, the penalty for avoiding static obstacles is the degree of intersection between the path segment in the obstacle area and the static obstacle when the UAV flies through a series of waypoints. The dynamic obstacle constraints include the threat cost of air defense radar and the threat cost of countering UAVs; The threat cost of the air defense radar is a penalty imposed on the degree of intersection between the drone and the air defense radar's detection area when the drone passes through a series of waypoints. The threat cost of countering drones includes the cost of inter-drone collisions and the cost of airborne radar threats. The inter-drone collision cost is the penalty for a drone flying through a series of waypoints and its distance from the counterdrone is less than the safe distance. The threat cost of airborne radar is the penalty for a drone entering the detection area of ​​the counterdrone's airborne radar while flying through a series of waypoints.

4. The multi-UAV four-dimensional spatiotemporal collaborative distributed path planning method according to claim 3 is characterized in that: The four-dimensional space-time coordination constraints in the individual objective function include time coordination constraints and space coordination constraints; Among them, in the time coordination constraint, the maximum value of the minimum arrival time calculated by each drone based on the path length and maximum speed is used as the cluster estimated arrival time. By coordinating the flight speed of each drone, all drones can reach their respective target locations at the same preset time; In spatial coordination constraints, the relative distance between each drone is monitored in real time, and penalties are imposed on route sections that are less than the safe distance to ensure that a safe distance is always maintained between drones.

5. The multi-UAV four-dimensional spatiotemporal collaborative distributed path planning method according to claim 4 is characterized in that: The path planning objective function is expressed as: Where, X i is the flight path of the i-th UAV; F(X i ) is the flight path X i The cost of n Represents the cost weight coefficient of the nth constraint, f n represents the nth constraint; among them, f1 represents the energy consumption cost, f2 represents the angle cost, f3 represents the height cost, f4 represents the cost of avoiding static obstacles, f5 represents the threat cost of air defense radar, f6 represents the cost of collision with the counter UAV, f7 represents the threat cost of the airborne radar of the counter UAV, and f8 represents the cost of spatiotemporal coordination of UAVs.

6. The multi-UAV four-dimensional spatiotemporal collaborative distributed path planning method according to claim 1 is characterized in that: The steps in the Lunar Motion Optimizer to solve the drone's flight path include: 1) Initialization: Initialize a population consisting of multiple paths, where each initial path is a random path within the upper and lower bounds of the search space; 2) Iterative optimization: The algorithm's iterative updates are characterized by changes in the net force acting on the moon. The net force acting on the moon includes the gravitational term due to the Earth, whose magnitude and direction change periodically with its position, and the gravitational term due to the Sun. To help the algorithm escape local optimal solutions, corresponding random variables are added to both the Earth's gravitational term and the Moon's gravitational term. 3) Elite strategy: Capture and retain the optimal configuration in the iterative optimization process through the elite strategy.

7. The multi-UAV four-dimensional spatiotemporal collaborative distributed path planning method according to claim 6 is characterized in that: In iterative optimization, the iterative update formula is: in, is the path of UAV i at the tth iteration, which represents the position of the moon at time t in the algorithm; G e is the gravitational force exerted on the moon by the earth, whose size and direction change periodically with its position, G s is the gravitational term of the moon exerted by the sun, whose size and direction change periodically with its position; r1 is a random number based on normal distribution, and α is a constant; Levy(d) is: Where γ is a constant and d is the data dimension of the solution.

8. The multi-UAV four-dimensional spatiotemporal collaborative distributed path planning method according to claim 7 is characterized in that: The moon, whose size and direction change periodically with its position, is subject to the gravitational force G of the earth. e for: Among them, X best represents the position of the Earth, T max Indicates the maximum number of iterations; the periodic function sin is used to simulate the periodic changes in the magnitude of the Earth's gravitational pull on the moon; Logo The periodic function sin multiplied by U1 is used to simultaneously reflect the periodic changes in the magnitude and direction of gravity, thereby more comprehensively simulating the dynamic characteristics of the moon under the influence of the earth's gravity; The moon, whose size and direction change periodically with its position, is subject to the gravitational force G of the sun. s for: Among them, X better represents the position of the sun, r2 is a random number based on normal distribution; the periodic function cos is used to simulate the periodic changes in the magnitude of the moon's gravitational pull on the sun; Logo The periodic function cos multiplied by U2 is used to simultaneously reflect the periodic changes in the magnitude and direction of gravity, thereby more comprehensively simulating the dynamic characteristics of the moon under the influence of the sun's gravity.

9. The multi-UAV four-dimensional spatiotemporal collaborative distributed path planning method according to claim 7, characterized in that: In the elite strategy, the selection mechanism is: in, Represents the position of individual i after the elite strategy processing at iteration t+1.

10. The multi-UAV four-dimensional spatiotemporal collaborative distributed path planning method according to claim 5, characterized in that: The adaptive population size adjustment mechanism activates the population attenuation mechanism by setting corresponding thresholds and adaptively adjusts the population size according to the evolutionary state of the population; The population size is adjusted as follows: Among them, N p is the size of the population, N′ p is the size of the adjusted population, represents the upper limit function; N min is the lower limit of the population size; β is the coefficient that controls the decay rate; R f is the current feasible solution ratio, which is the ratio of the number of feasible solutions to the total population; is the preset feasible solution threshold; R f Expressed as: in, represents the Euclidean distance from the starting point to the end point, is the scaling factor.

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