An unmanned aerial vehicle cluster shape reconstruction method based on a parameter mapping mechanism

Abstract

The application discloses a kind of based on parameter mapping mechanism's unmanned aerial vehicle cluster shape reconstruction method, belongs to unmanned aerial vehicle fleet autonomous decision control technical field, including establishing unmanned aerial vehicle cluster model and unmanned aerial vehicle single body model;Establish the basic behavior rule of unmanned aerial vehicle, including motion trend adjustment and dynamic position adjustment;Set cluster macro shape, according to the unmanned aerial vehicle cluster model and unmanned aerial vehicle single body model established by macro shape parameter mapping to micro rule parameter, determine neighborhood range, according to the basic behavior rule of unmanned aerial vehicle established, generate cluster macro three-dimensional shape, and the generated cluster macro three-dimensional shape is with preset shape Accuracy analysis, according to accuracy result completes unmanned aerial vehicle shape reconstruction.The application uses the above method, can make operator directly modify macro shape parameter to directly adjust the relative distance between unmanned aerial vehicle cluster machines, to form preset macro shape in three-dimensional space.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of autonomous decision-making control of unmanned aerial vehicle (UAV) swarms, and particularly relates to a UAV swarm shape reconstruction method based on a parameter mapping mechanism. BACKGROUND

[0002] With the development of unmanned system technology, UAV swarms have been increasingly widely applied in various fields. Meanwhile, the intelligentization of UAV swarms is also one of the important development directions in the future. The swarm can switch between different shapes or different sizes of the same shape. Autonomous shape transformation of the swarm has many application forms in the military field. On the one hand, a large-scale swarm of low-cost and small unmanned aerial vehicles can confuse the radar and detection systems of the enemy by constantly transforming the shape, increase the difficulty of identification of the enemy, and achieve the combat effect of jamming and deception; on the other hand, in a complex urban environment, the swarm can quickly shuttle between buildings by shape transformation, and quickly maneuver while effectively maintaining concealment.

[0003] Currently, there are relatively few studies on such shape transformation problems, and researchers pay more attention to the formation reconstruction problem of multiple unmanned aerial vehicles. For different research points in the formation reconstruction process, the problem can usually be described as a combinatorial optimization problem with complex constraint conditions and closely coupled variables, and then different optimization strategies or a combination of multiple strategies are used to solve the optimal or near-optimal solution. In the paper “Hybrid Particle Swarm Optimization and Genetic Algorithm for Multi-UAV Formation Reconfiguration”, Hai-bin Duan et al. proposed a combination optimization method of hybrid particle swarm optimization and genetic algorithm to solve the time-optimal solution of the multi-UAV formation reconstruction problem. In the three-dimensional space, the process of converting 5 aircraft from a random state to a V-shaped formation is verified by numerical simulation, and the superiority of this method compared with the particle swarm optimization method alone is verified.

[0004] Formation reconstruction is the process of converting multiple unmanned aerial vehicles from one certain formation to another certain formation, so the research on formation reconstruction is only applicable to a swarm of a fixed number of unmanned aerial vehicles, and it is difficult to cope with the case where the number of unmanned aerial vehicles changes dynamically. For example, if some unmanned aerial vehicles appear to be damaged or separated from the swarm during the flight of the swarm, the swarm cannot continue to maintain the preset formation, and the method based on behavior rules generally does not have restrictions on the number of unmanned aerial vehicles.

[0005] In the optimization of the formation reconfiguration problem or the optimization calculation of multiple behavior rule parameters, with the increase of the number of unmanned aerial vehicles, the resource consumption of the optimization iterative calculation is usually exponentially increased, and the cluster shape transformation only needs to specify the geometric shape that the cluster needs to maintain in the three-dimensional space, which is usually specified by the shape parameters of the geometric body, without the need to preset the relative positions of each unmanned aerial vehicle before and after the formation transformation. SUMMARY

[0006] The purpose of the present application is to provide a parameter mapping mechanism-based unmanned aerial vehicle cluster shape reconfiguration method to realize the macro shape reconfiguration of the unmanned aerial vehicle cluster in the three-dimensional space.

[0007] To achieve the above purpose, the present application provides a parameter mapping mechanism-based unmanned aerial vehicle cluster shape reconfiguration method, which comprises the following steps:

[0008] S1, establishing an unmanned aerial vehicle cluster model and an unmanned aerial vehicle individual model, the unmanned aerial vehicle cluster model comprising unmanned aerial vehicles and neighborhood relationships, and the unmanned aerial vehicle individual model comprising an unmanned aerial vehicle state model and an unmanned aerial vehicle friendly machine conversion model;

[0009] S2, establishing basic behavior rules of the unmanned aerial vehicle, including motion trend adjustment and dynamic position adjustment, which are respectively used to adjust the motion direction and relative position of the unmanned aerial vehicle relative to the neighborhood friendly machine;

[0010] S3, setting a cluster macro shape, mapping the macro shape parameters to the micro rule parameters according to the unmanned aerial vehicle cluster model and the unmanned aerial vehicle individual model, determining the neighborhood range, and generating a cluster macro three-dimensional shape according to the established basic behavior rules of the unmanned aerial vehicle, and performing accuracy analysis on the generated cluster macro three-dimensional shape and the preset shape, and completing the shape reconfiguration of the unmanned aerial vehicle according to the accuracy result.

[0011] Preferably, the establishment of the unmanned aerial vehicle cluster model in step S1 comprises:

[0012] Let the cluster size be N, U={U1, U2,...,Un} represents the unmanned aerial vehicle cluster set, and Ui represents the i-th unmanned aerial vehicle in the cluster, the neighborhood relationship of the unmanned aerial vehicle is determined based on the rule action range parameter of the unmanned aerial vehicle, and the neighborhood relationship includes the neighborhood friendly machine set C N centered on the unmanned aerial vehicle Ui, the neighborhood relationship includes the neighborhood friendly machine set C i consisting of other friendly unmanned aerial vehicles within the radius d i , the friendly unmanned aerial vehicle sub-set C r consisting of other friendly unmanned aerial vehicles within the radius d i , the friendly unmanned aerial vehicle sub-set C s consisting of other friendly unmanned aerial vehicles within the radius d dis，i , and the friendly unmanned aerial vehicle sub-set C c consisting of other friendly unmanned aerial vehicles within the radius d r , and the friendly unmanned aerial vehicle sub-set C coh，i consisting of other friendly unmanned aerial vehicles within the radius d

[0013] C i ={U k ∈U|||p i -p k ||≤d r};

[0014] C dis，i ={U k ∈C i |||p i -p k ||≤d s};

[0015] C coh，i ={U k ∈C i |d c ≤||p i -p k ||≤d r};

[0016] Where, p i and p k U represents the unmanned aerial vehicle (UAV) i and U k The three-dimensional position vector.

[0017] Preferably, the step S1 of establishing a single UAV model includes:

[0018] Based on ground coordinate system O g x g y g z g U-type drone i Position p i =[p x，i p y，i p z，i Speed ​​v i =[v x，i v y，i v z，i and the body coordinate system Ox b y b z b U-type drone i postureΘ i =[θ i , ψ i φ i Establish UAVs i The state model is represented as:

[0019] S i =[p i v i Θ i ] = [p x，ip y，i p z，i v x，i v y，i v z，i θ i , ψ i φ i ];

[0020] In the ground coordinate system, O g x g Pointing due east, O g y g Pointing due north, θ i , ψ i φ i U represents the unmanned aerial vehicle (UAV) i Pitch angle, yaw angle, and roll angle;

[0021] Based on ground coordinate system O g x g y g z g and U i relative coordinate system O i x i y i z i Establish a coordinate transformation model for the UAV and its friendly aircraft. i Located at the origin O i O i z i Axis and O g z g Axis coincidence, O i y i Axis and velocity consistency adjustment vector Δv ali，i Coincidence, O i x i Axis and O i y i z i If the planes are perpendicular and follow the right-hand rule, define the vector Δv. ali，i With O i y i The included angle of the axis is ψ ali，i Then the rotation matrix R i Defined as:

[0022]

[0023] Coordinate system transformation only occurs on the horizontal plane O. g x g y g The coordinate transformation process is performed internally and is represented as follows:

[0024]

[0025] where p xy，k represents the friendly U k in O g x g y g in the plane, represents the U k in O i x i axis component represents the U k in O i x i axis component represents the U k in O i x i y i in the plane, represents in O i x i y i in the plane, represents in O z，k x k in the plane. g x g in the plane.

[0026] Preferably, the motion trend adjustment in step S2 is used to keep the individual and the friendly individuals in the neighborhood relative consistent motion trend and advance to the target waypoint, including speed consistency adjustment and task heading adjustment.

[0027] Preferably, the speed consistency adjustment and task heading adjustment include:

[0028] The speed consistency adjustment represents the advancing direction of the UAV cluster at the current time, denoted as:

[0029]

[0030] where v xy，k represents the speed v k of the friendly U k in O g x g y g in the plane;

[0031] The UAV cluster has the same target heading p t , and the task heading of the UAV U i is denoted as:

[0032]

[0033] wherein p t，xy and p xy，i represent the position p t and the position p i of the target waypoint p i and U g in the O g x g y g plane, respectively;

[0034] According to the mission heading of the UAV U i and the heading of the UAV cluster at the current time, the motion tendency adjustment amount Δv i of the UAV U i is expressed as:

[0035]

[0036] wherein ω a and ω m represent the weight parameters of the velocity consistency rule and the mission heading rule, respectively.

[0037] Preferably, the dynamic position adjustment in step S2 is used to keep the UAV individual at a proper relative distance from the friendly UAVs in the neighborhood, and the position adjustment includes a dispersion rule, a gathering rule and a shape constraint rule, which are all calculated in the relative coordinate system O i x i y i z i of the UAV U i .

[0038] Preferably, the dispersion and gathering rules are respectively used to calculate the position adjustment amount of the UAV U i to move away from or close to the friendly UAVs in the neighborhood at different distance ranges, and the dispersion rule is expressed as:

[0039]

[0040] wherein Δp dis，i represents the position adjustment amount calculated by dispersion, represents the coordinates of the UAV U k in the U i relative coordinate system after coordinate system conversion;

[0041] The gathering rule is expressed as:

[0042]

[0043] wherein Δp coh，i represents the position adjustment amount calculated by gathering;

[0044] The basic quantity of position adjustment Δp′ is obtained based on the divergence and aggregation rules. i The expression is:

[0045] Δp i =Δp dis，i +Δp coh，i .

[0046] Preferably, the shape constraint rules include:

[0047] First, the drone swarm is calculated based on the transformation model, showing the entire swarm in the relative coordinate system O. i x i y i z i The desired centroid is used to intervene in and control the overall flight altitude of the cluster;

[0048] Secondly, the basic quantity Δp′ for three-dimensional position adjustment i Decompose the data according to shape constraints, when Δp′ i In O i x i z i The projection component Δp′ of the plane xz，i Located in shape O i x i z i External Ω of the cross-sectional region of the plane xz At that time, Δp′ i In O i x i z i In-plane and O i y i Adjust the direction;

[0049] Finally, relative coordinate system O i x i y i z i Δp′ below i Transform back to ground coordinate system O g x g y g z g The adjustment amount Δp i The conversion expression is:

[0050]

[0051] In the formula, R i -1 Let R be the rotation matrix. i The inverse matrix, Δp z，i Indicates the position adjustment amount Δp i In O g z gcomponent in the direction of p z，i represents the position adjustment amount Δp i in the O i z i direction.

[0052] Preferably, the Δp i in the O i x i z i plane and in the O i y i direction includes:

[0053] in the O i x i z i plane is represented as:

[0054]

[0055] where Intersect(·) represents a function of solving the intersection point of a vector and a geometric figure, Δp xz，i represents the Δp xz，i and the intersection point of the cross-sectional region boundary;

[0056] in the O i y i direction, first calculate Δp y，i the distance value beyond the Ω xy boundary is represented as:

[0057]

[0058] where dist(·) represents the shortest distance of Δp y，i in the O i y i direction and the cross-sectional region Ω xy Δp y，i represents the position adjustment amount Δp i in the O i y i direction;

[0059] convert the position adjustment amount into a speed adjustment amount σ v，i , and realize the forward or backward movement by acceleration or deceleration, wherein the forward or backward movement is relative to the whole cluster, and the unmanned aerial vehicle moves to the head or tail of the cluster by adjusting the relative speed, and the speed adjustment amount σ v，i is expressed as:

[0060]

[0061] where λv >0 is a constant coefficient, constrain(x, a, b) is a truncation function for limiting x in the interval [a, b], and are the minimum and maximum values of the speed adjustment amount, respectively.

[0062] Preferably, the parameter mapping relationship in step S3 is represented as:

[0063]

[0064] In the formula, represents a macro shape parameter set, when it is a cuboid, d L , d W and d H are the length, width and height of the cuboid, respectively; when it is a sphere, r represents the radius of the sphere; V sp represents the expected three-dimensional volume of the macro shape parameter definition set, represents the actual macro three-dimensional volume presented according to the micro rule parameters, and the function f(·) is a mapping relationship from the micro rule parameters to the actual three-dimensional volume, is a mapping relationship of the macro shape parameter to the set cluster three-dimensional volume.

[0065] Therefore, the unmanned aerial vehicle cluster shape reconstruction method based on the parameter mapping mechanism has the following beneficial effects:

[0066] (1) The method is based on behavior rules, which divides different rules into two categories of motion trend adjustment and dynamic position adjustment, and combines to generate the decision result of the unmanned aerial vehicle. Compared with the common way of using weight parameters to unify multiple rules, the number of parameters is greatly reduced, and the parameter optimization process is saved, reducing the real-time calculation amount of the decision process.

[0067] (2) The parameter mapping mechanism of the macro shape parameter to the micro rule parameter is used, and the three-dimensional volume of the cluster is affected by the rule action range parameter. By mapping the preset macro shape parameter to the rule action range parameter, the cluster can be indirectly controlled to spontaneously reconstruct to the preset three-dimensional shape. The parameter mapping mechanism is not sensitive to the number of unmanned aerial vehicles, and can be used for shape reconstruction of clusters of different sizes, and has strong scalability.

[0068] (3) The rule-based cluster decision method used in the present application is not limited by the size of the cluster, and the increase of the size of the cluster will not significantly increase the calculation amount of the decision process, so it can be applied to clusters of tens or even hundreds of sizes.

[0069] The technical solutions of the present application will be further described in detail through the drawings and examples. Attached Figure Description

[0070] Figure 1 This is a flowchart illustrating the reconstruction process according to an embodiment of the present invention;

[0071] Figure 2 This is a macroscopic shape reconstruction diagram of an embodiment of the present invention;

[0072] Figure 3 This is a diagram illustrating the scope of application of the basic behavioral rules in an embodiment of the present invention.

[0073] Figure 4 This is a diagram showing the position and attitude state of a UAV according to an embodiment of the present invention;

[0074] Figure 5 This is a schematic diagram of coordinate transformation according to an embodiment of the present invention;

[0075] Figure 6 The macroscopic shape of the embodiment of the present invention is in O i x i z i Shape constraint diagram in a plane;

[0076] Figure 7 The macroscopic shape of the embodiment of the present invention is in O i y i Shape constraint diagram in the direction;

[0077] Figure 8 This is a flowchart illustrating the macroscopic to microscopic parameter effects on the cuboid shape according to an embodiment of the present invention.

[0078] Figure 9 This is a diagram showing the average distance of the cluster in three directions under multiple sets of parameters according to an embodiment of the present invention.

[0079] Figure 10 d, as an embodiment of the present invention s With three-dimensional volume The relationship and the fitted curve. Detailed Implementation

[0080] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. 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 claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0081] Example

[0082] Reference Figure 1 This invention provides a method for reconstructing the shape of a UAV swarm based on a parameter mapping mechanism. The shape preservation and transformation involved in the reconstruction refer to the fact that during the flight of the UAV swarm in three-dimensional space, the swarm as a whole exhibits a relatively obvious spatial geometric structure at the macroscopic level. This invention's method is applicable to the reconstruction of cuboids and spheres, such as... Figure 2 As shown, Figure 2 (a) d L d W and d H These represent the length, width, and height of the cuboid, which are the distances spanned by the cluster in the horizontal, forward, and vertical directions. Figure 2 (b) represents the radius of the sphere, where r is the radius. d L d W d H and r can be used as macroscopic shape parameters of the cluster. Different combinations of parameters can make the cluster present as a cuboid or sphere of different geometric dimensions.

[0083] The specific steps of the method of the present invention include:

[0084] S1. Establish drone cluster models and drone individual models.

[0085] The drone swarm model includes drones and their neighborhood relationships. Establishing a drone swarm model involves:

[0086] Let the cluster size be N, and U = {U1, U2, ..., U...} N} represents a swarm of drones, U i Let i represent the i-th drone in the cluster. The neighborhood relationship of a drone is determined based on the drone rule's scope parameter. The scope of the drone rule is as follows: Figure 3 As shown, using U-type drones i Centered on the radius d, the neighborhood relationship includes the radius d. rC, a set of neighboring friendly drones within the range, together with other friendly drones. i Distance d s The set of friendly drones C within the range dis，i and distance d c ~d r The set of friendly drones C within the range coh，i , is represented as:

[0087] C i ={U k ∈U|||p i -p k ||≤d r};

[0088] C dis，i ={U k ∈C i |||p i -p k ||≤d s};

[0089] C coh，i ={U k ∈C i |d c ≤||p i -p k ||≤d r};

[0090] Where, p i and p k U represents the unmanned aerial vehicle (UAV) i and U k The three-dimensional position vector.

[0091] The individual UAV model includes the UAV state model and the coordinate transformation model of the UAV and its companion aircraft. A single UAV... i The motion state can be determined by Figure 4 express. Figure 4 (a) represents the ground coordinate system O g x g y g z g (O g x g Pointing due east, O g y g (Pointing due north) U-shaped drone i Position p i =[p x，i p y，i p z，i ], speed v i =[v x，i v y，i vz，i The three-axis components of the velocity vector are the first derivatives of the corresponding components of the position vector, expressed as:

[0092]

[0093] Figure 4 (b) is the body coordinate system Ox b y b z b U-type drone i postureΘ i =[θ i , ψ i , φ i ], where θ i , ψ i φ i U drones i The pitch angle, yaw angle, and roll angle.

[0094] Then the UAV i It can be derived from the state model S i express:

[0095] S i =[p i v i Θ i ] = [p x，i p y，i p z，i v x，i v y，i v z，i θ i , ψ i , φ i ].

[0096] State model S i This refers to the interaction information between individual drones within the cluster, which serves as the input information for the operation of the method proposed in this invention.

[0097] In the rule calculation of dynamic position adjustment, the UAV U i Neighborhood C i The location of the friendly machine within p k It needs to be from the ground coordinate system O g x g y g z g To U i relative coordinate system O i x i y i z i Relative position below Therefore, a coordinate transformation model needs to be established for the UAV U. iThe origin O i , O i z i axis coincides with O g z g axis, O i y i axis coincides with the velocity consistency adjustment vector Δv ali，i , O i x i axis coincides with O i y i z i plane is perpendicular and follows the right-hand rule, as shown in Figure 5 .

[0098] The vector Δv ali，i is defined as the angle ψ i between O i y ali，i axis, then the rotation matrix R i can be defined as:

[0099]

[0100] The coordinate system conversion is only performed in the horizontal plane O g x g y g , as shown in Figure 5 (a) and (b), the horizontal plane coordinates p k of the friend U xy，k are converted to the position in the relative coordinate system of U i The coordinate conversion process is expressed as:

[0101]

[0102] where the x i axis component represents the lateral orientation and distance of U k relative to U i , the y i axis component represents the front-back orientation and distance of U k relative to U i in the overall motion direction of the cluster, represents the component in the O i x i y i plane, represents the component in the O i z i direction, and p z，k represents p k in O​g z g on the component.

[0103] S2, establishing basic behavior rules of the UAV, including motion tendency adjustment and dynamic position adjustment, respectively used for adjusting the motion direction and relative position of the UAV relative to the neighbor friendly UAV.

[0104] The motion tendency adjustment is used for keeping the individual and the neighbor friendly individual consistent in the motion tendency and advancing to the target waypoint, including speed consistency adjustment and task heading adjustment.

[0105] The speed consistency adjustment represents the advancing direction of the UAV cluster at the current time, and is represented as:

[0106]

[0107] wherein v xy，k represents the speed v k of the neighbor friendly UAV U k in the O g x g y g plane.

[0108] The UAV cluster has the same target heading p t , and the task heading of the UAV U i is represented as:

[0109]

[0110] wherein p t，xy and p xy，i represent the component of the target waypoint p t and the position p i of the UAV U i in the O g x g y g plane, respectively.

[0111] According to the task heading of the UAV U i and the advancing direction of the UAV cluster at the current time, the motion tendency adjustment amount Δv i of the UAV U i is represented as:

[0112]

[0113] wherein ω a and ω m represent the weight parameters of the speed consistency rule and the task heading rule, respectively.

[0114] It should be noted that the adjustment of the motion tendency is only in the O g xg y g The plane is used because it contains z-axis. g When the three-dimensional velocity in the direction is calculated according to the rules, the adjustment amount of the height will conflict with the height adjustment amount of the dynamic position adjustment rule, which will lead to the instability of the overall movement of the cluster.

[0115] Dynamic position adjustment is used to maintain an appropriate relative distance between individual drones and friendly drones in the vicinity. Position adjustment includes dispersion rules, aggregation rules, and shape constraint rules, all of which are defined within the U-shaped area. i relative coordinate system O i x i y i z i The calculations will then be performed.

[0116] The scattering and clustering rules are used to calculate the UAV U. i This involves adjusting the position of friendly drones within different distance ranges in the neighborhood to maintain a suitable distance. The spread-out rule expression is:

[0117]

[0118] In the formula, Δp dis，i This represents the position adjustment amount calculated by spreading out the data. U k After coordinate system transformation, U i Coordinates in a relative coordinate system;

[0119] The aggregation rule expression is:

[0120]

[0121] In the formula, Δp coh，i This represents the position adjustment amount obtained from the aggregation calculation;

[0122] The basic quantity of position adjustment Δp′ is obtained based on the divergence and aggregation rules. i The expression is:

[0123] Δp′ i =Δp dis，i +Δp coh，i .

[0124] UAV i By adjusting its relative position within the cluster, the average distance between itself and neighboring friendly machines is made to be within d. s to d c Within a certain range, a relatively stable positional relationship is achieved. At this point, the cluster can spontaneously form a stable, specific macroscopic shape, along the direction of cluster movement, i.e., O. i y i Observing the axis, the cluster is in Oi x i z i The projection on the plane resembles a square or a circle.

[0125] Shape constraint rules include:

[0126] First, the drone swarm is calculated based on the transformation model, showing the entire swarm in the relative coordinate system O. i x i y i z i The desired centroid is used to intervene in and control the overall flight altitude of the cluster. It can be represented as:

[0127]

[0128] In the formula, h * For clustering, it is necessary to use the ground coordinate system O g x g y g z g The expected level to be maintained Indicates that the centroid is at O i x i y i Planar components, Indicates that the centroid is at O i z i The directional component. This is determined by setting the parameter h. * This keeps the centroid of the cluster at a fixed altitude, avoiding flight instability caused by constant changes in the average altitude of the cluster as a whole, and also makes it easier for people to intervene and control the overall flight altitude of the cluster.

[0129] Secondly, the basic quantity Δp′ for three-dimensional position adjustment i Decompose the data according to shape constraints, when Δp′ i In O i x i z i The projection component Δp′ of the plane xz，i Located in shape O i x i z i External Ω of the cross-sectional region of the plane xz At times, such as Figure 6 The region enclosed by the red dashed lines in (a) and (b), Δp′ i Need to O i x i z i In-plane and O i y i Adjust the direction.

[0130] In Oi x i z i Adjustment in the plane is represented as:

[0131]

[0132] where Intersect(·) represents a function of solving the intersection point of the vector and the geometric figure, Δp xz，i represents Δp′ xz，i and the intersection point of the section area boundary, the intersection point as the position adjustment amount after shape constraint.

[0133] Adjustment in the O i y i direction, as shown in Figure 7 . First, calculate Δp′ y，i the distance value beyond the Ω xy boundary is represented as:

[0134]

[0135] where dist(·) represents the shortest distance of Δp′ y，i in the O i y i direction to the section area Ω xy , Δp′ y，i represents the position adjustment amount Δp′ i in the O i y i direction;

[0136] Then, the position adjustment amount is converted into the speed adjustment amount σ v，i . In the O i x i z i plane, the UAV can move to the expected position by adjusting the attitude, but in the forward direction O i y i of the UAV, the UAV cannot adjust the front-back relationship with other friendly machines through attitude. Therefore, it is necessary to convert the position adjustment amount into the speed adjustment amount σ v，i , and realize forward or backward movement by accelerating or decelerating. Wherein forward or backward movement is relative to the whole cluster, by adjusting the relative speed to make the UAV move to the head or tail of the cluster, in the ground coordinate system, each UAV always flies towards the front.

[0137] The expression of the speed adjustment amount σ v，i is:

[0138]

[0139] In the formula, λ v >0 represents a constant coefficient, and consttrain(x, a, b) is a cutoff function used to restrict x to the interval [a, b]. and These represent the minimum and maximum speed adjustment values, respectively. It's important to note that from a control system perspective, the speed adjustment should not be too large, and the adjustment frequency should not be too frequent. Acceleration or deceleration will cause changes in the drone's flight altitude, and frequent speed changes will lead to flight instability, increase energy consumption, and reduce the drone's flight time.

[0140] Finally, due to the position adjustment Δp′ calculated by the macroscopic shape constraint rules i It cannot be used directly to generate waypoints; the relative coordinate system O needs to be changed. i x i y i z i Δp′ below i Transform back to ground coordinate system O g x g y g z g The adjustment amount Δp i The conversion expression is:

[0141]

[0142] In the formula, R i -1 Let R be the rotation matrix. i The inverse matrix, Δp z，i Indicates the position adjustment amount Δp i In O g z g Component in direction, Δp′ z，i This indicates the position adjustment amount Δp′ i In O i z i Components in direction.

[0143] S3. Set the macroscopic shape of the cluster. Based on the UAV cluster model and the UAV individual model, map the macroscopic shape parameters to the microscopic rule parameters, determine the neighborhood range, and generate the macroscopic three-dimensional shape of the cluster according to the established basic behavior rules of the UAV. Then, perform an accuracy analysis between the generated macroscopic three-dimensional shape of the cluster and the preset shape, and complete the UAV shape reconstruction based on the accuracy results.

[0144] Specifically, the parameter mapping relationship can be represented as:

[0145]

[0146] In the formula, represents the macroscopic shape parameter set, when it is a cuboid, d L , d W and d H are the length, width and height of the cuboid respectively; when it is a sphere, r represents the radius of the sphere; V sp represents the expected three-dimensional volume of the macroscopic shape parameter definition set, represents the actual macroscopic three-dimensional volume presented according to the microscopic rule parameters, the function f(·) is a mapping relationship from the microscopic rule parameters to the actual three-dimensional volume, is a mapping relationship of the macroscopic shape parameter to the set three-dimensional volume.

[0147] Taking the cuboid reconstruction as an example, the length, width and height of the cuboid are d L , d W and d H respectively, which represent the distance span of the cluster in the lateral, forward and longitudinal directions.

[0148] First, the unmanned aerial vehicle cluster model and the unmanned aerial vehicle single model are established. Then the basic behavior rules of the unmanned aerial vehicle are established, including motion trend adjustment (speed consistency and task heading adjustment) and dynamic position adjustment (aggregation rule, dispersion rule and shape constraint rule), in the shape constraint rule, d L , d W , d H represent the maximum span of the cluster in the lateral (O i x i ), forward (O i y i ) and longitudinal (O i z i ) directions respectively. The cuboid shape constraint rule specifically includes:

[0149] First, the expected centroid of the cluster as a whole in the relative coordinate system O i x i y i z i is calculated according to the formula.

[0150] Secondly, the three-dimensional position quantity is decomposed, first, the adjustment quantity in the O i x i z i plane is calculated, according to the shape constraints d L and d H , if Δp′ xz，i is located outside the rectangle, the intersection point of the vector Δp′ xz，i and the rectangle boundary is calculated, and the intersection point is taken as the position adjustment quantity Δp xz，i after shape constraint, which is represented as:

[0151]

[0152] In the formula, and The long side d of the rectangle L In O i x i Minimum and maximum values ​​in the direction, and The height d of the rectangle is respectively H In O i z i Minimum and maximum values ​​in the direction, Indicates macroscopic shape constraints in O i x i z i The rectangle is a projection of a plane. Intersect(·) represents the function that finds the intersection point of a vector with the geometric figure.

[0153] Calculate Δp′ i In O i y i The amount of directional adjustment, in O i y i In the direction, when Δp′ xy，i Exceeding the cluster shape constraint setting value d W upper and lower boundaries and If so, adjustments are needed. First, calculate Δp′. y，i Exceeding d W Distance values ​​between upper and lower bounds The expression is:

[0154]

[0155] Then, adjust the position amount. Converted into speed adjustment σ v，i .

[0156] Finally, relative coordinate system O i x i y i z i Δp′ below i Transform back to ground coordinate system O g x g y g z g The adjustment amount Δp i .

[0157] During reconstruction, the macroscopic shape of the cluster is defined, and the macroscopic shape parameter d is set. L d W and d HMapping to micro rule parameters d s , d c and d r , determining the neighborhood range, generating the cluster macro three-dimensional shape according to the established basic behavior rules of the unmanned aerial vehicle, and performing accuracy analysis on the generated cluster macro three-dimensional shape and the preset shape, and completing the shape reconstruction of the unmanned aerial vehicle according to the accuracy result, such as Figure 8 .

[0158] The parameter mapping relationship can be expressed as:

[0159]

[0160] f(·) has four independent variables d s , d c , d r and N, and the relationship of the four-variable multiple function is relatively complex. After a large number of repeated simulation experiments on the different relative relationships of the three parameters, it is found that when the rule action range intervals corresponding to d s , d c and d r are equal, the cluster can relatively quickly reach a stable state, that is:

[0161]

[0162] Based on the above formula, it can be simplified to the form of When the cluster size is determined, f(·) is a unary function. By setting multiple different values of d s , the corresponding is recorded and calculated to fit the expression of f(·).

[0163] Let the cluster size N = 20, d s = 5, 6,..., 40, d c = 10, 12,..., 80, d r = 15, 18,..., 120, a total of 36 groups of parameters, and each group of parameters is repeated 5 times to record the average distance of the cluster in three directions, as shown in Figure 9 It should be noted that this time the action of the macro shape constraint rule is cancelled, and the cluster only relies on the aggregation and dispersion rules to adjust the relative position, and the macro shape presented by the cluster is spontaneously formed and is not caused by the shape constraint set by humans. The average distances in the three directions are multiplied to obtain the three-dimensional volume, as shown in Figure 10The intuitive experience can be obtained that when the micro rule parameters are constant, each UAV individual maintains an approximate average relative distance with other friendly individuals in the neighborhood, so each UAV occupies an approximate volume in the three-dimensional space, and thus the three-dimensional shape volume of the swarm is linearly related to the swarm size, and the fitting of f(·) in the form of exponential function obtains the following formula.

[0164]

[0165] The values of the coefficients a, b, c, and d are shown in Table 1.

[0166] Table 1: Coefficients of the fitting function f(d s )

[0167] a b c d 0.21 0.05 9.83 -7405.12

[0168] The three-dimensional volume is mapped from the micro parameters, and according to the reconstruction process, the actual decision-making process is to calculate the micro parameters according to the three-dimensional volume. Therefore, the inverse function of the formula is needed to be calculated as shown in the following formula.

[0169]

[0170] According to the inverse function, the micro rule parameters can be calculated from the preset three-dimensional volume parameters and the swarm size, and then the shape transformation of the swarm is controlled.

[0171] Mapping relationship of the macro shape parameters to the set three-dimensional volume of the swarm The most intuitive form of V sp = d L d W d H . In theory, when two or three of the parameters d L , d W , and d H are transformed but the product, i.e., V sp , is constant, the corresponding micro rule parameters are also constant according to the formula and the inverse function formula. However, in the simulation study, the actual macro shape of the swarm does not always match the preset three-dimensional shape, and the actual shape volume is smaller than the preset shape volume, i.e.,

[0172] According to Figure 9When the cluster is not constrained by macro shape, the distances in the lateral, forward and longitudinal directions of the macro shape that the cluster presents spontaneously are approximately equal, i.e. the cluster presents a cubic shape. The cluster tends to transform into a shape with the largest three-dimensional volume. When the sum of the three sides of a cuboid is a constant value, only when the three sides are equal, the volume of the cuboid is the maximum value. Therefore, it is assumed that The expression is:

[0173]

[0174] The actual simulation test shows that, by using the mapping method of the inverse function formula and , the macro shape presented by the cluster can match the preset three-dimensional shape.

[0175] Therefore, the unmanned aerial vehicle cluster shape reconstruction method based on the parameter mapping mechanism has the advantages that the constant pressure treatment is performed on the brand-new cross-linked polyethylene sample to make it equivalent to the cross-linked polyethylene with pressure history, and the pressure resistance index of the cross-linked polyethylene with pressure history is obtained.

[0176] Finally, it should be noted that: the above examples are only used to illustrate the technical solutions of the present application but not to limit it, although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that: the technical solutions of the present application can still be modified or replaced by equivalents, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present application.

Claims

1. A method for reconstructing the shape of a UAV swarm based on a parameter mapping mechanism, characterized in that the steps include... include: S1. Establish a drone cluster model and a drone individual model. The drone cluster model includes drones and their neighborhood relationships, while the drone individual model includes a drone state model and a drone-friend transition model. S2. Establish basic behavioral rules for drones, including motion trend adjustment and dynamic position adjustment, which are used to adjust the drone's motion direction and relative position with respect to neighboring friendly drones, respectively. The dynamic position adjustment is used to maintain a suitable relative distance between individual UAVs and friendly UAVs in the vicinity. Position adjustment includes dispersion rules, aggregation rules, and shape constraint rules, all of which are within the UAV's... i relative coordinate system O i x i y i z i The following calculations are performed; The shape constraint rules include: First, the drone swarm is calculated based on the transformation model, showing the entire swarm in the relative coordinate system O. i x i y i z i The desired centroid is used to intervene in and control the overall flight altitude of the cluster; Secondly, the basic amount of position adjustment in three dimensions is Δp' i Decompose the data according to shape constraints, when Δp' i In O i x i z i The projection component Δp' of the plane xz,i Located in shape O i x i z i External Ω of the cross-sectional region of the plane xz At that time, Δp' i In O i x i z i In-plane and O i y i Adjust the direction; The Δp' i In O i x i z i In-plane and O i y i Adjustments to the direction include: In O i x i z i Adjustments within a plane are represented as: In the formula, Intersect(·) represents the function for finding the intersection point of a vector and a geometric figure, and Δp xz,i Indicates Δp' xz,i Intersection with the boundary of the cross-sectional region; In O i y i To adjust the direction, first calculate Δp' y,i Exceeding Ω xy Distance value of the boundary Represented as: In the formula, dist(·) represents Δp' y,i In O i y i Direction and cross-sectional region Ω xy The shortest distance, Δp' y,i Indicates the position adjustment amount Δp' i In O i y i Components in direction; Adjust position amount Converted into speed adjustment σ v,i The drones move forward or backward by accelerating or decelerating, with forward or backward movement relative to the cluster as a whole. Adjusting their relative speed allows the drones to move towards the head or tail of the cluster, with the speed adjustment amount σ. v,i The expression is: In the formula, λ v >0 represents a constant coefficient, and consttrain(x,a,b) is a cutoff function used to restrict x to the interval [a,b]. and These are the minimum and maximum speed adjustment amounts, respectively. Finally, relative coordinate system O i x i y i z i Δp' below i Transform back to ground coordinate system O g x g y g z g The adjustment amount Δp i The conversion expression is: In the formula, R i -1 Let R be the rotation matrix. i The inverse matrix, Δp z,i Indicates the position adjustment amount Δp i In O g z g The component in the direction, Δp' z,i Indicates the position adjustment amount Δp' i In O i z i Components in direction; S3. Set the macroscopic shape of the cluster. Based on the UAV cluster model and the UAV individual model, map the macroscopic shape parameters to the microscopic rule parameters, determine the neighborhood range, and generate the macroscopic three-dimensional shape of the cluster according to the established basic behavior rules of the UAV. Then, perform an accuracy analysis between the generated macroscopic three-dimensional shape of the cluster and the preset shape, and complete the UAV shape reconstruction based on the accuracy results.

2. The method for reconstructing the shape of a UAV swarm based on a parameter mapping mechanism according to claim 1, characterized in that, Step S1, establishing the drone swarm model, includes: Let the cluster size be N, and U = {U1, U2, ..., U...} N } represents a swarm of drones, U i Let U represent the i-th drone in the cluster. The neighborhood relationship of a drone is determined based on the drone rule's effective range parameter. i Centered on the radius d, the neighborhood relationship includes the radius d. r C, a set of neighboring friendly drones within the range, together with other friendly drones. i Distance d s The set of friendly drones C within the range dis,i and distance d c ~d r The set of friendly drones C within the range coh,i , represented as: C i ={U k ∈U|||p i -p k ||≤d r }; C dis,i ={U k ∈C i |||p i -p k ||≤d s }; C coh,i ={U k ∈C i |d c ≤||p i -p k ||≤d r }; Where, p i and p k U represents the unmanned aerial vehicle (UAV) i and U k The three-dimensional position vector.

3. The method for reconstructing the shape of a UAV swarm based on a parameter mapping mechanism according to claim 2, characterized in that, Step S1, which involves creating a single UAV model, includes: Based on ground coordinate system O g x g y g z g U-type drone i Position p i =[p x,i ,p y,i ,p z,i Speed ​​v i =[v x,i ,v y,i ,v z,i and the body coordinate system Ox b y b z b U-type drone i postureΘ i =[θ i ,ψ i ,φ i Establish UAVs i The state model is represented as: S i =[p i ,v i ,I i ]=[p x,i ,p y,i ,p z,i ,v x,i ,v y,i ,v z,i ,i i ,ψ i ,f i ]; In the ground coordinate system, O g x g Pointing due east, O g y g Pointing due north, θ i ,ψ i ,φ i U represents the unmanned aerial vehicle (UAV) i Pitch angle, yaw angle, and roll angle; Based on ground coordinate system O g x g y g z g and U i relative coordinate system O i x i y i z i Establish a coordinate transformation model for the UAV and its friendly aircraft. i Located at the origin O i O i z i Axis and O g z g Axis coincidence, O i y i Axis and velocity consistency adjustment vector Δv ali,i Coincidence, O i x i Axis and O i y i z i If the planes are perpendicular and follow the right-hand rule, define the vector Δv. ali,i With O i y i The included angle of the axis is ψ ali,i Then the rotation matrix R i Defined as: Coordinate system transformation only occurs on the horizontal plane O. g x g y g The coordinate transformation process is performed internally and is represented as follows: Where, p xy,k Indicates friendly machine U k In O g x g y g Coordinates in the plane U k After coordinate system transformation, U i Coordinates in a relative coordinate system, x i Axial components U k Relative to U i Lateral orientation and distance, y i Axial components U represents the direction of overall movement of the cluster. k Relative to U i The forward and backward orientation and distance, express In O i x i y i In-plane components, express In O i z i Components in direction, p z,k p k In O g z g The portion on top.

4. The method for reconstructing the shape of a UAV swarm based on a parameter mapping mechanism according to claim 3, characterized in that: In step S2, the motion trend adjustment is used to maintain a relatively consistent motion trend between the individual and friendly individuals in the neighborhood and move toward the target waypoint, including speed consistency adjustment and mission heading adjustment.

5. The method for reconstructing the shape of a UAV swarm based on a parameter mapping mechanism according to claim 4, characterized in that, The speed consistency adjustment and mission heading adjustment include: Speed ​​consistency adjustment indicates the current direction of movement of the drone swarm, represented as: Among them, v xy,k Indicates friendly U machines within the neighboring region k speed v k In O g x g y g Velocity components within a plane; The drone swarm has the same target heading p t UAV i The mission heading is represented as: Where, p t,xy and p xy,i These represent the target waypoints p. t and U i Position p i In O g x g y g In-plane components; According to U drone i The mission heading and the current direction of the drone swarm, U-shaped drones. i Motion trend adjustment amount Δv i Represented as: stω a +oh m =1.0≤ω a ,oh m ≤1 Where, ω a and ω m These represent the weight parameters for the speed consistency rule and the mission heading rule, respectively.

6. The method for reconstructing the shape of a UAV swarm based on a parameter mapping mechanism according to claim 5, characterized in that: The dispersion and aggregation rules are used to calculate the UAV U. i The position adjustment amount required for friendly drones to move away from or closer to each other within different distance ranges in the neighborhood is expressed by the following rule expression: In the formula, Δp dis,i This represents the position adjustment amount calculated by spreading out the data. U k After coordinate system transformation, U i Coordinates in a relative coordinate system; The aggregation rule expression is: In the formula, Δp coh,i This represents the position adjustment amount obtained from the aggregation calculation; The basic quantity of position adjustment Δp' is obtained based on the divergence and aggregation rules. i The expression is: Δp' i =Δp dis,i +Δp coh,i 。 7. The method for reconstructing the shape of a UAV swarm based on a parameter mapping mechanism according to claim 6, characterized in that, The parameter mapping relationship in step S3 is expressed as follows: In the formula, This represents the set of macroscopic shape parameters; when it is a cuboid, d L d W and d H These are the length, width, and height of a cuboid; when it is a sphere... r represents the radius of the sphere; V sp The macroscopic shape parameter defines the expected three-dimensional volume of the cluster. The function f(·) represents the macroscopic three-dimensional volume actually presented according to the microscopic regularity parameters, and is the mapping relationship from the microscopic regularity parameters to the actual three-dimensional volume. This represents the mapping relationship between macroscopic shape parameters and the defined three-dimensional volume of the cluster.

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