Unmanned aerial vehicle cluster shape reconstruction method based on parameter mapping mechanism

Abstract

The invention discloses an unmanned aerial vehicle cluster shape reconstruction method based on a parameter mapping mechanism, and belongs to the technical field of unmanned aerial vehicle cluster autonomous decision control. Establishing basic behavior rules of the unmanned aerial vehicle, wherein the basic behavior rules comprise motion trend adjustment and dynamic position adjustment; setting a cluster macroscopic shape, mapping macroscopic shape parameters to microscopic rule parameters according to the established unmanned aerial vehicle cluster model and the unmanned aerial vehicle monomer model, determining a neighborhood range, generating a cluster macroscopic three-dimensional shape according to the established unmanned aerial vehicle basic behavior rule, and performing accuracy analysis on the generated cluster macroscopic three-dimensional shape and a preset shape. And completing shape reconstruction of the unmanned aerial vehicle according to an accuracy result. By the adoption of the method, an operator can directly modify macroscopic shape parameters to visually adjust the relative distance between the unmanned aerial vehicles of the unmanned aerial vehicle cluster, and therefore the preset macroscopic shape is formed in the three-dimensional space.

Description

Technical Field

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

[0002] With the development of unmanned system technology, drone swarms have been used more and more widely in various fields. At the same time, the intelligence of drone 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. The autonomous shape transformation of the swarm has many applications in the military. On the one hand, large-scale swarms of low-cost, miniaturized drones can confuse the enemy's radar and detection systems by constantly changing their shapes, increase the difficulty of enemy identification, and achieve the combat effect of interference and deception; on the other hand, in complex urban environments, the swarm can use shape transformation to quickly shuttle between buildings, and can effectively maintain concealment while quickly maneuvering.

[0003] At present, there are relatively few studies on this type of shape transformation problem, and researchers pay more attention to the formation reconstruction problem of multiple UAVs. According to different research points in the formation reconstruction process, the problem can usually be expressed as a combinatorial optimization problem with complex constraints and tight coupling between variables, and then different optimization strategies or a combination of multiple strategies are used to solve the optimal or approximate optimal solution. In the paper "Hybrid Particle Swarm Optimization and Genetic Algorithm for Multi-UAV Formation Reconfiguration", Duan Haibin and others proposed a combined 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 process of converting five aircraft from random states to V-shaped formations in three-dimensional space, numerical simulation was used to verify the superiority of this method over the particle swarm optimization method alone.

[0004] Formation reconfiguration is the process of multiple drones transforming from one fixed formation to another. Therefore, the research on formation reconfiguration is only applicable to a fixed number of drone clusters, and it is difficult to cope with the situation where the number of drones changes dynamically. For example, if some drones fail and are damaged or leave the cluster during cluster flight, the cluster can no longer maintain the preset formation. However, the behavior rule-based method generally has no limit on the number of drones.

[0005] In the optimization process of formation reconstruction problems or the optimization calculation of multiple behavior rule parameters, as the number of drones increases, the resource consumption of optimization iterative calculations usually increases exponentially. The cluster shape transformation only needs to specify the geometric shape that the cluster needs to maintain in three-dimensional space, which is usually specified by the shape parameters of the geometric body, without the need to preset the relative position of each drone before and after the formation transformation. Summary of the invention

[0006] The purpose of the present invention is to provide a UAV cluster shape reconstruction method based on parameter mapping mechanism to achieve macroscopic shape reconstruction of UAV cluster in three-dimensional space.

[0007] To achieve the above object, the present invention provides a method for reconstructing the shape of a drone cluster based on a parameter mapping mechanism, the steps comprising:

[0008] S1. Establish a drone cluster model and a drone single model. The drone cluster model includes the relationship between drones and their neighborhoods, and the drone single model includes a drone state model and a drone-friendly aircraft conversion model.

[0009] S2. Establish basic behavior rules for drones, including motion trend adjustment and dynamic position adjustment, which are used to adjust the motion direction and relative position of drones relative to neighboring friendly aircraft respectively;

[0010] S3. Set the macroscopic shape of the cluster, map the macroscopic shape parameters to the microscopic rule parameters according to the UAV cluster model and the UAV single model, determine the neighborhood range, and generate the macroscopic three-dimensional shape of the cluster according to the established basic behavior rules of the UAV. Perform accuracy analysis on the generated cluster macroscopic three-dimensional shape and the preset shape, and complete the UAV shape reconstruction according to the accuracy results.

[0011] Preferably, establishing the drone cluster model in step S1 includes:

[0012] Assume that the cluster size is N, U = {U1, U2, ..., U N} represents the drone cluster set, U i represents the i-th drone in the cluster. The neighborhood relationship of the drone is determined based on the drone rule range parameter. i The neighborhood relationship includes the radius d r The neighboring friendly drone set C formed by other friendly drones in the range i , distance d s The subset of friendly drones C in the range dis，i and distance d c ~d r The subset of friendly drones C in the range coh，i , expressed as:

[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] Among them, p i and p k Respectively represent drone U i and U k The three-dimensional position vector of .

[0017] Preferably, establishing a single drone model in step S1 includes:

[0018] Based on the ground coordinate system O g x g y g z g Get off the drone i The 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 Get off the drone i The posture of Θ i =[θ i , ψ i ,φ i Build UAV i The state model is expressed as:

[0019] 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 ];

[0020] Among them, O in the ground coordinate system g x g Pointing due east, O g y g Pointing to due north, θ i , ψ i ,φ i Respectively represent drone U i Pitch, yaw and roll angles;

[0021] Based on the ground coordinate system O g x g y g z g and U i The relative coordinate system O i x i y i z i Establish the coordinate transformation model of UAV and friendly aircraft, U 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 speed consistency adjustment vector Δv ali，i Coincidence, O i x i Axis and O i y i z i The planes are perpendicular and follow the right-hand rule, defining the vector Δv ali，i With O i y i The angle between the axes is ψ ali，i , then the rotation matrix R i Defined as:

[0022]

[0023] Coordinate transformation is only in the horizontal plane O g x g y g The coordinate transformation process is expressed as:

[0024]

[0025] Among them, p xy，k Indicates friendly aircraft U k In O g x g y g Coordinates in the plane, Indicates U k After the coordinate system transformation, U i Coordinates in the relative coordinate system, x i Axis Component Indicates U k Relative to U i The lateral position and distance, y i Axis Component Indicates the overall movement direction of the cluster U k Relative to U i The forward and backward directions and distances, express In O i x i y i The components in the plane, express In O i z i The component in the direction, p z，k Indicates p k In O g z g The amount on.

[0026] Preferably, the motion trend adjustment in step S2 is used for the individual to maintain a relatively consistent motion trend with friendly individuals in the neighborhood and move toward the target waypoint, including speed consistency adjustment and mission heading adjustment.

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

[0028] Speed ​​consistency adjustment indicates the current direction of the drone cluster, expressed as:

[0029]

[0030] Among them, v xy，k represents the friendly machine U in the neighborhood k The speed v k In O g x g y g Velocity components in the plane;

[0031] The drone cluster has the same target heading p t , UAV i The mission heading is expressed as:

[0032]

[0033] Among them, p t，xy and p xy，i Represent the target waypoints p t and U i The position p i In O g x g y g Components in the plane;

[0034] According to UAV i The mission heading and the current direction of the UAV cluster, UAV U i The movement trend adjustment Δv i It is expressed as:

[0035]

[0036] Among them, ω a and ω m They represent the weight parameters of the speed consistency rule and the task heading rule respectively.

[0037] Preferably, the dynamic position adjustment in step S2 is used to maintain an appropriate relative distance between the individual drone and the friendly drones in the neighborhood. The position adjustment includes dispersion rules, aggregation rules and shape constraint rules. The rules are all in U i The relative coordinate system O i x i y i z i Calculate below.

[0038] Preferably, the dispersion and aggregation rules are used to calculate the UAV U i The position adjustment amount of friendly drones that need to be moved away or closer to different distance ranges in the neighborhood is expressed as follows:

[0039]

[0040] In the formula, Δp dis，i Represents the position adjustment amount obtained by scattered calculation, Indicates U k After the coordinate system transformation, U i Coordinates in relative coordinate system;

[0041] The aggregation rule expression is:

[0042]

[0043] In the formula, Δp coh，i Indicates the position adjustment amount obtained by aggregation calculation;

[0044] Based on the dispersion and aggregation rules, the position adjustment base Δp′ is obtained i , the expression is:

[0045] Δp i =Δp dis，i +Δp coh，i .

[0046] Preferably, the shape constraint rules include:

[0047] First, the UAV cluster is calculated according to the conversion model to calculate the overall coordinate system O i x i y i z i The desired centroid under the swarm is used to intervene and control the flight altitude of the entire swarm.

[0048] Next, adjust the base amount Δp′ for the three-dimensional position i Decompose, according to the shape constraint, when Δp′ i In O i x i z i The projected component of the plane Δp′ xz，i Located in shape O i x i z i The cross-sectional area of ​​the plane is external Ω xz When Δp′ i In O i x i z i In-plane and O i y i Adjust the direction;

[0049] Finally, the relative coordinate system O i x i y i z i Δp′ i Convert back to the ground coordinate system O again g x g y g z g Adjustment amount Δp i , the conversion expression is:

[0050]

[0051] In the formula, R i -1 is the rotation matrix R i The inverse matrix of z，i Indicates the position adjustment amount Δp i In O g z gComponent in the direction, Δp′ z，i Indicates the position adjustment amount Δp′ i In O i z i Directional weight.

[0052] Preferably, the Δp′ i In O i x i z i In-plane and O i y i Adjustments in direction include:

[0053] In O i x i z i The adjustment in the plane is expressed as:

[0054]

[0055] In the formula, Intersect(·) represents the function of finding the intersection of a vector and a geometric figure, Δp xz，i Denotes Δp′ xz，i The intersection with the boundary of the cross-section area;

[0056] In O i y i To adjust the direction, first calculate Δp′ y，i Exceed Ω xy The distance value of the boundary It is expressed as:

[0057]

[0058] Where dist(·) represents Δp′ y，i In O i y i Direction and cross-sectional area Ω xy The shortest distance, Δp′ y，i Indicates the position adjustment amount Δp′ i In O i y i Directional weight;

[0059] Adjust the position Converted into speed adjustment σ v，i , moving forward or backward is achieved by accelerating or decelerating, where the forward or backward movement is relative to the entire cluster. By adjusting the relative speed, the drone moves toward the head or tail of the cluster. The speed adjustment amount σ v，i The expression is:

[0060]

[0061] In the formula, λv >0 is a constant coefficient, and constrain(x, a, b) is a truncation function used to limit x to the interval [a, b]. and They are the minimum and maximum values ​​of the speed adjustment respectively.

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

[0063]

[0064] In the formula, Represents a set of macroscopic shape parameters. 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 macroscopic shape parameter defining the expected 3D volume of the cluster, represents the macroscopic three-dimensional volume actually presented according to the microscopic rule parameters, and the function f(·) is the mapping relationship from the microscopic rule parameters to the actual three-dimensional volume. It is the mapping relationship from the macroscopic shape parameters to the set three-dimensional volume of the cluster.

[0065] Therefore, the present invention adopts the above-mentioned UAV cluster shape reconstruction method based on parameter mapping mechanism, which has the following beneficial effects:

[0066] (1) The method of the present invention is based on behavioral rules, and different rules are divided into two categories: motion trend adjustment and dynamic position adjustment, and the decision results of the UAV are generated by combining them. Compared with the common method of unifying multiple rules by weight parameters, the number of parameters is greatly reduced, and the parameter optimization process is omitted, thereby reducing the real-time calculation amount of the decision-making process.

[0067] (2) Using the parameter mapping mechanism from macroscopic shape parameters to microscopic rule parameters, the three-dimensional volume of the cluster is affected by the rule scope parameters. By mapping the preset macroscopic shape parameters to the rule scope parameters, the cluster can be indirectly controlled to spontaneously reconstruct into a preset three-dimensional shape. The parameter mapping mechanism is insensitive to the number of drones and can be used for shape reconstruction of different cluster sizes, with strong scalability.

[0068] (3) The rule-based cluster decision method used in the present invention is not limited by the size of the cluster. The increase in the size of the cluster will not significantly increase the computational complexity of the decision-making process. Therefore, it can be expanded and applied to clusters of dozens or even hundreds of sizes.

[0069] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 is a reconstruction flow chart of an embodiment of the present invention;

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

[0072] Figure 3 This is a diagram showing the scope of action of basic behavior rules according to an embodiment of the present invention;

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

[0074] Figure 5 A schematic diagram of coordinate conversion according to an embodiment of the present invention;

[0075] Figure 6 The macroscopic shape of the embodiment of the present invention is shown in FIG. i x i z i Shape constraint graph in the plane;

[0076] Figure 7 The macroscopic shape of the embodiment of the present invention is shown in FIG. i y i Shape constraint graph in direction;

[0077] Figure 8 It is a flow chart of the effect of macroscopic to microscopic parameters of a rectangular parallelepiped in an embodiment of the present invention;

[0078] Fig. 9 It is an average distance diagram of clusters in three directions under multiple sets of parameters of an embodiment of the present invention;

[0079] Fig.10 is the embodiment of the present invention. s With three-dimensional volume The relationship and fitting curve diagram. DETAILED DESCRIPTION

[0080] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. The components of the embodiments of the present invention generally described and shown in the drawings herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0081] Example

[0082] Reference Figure 1 The present invention provides a method for reconstructing the shape of a drone cluster based on a parameter mapping mechanism. The cluster shape preservation and transformation involved in the reconstruction means that during the flight of the drone cluster in three-dimensional space, the cluster as a whole presents a relatively obvious spatial geometric structure at the macro level. The method of the present invention is used for the reconstruction of cuboids and spheres, such as Figure 2 As shown, Figure 2 (a) middle d L ,d W and d H are the length, width and height of the cuboid, i.e. the distance span of the cluster in the lateral, forward and longitudinal directions; Figure 2 (b) where r is the radius of the sphere. L ,d W ,d H and r can be used as macroscopic shape parameters of the cluster. Different parameter combinations can make the cluster present cuboids or spheres of different geometric sizes.

[0083] The method of the present invention specifically comprises the following steps:

[0084] S1. Establish UAV cluster model and UAV single model.

[0085] The drone cluster model includes the relationship between drones and neighborhoods. Building a drone cluster model includes:

[0086] Assume that the cluster size is N, U = {U1, U2, ..., U N} represents the drone cluster set, U i represents the i-th drone in the cluster. The neighborhood relationship of the drone is determined based on the drone rule scope parameter. The drone rule scope is as follows: Figure 3 As shown, the UAV i The neighborhood relationship includes the radius d rThe neighboring friendly drone set C formed by other friendly drones in the range i , distance d s The subset of friendly drones C in the range dis，i and distance d c ~d r The subset of friendly drones C in the range coh，i , expressed 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] Among them, p i and p k Respectively represent drone U i and U k The three-dimensional position vector of .

[0091] The single UAV model includes the UAV state model and the UAV-friendly coordinate conversion model. i The motion state of 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 Point to due north) i The 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-order 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 Get off the drone i The posture of Θ i =[θ i , ψ i ,φ i ], where θ i , ψ i ,φ i UAV i Pitch, yaw and roll angles.

[0094] UAV i 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] Status Model S i That is, the interactive information between individual drones in the cluster serves as input information for the operation process of the method proposed in the present invention.

[0097] In the rule calculation of dynamic position adjustment, the UAV U i Neighborhood C i Friendly aircraft position within p k Need to be based on the ground coordinate system O g x g y g z g To U i The relative coordinate system O i x i y i z i The relative position of Therefore, it is necessary to establish a coordinate transformation model. iLocated at the origin O i , O i z i Axis and O g z g Axis coincidence, O i y i Axis and speed consistency adjustment vector Δv ali，i Coincidence, O i x i Axis and O i y i z i The planes are perpendicular and follow the right-hand rule, such as Figure 5 shown.

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

[0099]

[0100] Coordinate transformation is only in the horizontal plane O g x g y g In-house, such as Figure 5 As shown in (a) and (b), the friendly aircraft U k The horizontal coordinate p xy，k , after the coordinate system is converted to U i Position in relative coordinate system The coordinate transformation process expression is:

[0101]

[0102] Among them, x i Axis Component Indicates U k Relative to U i The lateral position and distance, y i Axis Component Indicates the overall movement direction of the cluster U k Relative to U i The forward and backward directions and distances, express In O i x i y i The components in the plane, express In O i z i The component in the direction, p z，k Indicates p k In Og z g The amount on.

[0103] S2. Establish basic behavior rules for drones, including motion trend adjustment and dynamic position adjustment, which are used to adjust the motion direction and relative position of drones relative to neighboring friendly aircraft.

[0104] Motion trend adjustment is used to enable an individual to maintain a relatively consistent motion trend with friendly individuals in the neighborhood and move toward the target waypoint, including speed consistency adjustment and mission heading adjustment.

[0105] Speed ​​consistency adjustment indicates the current direction of the drone cluster, expressed as:

[0106]

[0107] Among them, v xy，k represents the friendly machine U in the neighborhood k The speed v k In O g x g y g Velocity components in the plane.

[0108] The drone cluster has the same target heading p t , UAV i The mission heading is expressed as:

[0109]

[0110] Among them, p t，xy and p xy，i Represent the target waypoints p t and U i The position p i In O g x g y g Components in the plane.

[0111] According to UAV i The mission heading and the current direction of the UAV cluster, UAV U i The movement trend adjustment Δv i It is expressed as:

[0112]

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

[0114] It should be noted that the adjustment of movement trend is only in O g xg y g plane, because the use of the g When the three-dimensional speed in the direction is calculated regularly, the height adjustment amount will conflict with the height adjustment amount of the dynamic position adjustment rule, resulting in instability in the overall movement of the cluster.

[0115] Dynamic position adjustment is used to keep the appropriate relative distance between individual drones and friendly drones in the neighborhood. Position adjustment includes dispersion rules, aggregation rules and shape constraint rules. The rules are all in U i The relative coordinate system O i x i y i z i Calculate below.

[0116] The dispersion and aggregation rules are used to calculate the UAV U i The position adjustment amount of friendly drones in different distance ranges in the neighborhood needs to be moved away or approached to maintain a suitable distance from friendly drones. The dispersion rule expression is:

[0117]

[0118] In the formula, Δp dis，i Represents the position adjustment amount obtained by scattered calculation, Indicates U k After the coordinate system transformation, U i Coordinates in relative coordinate system;

[0119] The aggregation rule expression is:

[0120]

[0121] In the formula, Δp coh，i Indicates the position adjustment amount obtained by aggregation calculation;

[0122] Based on the dispersion and aggregation rules, the position adjustment base Δp′ is obtained i , the expression is:

[0123] Δp′ i =Δp dis，i +Δp coh，i .

[0124] UAV i By adjusting the relative position within the cluster, the average distance between itself and friendly machines in the neighborhood is d s to d c Within the range, a relatively stable position relationship is reached. At this time, the cluster can spontaneously form a stable specific macroscopic shape, along the cluster's forward direction, that is, O i y i Axis observation, cluster in Oi x i z i The projection on a plane resembles a square or a circle.

[0125] Shape constraint rules include:

[0126] First, the UAV cluster is calculated according to the conversion model to calculate the overall coordinate system O i x i y i z i The expected centroid under the condition of It can be expressed as:

[0127]

[0128] In the formula, h * For clustering, the ground coordinate system O g x g y g z g The desired height to be maintained, Indicates that the centroid is at O i x i y i The weight of the plane, Indicates that the centroid is at O i z i By setting the parameter h * Keeping the centroid of the cluster near a fixed altitude can avoid unstable flight status caused by the constant changes in the average altitude of the cluster as a whole, and facilitate human intervention and control of the flight altitude of the cluster as a whole.

[0129] Next, adjust the base amount Δp′ for the three-dimensional position i Decompose, according to the shape constraint, when Δp′ i In O i x i z i The projected component of the plane Δp′ xz，i Located in shape O i x i z i The cross-sectional area of ​​the plane is external Ω xz When Figure 6 The area enclosed by the red dashed lines in (a) and (b), Δp′ i Need to be in O i x i z i In-plane and O i y i Adjust the direction.

[0130] In Oi x i z i The adjustment in the plane is expressed as:

[0131]

[0132] In the formula, Intersect(·) represents the function of finding the intersection of a vector and a geometric figure, Δp xz，i Denotes Δp′ xz，i The intersection point with the boundary of the cross-section area is used as the position adjustment amount after shape constraint.

[0133] In O i y i Adjust the direction, such as Figure 7 As shown. First calculate Δp′ y，i Exceed Ω xy The distance value of the boundary It is expressed as:

[0134]

[0135] Where dist(·) represents Δp′ y，i In O i y i Direction and cross-sectional area Ω xy The shortest distance, Δp′ y，i Indicates the position adjustment amount Δp′ i In O i y i Directional weight;

[0136] Then, adjust the position by Converted into speed adjustment σ v，i In O i x i z i The drone in the plane can move to the desired position by adjusting its attitude, but the drone’s forward direction O i y i In reality, the drone cannot adjust its position relative to other friendly aircraft by its attitude. Therefore, the position adjustment amount Converted into speed adjustment σ v，i , by accelerating or decelerating to achieve forward or backward movement. The forward or backward movement is relative to the entire cluster. By adjusting the relative speed, the drone moves toward the head or tail of the cluster. In fact, in the ground coordinate system, each drone always flies forward.

[0137] Speed ​​adjustment σ v，i The expression is:

[0138]

[0139] In the formula, λ v >0 is a constant coefficient, and constrain(x, a, b) is a truncation function used to limit x to the interval [a, b]. and They are the minimum and maximum values ​​of the speed adjustment. It should be noted that from the perspective of the control system, 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 flight altitude of the drone. Frequent changes in speed will lead to unstable flight, increase energy consumption, and reduce the endurance of the drone.

[0140] Finally, due to the position adjustment Δp′ calculated by the macro shape constraint rule i Cannot be used directly to generate waypoints. The relative coordinate system O i x i y i z i Δp′ i Convert back to the ground coordinate system O again g x g y g z g Adjustment amount Δp i , the conversion expression is:

[0141]

[0142] In the formula, R i -1 is the rotation matrix R i The inverse matrix of z，i Indicates the position adjustment amount Δp i In O g z g Component in the direction, Δp′ z，i Indicates the position adjustment amount Δp′ i In O i z i Directional weight.

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

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

[0145]

[0146] In the formula, Represents a set of macroscopic shape parameters. 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 macroscopic shape parameter defining the expected 3D volume of the cluster, represents the macroscopic three-dimensional volume actually presented according to the microscopic rule parameters, and the function f(·) is the mapping relationship from the microscopic rule parameters to the actual three-dimensional volume. It is the mapping relationship from the macroscopic shape parameters to the set three-dimensional volume of the cluster.

[0147] Take the reconstruction of a cuboid as an example. The length, width and height of the cuboid are d L ,d W and d H , represents the distance span of the cluster in the lateral, forward and longitudinal directions.

[0148] First, the UAV cluster model and the UAV single model are established. Then the basic behavior rules of the UAV are established, including motion trend adjustment (speed consistency and mission heading adjustment) and dynamic position adjustment (aggregation rules, dispersion rules and shape constraint rules). In the shape constraint rules, d L ,d W ,d H Represents the cluster in the lateral direction (O i x i ), forward (O i y i ) and longitudinal (O i z i ). The cuboid shape constraint rules specifically include:

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

[0150] Secondly, the three-dimensional position quantity is decomposed, and O is calculated first. i x i z i The amount of adjustment in the plane, according to the shape constraint d L and d H , if Δp′ xz，i is outside the rectangle, then calculate the vector Δp′ xz，i The intersection point with the rectangular boundary is used as the position adjustment amount Δp after the shape constraint. xz，i , expressed as:

[0151]

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

[0153] Calculation of Δp′ i In O i y i The adjustment amount in the direction of O i y i direction, when Δp′ xy，i Exceeding the cluster shape constraint setting value d W The upper and lower bounds of and When , adjustment is required. First, calculate Δp′ y，i Beyond d W The distance between the upper and lower bounds The expression is:

[0154]

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

[0156] Finally, the relative coordinate system O i x i y i z i Δp′ i Convert back to the ground coordinate system O again g x g y g z g Adjustment amount Δp i .

[0157] When reconstructing, set the cluster macro shape and change the macro shape parameter d L ,d W and d HTowards the microscopic rule parameter d s ,d c and d r Mapping is performed to determine the neighborhood range. According to the established basic behavior rules of the UAV, the macroscopic three-dimensional shape of the cluster is generated, and the accuracy of the generated macroscopic three-dimensional shape of the cluster is analyzed with the preset shape. According to the accuracy results, the shape reconstruction of the UAV is completed, such as Figure 8 shown.

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

[0159]

[0160] f(·) has d s ,d c ,d r The relationship between the four-variable multi-function and N is relatively complex. After a large number of repeated simulation experiments on the relative relationship between the three parameters, it is found that d s ,d c and d r When the corresponding rule scope intervals are equal, the cluster can reach a stable state relatively quickly, that is:

[0161]

[0162] Based on the above formula, Can be simplified to In the form of, when the cluster size is determined, f(·) is a univariate function. By setting multiple different d s Value, simulation record and calculate the corresponding To fit the representation of f(·).

[0163] Let the cluster size N = 20, d s =5, 6, ..., 40, then d c =10, 12, ..., 80, d r =15, 18, ..., 120, a total of 36 groups of parameters, each group of parameters repeated simulation 5 times to record the average distance of the cluster in three directions, such as Fig. 9 It should be noted that the role of macroscopic shape constraint rules is cancelled this time. The clusters only rely on the aggregation and dispersion rules to adjust their relative positions. The macroscopic shape presented by the clusters is formed spontaneously and is not subject to artificial shape constraints. The three-dimensional volume is obtained by multiplying the average distances in the three directions, as shown in Fig.10As shown in the figure. According to intuitive experience, when the micro-rule parameters remain unchanged, each drone will maintain an approximate average relative distance with other friendly aircraft in the neighborhood, so the volume occupied by each drone in the three-dimensional space is also approximate. Therefore, the three-dimensional shape volume of the cluster is linearly related to the cluster size. The exponential function is used to fit f(·) to obtain the following formula.

[0164]

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

[0166] Table 1 Fitting function f(d s ) coefficient value

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

[0168] The microscopic parameters are mapped to the three-dimensional volume. According to the reconstruction process, the actual decision process is to calculate the microscopic parameters based on the three-dimensional volume. Therefore, the formula Find the inverse function As shown in the following formula.

[0169]

[0170] According to the inverse function, the microscopic rule parameters can be calculated from the preset three-dimensional volume parameters and cluster size, thereby controlling the shape transformation of the cluster.

[0171] Mapping relationship between macroscopic shape parameters and set cluster 3D volume The most intuitive form is V sp =d L d W d H Theoretically, when d L d W and d H Parameters 2 or 3 of which are transformed but the product is V sp When unchanged, according to And the inverse function formula, the corresponding micro-rule parameters remain unchanged. However, in simulation research, the macroscopic shape of the actual cluster does not always match the preset three-dimensional shape, and the actual shape volume is smaller than the preset shape volume, that is,

[0172] according to Fig. 9, when there is no macroscopic shape constraint, the distances of the cluster in the lateral, forward and longitudinal directions are approximately equal, that is, it presents a cube shape. The cluster tends to transform into a shape with the largest three-dimensional volume. When the sum of the three sides of the cuboid is a constant, the volume of the cuboid is the maximum only when the three sides are equal. Therefore, assuming The expression is:

[0173]

[0174] Actual simulation tests show that the inverse function formula and The macroscopic shape of the cluster can match the preset three-dimensional shape.

[0175] Therefore, the present invention adopts the above-mentioned drone cluster shape reconstruction method based on parameter mapping mechanism, and equates the new cross-linked polyethylene sample with the cross-linked polyethylene with a pressurization history by subjecting it to constant pressurization treatment, so as to obtain the pressure resistance index of the cross-linked polyethylene with a pressurization history.

[0176] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for reconstructing the shape of a drone cluster based on a parameter mapping mechanism, characterized in that the steps include: S1. Establish a drone cluster model and a drone single model. The drone cluster model includes the relationship between drones and their neighborhoods, and the drone single model includes a drone state model and a drone-friendly aircraft conversion model. S2. Establish basic behavior rules for drones, including motion trend adjustment and dynamic position adjustment, which are used to adjust the motion direction and relative position of drones relative to neighboring friendly aircraft respectively; S3. Set the macroscopic shape of the cluster, map the macroscopic shape parameters to the microscopic rule parameters according to the UAV cluster model and the UAV single model, determine the neighborhood range, and generate the macroscopic three-dimensional shape of the cluster according to the established basic behavior rules of the UAV. Perform accuracy analysis on the generated cluster macroscopic three-dimensional shape and the preset shape, and complete the UAV shape reconstruction according to the accuracy results.

2. According to the parameter mapping mechanism-based UAV cluster shape reconstruction method of claim 1, it is characterized in that: The establishment of the drone cluster model in step S1 includes: Assume that the cluster size is N, U = {U1, U2, ..., U N } represents the drone cluster set, U i represents the i-th drone in the cluster. The neighborhood relationship of the drone is determined based on the drone rule range parameter. i The neighborhood relationship includes the radius d r The neighboring friendly drone set C formed by other friendly drones in the range i , distance d s A subset of friendly drones C within the range dis,i and distance d c ~d r The subset of friendly drones C in the range coh,i , expressed 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 }; Among them, p i and p k Respectively represent drone U i and U k The three-dimensional position vector of .

3. The method for reconstructing the shape of a drone cluster based on a parameter mapping mechanism according to claim 2 is characterized in that: The establishment of the drone monomer model in step S1 includes: Based on the ground coordinate system O g x g y g z g Get off the drone i The 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 Get off the drone i The posture of Θ i =[θ i ,ψ i ,φ i Build UAV i The state model is expressed 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 ]; Among them, O in the ground coordinate system g x g Pointing due east, O g y g Pointing to due north, θ i ,ψ i ,φ i Respectively represent drone U i Pitch, yaw and roll angles; Based on the ground coordinate system O g x g y g z g and U i The relative coordinate system O i x i y i z i Establish the coordinate transformation model of UAV and friendly aircraft, U 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 speed consistency adjustment vector Δv ali,i Coincidence, O i x i Axis and O i y i z i The planes are perpendicular and follow the right-hand rule, defining the vector Δv ali,i With O i y i The angle between the axes is ψ ali,i , then the rotation matrix R i Defined as: Coordinate transformation is only in the horizontal plane O g x g y g The coordinate transformation process is expressed as: Among them, p xy,k Indicates friendly aircraft U k In O g x g y g Coordinates in the plane, Indicates U k After the coordinate system transformation, U i Coordinates in the relative coordinate system, x i Axis Component Indicates U k Relative to U i The lateral position and distance, y i Axis Component Indicates the overall movement direction of the cluster U k Relative to U i The forward and backward directions and distances, express In O i x i y i The components in the plane, express In O i z i The component in the direction, p z,k Indicates p k In O g z g The amount on.

4. The method for reconstructing the shape of a drone cluster based on a parameter mapping mechanism according to claim 3 is characterized in that: The motion trend adjustment in step S2 is used to enable the individual to maintain a relatively consistent motion trend with 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 drone cluster based on a parameter mapping mechanism according to claim 4 is characterized in that: The speed consistency adjustment and mission heading adjustment include: Speed ​​consistency adjustment indicates the current direction of the drone cluster, expressed as: Among them, v xy,k represents the friendly machine U in the neighborhood k The speed v k In O g x g y g Velocity components in the plane; The drone cluster has the same target heading p t , UAV i The mission heading is expressed as: Among them, p t,xy and p xy,i Represent the target waypoints p t and U i The position p i In O g x g y g Components in the plane; According to UAV i The mission heading and the current direction of the UAV cluster, UAV U i The movement trend adjustment Δv i It is expressed as: stω a +oh m =1.0≤ω a ,oh m ≤1 Among them, ω a and ω m They represent the weight parameters of the speed consistency rule and the task heading rule respectively.

6. The method for reconstructing the shape of a drone cluster based on a parameter mapping mechanism according to claim 5, characterized in that: The dynamic position adjustment in step S2 is used to maintain an appropriate relative distance between individual drones and friendly drones in the neighborhood. The position adjustment includes dispersion rules, aggregation rules, and shape constraint rules. The rules are all in U i The relative coordinate system O i x i y i z i Calculate below.

7. The method for reconstructing the shape of a drone cluster based on a parameter mapping mechanism according to claim 6, characterized in that: The dispersion and aggregation rules are used to calculate the UAV U i The position adjustment amount of friendly drones that need to be moved away or closer to different distance ranges in the neighborhood is expressed as follows: In the formula, Δp dis,i Represents the position adjustment amount obtained by scattered calculation, Indicates U k After the coordinate system transformation, U i Coordinates in relative coordinate system; The aggregation rule expression is: In the formula, Δp coh,i Indicates the position adjustment amount obtained by aggregation calculation; Based on the dispersion and aggregation rules, the position adjustment base Δp' is obtained i , the expression is: Δp′ i =Δp dis,i +Δp coh,i 。 8. The method for reconstructing the shape of a drone cluster based on a parameter mapping mechanism according to claim 7, characterized in that: The shape constraint rules include: First, the UAV cluster is calculated according to the conversion model to calculate the overall coordinate system O i x i y i z i The desired centroid under the swarm is used to intervene and control the flight altitude of the entire swarm. Next, adjust the base amount Δp' for the three-dimensional position i Decompose, according to the shape constraint, when Δp' i In O i x i z i The projected component of the plane Δp' xz,i Located in shape O i x i z i The cross-sectional area of ​​the plane is external Ω xz When Δp' i In O i x i z i In-plane and O i y i Adjust the direction; Finally, the relative coordinate system O i x i y i z i Δp' i Convert back to the ground coordinate system O again g x g y g z g Adjustment amount Δp i , the conversion expression is: In the formula, R i -1 is the rotation matrix R i The inverse matrix of z,i Indicates the position adjustment amount Δp i In O g z g Component in the direction, Δp' z,i Indicates the position adjustment amount Δp' i In O i z i Directional weight.

9. The method for reconstructing the shape of a drone cluster based on a parameter mapping mechanism according to claim 8, characterized in that: The Δp' i In O i x i z i In-plane and O i y i Adjustments in direction include: In O i x i z i The adjustment in the plane is expressed as: In the formula, Intersec(·) represents the function of finding the intersection point between the vector and the geometric figure, Δp xz,i Denotes Δp' xz,i The intersection with the boundary of the cross-section area; In O i y i To adjust the direction, first calculate Δp' y,i Exceed Ω xy The distance value of the boundary It is expressed as: Where dist(·) represents Δp' y,i In O i y i Direction and cross-sectional area Ω xy The shortest distance, Δp' y,i Indicates the position adjustment amount Δp' i In O i y i Directional weight; Adjust the position Converted into speed adjustment σ v,i , moving forward or backward is achieved by accelerating or decelerating, where the forward or backward movement is relative to the entire cluster. By adjusting the relative speed, the drone moves toward the head or tail of the cluster. The speed adjustment amount σ v,i The expression is: In the formula, λ v >0 is a constant coefficient, and constrain(x,a,b) is a truncation function used to limit x to the interval [a,b]. and They are the minimum and maximum values ​​of the speed adjustment respectively.

10. The method for reconstructing the shape of a drone cluster based on a parameter mapping mechanism according to claim 9, characterized in that: The parameter mapping relationship in step S3 is expressed as: In the formula, Represents a set of macroscopic shape parameters. 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 macroscopic shape parameter defining the expected 3D volume of the cluster, represents the macroscopic three-dimensional volume actually presented according to the microscopic rule parameters, and the function f(·) is the mapping relationship from the microscopic rule parameters to the actual three-dimensional volume. It is the mapping relationship from the macroscopic shape parameters to the set three-dimensional volume of the cluster.

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