Universal multi-unmanned aerial vehicle formation method

Abstract

The invention discloses a universal multi-unmanned aerial vehicle formation method, and belongs to the field of unmanned aerial vehicle formation control. The method specifically comprises the following steps: firstly, giving an unmanned aerial vehicle formation image, and selecting a minimum number of unmanned aerial vehicles as a basic formation under the condition of guaranteeing the safe spacing of the unmanned aerial vehicles; then the basic formation is disassembled into one simple formation according to user requirements, the priority of the formation is stipulated, and one-by-one expansion is carried out; for the simple formation of edge expansion, traversing each edge in sequence, and determining the number of unmanned aerial vehicle points inserted into each edge according to different numbers of vertexes of each edge in a vertex set; carrying out equal-ratio amplification by k times on the simple formation containing internal expansion based on a recursion method, and calculating the number of inserted unmanned aerial vehicle points; after the l simple formations are expanded respectively, coordinate sets of all the unmanned aerial vehicle points are subjected to union operation and are inserted into an original basic formation by adopting a recursion method, and a new formation is formed; according to the invention, flexible design and adjustment of various formations are realized.

Description

Technical Field

[0001] The present invention belongs to the field of unmanned aerial vehicle (UAV) formation control, and particularly relates to a general multi-UAV formation method. Background Art

[0002] In recent years, UAV formation technology has been widely applied in multiple fields, including military reconnaissance, disaster relief, logistics transportation, and environmental monitoring. In these applications, UAVs perform complex tasks through formation cooperation, which can not only improve task efficiency but also significantly enhance the reliability and flexibility of the tasks.

[0003] However, the requirements for flight formations are different when UAVs perform different tasks. Currently, common UAV formation shapes mainly include triangles, rectangles, "one"-shaped, "human"-shaped, diamonds, wedges, and arcs. Complex formations include multiple types for fighter jets alone.

[0004] Different UAV formation methods vary greatly, and the design and expansion implementation methods of various formations are often different. This differential formation method makes it complex and difficult for UAVs to switch and adjust formations when facing dynamic environments or changes in task requirements during the task execution process, thereby increasing the uncertainty of task execution.

[0005] Therefore, researching a flexible and efficient UAV formation method to simplify the formation switching process and improve the ability of UAV formations to adapt to changing task environments has important theoretical value and practical significance. Summary of the Invention

[0006] In view of the above problems, the present invention proposes a general multi-UAV formation method. By using geometric and graph theory knowledge, through the precise description of the basic formation points, edges, and expansion types of UAVs, flexible design and adjustment of various formations are realized.

[0007] The general multi-UAV formation method includes the following steps:

[0008] Step 1: Given a UAV formation image, under the condition of ensuring the safe spacing between UAVs, select the minimum number of UAVs as the basic formation according to the image;

[0009] The specific selection process is as follows:

[0010] First, set the minimum spacing d between UAVs min , sample along the boundary points, and interpolate according to the spacing d min to generate a preliminary set of UAV positions.

[0011] Then, according to the need, use triangular mesh division or sparse point filling method to select the internal area for point filling.

[0012] Finally, based on the key point positions and curvature changes, gradually adjust the UAV positions to describe the formation boundary with the fewest UAV points.

[0013] Step 2: Determine whether the basic formation is a simple formation. If so, proceed to Step 3; otherwise, disassemble it into l simple formations according to the user's requirements, specify the formation priorities, and expand them one by one.

[0014] Simple formations are common triangular, rectangular, horizontal line, vertical line, diamond, wedge, or cross-shaped formation patterns.

[0015] Step 3: Describe the simple formation of the UAVs through three basic elements: points, edges, and expansion types;

[0016] Regard each UAV in the formation as a point. The description specifically includes the coordinates of vertices and intersections, the lengths and directions of edges, and the expansion types;

[0017] Description of points: Among the n UAVs in the basic formation, let the spatial position coordinates of the i-th UAV be P i (x i ,y i ,z i ), where i = 0, 1, 2, …, n. Denote the position of the lead UAV as P0(x0, y0, z0), and set x0 = y0 = z0 = 0, which is defined as the intersection point.

[0018] The vertices (excluding the intersection point) of the basic formation form the vertex set V, and the complex formation is disassembled into multiple simple formations to form the intersection point set I.

[0019] Description of edges: Let the connection vector between two points P i and P j be denoted as v ij =(x j -x i ,y j -y i ,z j -z i ), and the direction points from point P i to P j . For the i-th edge of the basic formation with q i UAVs, denote the length of the i-th edge as λ i =q i -1;

[0020] Expansion type: Let S ∈ {0, 1}, where 0 represents edge expansion and 1 represents inclusion internal expansion.

[0021] Step 4: For each sorted simple formation, determine whether the expansion type of each simple formation is edge expansion. If so, go to Step 5; otherwise, go to Step 6;

[0022] Step 5: Traverse each edge in the simple formation in sequence. According to the different numbers of vertices of each edge in the vertex set, determine the number of insertion points for each edge;

[0023] First, determine the number of vertices of the current edge in the vertex set, and then magnify the coordinates of all points in the vertex set and the intersection point set by k times; if the number of vertices in the vertex set is 1, the number of points to be inserted for this edge is m = λ i (k - 1) - 1; if the number is 2, the number of points to be inserted for this edge is m = λ i k - 1.

[0024] When all the edges of the simple formation are completed in expansion, the coordinates of all drone points after being magnified by k times in equal ratio are obtained.

[0025] Step 6: The expansion type of the simple formation is inclusion internal expansion. Based on the recursive method, the simple formation is magnified by k times in equal ratio, and the number of insertion points for inclusion internal expansion is calculated;

[0026] First, according to the operation process of the simple formation with edge expansion type, expand the edge of the simple formation by k times to obtain the number of drone points to be inserted and the coordinates of the drone points for each edge after being magnified by k times;

[0027] Then, expand the edge of the simple formation by k - 1 times to obtain the number of drone points to be inserted and the coordinates of the drone points for each edge after being magnified by k - 1 times;

[0028] And so on. Finally, expand the edge of the simple formation by 2 times to determine the number of drone points to be inserted and the coordinates of the drone points for each edge after being magnified by 2 times.

[0029] Perform a union operation on the set of the coordinates of all points in the vertex set and the intersection point set after being magnified by k times and the above set of the coordinates of the inserted drone points, and the coordinates of all drone points after the simple basic formation is magnified by k times in inclusion internal expansion can be obtained.

[0030] Step 7: When l simple basic formations are expanded according to their respective expansion types respectively, perform a union operation on the sets of the coordinates of all drone points.

[0031] Step 8: Insert all the drones after the union operation into the original basic formation by using the recursive method to form a new formation;

[0032] First, a distortion metric function Δ(G1, G2) is defined to calculate the geometric difference between the two formations before and after expansion. The smaller the value, the higher the similarity between the two formations. Weighted Euclidean distance is usually used as the similarity indicator.

[0033] To the original formation G k-1 and the new formation G′ k-1 The distortion metric between is calculated as follows:

[0034]

[0035] Among them, P′ i is the formation G′ k-1 The coordinates of the drone point, P j It is formation G k-1 The coordinates of the drone point, w ij is the weight coefficient.

[0036] Then, based on the original formation G expanded k-1 times k-1 Insert points one by one, that is, number the known drone coordinates to ensure that within the range of selectable drones, each numbering makes the distortion metric function Δ(G′ k-1 ,G k-1 ) is the smallest, until all numbers are completed, and the new formation G is obtained. k .

[0037] Finally, given the numbers of all drones after the k-fold expansion, repeat the above numbering steps one by one to obtain the numbers of all drones after the k+1-fold expansion.

[0038] The advantages of the present invention are:

[0039] 1) A general multi-UAV formation method that, while ensuring safe spacing between UAVs, performs edge expansion or internal expansion based on the minimum UAV basic formation, ensuring that the formation and geometric features are not significantly distorted;

[0040] 2) A general multi-UAV formation method is simple to implement. By decomposing a complex formation into multiple simple formations and then forming them separately and then combining them, the algorithm complexity is reduced, and ultimately the rapid construction and adjustment of complex formations is achieved. It has the characteristics of strong applicability and high scalability. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 The present invention provides a flow chart of a general multi-UAV formation method.

[0042] Figure 2 This is a schematic diagram of a diamond formation used in a simple formation in an embodiment of the present invention;

[0043] Figure 3Schematic diagram of rhombus edge expansion for simple formation in the embodiments of the present invention;

[0044] Figure 4 Schematic diagram of internal expansion of the rhombus for simple formation in the embodiments of the present invention;

[0045] Figure 5 Schematic diagram of the position of rhombus positioning numbers for simple formation in the embodiments of the present invention;

[0046] Figure 6 Schematic diagram of fighter aircraft formation for complex formation in the embodiments of the present invention;

[0047] Figure 7 Schematic diagram of the breakdown of the fighter aircraft formation for complex formation in the embodiments of the present invention;

[0048] Figure 8 Result diagram of quadrupling the internal expansion of triangle ① after the breakdown of the complex formation in the embodiments of the present invention

[0049] Figure 9 Result diagram of quadrupling the internal expansion of wedge ⑤ after the breakdown of the complex formation in the embodiments of the present invention

[0050] Figure 10 Schematic diagram of the position of fighter aircraft positioning numbers for complex formation in the embodiments of the present invention. Detailed implementation manners

[0051] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the following further elaborates on the technical solutions of the present invention in conjunction with the accompanying drawings and embodiments.

[0052] The described general multi-UAV formation method, as Figure 1 shown, includes the following steps:

[0053] Step 1: Given a UAV formation image, under the condition of ensuring the safe distance between UAVs, select the minimum number of UAVs as the basic formation according to the image;

[0054] Determine to use the minimum number of UAVs to approximately describe the basic formation of the image while ensuring that the visual and geometric features do not undergo obvious distortion; the specific selection process is as follows:

[0055] First, set the minimum distance d min between UAVs to ensure safety, sample along the boundary points, and interpolate according to the distance d min to generate a preliminary set of UAV positions; for local curve regions, appropriately densify the sampling to avoid visual distortion.

[0056] Then, according to the need, use the triangular grid division or sparse point filling method to select the internal area for point filling.

[0057] Finally, based on the key point positions and curvature changes, gradually adjust the UAV positions to describe the formation boundary with as few UAV points as possible.

[0058] Compare the UAV point sets before and after simplification with the original boundary to ensure that the shape distortion is within an acceptable range.

[0059] Step 2: Determine whether the basic formation is a simple formation. If so, proceed to Step 3; otherwise, disassemble it into l simple formations according to the user's requirements, specify the formation priorities, and expand them one by one.

[0060] Simple formations are common triangular, rectangular, horizontal line, vertical line, diamond-shaped, wedge-shaped, or cross-shaped formation shapes.

[0061] Step 3: Describe the simple formation of UAVs through three basic elements: points, edges, and expansion types;

[0062] Specifically, it includes the coordinates of vertices and intersection points, the length and direction of edges, and the expansion type;

[0063] Description of points: Among the n UAVs in the basic formation, the position of each UAV is a point. The spatial position coordinates of the i-th UAV are represented as P i (x i , y i , z i ), where i = 0, 1, 2, …, n. The position of the lead UAV is denoted as P0(x0, y0, z0), and x0 = y0 = z0 = 0 is set to ensure that the original UAV positions do not shift as a whole during subsequent formation expansion, and it is defined as the intersection point.

[0064] The vertices (except the intersection point) of the basic formation form the vertex set V, and the complex formation is disassembled into multiple simple formations to form the intersection point set I.

[0065] Description of edges: Let the connection vector between two points of UAV P i and P j be represented as v ij = (x j - x i , y j - y i , z j - z i ), and the direction is from point P i to P j . If the i-th edge of the basic formation has q i UAVs, then the length of the i-th edge is denoted as λ i = q i-1; Sometimes, in order to describe the details of the basic formation in more detail, virtual points may be set, and virtual points cannot be regarded as normal drone formation points. Therefore, the side length where the virtual point is located is λ i It can be set as a decimal according to needs.

[0066] Expansion type: Let S ∈ {0, 1}, 0 represents edge expansion, and 1 represents including internal expansion.

[0067] Step 4: For each simple formation after priority sorting, respectively judge whether the expansion type of each simple formation is edge expansion. If it is, enter Step 5; otherwise, enter Step 6;

[0068] Step 5: The simple formation expansion type is edge expansion. Traverse each edge in the simple formation in turn. According to the different numbers of vertices of each edge in the vertex set, determine the number and coordinates of the insertion points of each edge;

[0069] Each edge has two vertices, or one vertex and one intersection point; after the formation expands, the edge will extend, the original vertex position remains unchanged, and the new vertex coordinates are k times the original vertex coordinates, but the vertex set and intersection point set do not change, and are still the vertex and intersection point sets corresponding to the original formation.

[0070] If it is edge expansion, multiply the coordinates of all points in the vertex set and intersection point set by k. Select any one edge and judge the number of vertices of this edge in the vertex set:

[0071] (1) If it is 1, the number of points to be inserted for this edge is m = λ i (k - 1) - 1;

[0072] (2) If it is 2, the number of points to be inserted for this edge is m = λ i k - 1.

[0073] Let P a (x a , y b , z c ) and P b (x b , y b , z b ) be the two vertices of a certain edge in the simple basic formation, and the length of this edge is 1, that is, the vertices P a and P b are adjacent. According to the description of the opposite side, the coordinate representation of the connection vector between the two drones P a and P b is v ab = (x b - x a , y b - y a , z b-z a )。

[0074] a) If P a and P b both belong to the vertex set V and are not virtual points, then the vertex coordinates after magnifying this edge by k times are (kx a , ky a , kz a ), (kx b , ky b , kz b ), the number of points to be inserted is m = λ i k - 1, and the coordinates of the inserted points are successively (kx b , ky b , kz b ) - v ab / λ i , (kx b , ky b , kz b ) - 2×v ab / λ i 、…、(kx b , ky b , kz b ) - m×v ab / λ i 。

[0075] b) If P a and P b both belong to the vertex set V and P b is a virtual point, then the vertex coordinates after magnifying this edge by k times are (kx a , ky a , kz a ), (kx b , ky b , kz b ), the number of points to be inserted is m = λ i k - 1. At this time, m is a decimal. Denote the decimal part of m as {m}. The coordinates of the inserted points are successively (kx b , ky b , kz b ) - {m}v ab / λ i , (kx b , ky b , kz b ) - ({m} + 1)×v ab / λ i 、…、(kx b , ky b , kz b ) - m×v ab / λ i 。

[0076] Then select another side of the basic formation and repeat until all sides are expanded. After that, the coordinates of all UAV points after being enlarged by a factor of k in equal proportion can be obtained.

[0077] Step 6: The simple formation expansion type includes internal expansion. Based on the recursive method, the simple formation is enlarged by a factor of k in equal proportion, and the number and coordinates of the insertion points including internal expansion are calculated.

[0078] Specifically:

[0079] (1) According to the operation process of the simple formation expansion type being the edge, first expand the edge of the simple formation by a factor of k, and determine the number and coordinates of the UAV points to be inserted for each side after being enlarged by a factor of k.

[0080] (2) Then expand the edge of the simple formation by a factor of k - 1, and repeat to determine the number and coordinates of the UAV points to be inserted for each side after being enlarged by a factor of k - 1.

[0081] ……

[0082] (k - 1) Finally, expand the edge of the simple formation by a factor of 2, and repeat to determine the number and coordinates of the UAV points to be inserted for each side after being enlarged by a factor of 2.

[0083] Finally, perform the union operation on the set of the coordinates of all points in the vertex set and intersection point set after being enlarged by a factor of k, and the set of the coordinates of the inserted UAV points above, then the coordinates of all UAV points after the simple basic formation is enlarged by a factor of k including internal expansion can be obtained.

[0084] Step 7: When l simple basic formations are expanded respectively according to their respective expansion types, perform the union operation on the sets of the coordinates of all UAV points.

[0085] When the UAV basic formation is disassembled into l simple basic formations F1, F2, …, F l , after being expanded by a factor of k respectively as above, determine the sets of the coordinates of all UAV points M1, M2, …, M l , and perform the union operation to obtain the set of the coordinates of all UAV points M = M1 ∪ M2 ∪ … ∪ M l .

[0086] Step 8: Insert all the UAVs after the union operation into the original basic formation by the recursive method to form a new formation.

[0087] For the UAV formation that has been expanded by a factor of k - 1, the initial value of k is taken as 2; insert new UAV points according to the following rules:

[0088] Geometric feature preservation: The formation G′ after inserting new points k-1 should be as close as possible to the original formation Gk-1 ;

[0089] The insertion order is reasonable: The number of the insertion point should meet the requirements of path planning and obstacle avoidance during task execution;

[0090] The specific insertion process is as follows:

[0091] First, define the distortion metric function Δ(G1, G2) to calculate the geometric difference between the two formations before and after expansion. The smaller this value, the higher the similarity between the two formations. Usually, the weighted Euclidean distance is used as the similarity index;

[0092] For the original formation G k-1 and the new formation G' k-1 The calculation of the distortion metric between them is as follows:

[0093]

[0094] where P' i is the UAV point coordinate of the formation G' k-1 , P j is the UAV point coordinate of the formation G k-1 , and w ij is the weight coefficient.

[0095] Then, based on the original formation G expanded by k - 1 times k-1 insert points one by one, that is, number the known UAV coordinates. Ensure that within the range of selectable UAVs, each time a number is assigned, the distortion metric function Δ(G' k-1 , G k-1 ) is minimized until all numbers are assigned, obtaining the new formation G k .

[0096] Finally, given the numbers of all UAVs after expanding by k times, repeat the above step of numbering one by one to obtain the numbers of all UAVs after expanding by k + 1 times.

[0097] The number of UAV points in the new formation G k is m k . When obtaining the coordinate position of the UAV with the specified number q, only need to judge whether it satisfies m k-1 < q + 1 ≤ m k . If so, the UAV with the number q is in the formation after expanding by k times, and then the coordinate position of any numbered UAV in the formation after expanding by k times can be obtained.

[0098] Example:

[0099] 1) Formation for a simple formation:

[0100] Given a rhombus formation image, the obtained basic formation of UAVs is a simple formation;

[0101] Describe a simple formation using basic elements: It consists of 4 drones. As shown Figure 2 below, the position of the lead drone is denoted as P0(0, 0, 0), and the drones at other positions are denoted as the vertex set V = {P1, P2, P3}, and the intersection set I = {P0}.

[0102] The vector representation of the line connecting two points P0 and P1 of the drone is The side length is denoted as λ1 = 1; the vector representation of the line connecting two points P0 and P2 of the drone is The side length is denoted as λ2 = 1; the vector representation of the line connecting two points P1 and P3 of the drone is The side length is denoted as λ3 = 1; the vector representation of the line connecting two points P2 and P3 of the drone is The side length is denoted as λ4 = 1; the expansion type S = 1.

[0103] Since the expansion type of the rhombus formation is internal expansion, let the magnification factor k = 4;

[0104] (1) First, expand the rhombus edge by 4 times, determine the number of drone points to be inserted and the coordinates of the drone points required to magnify each side by 4 times, and obtain the coordinates of the new vertices:

[0105] The number of vertices in the vertex set of side P0P1 is 1, so the number of points to be inserted on this side is m1 = λ1(4 - 1) - 1 = 2;

[0106] The coordinates of the inserted points are respectively That is

[0107] The number of vertices in the vertex set of side P0P2 is 1, so the number of points to be inserted on this side is m2 = λ2(4 - 1) - 1 = 2; The coordinates of the inserted points are respectively That is

[0108] The number of vertices in the vertex set of side P1P3 is 2, so the number of points to be inserted on this side is m3 = λ3×4 - 1 = 3; The coordinates of the inserted points are respectively That is

[0109]

[0110] The number of vertices in the vertex set of side P2P3 is 2, so the number of points to be inserted on this side is m4 = λ4×4 - 1 = 3. The coordinates of the inserted points are respectively That is

[0111]

[0112] The result of quadrupling the edge expansion is as follows Figure 3 shown. The orange dots are the new vertices, and the green dots are the insertion points.

[0113] (2) Then expand the rhombus edge by 3 times, and determine the number of UAV points to be inserted and the coordinates of the UAV points required for each side to be magnified by 3 times: Obtain the coordinates of the new vertices:

[0114] The number of points to be inserted for side P0P1 is 1, and the coordinates of the insertion point are which is

[0115] The number of points to be inserted for side P0P2 is 1, and the coordinates of the insertion point are which is

[0116] The number of points to be inserted for side P1P3 is 2, and the coordinates of the insertion point are which is

[0117] The number of points to be inserted for side P2P3 is 2, and the coordinates of the insertion point are which is

[0118] (3) Finally, expand the rhombus edge by 2 times, and repeat to determine the number of UAV points to be inserted and the coordinates of the UAV points required for each side to be magnified by 2 times: Obtain the coordinates of the new vertices:

[0119] The number of points to be inserted for side P0P1 and side P0P2 is 0;

[0120] The number of points to be inserted for side P1P3 and side P2P3 is 1, and the coordinates of the insertion point are and

[0121] After multiple edge expansions, the result graph of the 4-fold internal expansion of the rhombus is obtained, as shown in Figure 4 shown.

[0122] Finally, first form a formation for the rhombus formation expanded by 2 times, insert it into the nodes of the original simple formation, consider the criterion of basically maintaining the geometric characteristics, and number the UAVs; then, based on the numbering of the 2-fold expanded formation, insert points one by one, repeat the above operations, obtain the numbers of all UAVs after expanding by 3 times, and finally determine the numbers of the UAVs in the rhombus formation after expanding by 4 times.

[0123] As shown in Figure 5As shown in the figure, when the position of the UAV numbered 19 in the diamond formation is required, since the maximum UAV number after the diamond basic formation is expanded by 3 times is 15, the UAV numbered 19 is in the formation where the diamond basic formation is expanded by 4 times. Furthermore, the positions corresponding to the numbers of all UAVs after the diamond formation is expanded by 4 times can be determined, and through indexing, the position of the UAV numbered 19 can be obtained.

[0124] 2) For the formation of complex formations:

[0125] Given the fighter formation image, the obtained UAV basic formation is as Figure 6 shown, and it is disassembled into multiple simple basic formations, such as Figure 7 shown, that is, the fighter formation can be regarded as a combination of 4 triangles and 2 wedges; the expansion simple formation priority is the same as the number.

[0126] Describe the characteristics of the fighter basic formation: It consists of 8 UAVs. The position of the lead aircraft is recorded as P0(0,0,0), and the UAVs at other positions are recorded as P1(1,-1,0), P2(2,0,0), P3(1,-2,0), P4(-1,0,0), P5(3,0,0), P6(0,1,0), P7(2,1,0). For the convenience of description, set 5 virtual points P8(1,0,0), P9(-0.5,0,0), P 10 (0.5,0,0), P 11 (1.5,0,0), P 12 (2.5,0,0).

[0127] For triangular formation ①, the vertex set V1 = {P3, P8}, and the intersection set I1 = {P0}. The vector representation of the line connecting the two points P3 and P8 of the UAV is v 38 =(0,2,0), and the side length is recorded as λ1 = 2; the expansion type S1 = 1.

[0128] For triangular formation ②, the vertex set V2 = {P3, P8}, and the intersection set I2 = {P2}. The vector representation of the line connecting the two points P3 and P8 of the UAV is v 38 =(0,2,0), and the side length is recorded as λ2 = 2; the expansion type S2 = 1.

[0129] For triangular formation ③, the vertex set V3 = {P4, P8}, and the intersection set I3 = {P1}. The vector representation of the line connecting the two points P4 and P8 of the UAV is v 48 =(2,0,0), and the side length is recorded as λ3 = 2; the expansion type S3 = 1.

[0130] For triangular formation ④, the vertex set V4 = {P5, P8}, and the intersection set I4 = {P1}. The vector representation of the line connecting the two points P5 and P8 of the UAV is v58 = (-2, 0, 0), and the side length is denoted as λ4 = 2; the expansion type S4 = 1.

[0131] For wedge ⑤, the vertex set V5 = {P6, P9, P 10}, and the intersection set I5 is empty. The vector representation of the line connecting the two points P6 and P9 of the UAV is v 69 = (-0.5, -1, 0), and the side length is denoted as λ5 = 0.5; the vector representation of the line connecting the two points P6 and P 10 is v 610 = (0.5, -1, 0), and the side length is denoted as λ6 = 0.5; the expansion type S5 = 1.

[0132] For wedge ⑥, the vertex set V6 = {P7, P 11 , P 12}, and the intersection set I6 is empty. The vector representation of the line connecting the two points P7 and P 11 is v 711 = (-0.5, -1, 0), and the side length is denoted as λ7 = 0.5; the vector representation of the line connecting the two points P7 and P 12 is v 712 = (0.5, -1, 0), and the side length is denoted as λ8 = 0.5; the expansion type S6 = 1.

[0133] The expansion types of the 6 disassembled basic formations are all internal expansions, and let the magnification factor k = 4. Since the basic formations of formation ①,

[0134] ②, ③, and ④ are pairwise symmetric, therefore, only the expansions of formation ① and ⑤ are introduced in specific examples.

[0135] For triangular formation ①, calculate the number of UAV points to be inserted and the coordinates of the UAV points when magnified by 4:

[0136] (1) Magnify the vertex and intersection coordinates by 4 to obtain the new coordinates: (4, -8, 0), (4, 0, 0), (0, 0, 0);

[0137] The number of vertices of side P3P8 in the vertex set is 2, so the number of points to be inserted on this side is m1 = λ1 × 4 - 1 = 7; the coordinates of the inserted points are (4, 0, 0) - v 38 / λ1, (4, 0, 0) - 2 × v 38 / λ1,..., (4, 0, 0) - 7 × v 38 / λ1, which are (4, -1, 0), (4, -2, 0),..., (4, -7, 0);

[0138] (2) Magnify the vertex and intersection coordinates by 3 to obtain the new vertex coordinates: (3, -6, 0), (3, 0, 0), (0, 0, 0);

[0139] Similarly, the number of points to be inserted on the side P3P8 is m2 = λ1×3 - 1 = 5; the coordinates of the inserted points are (3,0,0) -

[0140] v 38 / λ1, (3,0,0) - 2×v 38 / λ1,..., (3,0,0) - 5×v 38 / λ1 are (3, -1,0), (3, -2,0),..., (3, -5,0);

[0141] (3) Magnify the coordinates of the vertices and intersection points by 2 times to obtain the coordinates of the new vertices: (2, -4,0), (2,0,0), (0,0,0);

[0142] Similarly, the number of points to be inserted on the side P3P8 is m3 = λ1×2 - 1 = 3; the coordinates of the inserted points are (2,0,0) -

[0143] v 38 / λ1, (2,0,0) - 2×v 38 / λ1, (2,0,0) - 3×v 38 / λ1 are (2, -1,0), (2, -2,0), (2, -3,0);

[0144] After multiple edge expansions, the result graph of the 4 - fold internal expansion of triangle ① is obtained, as Figure 8 shown.

[0145] For wedge ⑤, calculate the number of UAV points to be inserted and the coordinates of the UAV points after magnifying by 4 times:

[0146] (1) Expand the edge of wedge ⑤ by 4 times, repeat steps 4 and 5 to determine the number of UAV points to be inserted on each side after magnifying by 4 times and the coordinates of the UAV points: obtain the coordinates of the new vertices: (-2,0,0), (2,0,0), (0,4,0);

[0147] The number of points to be inserted on the side P6P9 is m4 = λ5×4 - 1 = 1, and the coordinate of the inserted point is (-2,0,0) - v 69 / λ5, which is (-1,2,0); for the side P6P 10 The number of points to be inserted is m5 = λ6×4 - 1 = 1, and the coordinate of the inserted point is (2,0,0) -

[0148] v 610 / λ6, which is (1,2,0);

[0149] (2) Expand the edge of the wedge ⑤ by 3 times, repeat steps 4 and 5, and determine the number of UAV points to be inserted and the coordinates of the UAV points required for each side to be enlarged by 3 times: Obtain the coordinates of the new vertices: (-1.5, 0, 0), (1.5, 0, 0), (0, 3, 0);

[0150] The number of points to be inserted on the edge P6P9 is m6 = λ5×3 - 1 = 0.5, 0 < m6 < 1, and the coordinates of the inserted point are (-1.5, 0, 0) - {m6}v 69 / λ5, which is (-1, 1, 0); similarly, for the edge P6P 10 The number of points to be inserted is m7 = λ6×3 - 1 = 0.5, and the coordinates of the inserted point are (1.5, 0, 0) - {m7}v 610 / λ6, which is (1, 1, 0);

[0151] (3) Expand the edge of the wedge ⑤ by 2 times, repeat steps 4 and 5, and determine the number of UAV points to be inserted and the coordinates of the UAV points required for each side to be enlarged by 2 times: Obtain the coordinates of the new vertices: (-1, 0, 0), (1, 0, 0), (0, 2, 0);

[0152] The number of points to be inserted on the edge P6P9 is m8 = λ5×2 - 1 = 0; the number of points to be inserted on the edge P6P 10 is m9 =

[0153] λ6×2 - 1 = 0;

[0154] After multiple expansions of the simple basic formation, a schematic diagram of the internal expansion of the fighter formation by 4 times is obtained, as Figure 9 shown.

[0155] According to the priority ① > ② > ③ > ④ > ⑤ > ⑥, the simple formation is changed in sequence: First, form a formation for the diamond formation expanded by 2 times. During the process of inserting nodes, considering the criterion of basically maintaining the geometric characteristics, number the UAVs; then, based on the numbering of the 2-fold expanded formation, insert points one by one, repeat the above operations, and obtain the numbers of all UAVs after expansion by 3 times. After completing the numbering of one simple formation, proceed to the numbering of the next simple formation and retain the results of the previous numbering. According to the criterion of basically maintaining the geometric characteristics, insert points one by one, and finally determine the numbers of the UAVs in the fighter formation with an internal expansion of 4 times.

[0156] As Figure 10 shown, finally, the position of the UAV numbered 60 in the fighter formation is required: First, it is necessary to know that for the fighter to expand internally by k times according to the foregoing steps, the minimum number of UAVs required is X kSince X3 < 60 < X4, it is determined that the UAV numbered 60 is in the formation where the fighter formation is expanded by 4 times. Furthermore, determine the positions corresponding to all UAV numbers after the fighter formation is expanded by 4 times, and perform indexing to obtain the position of the UAV numbered 60.

[0157] The above embodiments are only used to illustrate the present invention and not to limit it. Those of ordinary skill in the art should understand that any modifications, deformations, or equivalent replacements made to the present invention without departing from the spirit of the present invention shall be covered by the claims of the present invention. To make the purpose, technical solution, and advantages of the present invention clearer and more understandable, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

Claims

1. A general multi-UAV formation method, characterized in that It includes the following steps: Step 1: Given the UAV formation image, under the condition of ensuring the safe distance between UAVs, select the minimum number of UAVs as the basic formation according to the image; Step 2: Judge whether the basic formation is a simple formation. If it is, go to Step 3; otherwise, disassemble it into l simple formations according to the user's needs, specify the formation priority, and expand them one by one; Step 3: Describe the simple formation of UAVs through three basic elements: points, edges, and expansion types; Each UAV in the formation is regarded as a point, and the description specifically includes the coordinates of vertices and intersection points, the length and direction of edges, and the expansion type is edge expansion or includes internal expansion; Step 4: For each sorted simple formation, judge whether the expansion type of each simple formation is edge expansion. If it is, go to Step 5; otherwise, go to Step 6; Step 5: Traverse each edge in the simple formation in turn. According to the different numbers of vertices of each edge in the vertex set, determine the number and coordinates of the insertion points of each edge; First, determine the number of vertices of the current edge in the vertex set, and then magnify the coordinates of all points in the vertex set and the intersection point set by k times; if the number of vertices in the vertex set is 1, the number of points to be inserted for this edge is m = λ i (k - 1) - 1; if the number is 2, the number of points to be inserted for this edge is m = λ i k - 1; λ i is the side length of the i-th side of the basic formation; When all the edges of the simple formation are completed for expansion, obtain the coordinates of all UAV points after being enlarged by k times in equal proportion; Step 6: The expansion type of the simple formation is internal expansion. Based on the recursive method, enlarge the simple formation by k times in equal proportion, and calculate the number and coordinates of the insertion points for internal expansion; First, according to the operation process of the simple formation with the expansion type of edge, expand the edge of the simple formation by k times, and obtain the number of UAV points to be inserted and the coordinates of UAV points required for each edge to be enlarged by k times; Then, expand the edge of the simple formation by k - 1 times, and obtain the number of UAV points to be inserted and the coordinates of UAV points required for each edge to be enlarged by k - 1 times; And so on. Finally, expand the edge of the simple formation by 2 times, and determine the number of UAV points to be inserted and the coordinates of UAV points required for each edge to be enlarged by 2 times; Perform a union operation on the set of coordinates of all points in the vertex set and intersection point set after being enlarged by k times and the above set of coordinates of inserted UAV points, and then the coordinates of all UAV points after the simple basic formation is enlarged by k times with internal expansion can be obtained; Step 7: When the l simple basic formations are expanded according to their respective expansion types respectively, perform a union operation on the coordinate sets of all UAV points; Step 8: Insert all the UAVs after the union operation into the original basic formation by using the recursive method to form a new formation; First, define the distortion metric function Δ(G1, G2) to calculate the geometric difference between the two formations before and after expansion; For the original formation G k-1 and the new formation G′ k-1 the distortion metric between them is calculated as follows: Among them, P' i is the UAV point coordinate of formation G' k-1 , P j is the UAV point coordinate of formation G k-1 , and w ij is the weight coefficient;; Then, based on the original formation G expanded by k - 1 times k-1 Insert points one by one, that is, number the known UAV coordinates, ensuring that within the range of selectable UAVs, each time a number is assigned, the distortion metric function Δ(G′ k-1 , G k-1 ) is minimized until all numbers are assigned, obtaining the new formation G k ; Finally, given the numbers of all UAVs after being enlarged by k times, repeat the above steps of numbering one by one to obtain the numbers of all UAVs after being enlarged by k + 1 times.

2. The general multi-UAV formation method according to claim 1, characterized in that In the above Step 1, the specific selection process is as follows: First, set the minimum distance d between drones min , sample along the boundary points, and interpolate at intervals of d min to generate a preliminary set of drone positions; Then, according to the need, use the triangular grid division or sparse point filling method to select the internal area for point filling; Finally, based on the key point positions and curvature changes, gradually adjust the UAV positions to describe the formation boundary with the minimum number of UAV points.

3. A general multi-UAV formation method as claimed in claim 1, characterized in that, In the above Step 2, the simple formation refers to a triangular, rectangular, horizontal line, vertical line, rhombic, wedge-shaped or cross-shaped formation.

4. A general multi-UAV formation method according to claim 1, characterized in that In the above Step 3, Description of points: Among the n drones in the basic formation, the spatial position coordinates of the i-th drone are expressed as P i (x i , y i , z i ), where i = 0, 1, 2, …, n; the position of the leader drone is denoted as P0(x0, y0, z0), and it is set that x0 = y0 = z0 = 0, which is defined as the intersection point; The vertices of the basic formation except the intersection points form the vertex set V, and the complex formation is disassembled into multiple simple formations to form the intersection set I; Description of the side: Let the UAV P i and P j The connection vector between the two points is represented as v ij =(x j -x i ,y j -y i ,z j -z i ), and the direction is from point P i to P j [[ID=2The i-th side of the basic formation has q i UAVs, then the side length of the i-th side is denoted as λ i =q i -1; To describe the details of the basic formation in more detail, virtual points can be set, and the side length where the virtual points are located is λ i Set as a decimal as needed.​ Expansion type: Let S ∈ {0, 1}, where 0 represents edge expansion and 1 represents internal expansion including.

5. A general multi-UAV formation method according to claim 1, characterized in that In the fifth step, for two adjacent vertices on a certain side in the simple formation, let P a (x a , y a , z a ) and P b (x b , y b , z b ). The coordinate of the connection vector between the two points is v ab = (x b - x a , y b - y a , z b - z a ); a) If P a and P b both belong to the vertex set V and are not virtual points, then the vertex coordinates after magnifying this edge by k times are (kx a , ky a , kz a ), (kx b , ky b , kz b ). The number of points to be inserted is m = λ i k - 1. The coordinates of the inserted points are successively (kx b , ky b , kz b ) - v ab / λ i , (kx b , ky b , kz b ) - 2×v ab / λ i , …, (kx b , ky b , kz b ) - m×v ab / λ i ; b) If P a and P b both belong to the vertex set V, and P b is a virtual point, then the vertex coordinates after magnifying this edge by k times are (kx a , ky a , kz a ), (kx b , ky b , kz b ). The number of points to be inserted is m = λ i k - 1. At this time, m is a decimal. Denote the decimal part of m as {m}. The coordinates of the inserted points are successively (kx b , ky b , kz b ) - {m}v ab / λ i , (kx b , ky b , kz b ) - ({m} + 1) × v ab / λ i , …, (kx b , ky b , kz b ) - m × v ab / λ i .

6. A general multi-UAV formation method as claimed in claim 1, wherein In step eight, for the UAV formation that has been expanded k - 1 times, the initial value of k is taken as 2; Insert new UAV points according to the following rules: Geometric feature preservation: Formation G' after inserting new points k-1 should be as close as possible to the original formation G k-1 ; The insertion order is reasonable: The numbers of the inserted points should meet the requirements of path planning and obstacle avoidance during mission execution.

7. The general multi-UAV formation method according to claim 1, characterized in that, In the eighth step, the new formation G k The number of UAV points is m k , when it is necessary to obtain the coordinate position of the UAV with the specified number q, it is only necessary to judge whether it satisfies m k-1 <q + 1 ≤ m k , if so, the UAV with the number q is in the formation expanded by k times, and then the coordinate positions of the UAVs with any number in the formation expanded by k times can be obtained.

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