A spacecraft component layout optimization method based on three-dimensional Φ function

Abstract

The present invention discloses a spacecraft component layout optimization method based on a three-dimensional Φ function. The method presets the dimensions of a spacecraft cabin and a plurality of components to be arranged and performs an approximate description, obtains an approximate cuboid of the spacecraft cabin and the plurality of components to be arranged, presets the position parameters of the approximate cuboid corresponding to each component to be arranged in the approximate cuboid of the spacecraft cabin, and uses a method based on the three-dimensional Φ function to set the position parameters of any two components to be arranged and the position of each component to be arranged with the spacecraft cabin in the three-dimensional space R 3 The method uses a three-dimensional Φ function between the complements of the spacecraft and constructs non-interference constraints for the spacecraft cabin's internal layout. A target function is constructed based on the spacecraft's desired and actual center of mass. Based on this target function and the non-interference constraints for the spacecraft cabin's internal layout, a spacecraft component layout optimization model is constructed and solved, yielding an optimized solution for the spacecraft component layout that satisfies the constraints. This method enables more efficient and accurate optimization of component layouts.

Description

Technical Field

[0001] The present invention relates to the technical field of spacecraft design, and in particular to a spacecraft component layout optimization method based on a three-dimensional Φ function. Background Art

[0002] With the rapid advancement of aerospace technology and industrialization, the requirements for spacecraft design are increasing. Shorter design cycles, lower development costs, and higher design reliability have become the primary goals of current spacecraft design. A spacecraft consists of a cabin and the components arranged within it. These components are the equipment and instruments installed within the cabin to support the spacecraft's flight mission and complete various experimental requirements. A key task in spacecraft design is to optimize the component layout design within limited mass, volume, and other relevant constraints to ensure long-term stable operation in orbit. The spacecraft component layout optimization problem is a typical multidisciplinary system design problem, involving both continuous variables (such as component position coordinates) and discrete variables (such as component distribution bay panels) and complex performance constraints. This results in a highly nonlinear, strongly constrained, and multimodal design space, significantly increasing the difficulty of the optimization search.

[0003] Scholars have proposed and applied various methods to address layout interference. These methods all establish geometric mathematical models of spacecraft and transform the geometric positional relationships between components into geometric positional relationships between shapes, which, to some extent, address the strong constraint of geometric non-interference between components. For example, the unsuitable polygon method determines whether two polygons interfere with each other by constructing a critical geometric figure where their boundaries just touch; the finite enveloping circle method uses multiple enveloping circles or spheres to approximate device components of arbitrary geometric shapes; and the level set function method uses the zero surface of the level set function to represent geometric boundaries. Among these methods, the unsuitable polygon method transforms the geometric relationship between two shapes into a positional relationship between points and shapes, but is limited to handling two-dimensional component layouts placed perpendicular to the coordinate axes. The finite enveloping circle method evaluates interference between components by calculating the minimum distance between clusters of circles or spheres. While simple to implement, it inherently suffers from large errors and can lead to wasted design space. The level set function method can effectively construct arbitrary geometric shapes, but can lead to inaccurate geometric descriptions and interference calculations when objects have sharp corners. The above methods are mostly applied to the layout optimization problem of spacecraft cabin components in a two-dimensional plane. There is still great difficulty in solving the layout scheme design problem in three-dimensional space, and there are certain accuracy errors.

[0004] Currently, the design of three-dimensional layout schemes for spacecraft cabin components mainly relies on the experience of engineers. The initial optimization method often simplifies the three-dimensional layout problem in the instrument cabin into a two-dimensional layout problem on the cabin plane. Although several better solutions that meet the requirements of the spacecraft flight mission can be given, how to theoretically prove that the proposed solution is the optimal solution and how to obtain the optimal three-dimensional layout through theory remains a challenge. The research focus is on how to describe the interference calculation between components. Summary of the Invention

[0005] In order to solve the three-dimensional interference calculation problem involved in the layout of instrument and equipment components installed on different panels of the spacecraft cabin in a box-type spacecraft, the present invention application proposes a spacecraft component layout optimization method based on a three-dimensional Φ function to optimize the design of the spacecraft component layout.

[0006] A spacecraft component layout optimization method based on a three-dimensional Φ function, the method comprising the following steps:

[0007] S1. Preset the dimensions of the spacecraft cabin and multiple components to be laid out, perform approximate descriptions of the spacecraft cabin and the multiple components to be laid out based on the dimensions, obtain approximate rectangular parallelepipeds of the spacecraft cabin and the multiple components to be laid out, construct a three-dimensional rectangular coordinate system with any vertex of the approximate rectangular parallelepiped of the spacecraft cabin as the coordinate origin, and preset position parameters of the approximate rectangular parallelepiped corresponding to each component to be laid out within the approximate rectangular parallelepiped of the spacecraft cabin;

[0008] S2, according to the position parameters, a method based on the three-dimensional Φ function is used to set the three-dimensional Φ function between the approximate cuboids corresponding to any two components to be laid out, and the approximate cuboid of each component to be laid out and the approximate cuboid of the spacecraft cabin in the three-dimensional space R 3 The three-dimensional Φ function between the complement of ;

[0009] S3, according to the three-dimensional Φ function between the approximate cuboids corresponding to any two components to be laid out and the approximate cuboid of each component to be laid out and the approximate cuboid of the spacecraft cabin in the three-dimensional space R 3 The three-dimensional Φ function between the complements of is used to construct the non-interference constraints for the interior layout of the spacecraft cabin;

[0010] S4. Taking the geometric center of the spacecraft as the expected center of mass, taking the center of mass of the spacecraft obtained after layout as the actual center of mass, and constructing the objective function based on the expected center of mass and the actual center of mass;

[0011] S5. Construct a spacecraft component layout optimization model based on the objective function and the non-interference constraints of the internal layout of the spacecraft cabin, optimize and solve the spacecraft component layout optimization model, and obtain a spacecraft component layout optimization solution that meets the constraints.

[0012] Preferably, the approximate rectangular parallelepiped of the spacecraft cabin and the multiple components to be laid out in S1 is specifically expressed by the formula:

[0013] P0=(a0,b0,h0)

[0014] P i =(a i ,b i ,h i )

[0015] Among them, P0 is the approximate rectangular parallelepiped of the spacecraft cabin, a0, b0, and h0 represent the half length, half width, and half height of the approximate rectangular parallelepiped of the spacecraft cabin, respectively. i is the approximate cuboid of the i-th component to be laid out, a i 、b i 、h i Respectively represent the half-length, half-width, and half-height of the approximate cuboid of the i-th component to be laid out.

[0016] Preferably, in S1, position parameters of the approximate cuboid corresponding to each component to be laid out in the approximate cuboid of the spacecraft cabin are preset. The position parameters are specifically expressed by the formula:

[0017] X={X i =(a i ,x i ,y i ,z i )|i=1,2,...,N,a i ∈[1,2,3,4,5,6]}

[0018] Where X represents a set of layout schemes of the components to be laid out in the spacecraft cabin, X i Indicates the position parameter of the i-th component to be laid out, a i represents the installation surface of the i-th component to be laid out on the 3D geometric model, x i ,y i ,z i They represent the centroid coordinates of the i-th component to be laid out in the three-dimensional rectangular coordinate system, and N represents the total number of components to be laid out.

[0019] Preferably, S2 specifically includes the following:

[0020] S21, determine the position of any two components to be laid out in the three-dimensional space R according to the position parameters of the two components to be laid out and the approximate cuboid. 3 The possible spatial range of intersection;

[0021] S22, set the approximate cuboids corresponding to any two components to be laid out in the three-dimensional space R 3 The three-dimensional Φ function in the space where the two may intersect;

[0022] S23. Determine the approximate rectangular parallelepiped of the spacecraft cabin in the three-dimensional space R 3 The complement of the set, the approximate cuboid of any component to be laid out and the approximate cuboid of the spacecraft cabin in the three-dimensional space R 3 The complement of in three-dimensional space R 3 The possible spatial range of intersection;

[0023] S24, set the approximate cuboid of any component to be laid out and the approximate cuboid of the spacecraft cabin in the three-dimensional space R 3 The complement of in three-dimensional space R 3 The three-dimensional Φ function in the range of possible intersection spaces.

[0024] Preferably, S22 is specifically expressed by the formula:

[0025] Φ 1 (u i ,u j )=Φ 1 (u)=max{xA,yB,-xA,-yB,zH,-zH}

[0026] Among them, u=u j -u i ,u j =(x j ,y j ,z j ),u i =(x i ,y i ,z i ), u=(x,y,z)∈R 3

[0027] A=a i +a j , B=b i +b j , H=h i +h j

[0028] Where, Φ 1 (u i ,u j ) represents the three-dimensional Φ function between the i-th component to be laid out and the approximate cuboid corresponding to the j-th component to be laid out, Φ 1 (u) is the intermediate process variable, u i and u jThey represent the centroid coordinates of the approximate rectangular parallelepipeds corresponding to the i-th component to be laid out and the j-th component to be laid out, u represents the difference between the centroid coordinates of the i-th component to be laid out and the j-th component to be laid out, A, B, and H represent the sum of the half-length, half-width, and half-height of the approximate rectangular parallelepipeds corresponding to the i-th component to be laid out and the j-th component to be laid out, respectively.

[0029] Preferably, S24 is specifically expressed by the formula:

[0030] Φ 2 (u0,u i )=Φ 2 (u′)=min{-x+A′,-y+B′,x+A′,y+B′,-z+H′,z+H′}

[0031] Among them, u′=u0-u i ,u0=(x0,y0,z0),u i =(x i ,y i ,z i ), u′=(x,y,z)∈R 3

[0032] A′=a0-a i , B′=b0-b i , H′=h0-h i

[0033] Where, Φ 2 (u0,u i ) represents the approximate cuboid of the spacecraft cabin in the three-dimensional space R 3 The three-dimensional Φ function between the complement of and the approximate cuboid of the i-th component to be laid out, Φ 2 (u′) is an intermediate process variable, u0 represents the coordinates of the center of mass of the approximate rectangular parallelepiped of the spacecraft cabin, u i represents the coordinates of the center of mass of the approximate rectangular parallelepiped of the i-th component to be laid out, u′ represents the difference between the coordinates of the center of mass of the spacecraft cabin and the i-th component to be laid out, A′, B′, and H′ represent the differences in half length, half width, and half height between the approximate rectangular parallelepiped of the spacecraft cabin and the i-th component to be laid out, respectively.

[0034] Preferably, the non-interference constraint of the internal layout of the spacecraft cabin in S3 is specifically expressed by the formula:

[0035] c1(X)=Φ 1 (u i ,u j )≥0,i,j=1,2,...,N,i≠j

[0036] c2(X)=Φ 2 (u0,ui )≥0,i=1,2,...,N

[0037] Where c1(X) represents the non-interference constraint between the approximate cuboids corresponding to any two components to be laid out, and c2(X) represents the approximate cuboid of any one component to be laid out and the approximate cuboid of the spacecraft cabin in the three-dimensional space R 3 Non-interference constraints between the complements of .

[0038] Preferably, the objective function in S4 is specifically expressed as:

[0039] f(X)=|x c -x e |+|y c -y e |+|z c -z e |

[0040] Where f(X) represents the center of mass error of the spacecraft after the components to be laid out are laid out according to the layout plan X, (x c ,y c ,z c ) represents the actual center of mass of the spacecraft after the components to be laid out are laid out according to the layout scheme X, (x e ,y e ,z e ) represents the desired center of mass of the spacecraft.

[0041] Preferably, the spacecraft component layout optimization model in S5 is specifically expressed by the formula:

[0042]

[0043] Where X represents a set of layout schemes of the components to be laid out in the spacecraft cabin.

[0044] The above-mentioned spacecraft component layout optimization method based on the three-dimensional Φ function presets the outer dimensions of the spacecraft cabin and multiple components to be arranged and performs an approximate description to obtain an approximate rectangular parallelepiped of the spacecraft cabin and multiple components to be arranged, presets the position parameters of the approximate rectangular parallelepiped corresponding to each component to be arranged in the approximate rectangular parallelepiped of the spacecraft cabin, and uses the method based on the three-dimensional Φ function to set the position parameters of any two components to be arranged and each component to be arranged and the spacecraft cabin in the three-dimensional space R 3The method uses a three-dimensional Φ function between the complements of the spacecraft and constructs non-interference constraints for the interior layout of the spacecraft cabin. A target function is constructed based on the desired and actual center of mass of the spacecraft. A spacecraft component layout optimization model is constructed based on the target function and the non-interference constraints of the interior layout of the spacecraft cabin, and the optimization solution is optimized to obtain a spacecraft component layout optimization solution that meets the constraints. This method introduces integer variables to determine the specific installation surfaces of the components to be laid out. The three-dimensional Φ function is used to calculate geometric interference and perform layout optimization. The integer variables can influence the coordinate variables of the components after layout, thereby achieving more efficient and accurate optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 is a flow chart of a method for optimizing spacecraft component layout based on a three-dimensional Φ function in one embodiment of the present invention;

[0046] Figure 2 is a schematic diagram of the layout structure in one embodiment of the present invention;

[0047] Figure 3 is a schematic diagram of a layout optimization result in one embodiment of the present invention, wherein: Figure 3 (a) is a three-dimensional isometric drawing. Figure 3 (b) is the isometric drawing on the YOZ plane. Figure 3 (c) is the isometric drawing on the XOZ plane. Figure 3 (d) is the isometric view on the XOY plane. DETAILED DESCRIPTION

[0048] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention is further described in detail below with reference to the accompanying drawings.

[0049] See also Figure 1 , a spacecraft component layout optimization method based on a three-dimensional Φ function, the method comprising the following steps:

[0050] S1. Preset the outer dimensions of the spacecraft cabin and multiple components to be arranged, make approximate descriptions of the spacecraft cabin and the multiple components to be arranged based on their outer dimensions, obtain approximate rectangular parallelepipeds of the spacecraft cabin and the multiple components to be arranged, construct a three-dimensional rectangular coordinate system with any vertex of the approximate rectangular parallelepiped of the spacecraft cabin as the coordinate origin, and preset the position parameters of the approximate rectangular parallelepiped corresponding to each component to be arranged in the approximate rectangular parallelepiped of the spacecraft cabin.

[0051] Furthermore, the approximate cuboid of the spacecraft cabin and multiple components to be laid out in S1 is specifically expressed by the formula:

[0052] P0=(a0,b0,h0)

[0053] P i =(ai ,b i ,h i )

[0054] Among them, P0 is the approximate rectangular parallelepiped of the spacecraft cabin, a0, b0, and h0 represent the half length, half width, and half height of the approximate rectangular parallelepiped of the spacecraft cabin, respectively. i is the approximate cuboid of the i-th component to be laid out, a i 、b i 、h i They represent the half length, half width, and half height of the approximate rectangular parallelepiped of the i-th component to be laid out, respectively. The half length, half width, and half height are half of the length, width, and height of the approximate rectangular parallelepiped.

[0055] Specifically, this embodiment mainly conducts component layout optimization design research on the spacecraft cabin structure. The components to be laid out can be installed on different panels in the spacecraft cabin. During the simulation process, the space occupied by components with complex geometric shapes is approximated as a rectangular parallelepiped with uniform mass distribution. Its center of mass coincides with the centroid, and the sides of the rectangular parallelepiped are considered to be parallel to the sides of the instrument cabin rectangular parallelepiped.

[0056] Furthermore, S1 presets the position parameters of the approximate cuboid corresponding to each component to be laid out in the approximate cuboid of the spacecraft cabin. The position parameters are specifically expressed by the formula:

[0057] X={X i =(a i ,x i ,y i ,z i )|i=1,2,...,N,a i ∈[1,2,3,4,5,6]}

[0058] Where X represents a set of layout schemes of the components to be laid out in the spacecraft cabin, X i Indicates the position parameter of the i-th component to be laid out, a i represents the installation surface of the i-th component to be laid out on the 3D geometric model, x i ,y i ,z i They represent the centroid coordinates of the i-th component to be laid out in the three-dimensional rectangular coordinate system, and N represents the total number of components to be laid out.

[0059] Specifically, suppose there are N components to be arranged, and these N components can be arbitrarily installed on the six mounting surfaces in the spacecraft cabin. A three-dimensional rectangular coordinate system is established with a vertex of the spacecraft cabin as the origin. According to the above uniform mass distribution assumption, the centroid or center of mass coordinates of each component to be arranged uniquely determine the geometric position of the component in the spacecraft cabin. This set of center of mass coordinates is denoted as {(x i ,y i,z i )|i=1,2,...,N}. In addition, since each component to be laid out must and can only be installed on the six mounting surfaces in the spacecraft cabin, that is, each component to be laid out cannot be "suspended" in the spacecraft cabin, an integer variable is introduced based on the aforementioned centroid coordinates to indicate on which mounting surface each component to be laid out is installed in the spacecraft cabin, thereby obtaining the position parameter of each component to be laid out: X={X i =(a i ,x i ,y i ,z i )|i=1,2,...,N,a i ∈[1,2,3,4,5,6]}. During the optimization process, once a component i to be laid out is located on the mounting surface a in the spacecraft cabin, i OK, then the centroid coordinates (x i ,y i ,z i ) will also be determined accordingly, that is, it will be limited to half the length of the component i in the height direction (that is, the direction perpendicular to the mounting surface). For example, if the component is mounted on the xoy plane, the coordinate of the component in the z direction is fixed to half the height of its approximate rectangular parallelepiped in the z direction, that is, half the height.

[0060] S2, according to the position parameters, a method based on the three-dimensional Φ function is used to set the three-dimensional Φ function between the approximate cuboids corresponding to any two components to be laid out, and the approximate cuboid of each component to be laid out and the approximate cuboid of the spacecraft cabin in the three-dimensional space R 3 The three-dimensional Φ function between the complements of .

[0061] Specifically, the three-dimensional Φ function describes the geometric information of the components and the geometric constraints between the components through an explicit functional analytical expression, and the geometric interference constraints between the components can be easily quantified according to the three-dimensional Φ function value.

[0062] Furthermore, S2 specifically includes the following:

[0063] S21, determine the position of any two components to be laid out in the three-dimensional space R according to the position parameters of the two components to be laid out and the approximate cuboid. 3 The possible intersecting space range.

[0064] S22, set the approximate cuboids corresponding to any two components to be laid out in the three-dimensional space R 3 The three-dimensional Φ function in the range of possible intersection spaces.

[0065] S23. Determine the approximate rectangular parallelepiped of the spacecraft cabin in the three-dimensional space R 3The complement of the set, the approximate cuboid of any component to be laid out and the approximate cuboid of the spacecraft cabin in the three-dimensional space R 3 The complement of in three-dimensional space R 3 The possible intersecting space range.

[0066] Specifically, first determine the approximate cuboid of the spacecraft cabin in the three-dimensional space R 3 Then determine the complement of the approximate cuboid of the component to be laid out and the approximate cuboid of the spacecraft cabin in three-dimensional space. The two are in three-dimensional space R 3 The possible intersecting space range.

[0067] S24, set the approximate cuboid of any component to be laid out and the approximate cuboid of the spacecraft cabin in the three-dimensional space R 3 The complement between the three-dimensional space R 3 The three-dimensional Φ function in the complement of the possible intersecting space range.

[0068] Specifically, after the position parameters of the components to be arranged are determined, the interference amount can be calculated according to the size of the approximate cuboid of the components to be arranged. In this embodiment, a method based on a three-dimensional Φ function is used for calculation. For a given approximate cuboid It is only allowed to move along the vector u=(x,y,z)∈R 3 Perform translation and record the approximate cuboid after translation along vector u as:

[0069] P(u)={v∈R 3 :v=u+w,w∈P}

[0070] Where w represents the coordinates of any point inside the approximate cuboid P before translation, v represents the coordinates of the point inside the approximate cuboid P(u) after translation corresponding to w, and vector u is called the centroid coordinates of the approximate cuboid P(u).

[0071] For a continuous function Φ:R defined everywhere 6 →R 1 , that is, the input variable is six-dimensional, the output is one-dimensional, and the Φ function between the approximate cuboid P1(u1) and the approximate cuboid P2(u2) (that is, the three-dimensional Φ function) has the following properties:

[0072] When two approximate cuboids do not intersect, the Φ function between the two approximate cuboids is greater than 0, that is:

[0073] like Then Φ(u1,u2)>0;

[0074] When two approximate cuboids are tangent, that is, when the boundaries of the two approximate cuboids just touch, the Φ function between the two approximate cuboids is equal to 0, that is:

[0075] like and Then Φ(u1,u2)=0;

[0076] When two approximate cuboids intersect, the Φ function between the two approximate cuboids is less than 0, that is:

[0077] like Then Φ(u1,u2)<0.

[0078] Among them, Φ(u1,u2) represents the Φ function between the approximate cuboid P1(u1) and the approximate cuboid P2(u2), clP represents the topological closure of the approximate cuboid P (the topological closure includes the interior and boundary of the cuboid), intP represents the interior of the approximate cuboid P, and frP represents the boundary of the approximate cuboid P.

[0079] Taking the first and second components to be laid out as examples, the process of setting the three-dimensional Φ function between the approximate cuboids corresponding to the two components to be laid out is described as follows:

[0080] The approximate cuboids of the first component to be laid out and the second component to be laid out are described as P1 = (a1, b1, h1) and P2 = (a2, b2, h2), respectively, where P1 and P2 represent the approximate cuboids of the first and second components to be laid out, respectively. 2a1, 2b1, and 2h1 are the length, width, and height of the approximate cuboid of the first component to be laid out, respectively. 2a2, 2b2, and 2h2 represent the length, width, and height of the approximate cuboid of the second component to be laid out, respectively.

[0081] The position parameters of the first component to be laid out and the second component to be laid out are: (a1, x1, y1, z1) and (a2, x2, y2, z2), where a1, a2∈[1, 2, 3, 4, 5, 6].

[0082] The approximate cuboids of the first component to be laid out and the second component to be laid out are in the three-dimensional space R 3 The possible intersecting spaces are as follows:

[0083] {(-A,A), (-B,B), (-H,H)},

[0084] Among them, A=a1+a2,B=b1+b2,H=h1+h2

[0085] Where A, B, and H represent the sum of half-lengths, half-widths, and half-heights of the approximate rectangular parallelepipeds corresponding to the first component to be laid out and the second component to be laid out, respectively.

[0086] The approximate cuboids of the first component to be laid out and the second component to be laid out are in the three-dimensional space R3 The three-dimensional Φ function in the possible intersecting space is:

[0087] Φ 1 (u1,u2)=Φ 1 (u)=max{xA,yB,-xA,-yB,zH,-zH}

[0088] Among them, u=u2-u1, u2=(x2,y2,z2), u1=(x1,y1,z1), u=(x,y,z)∈R 3

[0089] Where, Φ 1 (u1,u2) represents the three-dimensional Φ function between the approximate cuboids corresponding to the first component to be laid out and the second component to be laid out, Φ 1 (u) is an intermediate process variable, u1 and u2 represent the centroid coordinates of the approximate rectangular blocks P1(u1) and P2(u2) corresponding to the first and second components to be laid out, respectively, and u represents the difference between the centroid coordinates of the first and second components to be laid out.

[0090] By using the same method as above, the approximate cuboids of any two components to be laid out among the N components to be laid out can be set in the three-dimensional space R 3 The three-dimensional Φ function in the range of possible intersection spaces.

[0091] Similarly, taking the spacecraft cabin and the first component to be laid out as an example, the approximate cuboid of the first component to be laid out and the approximate cuboid of the spacecraft cabin are placed in the three-dimensional space R 3 The complement of in three-dimensional space R 3 The setting process of the three-dimensional Φ function in the possible intersecting space is as follows:

[0092] The approximate rectangular parallelepiped of the spacecraft cabin is described as P0 = (a0, b0, h0), where P0 represents the approximate rectangular parallelepiped of the spacecraft cabin, 2a0, 2b0 and 2h0 represent the length, width and height of the approximate rectangular parallelepiped of the spacecraft cabin respectively, and a0>a1, b0>b1, h0>h1 must be satisfied.

[0093] The approximate cuboid of the spacecraft cabin is in the three-dimensional space R 3 The complement of the first component to be laid out and the approximate cuboid between them are in the three-dimensional space R 3 The possible intersection ranges are as follows:

[0094] {(-A′,A′),(-B′,B′),(-H′,H′)}

[0095] Among them, A′=a0-a1, B′=b0-b1, H′=h0-h1

[0096] Where A′, B′, and H′ represent the difference in half length, half width, and half height between the approximate cuboid of the spacecraft cabin and the approximate cuboid of the first component to be laid out, respectively.

[0097] The approximate cuboid of the spacecraft cabin is in the three-dimensional space R 3 The three-dimensional Φ function between the complement of and the approximate cuboid of the first component to be laid out is:

[0098] Φ 2 (u0,u1)=Φ 2 (u′)=min{-x+A′,-y+B′,x+A′,y+B′,-z+H′,z+H′}

[0099] Among them, u′=u0-u1, u0=(x0,y0,z0), u1=(x1,y1,z1), u′=(x,y,z)∈R 3

[0100] Where, Φ 2 (u0,u1) represents the approximate cuboid of the spacecraft cabin in the three-dimensional space R 3 The three-dimensional Φ function between the complement of and the approximate cuboid of the first component to be laid out, Φ 2 (u′) is an intermediate process variable, u0 represents the coordinates of the center of mass of the approximate rectangular parallelepiped of the spacecraft cabin, u1 represents the coordinates of the center of mass of the approximate rectangular parallelepiped of the first component to be laid out, and u′ represents the difference between the coordinates of the center of mass of the spacecraft cabin and the first component to be laid out.

[0101] By using the method described above, the approximate cuboid of any one of the N components to be laid out and the approximate cuboid of the spacecraft cabin can be set in the three-dimensional space R 3 The three-dimensional Φ function between the complements of .

[0102] S3, according to the three-dimensional Φ function between the approximate cuboids corresponding to any two components to be laid out and the approximate cuboid of each component to be laid out and the approximate cuboid of the spacecraft cabin in the three-dimensional space R 3 The three-dimensional Φ function between the complements of is used to construct the non-interference constraints for the interior layout of the spacecraft cabin.

[0103] Furthermore, the non-interference constraint of the internal layout of the spacecraft cabin in S3 is specifically expressed by the formula:

[0104] c1(X)=Φ 1 (u i ,u j )≥0,i,j=1,2,...,N,i≠j

[0105] c2(X)=Φ 2(u0,u i )≥0,i=1,2,...,N

[0106] Where c1(X) represents the non-interference constraint between the approximate cuboids corresponding to any two components to be laid out, and c2(X) represents the approximate cuboid of any one component to be laid out and the approximate cuboid of the spacecraft cabin in the three-dimensional space R 3 Non-interference constraints between the complements of .

[0107] Specifically, after obtaining the three-dimensional Φ function between any two approximate cuboids of components to be laid out, the approximate cuboid of each component to be laid out and the approximate cuboid of the spacecraft cabin are in the three-dimensional space R 3 After the three-dimensional Φ function between the complements of , each given a set of design variables in step S1

[0108] X={X i =(a i ,x i ,y i ,z i )|i=1,2,...,N,a i ∈[1,2,3,4,5,6]}, you can get the centroid coordinates u corresponding to the component to be laid out i (The center of mass coordinates u0 of the spacecraft cabin is fixed), according to the center of mass coordinates, the three-dimensional Φ function between the approximate cuboids of all components to be laid out, the approximate cuboid of each component to be laid out and the approximate cuboid of the spacecraft cabin in the three-dimensional space R 3 The interference of component layout is obtained by calculating the three-dimensional Φ function between the complements of .

[0109] According to the above definition, if Φ 1 (u1,u2)≥0, it means that the first component to be laid out and the second component to be laid out do not interfere with each other. Otherwise, if Φ 1 (u1,u2)<0, it means that the first component to be laid out and the second component to be laid out will interfere with each other; similarly, if Φ 2 (u0,u1)≥0, it means that the spacecraft cabin and the first component to be laid out do not interfere with each other. Otherwise, if Φ 2 If (u0,u1)<0, it means that the spacecraft cabin interferes with the first component to be laid out.

[0110] During component layout, the three-dimensional Φ function value of each item is required to be greater than or equal to 0.

[0111] S4. The geometric center of the spacecraft is taken as the expected center of mass, the center of mass of the spacecraft obtained after layout is taken as the actual center of mass, and the objective function is constructed based on the expected center of mass and the actual center of mass.

[0112] Specifically, after setting the non-interference constraints in the layout optimization process, the optimization target can be designed. In this embodiment, the center of mass target of the spacecraft is mainly considered. If the static stability of the spacecraft is too large, it will inevitably affect the maneuverability of the spacecraft. Therefore, when designing the spacecraft, it is required that the center of mass deviation of the entire spacecraft be kept within an allowable error range, and the error between the actual center of mass of the spacecraft and the expected center of mass is required to be as small as possible. Generally, the geometric center of the spacecraft is taken as the expected center of mass. The objective function is expressed as follows:

[0113] f(X)=|x c -x e |+|y c -y e |+|z c -z e |

[0114] Where f(X) represents the center of mass error of the spacecraft after the components to be laid out are laid out according to the layout plan X, (x c ,y c ,z c ) represents the actual center of mass of the spacecraft after the components to be laid out are laid out according to the layout scheme X, (x e ,y e ,z e ) represents the desired center of mass of the spacecraft.

[0115] S5. Construct a spacecraft component layout optimization model based on the objective function and the non-interference constraints of the internal layout of the spacecraft cabin, optimize and solve the spacecraft component layout optimization model, and obtain a spacecraft component layout optimization solution that meets the constraints.

[0116] Furthermore, the spacecraft cabin component layout optimization problem can be described as:

[0117]

[0118] Where X represents a set of layout schemes of the components to be laid out in the spacecraft cabin.

[0119] By optimizing and solving the above optimization model, we can obtain the optimal layout solution of spacecraft components that meets the constraints, that is, the set of position parameters of each component to be laid out.

[0120] Furthermore, a spacecraft component layout optimization method based on a three-dimensional Φ function in the present invention is verified through numerical simulation.

[0121] Consider a spacecraft component layout problem consisting of 11 components, the layout structure of which is shown as follows: Figure 2The dimensions of the spacecraft cabin cuboid are [10, 20, 10]. Considering the spacecraft cabin as a uniformly massed geometric body, its center of mass is its geometric center [5, 10, 5]. The approximate dimensions of the cuboids for the components to be laid out are shown in Table 1. The desired center of mass coordinates for layout optimization are set to [5, 10, 5]. Non-interference constraints between components and between components and the spacecraft cabin are set and optimized using the same method as described above.

[0122] Table 1 Data of the approximate cuboids of the 11 components to be laid out

[0123]

[0124]

[0125] After multiple optimization iterations, a layout design scheme that satisfies the design constraints and minimizes the objective function is obtained. The layout result diagram and its three-view drawing are shown in the figure. Figure 3 The corresponding layout scheme is shown in Table 2.

[0126] According to the position parameters and mass of each component in Table 2, the actual center of mass of the spacecraft can be calculated as:

[0127] [4.999959551963589,10.000021164830644,4.999981943191803], it can be considered that the desired target centroid [5,10,5] is within the allowable error range.

[0128] Table 2 Component position parameters obtained after layout optimization

[0129] Component Number a x y z 1 6 5.773 11.216 8.500 2 2 4.886 2.000 8.501 3 2 8.943 2.500 8.491 4 3 4.334 13.170 2.000 5 3 6.192 18.304 1.500 6 3 3.023 16.266 1.500 7 3 6.696 2.942 1.500 8 3 1.734 11.191 2.500 9 1 1.500 4.843 8.495 10 4 6.000 8.091 3.221 11 5 7.392 19.000 8.986

[0130] The above-mentioned spacecraft component layout optimization method based on the three-dimensional Φ function presets the outer dimensions of the spacecraft cabin and multiple components to be arranged and performs an approximate description to obtain an approximate rectangular parallelepiped of the spacecraft cabin and multiple components to be arranged, presets the position parameters of the approximate rectangular parallelepiped corresponding to each component to be arranged in the approximate rectangular parallelepiped of the spacecraft cabin, and uses the method based on the three-dimensional Φ function to set the position parameters of any two components to be arranged and each component to be arranged and the spacecraft cabin in the three-dimensional space R 3The method uses a three-dimensional Φ function between the complements of the spacecraft and constructs non-interference constraints for the interior layout of the spacecraft cabin. A target function is constructed based on the desired and actual center of mass of the spacecraft. A spacecraft component layout optimization model is constructed based on the target function and the non-interference constraints of the interior layout of the spacecraft cabin, and the optimization solution is obtained to obtain an optimized layout solution for the spacecraft components that meets the constraints. This method introduces integer variables to determine the specific installation surfaces of the components to be laid out. The introduction of integer variables provides more possibilities and flexibility for solving the layout optimization problem. By calculating geometric interference using the three-dimensional Φ function and performing layout optimization, the positional relationships of each component in three-dimensional space are comprehensively and meticulously considered, avoiding unreasonable layout problems caused by inaccurate calculations. Taking the center of mass requirement of the spacecraft design as the optimization target, the stability and reliability of the spacecraft during operation are ensured.

[0131] The above describes in detail the spacecraft component layout optimization method based on a three-dimensional Φ function provided by the present invention. This article uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only intended to facilitate understanding of the core concepts of the present invention. It should be noted that those skilled in the art will be able to make various improvements and modifications to the present invention without departing from the principles of the present invention, and such improvements and modifications are also within the scope of protection of the claims.

Claims

1. A spacecraft component layout optimization method based on three-dimensional Φ function, characterized in that: The method comprises: S1. Preset the dimensions of the spacecraft cabin and multiple components to be laid out, perform approximate descriptions of the spacecraft cabin and the multiple components to be laid out based on the dimensions, obtain approximate rectangular parallelepipeds of the spacecraft cabin and the multiple components to be laid out, construct a three-dimensional rectangular coordinate system with any vertex of the approximate rectangular parallelepiped of the spacecraft cabin as the coordinate origin, and preset position parameters of the approximate rectangular parallelepiped corresponding to each component to be laid out within the approximate rectangular parallelepiped of the spacecraft cabin; S2, according to the position parameters, a method based on the three-dimensional Φ function is used to set the three-dimensional Φ function between the approximate cuboids corresponding to any two components to be laid out, and the approximate cuboid of each component to be laid out and the approximate cuboid of the spacecraft cabin in the three-dimensional space R 3 The three-dimensional Φ function between the complement of ; S3, according to the three-dimensional Φ function between the approximate cuboids corresponding to any two components to be laid out and the approximate cuboid of each component to be laid out and the approximate cuboid of the spacecraft cabin in the three-dimensional space R 3 The three-dimensional Φ function between the complements of is used to construct the non-interference constraints for the interior layout of the spacecraft cabin; S4. Taking the geometric center of the spacecraft as the expected center of mass, taking the center of mass of the spacecraft obtained after layout as the actual center of mass, and constructing the objective function based on the expected center of mass and the actual center of mass; S5. Construct a spacecraft component layout optimization model based on the objective function and the non-interference constraints of the spacecraft cabin internal layout, optimize and solve the spacecraft component layout optimization model, and obtain a spacecraft component layout optimization solution that meets the constraints; S2 specifically includes the following: S21, determine the position of any two components to be laid out in the three-dimensional space R according to the position parameters of the two components to be laid out and the approximate cuboid. 3 The possible spatial range of intersection; S22, set the approximate cuboids corresponding to any two components to be laid out in the three-dimensional space R 3 The three-dimensional Φ function in the space where the two may intersect; S23. Determine the approximate rectangular parallelepiped of the spacecraft cabin in the three-dimensional space R 3 The complement of the set, the approximate cuboid of any component to be laid out and the approximate cuboid of the spacecraft cabin in the three-dimensional space R 3 The complement of in three-dimensional space R 3 The possible spatial range of intersection; S24, set the approximate cuboid of any component to be laid out and the approximate cuboid of the spacecraft cabin in the three-dimensional space R 3 The complement of in three-dimensional space R 3 The three-dimensional Φ function in the range of possible intersection spaces.

2. The spacecraft component layout optimization method based on three-dimensional Φ function according to claim 1, characterized in that: The approximate cuboid of the spacecraft cabin and multiple components to be laid out in S1 is specifically expressed by the formula: P0=(a0,b0,h0) P i =(a i ,b i ,h i ) Among them, P0 is the approximate rectangular parallelepiped of the spacecraft cabin, a0, b0, and h0 represent the half length, half width, and half height of the approximate rectangular parallelepiped of the spacecraft cabin, respectively. i is the approximate cuboid of the i-th component to be laid out, a i 、b i 、h i Respectively represent the half-length, half-width, and half-height of the approximate cuboid of the i-th component to be laid out.

3. The spacecraft component layout optimization method based on three-dimensional Φ function according to claim 2, characterized in that: In S1, the position parameters of the approximate cuboid corresponding to each component to be laid out in the approximate cuboid of the spacecraft cabin are preset. The position parameters are specifically expressed by the formula: X={X i =(a i ,x i ,y i ,z i )|i=1,2,...,N,a i ∈[1,2,3,4,5,6]} Where X represents a set of layout schemes of the components to be laid out in the spacecraft cabin, X i Indicates the position parameter of the i-th component to be laid out, a i represents the installation surface of the i-th component to be laid out on the 3D geometric model, x i ,y i ,z i They represent the centroid coordinates of the i-th component to be laid out in the three-dimensional rectangular coordinate system, and N represents the total number of components to be laid out.

4. The spacecraft component layout optimization method based on three-dimensional Φ function according to claim 3, characterized in that: S22 is specifically expressed by the formula: Φ 1 (u i ,u j )=Φ 1 (u)=max{xA,yB,-xA,-yB,zH,-zH} where \(u = u\) j -u i , \(u\) j =(x j , y j , z j ), \(u\) i =(x i , y i , z i ), \(u=(x,y,z)\in R\) 3 A=a i +a j ,B=b i +b j ,H=h i +h j Where, Φ 1 (u i ,u j ) represents the three-dimensional Φ function between the i-th component to be laid out and the approximate cuboid corresponding to the j-th component to be laid out, Φ 1 (u) is the intermediate process variable, u i and u j They represent the centroid coordinates of the approximate rectangular parallelepipeds corresponding to the i-th component to be laid out and the j-th component to be laid out, u represents the difference between the centroid coordinates of the i-th component to be laid out and the j-th component to be laid out, A, B, and H represent the sum of the half-length, half-width, and half-height of the approximate rectangular parallelepipeds corresponding to the i-th component to be laid out and the j-th component to be laid out, respectively.

5. The spacecraft component layout optimization method based on three-dimensional Φ function according to claim 4, characterized in that: S24 is specifically expressed by the formula: Φ 2 (u0,u i )=Φ 2 (u′)=min{-x+A′,-y+B′,x+A′,y+B′,-z+H′,z+H′} where \(u' = u_0 - u\) i , \(u_0=(x_0,y_0,z_0)\), \(u\) i \(=(x i ,y i ,z i )\), \(u'=(x,y,z)\in R 3 A′=a0-a i ,B′=b0-b i ,H′=h0-h i Where, Φ 2 (u0,u i ) represents the approximate cuboid of the spacecraft cabin in the three-dimensional space R 3 The three-dimensional Φ function between the complement of and the approximate cuboid of the i-th component to be laid out, Φ 2 (u′) is an intermediate process variable, u0 represents the coordinates of the center of mass of the approximate rectangular parallelepiped of the spacecraft cabin, u i represents the coordinates of the center of mass of the approximate rectangular parallelepiped of the i-th component to be laid out, u′ represents the difference between the coordinates of the center of mass of the spacecraft cabin and the i-th component to be laid out, A′, B′, and H′ represent the differences in half length, half width, and half height between the approximate rectangular parallelepiped of the spacecraft cabin and the i-th component to be laid out, respectively.

6. The spacecraft component layout optimization method based on three-dimensional Φ function according to claim 5, characterized in that: The non-interference constraint of the internal layout of the spacecraft cabin in S3 is specifically expressed by the formula: c1(X)=Φ 1 (you i ,u j )≥0,i,j=1,2,...,N,i≠j c2(X)=Φ 2 (u0,u i )≥0,i=1,2,...,N Where c1(X) represents the non-interference constraint between the approximate cuboids corresponding to any two components to be laid out, and c2(X) represents the approximate cuboid of any one component to be laid out and the approximate cuboid of the spacecraft cabin in the three-dimensional space R 3 Non-interference constraints between the complements of .

7. The spacecraft component layout optimization method based on three-dimensional Φ function according to claim 6, characterized in that: The objective function in S4 is specifically expressed as follows: f(X)=|x c -x e |+|y c -y e |+|z c -z e | Where f(X) represents the center of mass error of the spacecraft after the components to be laid out are laid out according to the layout plan X, (x c ,y c ,z c ) represents the actual center of mass of the spacecraft after the components to be laid out are laid out according to the layout scheme X, (x e ,y e ,z e ) represents the desired center of mass of the spacecraft.

8. The spacecraft component layout optimization method based on three-dimensional Φ function according to claim 7, characterized in that: The spacecraft component layout optimization model in S5 is specifically expressed by the formula: Where X represents a set of layout schemes of the components to be laid out in the spacecraft cabin.

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