Robot in-orbit space structure assembly optimization method

Abstract

The invention discloses a robot in-orbit space structure assembly optimization method, and belongs to the field of large-scale in-orbit space structure assembly strategy optimization. The problems that in the structure assembling process, external force impact can cause assembling errors, and vibration is caused are solved. According to the method, a dynamic substructure method and finite element analysis are adopted, a dynamic model in the assembly process is calculated, vibration of a robot to a structure is accurately calculated through a Newton-Euler method, high precision and reliability of the whole model are ensured, the genetic algorithm and the dynamic substructure technology are combined, the assembly sequence and path planning are optimized, and the assembly efficiency is improved. The influence of vibration on the structure is reduced, errors caused by vibration are effectively reduced, the assembly precision is improved, and the multi-robot cooperation efficiency is improved. The method can be applied to large-scale in-orbit space structure assembly strategy optimization.

Description

Technical Field

[0001] The present invention belongs to the field of large-scale on-orbit space structure assembly strategy optimization, and in particular relates to a robot on-orbit space structure assembly optimization method. Background Art

[0002] As the diameter of space antennas continues to increase, traditional assembly methods are gradually becoming inadequate, vibration issues are becoming increasingly prominent, and computational complexity increases dramatically with the expansion of system scale. Therefore, how to efficiently and accurately assemble these complex structures has become a critical issue that needs to be addressed. Due to the limited carrying capacity of rockets, existing pre-launch folding and post-orbital deployment technologies face the following problems: First, the folded structure is too large to be transported in a single launch; second, the design of the structural deployment mechanism and its drive present significant challenges; and finally, the surface accuracy of the deployed structure is low. To address these issues, especially the demand for large-scale space antennas with a diameter of hundreds of meters, future solutions will need to rely on designing the structure as a combination of multiple modules, launching these structural modules into orbit via a launch vehicle, and then relying on space robots to complete the modular assembly in orbit. This assembly method not only solves the problems of transportation and deployment, but also helps to improve assembly precision and flexibility.

[0003] Very large spatial structures are often composed of multiple identical modules. Precise assembly of these large modules requires the coordinated coordination and assembly of multiple assembly mechanisms. However, the structural assembly process often encounters periodic external impacts, which not only lead to assembly errors but also cause vibration and other problems, posing a significant challenge to circular assembly. Summary of the Invention

[0004] The purpose of the present invention is to solve the problem that external force impact during the structural assembly process may cause assembly errors and induce vibrations, and to propose a robot on-orbit spatial structure assembly optimization method to reduce vibrations during the structural assembly process.

[0005] The technical solution adopted by the present invention to solve the above technical problems is:

[0006] A method for optimizing on-orbit spatial structure assembly by a robot, the method specifically comprising the following steps:

[0007] Step 1: Construct the dynamic equation of a single assembly module based on the thin plate finite element principle;

[0008] Step 2: Use the dynamic substructuring method to assemble the two independent assembly modules into a whole, and establish the dynamic differential equation after the assembly is completed based on the dynamic equation of the individual assembly modules;

[0009] Step 3: Plan the robot's path from the assembly module storage location to the target installation location, and optimize the assembly sequence based on the genetic algorithm and the dynamic differential equation of step 2.

[0010] The beneficial effects of the present invention are:

[0011] 1. This invention optimizes the assembly of space structures through dynamic substructuring and finite element analysis. This method uses dynamic substructuring and finite element analysis to calculate the dynamic model during the assembly process. The Newton-Euler method is also used to accurately calculate the vibration of the robot on the structure, ensuring high accuracy and reliability of the overall model. This solves the complexity problem in assembling large space antenna structures.

[0012] 2. This invention reduces vibration through multi-robot collaboration, improving assembly precision and efficiency. This invention combines multi-robot collaboration with dynamic substructuring technology to optimize assembly sequence and path planning, reducing the impact of vibration on the structure and improving assembly precision. Through vibration control and path optimization, the precision and stability of spatial structure assembly are significantly improved, ensuring smooth execution of the task.

[0013] 3. The present invention optimizes assembly sequence and robot path planning through genetic algorithms. The present invention effectively reduces errors caused by vibration, reduces damage to precision equipment, improves the efficiency of multi-robot collaboration, shortens assembly time, reduces costs, and is suitable for high-precision space missions.

[0014] 4. This invention improves the long-term stability and reliability of space structures. By effectively suppressing vibration and optimizing the module installation sequence, this invention enhances the stability and long-term reliability of space structures, extends their service life, reduces maintenance costs, and provides a stable technical guarantee for future large-scale space missions. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a flow chart of a robot on-orbit spatial structure assembly optimization method of the present invention;

[0016] Figure 2 It is a schematic diagram of the assembly process;

[0017] Figure 3a It is the finite element cloud diagram of a single assembly module;

[0018] In the figure, X represents the X-axis coordinate in a two-dimensional Cartesian coordinate system, and Y represents the Y-axis coordinate in a two-dimensional Cartesian coordinate system, and the unit is m;

[0019] Figure 3b It is a finite element cloud diagram of multiple assembly modules;

[0020] Figure 4 It is a schematic diagram of module assembly planning;

[0021] Figure 5a It is a genetic algorithm adaptation curve in the case of a robot;

[0022] Fitness represents fitness, and iteration represents the number of iterations;

[0023] Figure 5b is the adaptation curve of the genetic algorithm in the case of two robots;

[0024] Figure 5c is the adaptation curve of the genetic algorithm in the case of three robots;

[0025] Figure 5d is the adaptation curve of the genetic algorithm in the case of six robots;

[0026] Figure 6a It is a graph of the maximum vibration point of the structure in the case of a robot under randomly generated assembly sequences;

[0027] Vibration indicates the vibration amplitude;

[0028] Figure 6b This is a graph of the maximum vibration point of the structure in the case of two robots under randomly generated assembly orders;

[0029] Figure 6c This is a graph of the maximum vibration point of the structure in the case of three robots under randomly generated assembly orders;

[0030] Figure 6d This is a graph of the maximum vibration point of the structure in the case of six robots under randomly generated assembly orders;

[0031] Figure 7a It is a graph of the maximum vibration point of the structure in the case of one robot under the optimized assembly sequence;

[0032] Figure 7b It is a graph of the maximum vibration point of the structure in the case of two robots under the optimized assembly sequence;

[0033] Figure 7c It is a graph of the maximum vibration point of the structure in the case of three robots under the optimized assembly sequence;

[0034] Figure 7d It is a graph of the maximum vibration point of the structure in the case of six robots under the optimized assembly sequence. DETAILED DESCRIPTION

[0035] Specific implementation method 1. Combination Figure 1 This embodiment describes a method for optimizing the on-orbit spatial structure assembly of a robot, which specifically includes the following steps:

[0036] Step 1: Construct the dynamic equation of a single assembly module based on the thin plate finite element principle;

[0037] Step 2: Use the dynamic substructure method to assemble the two independent assembly modules into a whole. According to the dynamic equation of a single assembly module, the dynamic differential equation after assembly is established. The finite element cloud diagram of a single assembly module is as follows: Figure 3a As shown, the finite element cloud diagrams of multiple assembly modules are as follows Figure 3b shown.

[0038] Step 3: Plan the robot's path from the assembly module storage location to the target installation location, and optimize the assembly sequence based on the genetic algorithm and the dynamic differential equation of step 2.

[0039] After assembling two independent assembly modules together using the method of the present invention, the assembled whole and a new independent assembly module are respectively regarded as independent parts, and the two independent parts are assembled again using the method of the present invention, and so on, until the entire assembly process is completed.

[0040] Specific embodiment 2: This embodiment differs from specific embodiment 1 in that the specific process of step 1 is as follows:

[0041] Step 1: The shape function matrix N of the triangular thin plate element in a single assembly module is:

[0042] N=[N1 N2 N3] (1)

[0043] Where N1, N2 and N3 represent the shape functions of the three vertices of the triangular thin plate element;

[0044] Step 1 and 2: The displacement matrix B of the triangular thin plate finite element is:

[0045]

[0046] Wherein, x and y are two coordinate axes of a two-dimensional Cartesian coordinate system;

[0047] The material elastic matrix D is:

[0048]

[0049] Where E is the elastic modulus of the material, μ is the Poisson's ratio of the material;

[0050] Then the undamped vibration dynamic equation of the triangular thin plate element is:

[0051]

[0052] Among them, M eis the mass matrix of the triangular thin plate element, K e is the stiffness matrix of the triangular thin plate element, u e is the displacement vector of the triangular thin plate element, Indicates u e The second derivative of e is the external force acting on the triangular thin plate element;

[0053]

[0054] Where t is the thickness of the triangular thin plate element, ρ is the density of the triangular thin plate element material, A represents the total area of ​​the triangular thin plate element, and the superscript T represents transposition;

[0055] Step 1-3: Assemble the triangular thin plate elements by numbering. The finite element dynamic model of a single assembly module composed of triangular thin plate elements is:

[0056]

[0057] Where M represents the mass matrix of a single assembly module, K represents the stiffness matrix of a single assembly module, f represents the external force applied to a single assembly module, and u represents the displacement vector of a single assembly module. represents the second-order derivative of u.

[0058] Other steps and parameters are the same as those in the first embodiment.

[0059] Specific embodiment three: This embodiment differs from specific embodiment one or two in that the shape functions of the three vertices of the triangular thin plate unit are:

[0060]

[0061]

[0062] Where b1, b2, b3, c1, c2, and c3 are all constants in the area coordinate transformation, and the areas of the triangles L1, L2, and L3 satisfy L1+L2+L3=1;

[0063] For any point p(x,y) in the triangular thin plate element, the area of ​​the sub-triangle formed by p(x,y) and vertices 1 and 2 of the triangular thin plate element is recorded as A1, the area of ​​the sub-triangle formed by p(x,y) and vertices 2 and 3 of the triangular thin plate element is recorded as A2, and the area of ​​the sub-triangle formed by p(x,y) and vertices 1 and 3 of the triangular thin plate element is recorded as A3. The triangle areas L1, L2 and L3 are:

[0064]

[0065] Where A represents the total area of ​​the triangular plate element.

[0066] Other steps and parameters are the same as those in the first or second embodiment.

[0067] Specific embodiment 4: This embodiment differs from any one of specific embodiments 1 to 3 in that the specific process of step 2 is as follows:

[0068] Step 2.1 Expand formula (7) to:

[0069]

[0070] Among them, M II 、M IJ 、M JI and M JJ are all submatrices of M, K II , K IJ , K JI and K JJ are all submatrices of K, u I Represents the displacement vector of the non-connected edge, u J represents the displacement vector of the connecting edge, Indicates u I The second derivative of Indicates u J The second derivative of I represents the external force acting on the non-connected edge, f J Indicates the external force acting on the connecting edge;

[0071] The structural dynamics model obtained after modal decomposition of formula (7) is:

[0072]

[0073] in, represents the modal decomposition result of M, represents the modal decomposition result of K, Express in The result after modal decomposition (i.e. Depend on The modal decomposition results and composition), p represents the u in u I The result after modal decomposition (i.e. p is composed of u I The modal decomposition results and u J composition), Indicates the f in f I The result after modal decomposition (i.e. By f IThe modal decomposition results and f J composition); after modal decomposition and The order of is much smaller than that of M and K;

[0074] According to equations (12) and (13), the undamped dynamic equation of a single assembly module after modal decomposition is obtained:

[0075]

[0076] Among them, p k Indicates u I The modal decomposition results are: express The modal decomposition results, f k represents f I The modal decomposition results of the normalized processing are as follows: I kk is the identity matrix;

[0077]

[0078] Among them, Φ Ik is the main mode of the fixed interface, the superscript -1 represents the inverse of the matrix, ψ IJ It represents the influence of the freedom degree of the connecting edge on the freedom degree of the non-connecting edge when the freedom degree of the connecting edge produces a unit displacement, Φ k and Ψ C represents the intermediate variable, ω kk Represents the frequency of the kth mode of the stiffness matrix and mass matrix;

[0079] Step 2: When assembling two assembly modules, the transfer matrix Φ′, stiffness matrix K′ and mass matrix M′ before assembly are respectively:

[0080]

[0081] in, (1) Φ=[ (1) Φ k (1) Ψ C ], (2) Φ=[ (2) Φ k (2) Ψ C ], (1) Φ represents the intermediate variable corresponding to the first assembly module, (2) Φ represents the intermediate variable corresponding to the second assembly module, (1) M represents the mass matrix of the first assembled module, (2) M represents the mass matrix of the second assembly module, (1)K represents the stiffness matrix of the first assembly module, (2) K represents the stiffness matrix of the second assembly module;

[0082] The interface coordinates are repeated evenly in u (i.e., the coordinates in u are not independent of each other), so a set of non-coupled and non-independent overall motion equations is established as shown in formula (22).

[0083]

[0084] in, represents the modal decomposition result of M′, represents the modal decomposition result of K′, The modal decomposition results of the external forces applied to the two assembly modules after assembly;

[0085] The parameters in formula (22) are as follows:

[0086]

[0087] The overall displacement vector of the two assembly modules after assembly is:

[0088]

[0089] in, (1) u represents the displacement vector of the first assembly module, ( 1) u I represents the displacement vector of the non-connected edge of the first assembly module, ( 1) u J represents the displacement vector of the connecting edge of the first assembled module, (2) u represents the displacement vector of the second assembly module, ( 2) u I represents the displacement vector of the non-connected edge of the second assembly module, ( 2) u J represents the displacement vector of the connecting edge of the second assembly module;

[0090] Since p in the modal coordinates c Interface docking displacement vector u in physical coordinates of the docking surface J The same, so the displacement continuity condition of the docking interface is (1) p c = (2) p c =u J , then the two assembly modules are assembled using formula (25):

[0091]

[0092] in, (1) p k Indicates the first assembly module pair (1) u I The modal decomposition results are: (2) p k Indicates the second assembly module pair (2) u I The modal decomposition result of , I represents the identity matrix,

[0093] By linearly changing formula (22) through formula (25), the dynamic differential equation after assembly is obtained:

[0094]

[0095] in, express The linear change result of express The linear change result of express The linear change result, p * Represents the linear change result of p, express The linear change results.

[0096] The other steps and parameters are the same as those in the first to third embodiments.

[0097] Specific embodiment 5: This embodiment differs from any one of specific embodiments 1 to 4 in that the modal decomposition form of u of the single assembly module is:

[0098]

[0099] Among them, I JJ represents the identity matrix, O Jk Represents a matrix of all zeros, an intermediate variable

[0100]

[0101] ψ IJ =-K II -1 K IJ (29)

[0102] The other steps and parameters are the same as those in the first to fourth embodiments.

[0103] Specific embodiment 6: This embodiment is different from the specific embodiments 1 to 5 in that the path of the planning robot from the assembly module storage position to the target installation position adopts A* algorithm.

[0104] The other steps and parameters are the same as those in the first to fifth embodiments.

[0105] It is assumed that the robot moves only one module at a time and that the forces exerted on the structure are evenly distributed.

[0106] Specific embodiment seven: This embodiment differs from any one of specific embodiments one to six in that the assembly sequence is optimized using a genetic algorithm, specifically:

[0107] Step 3.1. Solve the force exerted by the robot on the structure using the Newton-Euler method

[0108] The Newton-Euler method is based on the kinematics of rigid bodies and the fact that force transmission is a combination of translation and rotation. First, the method is derived from the inner link to the outer link:

[0109]

[0110]

[0111] in, i ω i is the angular velocity of the end of the i-th link of the robot, i+1 ω i+1 is the angular velocity of the end of the robot's i+1th link, is the transfer matrix from the robot's i-th joint to the i+1-th joint, is the relative angular velocity of the robot's i+1 joint, z i+1 is the z-axis vector of the i+1th joint, for i ω i The first derivative of is the relative angular acceleration of the robot's i+1 joint, is the speed of the end of the i+1th link of the robot, is the velocity of the end of the i-th link of the robot, i p i+1 Indicates the position of the i-th joint based on the coordinate system of the i+1-th joint. is the velocity of the center of mass of the robot's i+1th link, for i+1 ω i+1 The first derivative of i+1 r ci+1 is the vector of the center of mass of the i+1th link based on the coordinate system of the i+1th joint, i+1 f ci+1 is the force acting on the mass center of the robot's i+1th link, m i+1is the mass of the robot's i+1th link, i+1 τ ci+1 is the bending moment value of the mass center of the robot's i+1th link, Ci+1 I i+1 is the moment of inertia of the robot's i+1th link around its center of mass;

[0112] The joint relative angular velocity θ is solved by fourth-order polynomial programming, and dynamic programming is performed on the robot's joint angles, angular velocities, and angular accelerations:

[0113]

[0114] Among them, a0…a4 can be solved by robot inverse kinematics.

[0115] Then the reaction force of each joint is derived from the external link to the internal link, and the force f generated by the robot on the base during movement is r for:

[0116]

[0117] in, i+1 f i+1 is the force acting on the end of the robot’s i+1th link, i f ci is the force acting on the center of mass of the ith link of the robot;

[0118] Step 3.2: Generate an assembly sequence randomly through genetic algorithm. Then the force under the generated current assembly sequence is for:

[0119]

[0120] in, for The value at t = g, n is the number of robots, p is the number of assembled modules, f 1k …f jk …f pk is the unit load for each assembly module. When the kth robot is in the jth module at t = g, f jk =f, when the kth robot is not in the jth module at t = g, f jk =0,f r (g) is f r The value at t = g; it should be noted that g represents any moment corresponding to the current assembly sequence. When g takes different values, the force at each moment in the assembly process can be obtained;

[0121] Therefore, under different numbers of robots and different assembly sequences There will be different values, which will produce different forces on the structure;

[0122] Step 3: Apply force Substituting into formula (22), we can obtain the displacement under the current assembly sequence;

[0123] Return to step 32 and stop iterating until the maximum value of the displacement (vibration) no longer decreases. The assembly sequence corresponding to the minimum displacement is the final assembly sequence.

[0124] The other steps and parameters are the same as those in the first to sixth embodiments.

[0125] The present invention divides the entire assembly process into a series of sub-stages, each of which begins only after the vibrations from the previous stage have completely dissipated. The first stage involves installing a circle of modules around the storage location. The second stage builds on the first stage by connecting the edges of the unconnected modules to form a new structure. For example, in the second stage, Figure 4 As shown, modules 7, 9, 11, 13, 15, and 17 are installed at the hexagonal vertex positions determined by the first stage (for example, module 7 can only be installed at the position of module 1), while modules 8, 10, 12, 14, 16, and 18 are installed between adjacent modules (for example, module 8 can be installed at the position of module 1 or module 2). The red and yellow arrows indicate the specific installation positions, and different installation positions have different effects on structural vibration. The advantage of genetic algorithms in assembly sequence planning lies in their powerful global search capabilities, flexibility, and adaptability. They can effectively handle complex and multi-objective optimization problems. Optimizing the assembly sequence through genetic algorithms not only improves assembly efficiency, but also greatly reduces potential problems caused by vibration, ensuring the smooth installation of the entire structure. This shows that using genetic algorithms to optimize the assembly sequence is of great significance for controlling structural vibration.

[0126] Experimental part

[0127] The algorithm of the present invention is verified in a simulation environment. The present invention randomly generates an assembly sequence for one robot, two robots, three robots, and six robots. The specific simulation results are as follows: Figures 6a to 6d By comparing the assembly efficiency and path optimization effects when different numbers of robots are involved, we can better evaluate the improvement effect of multi-robot collaboration on assembly tasks.

[0128] A genetic algorithm was used to optimize the assembly sequence, aiming to minimize structural vibration. During this process, we selected an initial population of 100 individuals and set 200 iterations, a crossover probability of 0.9, a mutation probability of 0.2, and a generation gap of 0.9. These parameters helped increase population diversity and, in turn, accelerated convergence to the optimal solution.

[0129] We optimized one, two, three, and six robots respectively, aiming to reduce the vibration generated during the installation process at each stage by properly adjusting the assembly sequence. Figures 5a to 5d The evolution of fitness as the number of iterations during the assembly process is shown. It can be observed that fitness is close to convergence before reaching 100 iterations, demonstrating that the genetic algorithm has achieved significant results in optimizing the assembly sequence. After optimization, the structural vibration amplitude is significantly reduced, and the optimization results are improved by over 50%, effectively enhancing the stability of the assembly process.

[0130] Figures 7a to 7d The curves showing the time-varying vibration amplitude at the structure's maximum vibration point after optimizing the installation sequence are shown. The graphs show that the optimized maximum vibration amplitude remains around 0.01 m for each robot number, demonstrating that the optimized assembly sequence effectively controls the vibration amplitude and avoids excessive structural vibration. Although the installation time varies with the number of robots, the vibration amplitude remains stable, demonstrating the advantages of multi-robot collaboration.

[0131] Compared to a randomly generated installation sequence, the optimized assembly sequence significantly reduced the vibration amplitude of the structure, reducing it by about half. This demonstrates that optimizing the assembly sequence through a genetic algorithm not only improves assembly efficiency but also effectively reduces potential problems caused by vibration, making the entire assembly process smoother and more efficient.

[0132] In summary, optimizing the assembly sequence can effectively reduce vibration in a multi-robot collaborative environment, improve the stability of structural assembly, and maintain a relatively consistent vibration amplitude with different numbers of robots, providing a feasible solution for practical applications.

[0133] The above examples are merely illustrative of the calculation model and process of the present invention and are not intended to limit the embodiments of the present invention. Persons skilled in the art will readily appreciate that other variations or modifications based on the above description are possible. This list of embodiments is not exhaustive; however, any obvious variations or modifications derived from the technical solution of the present invention remain within the scope of protection of the present invention.

Claims

1. A robot on-orbit spatial structure assembly optimization method, characterized in that: The method specifically comprises the following steps: Step 1: Construct the dynamic equation of a single assembly module based on the thin plate finite element principle; Step 2: Use the dynamic substructuring method to assemble the two independent assembly modules into a whole, and establish the dynamic differential equation after the assembly is completed based on the dynamic equation of the individual assembly modules; Step 3: Plan the robot's path from the assembly module storage location to the target installation location, and optimize the assembly sequence based on the genetic algorithm and the dynamic differential equation of step 2.

2. The method for optimizing the on-orbit spatial structure assembly of a robot according to claim 1, characterized in that: The specific process of step one is: Step 1: The shape function matrix N of the triangular thin plate element in a single assembly module is: N=[N1 N2 N3] (1) Where N1, N2 and N3 represent the shape functions of the three vertices of the triangular thin plate element; Step 1 and 2: The displacement matrix B of the triangular thin plate finite element is: The material elastic matrix D is: Where E is the elastic modulus of the material, μ is the Poisson's ratio of the material; Then the undamped vibration dynamic equation of the triangular thin plate element is: Among them, M e is the mass matrix of the triangular thin plate element, K e is the stiffness matrix of the triangular thin plate element, u e is the displacement vector of the triangular thin plate element, Indicates u e The second derivative of e is the external force acting on the triangular thin plate element; M e =t∫ A ρN T NdA (6) Where t is the thickness of the triangular thin plate element, ρ is the density of the triangular thin plate element material, A represents the total area of ​​the triangular thin plate element, and the superscript T represents transposition; Step 1-3: Assemble the triangular thin plate elements by numbering. The finite element dynamic model of a single assembly module composed of triangular thin plate elements is: Where M represents the mass matrix of a single assembly module, K represents the stiffness matrix of a single assembly module, f represents the external force applied to a single assembly module, and u represents the displacement vector of a single assembly module. represents the second-order derivative of u.

3. The method for optimizing the on-orbit spatial structure assembly of a robot according to claim 2, characterized in that: The shape functions of the three vertices of the triangular thin plate element are: Where b1, b2, b3, c1, c2, and c3 are all constants in the area coordinate transformation, and the areas of the triangles L1, L2, and L3 satisfy L1+L2+L3=1; For any point p(x,y) in the triangular thin plate element, the area of ​​the sub-triangle formed by p(x,y) and vertices 1 and 2 of the triangular thin plate element is recorded as A1, the area of ​​the sub-triangle formed by p(x,y) and vertices 2 and 3 of the triangular thin plate element is recorded as A2, and the area of ​​the sub-triangle formed by p(x,y) and vertices 1 and 3 of the triangular thin plate element is recorded as A3. The triangle areas L1, L2 and L3 are: Where A represents the total area of ​​the triangular plate element.

4. The method for optimizing on-orbit spatial structure assembly of a robot according to claim 3, characterized in that: The specific process of step 2 is as follows: Step 2.1 Expand formula (7) to: Among them, M II 、M IJ 、M JI and M JJ are all submatrices of M, K II , K IJ , K JI and K JJ are all submatrices of K, u I Represents the displacement vector of the non-connected edge, u J represents the displacement vector of the connecting edge, Indicates u I The second derivative of Indicates u J The second derivative of I represents the external force acting on the non-connected edge, f J Indicates the external force acting on the connecting edge; The structural dynamics model obtained after modal decomposition of formula (7) is: in, represents the modal decomposition result of M, represents the modal decomposition result of K, Express in The result after modal decomposition, p represents the u in u I The result after modal decomposition is: Indicates the f in f I The results after modal decomposition; According to equations (12) and (13), the undamped dynamic equation of a single assembly module after modal decomposition is obtained: Among them, p k Indicates u I The modal decomposition results are: express The modal decomposition results, f k represents f I The modal decomposition results, I kk is the identity matrix; Among them, Φ Ik is the main mode of the fixed interface, the superscript -1 represents the inverse of the matrix, ψ IJ It represents the influence of the freedom degree of the connecting edge on the freedom degree of the non-connecting edge when the freedom degree of the connecting edge produces a unit displacement, Φ k and Ψ C represents the intermediate variable, ω kk Represents the frequency of the kth mode of the stiffness matrix and mass matrix; Step 2: When assembling two assembly modules, the transfer matrix Φ′, stiffness matrix K′ and mass matrix M′ before assembly are respectively: in, (1) Φ=[ (1) Φ k (1) Ψ C ], (2) Φ=[ (2) Φ k (2) Ψ C ], (1) Φ represents the intermediate variable corresponding to the first assembly module, (2) Φ represents the intermediate variable corresponding to the second assembly module, (1) M represents the mass matrix of the first assembled module, (2) M represents the mass matrix of the second assembly module, (1) K represents the stiffness matrix of the first assembly module, (2) K represents the stiffness matrix of the second assembly module; in, represents the modal decomposition result of M′, represents the modal decomposition result of K′, The modal decomposition results of the external forces applied to the two assembly modules after assembly; The parameters in formula (22) are as follows: The overall displacement vector of the two assembly modules after assembly is: in, (1) u represents the displacement vector of the first assembly module, (1) u I represents the displacement vector of the non-connected edge of the first assembly module, (1) u J represents the displacement vector of the connecting edge of the first assembled module, (2) u represents the displacement vector of the second assembly module, (2) u I represents the displacement vector of the non-connected edge of the second assembly module, (2) u J represents the displacement vector of the connecting edge of the second assembly module; The displacement continuity condition of the docking interface is (1) p c = (2) p c =u J , then the two assembly modules are assembled using formula (25): in, (1) p k Indicates the first assembly module pair (1) u I The modal decomposition results are: (2) p k Indicates the second assembly module pair (2) u I The modal decomposition result of , I represents the identity matrix, By linearly changing formula (22) through formula (25), the dynamic differential equation after assembly is obtained: in, express The linear change result of express The linear change result of express The linear change result, p * Represents the linear change result of p, express The linear change results.

5. The method for optimizing on-orbit spatial structure assembly of a robot according to claim 4, characterized in that: The modal decomposition form of u of the single assembly module is: Among them, I JJ represents the identity matrix, O Jk Represents a matrix of all zeros, an intermediate variable ψ IJ =-K II -1 K IJ (29).

6. The method for optimizing on-orbit spatial structure assembly of a robot according to claim 5, characterized in that: The path of the planning robot from the assembly module storage position to the target installation position adopts A * algorithm.

7. The method for optimizing on-orbit spatial structure assembly of a robot according to claim 6, characterized in that: The genetic algorithm is used to optimize the assembly sequence, specifically: Step 3.

1. Solve the force exerted by the robot on the structure using the Newton-Euler method in, i ω i is the angular velocity of the end of the i-th link of the robot, i+1 ω i+1 is the angular velocity of the end of the robot's i+1th link, is the transfer matrix from the robot's i-th joint to the i+1-th joint, is the relative angular velocity of the robot's i+1 joint, z i+1 is the z-axis vector of the i+1th joint, for i ω i The first derivative of is the relative angular acceleration of the robot's i+1 joint, is the speed of the end of the i+1th link of the robot, is the velocity of the end of the i-th link of the robot, i p i+1 Indicates the position of the i-th joint based on the coordinate system of the i+1-th joint. is the velocity of the center of mass of the robot's i+1th link, for i+1 ω i+1 The first derivative of i+1 r ci+1 is the vector of the center of mass of the i+1th link based on the coordinate system of the i+1th joint, i+1 f ci+1 is the force acting on the mass center of the robot's i+1th link, m i+1 is the mass of the robot's i+1th link, i+1 τ ci+1 is the bending moment value of the mass center of the robot's i+1th link, Ci+1 I i+1 is the moment of inertia of the robot's i+1th link around its center of mass; Then the reaction force of each joint is derived from the external link to the internal link, and the force f generated by the robot on the base during movement is r for: in, i+1 f i+1 is the force acting on the end of the robot’s i+1th link, i f ci is the force acting on the center of mass of the ith link of the robot; Step 3.2: Generate an assembly sequence randomly through genetic algorithm. Then the force under the generated current assembly sequence is for: in, for The value at t = g, n is the number of robots, p is the number of assembled modules, f 1k …f jk …f pk is the unit load for each assembly module. When the kth robot is in the jth module at t = g, f jk =f, when the kth robot is not in the jth module at t = g, f jk =0,f r (g) is f r The value at t = g; Step 3: Apply force Substituting into formula (22), we can obtain the displacement under the current assembly sequence; Return to step 32 and stop iterating until the maximum displacement value no longer decreases. The assembly order corresponding to the minimum displacement is the final assembly order.

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