Evaluation method for topological configuration reconstruction of floating base assembly system

Abstract

An evaluation method for topological configuration reconstruction of a floating-based assembly system comprises the steps of obtaining a mapping relation between kinetic parameters of the floating-based assembly system and evaluation parameters of topological configuration of the assembly, and then analyzing the mapping relation of the floating-based assembly system. Analyzing the design variables according to the mapping relation; and constructing an assembly system constraint function by using the mapping relation of the assembly parameters, and further constructing a floating base assembly topological configuration evaluation model. An approximation rule of a brachistochrone of a robot-reconstructed target combination configuration is researched through a minimum action quantity principle, and then normalization and linearization of a proposed topological configuration evaluation model are analyzed by adopting a sequential quadratic programming method. Therefore, the finally proposed reconstruction topological configuration evaluation method can accurately evaluate the system stability, the reconstruction precision and the task energy efficiency improvement potential of the floating base assembly under different reconstruction paths.

Description

Technical Field

[0001] The invention relates to an evaluation method for topological configuration reconstruction of a floating base assembly system, and relates to the application field of space robots. Background Art

[0002] With the development of aerospace technology, the scenarios of aerospace missions have become more complex and diverse, which requires the payload of spacecraft to be diverse and make the system multifunctional. However, the traditional system design makes the topological structure and activity of spacecraft relatively fixed, which is difficult to use in mission scenarios with variable environment and multiple working conditions. It is also limited by the multi-vessel launch and direct orbit entry capabilities of the launch vehicle and the structural bearing performance. This makes space cell robots one of the hot spots in the current aerospace research field. The advantage of cell robots is that they can change their configuration to meet the environmental and mission requirements in the face of mission scenarios with variable environment and multiple working conditions. At the same time, due to the reconfigurability of cell robots, their activity is greatly improved, and the structural bearing performance is relieved to the greatest extent. Among them, the key to reconstruction is to reasonably and effectively evaluate the configuration process. However, it is difficult to clearly define the mapping relationship between the dynamic parameters of the floating base assembly system and the evaluation parameters of the assembly topological configuration under different reconstruction conditions, and it is difficult to clearly define the evaluation benchmark parameters and the evaluation parameter weights, which leads to considerable difficulty in proposing the evaluation method.

[0003] In summary, the problems existing in the prior art are:

[0004] (1) Due to the instantaneous contact impact between the target and the cell robot during the continuous reconstruction process, the gap collision and inertia mutation of the joint multi-contact state, and the posture disturbance involved in the dragging process, the dynamic and inertial characteristics of the assembly system in the variable topology and variable inertia reconstruction process are time-varying, making it difficult to determine the mapping relationship between the system dynamic response characteristics and the topological configuration evaluation parameters of the assembly system.

[0005] (2) During the on-orbit reconstruction process of the floating-based cellular robot, the variable benchmark is affected by the time-varying load-bearing structure and dynamic benchmark characteristics of the assembly system, which makes it difficult to determine the evaluation benchmark parameters and evaluation parameter weights of the entire on-orbit reconstruction process.

[0006] (3) Since the evaluation benchmark parameters and evaluation parameter weights of the on-orbit reconstruction process are difficult to determine, it is difficult to accurately evaluate the stability of the floating-based assembly system, reconstruction accuracy, and mission energy efficiency improvement potential under different reconstruction paths.

[0007] Difficulty in solving the above mentioned technologies:

[0008] (1) The dynamic model of a cellular robot is usually very complex and difficult to model accurately. Therefore, it is difficult to accurately map the dynamic response characteristics of the system with the evaluation parameters of the topological configuration of the assembly system.

[0009] (2) The evaluation parameters of the topological configuration of the floating base assembly system are usually high-dimensional, including geometric configuration, material properties, connection methods, etc. These high-dimensional parameter spaces increase the difficulty of establishing mapping relationships.

[0010] (3) Uncertainties in the space environment (such as tiny forces and thermal disturbances) and manufacturing and operational errors in the system itself make it difficult to rationalize the weights of each parameter.

[0011] The significance of solving the above problems:

[0012] Due to the complexity of the space environment and the diversity of mission requirements, it is difficult to reasonably design the on-orbit reconstruction process of a floating-based cellular robot. Solving the above problems can well solve the evaluation problem of the on-orbit reconstruction process of a floating-based cellular robot, and has good promotion and application value in the modeling and analysis of complex spacecraft dynamics and the evaluation of the topological configuration of space deployable structures. Summary of the invention

[0013] The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and solve the evaluation problem of topological configuration reconstruction of a floating base assembly system.

[0014] The purpose of the present invention is achieved through the following technical solutions:

[0015] An evaluation method for topological configuration reconstruction of a floating base assembly system, comprising:

[0016] Step 1: Perform dynamic modeling on the assembly system to obtain the dynamic parameters of the assembly system including stiffness, mass, inertia, etc.

[0017] Step 2: Determine the key parameters for evaluating the system topology, such as connection strength, topological stability, structural stiffness, mass distribution, redundancy, etc.

[0018] Step three, analyze the mapping relationship of the floating base assembly system to obtain the mapping relationship between the dynamic parameters of the floating base assembly system and the evaluation parameters of the assembly topology configuration under different reconstruction conditions.

[0019] Step 4: Construct constraint functions for design variables such as the cell robot's driving parameters, the assembly system's vibration parameters, the assembly's orbital parameters, and the stability of the topological configuration reconstruction process.

[0020] Step five, using the proposed mapping relationship of the floating base assembly system and the design variable constraint function under the actual background, a topological configuration evaluation model of the floating base assembly system is proposed.

[0021] Step six, by constructing the action equation and using the gradient descent method to give the steepest descent line of the assembly configuration, the minimum action path can be obtained to achieve the optimal configuration evaluation model.

[0022] Step seven, normalize and linearize the configuration evaluation model, perform sequential quadratic programming on the processed configuration evaluation model, and obtain the configuration evaluation result.

[0023] Further, in step 4, each design variable and its constraint conditions are as follows: driving parameters include motor torque, motor speed, joint angle, etc. The settings of these parameters need to be within their maximum and minimum ranges. Vibration parameters include resonant frequency, vibration amplitude, damping ratio, etc. The minimum threshold and maximum threshold of each vibration parameter are solved by the system matrix equation to obtain the constraint function of the vibration parameter. Orbital parameters include orbital height, orbital inclination, orbital period, etc. The constraints of the orbital parameters are determined by the orbit of the cell robot. Reasonable orbital parameters are set according to the orbit of the cell robot and the task requirements to couple the proposed reconfigurable evaluation method. Stability parameters include structural deformation, stress distribution, stability factor, etc. The stability parameters are determined by the dynamic characteristics of the assembly system. The structure is subjected to force analysis to obtain the dynamic response of the structure. The minimum threshold and maximum threshold of each parameter are solved to obtain the constraint function of the stability parameter.

[0024] Furthermore, in step five, the reachability and dexterity of the cell robot are mainly evaluated.

[0025] Furthermore, in step six, the Lagrangian is first established, the action is defined as the integral of the system Lagrangian over time, the initial and final positions of the cell robot and the target assembly are determined, the boundary conditions are set, and the motion equation is solved to calculate the path that minimizes the action. The approximation law of the brachistocentre of the assembly configuration is obtained by gradient descent analysis to ensure that the approximated brachistocentre meets the system dynamic and stability requirements.

[0026] Furthermore, in step 7, the variables of different dimensions of the evaluation model are converted into dimensionless unified scales to achieve normalization of the model for the convenience of optimization algorithm processing. The nonlinear constraints and objective functions are then approximated into linear forms to achieve linearization of the model so that each iteration can be solved using linear or quadratic programming methods. The model is then solved by sequential quadratic programming and the optimized variable x is output. * 、The optimal objective function value f(x * ) and the constraint value g j (x*), the obtained x * This is the model evaluation result. By comparing it with the standard indicators, the evaluation result of the topological configuration can be obtained.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] (1) The evaluation method provided by the present invention includes obtaining the mapping relationship between the dynamic parameters of the floating base assembly system and the evaluation parameters of the assembly topological configuration, and then analyzing the mapping relationship of the floating base assembly system. According to the mapping relationship, the design variables are analyzed, including the cell robot driving parameters, the assembly system vibration parameters, the assembly orbit parameters, the stability of the topological configuration reconstruction process, etc. The evaluation method of the present invention solves the problems of low efficiency, poor precision and inaccuracy in the prior art when analyzing the assembly parameter mapping relationship.

[0029] (2) Through the present invention, the mapping relationship of the assembly parameters is used to construct the assembly system constraint function, and then the floating base assembly topological configuration evaluation model is constructed. Compared with the evaluation model proposed by the existing evaluation method, it has higher evaluation precision and accuracy due to the accurate parameter mapping relationship.

[0030] (3) In the present invention, the approximation law of the shortest descent line of the robot-reconstruction target assembly configuration is studied by the principle of minimum action, and then the normalization and linearization of the proposed topological configuration evaluation model are analyzed by the sequential quadratic programming method, so that the reconstructed topological configuration evaluation method finally proposed can accurately evaluate the stability of the floating base assembly system under different reconstruction paths, the reconstruction accuracy and the potential for improving the task energy efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is a flow chart of an evaluation method for reconstructing the topological configuration of a floating base assembly system provided in an embodiment of the present invention.

[0032] Figure 2 It is a schematic diagram of the full envelope configuration and reconstruction process of the floating base assembly system in Example 1 provided in an embodiment of the present invention.

[0033] Figure 3 It is a schematic diagram of the point envelope configuration and reconstruction process of the floating base assembly system in Example 1 provided in an embodiment of the present invention.

[0034] In the figure: 111 is a floating base assembly system, 112 is a cell robot, and 113 is a target. DETAILED DESCRIPTION

[0035] To make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0036] Affected by the instantaneous contact impact between the target and the cell robot during the continuous reconstruction process, the gap collision and inertia mutation of the joint multi-contact state, and the posture disturbance involved in the dragging process, the dynamics and inertial characteristics of the floating base assembly system in the variable topology and variable inertia reconstruction process are time-varying, which makes it difficult to determine the mapping relationship between the system dynamic response characteristics and the evaluation parameters of the assembly system topology configuration. During the variable reference on-orbit reconstruction of the cell robot, the load-bearing structure and dynamic reference characteristics of the floating base assembly system are time-varying, making it difficult to determine the evaluation reference parameters and evaluation parameter weights of the entire on-orbit reconstruction process. Since the evaluation reference parameters and evaluation parameter weights of the on-orbit reconstruction process are difficult to determine, it is difficult to accurately evaluate the stability of the assembly system, reconstruction accuracy, and mission energy efficiency improvement potential under different reconstruction paths.

[0037] In order to solve the above problems, the present invention provides an evaluation method for reconstructing the topological configuration of a floating base assembly system, comprising:

[0038] Step 1: Perform dynamic modeling on the floating base assembly system to obtain dynamic parameters of the floating base assembly system including stiffness, mass, inertia, etc.

[0039] Step 2: Determine the key parameters for evaluating the topological configuration of the system, such as connection strength, topological stability, structural stiffness, mass distribution, redundancy, etc.

[0040] Step three, analyze the mapping relationship of the floating base assembly system to obtain the mapping relationship between the dynamic parameters of the floating base assembly system and the evaluation parameters of the assembly topology configuration under different reconstruction conditions.

[0041] Step 4: Construct constraint functions for design variables such as the cell robot driving parameters, the vibration parameters of the floating base assembly system, the assembly orbit parameters, and the stability of the topological configuration reconstruction process.

[0042] Among them, the driving parameters include: motor torque, motor speed, joint angle, etc. The vibration parameters include: resonance frequency, vibration amplitude, damping ratio, etc. The settings of these parameters need to be within their maximum and minimum value ranges.

[0043] The resonant frequency of the system is solved by the matrix equation of the system, which is written as:

[0044]

[0045] Among them, M is the system mass, C is the system damping, K is the system stiffness, F is the system force, X is the system displacement, and t is the time of external force. Calculate the eigenvalue of the equation and get the equation about the resonant frequency. Solve the following equation to get the resonant frequency ω:

[0046] det(K-ω 2 M)=0

[0047] Among them, det() is used to find the value of the determinant in the brackets.

[0048] for Figure 2 The system equation of the floating base assembly shown in the figure is solved by solving the frequency response function to obtain the vibration amplitude:

[0049]

[0050] Among them, F0 is the force of the floating base assembly system in the variable topology process. The damping ratio can be directly calculated by the damping ratio calculation formula:

[0051]

[0052] The orbital parameters include orbital height, orbital inclination, orbital period, etc. The constraints of the orbital parameters are determined by the orbit of the cell robot. Reasonable orbital parameters are set according to the orbit of the cell robot and the task requirements to couple the proposed reconfigurable evaluation method.

[0053] Stability parameters include: structural deformation, stress distribution, stability factor, etc. Structural deformation is a type of structural coupling, including axial deformation, shear deformation, bending deformation, etc. of the cell robot. The structural deformation must be less than the maximum allowable deformation of the system. The stress distribution is calculated using the finite element method. A cell robot model is established in the modeling software, material properties are input, the grid is divided, loads are applied, and boundary conditions are set. Finally, the stress and deformation distribution of the cell robot under various load conditions are solved. The stress must be less than the maximum allowable stress of the system. The stability factor is used to evaluate the stability of the structure under different load conditions. For cell robots, the critical stress is used to represent the structural stability factor. The calculation formula is as follows:

[0054]

[0055] Among them, σ cr is the critical stress, P cr is the critical force, π is the circumference, E is the elastic modulus of the cell robot material, β is the critical stress proportional factor, l is the axis diameter of the cell robot, A is the cross-sectional area, and r is the cross-sectional radius of gyration, satisfying:

[0056]

[0057] Where I is the moment of inertia of the cell robot. The stability factor must be greater than the minimum allowable stability factor of the system.

[0058] Step five, using the proposed mapping relationship of the floating base assembly system and the design variable constraint function under the actual background, a topological configuration evaluation model of the floating base assembly system is proposed.

[0059] For cellular robots, kinematic and dynamic evaluation indicators mainly include reachability and dexterity.

[0060] S51, conduct dexterity modeling analysis. By studying the Jacobian matrix of the cell robot, a variety of dexterity measurement indicators can be obtained. Solve the condition number k to obtain the ratio of the maximum singular value to the minimum singular value of the matrix.

[0061] k(J)=α1 / α2

[0062] Where J is the Jacobian matrix, α1 and α2 are the maximum and minimum singular values ​​of J.

[0063] The condition number of the matrix ranges from 1 ≤ k ≤ 100. When k = 1, the configuration is called isotropic.

[0064] S52, solving the minimum singular value to obtain the minimum workspace velocity corresponding to the unit joint velocity vector. The larger the minimum singular value, the faster the configuration responds to the joint motion.

[0065] S53, solve the inverse of the condition number to obtain the sensitivity of the velocity of the end effector to the joint velocity vector. Because the Jacobian matrix is ​​a quantity related to the shape and position of the configuration, the minimum condition number k is used. m The dexterity index D is defined by the reciprocal of

[0066]

[0067] Among them, k m =min(K(J))

[0068] S54, solve the operability, and define the determinant of the product of the Jacobian matrix and its transpose as the operability metric ρ. That is:

[0069]

[0070] S55, conduct reachability analysis of the cell robot and define the workspace of the cell robot. The workspace of the cell robot is defined as the set of all configurations of the end effector reached by different joint rotation angles. If Q is the configuration space of the cell robot, SE(3) is the displacement and rotation angle of the cell robot, g ts :Q→SE(3) is a positive solution of the kinematic mapping, then the workspace W is defined as the set:

[0071]

[0072] Among them, φ is the joint rotation angle of the cell robot.

[0073] S56, define the reachability description of the cell robot. The reachability description of the cell robot is:

[0074] If the given task is a task space W with pose requirements TPO = {P d ∈SE(3)}, where P d is the required posture position of the cell robot. For a given cell robot, its working space is W RPO Then: The accessibility evaluation problem is to judge W TPO Is it in the reachable space W? RPO Inside.

[0075] Right now: There is P di ∈W RPO (i=1,2,…,n), where n is the number of joints of the floating base assembly system, i is the joint of the i-th cell robot, P di is the expected posture position of the i-th cell robot joint.

[0076] S57, define the evaluation task of the cell robot reachability. The evaluation task of the cell robot reachability is: Make P d With P r coincidence, where P r It is the posture position that the cellular robot can reach in the floating base assembly system under the mission requirements.

[0077] That is, P d With P r The distance measure d between p (P d ,P r )=0, the cell robot is considered to meet the reachability requirement.

[0078] set up R do ,R ro ∈SO(3), respectively representing the desired posture and reachable posture of the cell robot, P dp ,P rp ∈R 3 , respectively represent the desired position and reachable position of the cell robot.

[0079] Then the distance measure is defined as:

[0080]

[0081] Where y is a constant related to the structural size of the cell robot.

[0082] S58, construct a reachability evaluation function. According to the evaluation task, construct a reachability evaluation function:

[0083] G(P d ,q)=d(P d ,P r ),q=[q1 q2 … q4] T

[0084] Where q is the quaternion of the cell robot joint. If G(P d ,q)=0, then the reachability requirement is met.

[0085] S59, establish an optimization model. According to the evaluation task of the cell robot, establish the following optimization model: for each P di ∈W TPO :

[0086] minimize G(P di ,q)

[0087] subject to:q imin ≤q i ≤q imax ,i=1,...,n

[0088] If Max{Min G(P di ,q)|P di ∈W TPO}≤ε (ε is the calculation accuracy) holds true, then the cell robot has a task space W TPO reachable.

[0089] Step 6: Based on the principle of minimum action, study the approximation law of the brachistocentre of the configuration of the cell robot-target combination. By constructing the action equation and using the gradient descent method to give the brachistocentre of the configuration of the combination, the minimum action path can be obtained to achieve the optimal configuration evaluation model. The specific steps are as follows:

[0090] S61, establish the Lagrangian. Calculate the kinetic energy of the cell robot, the kinetic energy of the target assembly, the gravitational potential energy and the elastic potential energy respectively.

[0091] Cell robot kinetic energy:

[0092]

[0093] Among them, m ce ll is the mass of the cell robot, r ce ll is its position vector.

[0094] Target combination kinetic energy:

[0095]

[0096] Among them, mtarget is the mass of the target assembly, r target is its position vector.

[0097] In orbit near the earth, the gravitational potential energy of the floating base assembly system is:

[0098]

[0099] Where G is the gravitational constant, m e is the mass of the Earth, m c is the mass of the floating base assembly system, r e,c is the distance from the center of the earth.

[0100] The Lagrangian L is usually expressed as the kinetic energy E v and potential energy E g The difference:

[0101] L=TV L=E v -E g

[0102] S62, define the action, the action S is the time integral of the system Lagrangian L:

[0103]

[0104] Among them, t0 is the time when the floating base assembly system starts to change its configuration, t f It is the time when the configuration change of the floating base assembly system is completed.

[0105] S63, using the above Lagrangian equation to solve the motion trajectory of the system. Substitute the Lagrangian into the Lagrangian equation to obtain the motion equation to establish the motion equation, then determine the initial and final positions of the cell robot and the target assembly, set the boundary conditions, and solve the action path. The motion equation is as follows:

[0106]

[0107] Among them, q i are generalized coordinates, is the generalized speed.

[0108] S64 uses the gradient descent method to iteratively approximate the steepest descent line. The path is adjusted to minimize the action and ensure that the path is smooth and meets the physical constraints. The effectiveness of the path is verified through numerical simulation to ensure that the approximated steepest descent line meets the system dynamic and stability requirements.

[0109] For a given objective function f(θ), the update formula for gradient descent is:

[0110]

[0111] where θ λ is the parameter vector for the λth iteration, θ λ+1 is the parameter vector for the λ+1th iteration, η is the learning rate, is the objective function at θ λ The gradient at .

[0112] Step 7: Based on the sequential quadratic programming method, a normalization and linearization method for the topological configuration evaluation model is given. The following is a detailed description:

[0113] S71, normalize the evaluation model. The purpose of normalization is to convert variables of different dimensions into a dimensionless unified scale to facilitate optimization algorithm processing. Usually, the variables are mapped to the range of [0, 1] or [-1, 1] through linear transformation. First, determine the normalization range. For each variable x i , determine the maximum value x i,max and the minimum value x i,min . i Normalized to z i :

[0114]

[0115] Normalized variable z i The value range is [0,1].

[0116] S72, linearize the normalized model. The purpose of linearization is to approximate the nonlinear constraints and objective functions into linear forms, so that each iteration can be solved using linear or quadratic programming methods. First, linearize the objective function. Assume that the original nonlinear objective function is f(x). At the current iteration point x k Perform a first-order Taylor expansion at:

[0117]

[0118] in, is the objective function at x k The gradient at . Reconstruct the linearized constraint function, assuming that the original nonlinear constraint is g j (x)≤0, at the current iteration point x k Perform a first-order Taylor expansion at:

[0119]

[0120] in, is the constraint function at x k The gradient at .

[0121] S73, perform sequential quadratic programming on the processed evaluation model. Select the initial point x0, calculate the initial objective function value f(x) and constraint gj (x0). Then iterate and calculate at the current iteration point x k At , construct and solve the quadratic programming subproblem:

[0122]

[0123] Where d is the step vector, H k is a matrix of quadratic terms (which can be an approximation of the second-order derivative of the objective function).

[0124] Update iteration point:

[0125] x k+1 =x k +α k d k

[0126] Among them, α k is the step size factor, usually determined by a line search method.

[0127] Then check the changes in the objective function value and constraints. If the convergence criteria are met (such as the change in the objective function value is less than the preset threshold), terminate the iteration, and finally calculate the new Lagrange multiplier for the construction of the next quadratic programming subproblem.

[0128] S74, output optimized variable x * 、The optimal objective function value f(x * ) and the constraint value g j (x*), the obtained x * This is the model evaluation result.

[0129] S75, evaluate the obtained model result x * Compare standard indicators. * For the normalized and dimensionless evaluation, the evaluation indicators are as follows:

[0130] When the constraint value g j When the value of (x*) is less than or equal to 0, it indicates that the reconstructed model does not meet the task requirements or cannot satisfy the constraints, and it is evaluated as not being able to be reconstructed.

[0131] When the constraint value g j The value of (x*) is greater than 0 and the optimal objective function value f(x * ) is less than or equal to 1, indicating that the reconstructed model meets the task requirements and satisfies the constraints. At this time, the reconstructed model is a single-factor optimal model. This model is the optimal solution in a local range and is easy to obtain, but it has a large loss compared to the global task and is not the global optimal reconstruction model.

[0132] When j The value of (x*) is greater than 0 and the optimal objective function value f(x* ) is greater than 1, indicating that the reconstructed model meets the task requirements and satisfies the constraints. At this time, the reconstructed model is a two-factor optimal model, which is the optimal solution in the global scope and has the smallest loss function.

[0133] The present invention will be further described below in conjunction with specific embodiments.

[0134] Embodiment 1

[0135] like Figure 1 As shown, the evaluation method for reconstructing the topological configuration of a floating base assembly system according to an embodiment of the present invention includes the following steps S101 to S107.

[0136] S101, dynamic modeling of the floating base assembly system is performed to obtain dynamic parameters of the floating base assembly system including stiffness, mass, inertia, etc. Figure 2 and Figure 3 In the case of , the floating base assembly system of the full envelope configuration and the point envelope configuration is measured respectively, and the masses of the two are obtained as M q and M d , inertia J q and J d , system damping C q and C d , system stiffness K q and K d Equikinetic parameters.

[0137] S102, determine the key parameters for evaluating the topological configuration of the system, such as connection strength, topological stability, structural stiffness, mass distribution, redundancy, etc. Figure 2 and Figure 3 From the working conditions of the case, it can be seen that the connection strength of the components of the reconfigurable robot is qualified, the topological stability is high, the elastic deformation in the working state is within the allowable range, the mass distribution is uniform and reasonable, and it has the ability to work in a certain degree of abnormal environment.

[0138] S103, analyze the mapping relationship of variable topology and variable inertia combination system, combined with Figure 2 and Figure 3 The two different configurations in the case solve the mapping functions of dynamic parameters and evaluation parameters respectively: Y τ (x),τ=1,2. Where τ is the case number.

[0139] S104, constructing constraint functions for design variables such as cell robot driving parameters, floating base assembly system vibration parameters, assembly orbit parameters, and stability of topological configuration reconstruction process. Figure 2 and Figure 3 In the case of the allosteric process, the motor torque T is obtained by analysis. q and Td , motor speed N q and N d , joint angle and The resonant frequency is solved by the matrix equation of the system, which is written as:

[0140]

[0141] Where M is the system mass, C is the system damping, and K is the system stiffness. The eigenvalue of the equation is calculated to obtain the equation about the resonant frequency. Solving the following equations can obtain the resonant frequency ω, vibration amplitude X, and damping ratio ζ:

[0142] det(K-ω 2 M)=0

[0143]

[0144] The orbital parameters can be obtained according to the orbit of the floating base assembly system and the mission requirements. The orbital height is h, the orbital inclination is Φ, and the orbital period is T0. The stability parameters of the floating base assembly system mainly include structural deformation, stress distribution and stability factor. The finite element method is used for calculation. The cell robot model is established in the modeling software, the material properties are input, the grid is divided, the load is applied and the boundary conditions are set. Finally, the stress and deformation distribution of the cell robot under various load conditions are solved, and the axial deformation of the floating base assembly system under the two configurations is δl q and δl d , the shear deformations are δγ q and δγ d , the bending deformations are δb q and δb d , the three deformations are all less than the maximum allowable deformation of the system. At the same time, the critical stress σ cr It is also greater than the minimum allowable stability factor of the system.

[0145] S105, using the proposed mapping relationship of the floating base assembly system and the design variable constraint function in the actual background, a topological configuration evaluation model of the floating base assembly system is proposed. For the cell robot, the kinematic and dynamic evaluation indicators mainly include accessibility and dexterity. The first step is to analyze dexterity. Based on the Jacobian matrix of the cell robot, the condition number is obtained by dividing the maximum singular value and the minimum singular value.

[0146] k(J)=α1 / α2

[0147] Where J is the Jacobian matrix, α1 and α2 are the maximum and minimum singular values ​​of J. Solve for the minimum singular value to obtain the minimum workspace velocity corresponding to the unit joint velocity vector. Use the minimum condition number k m The dexterity index is defined as the reciprocal of

[0148]

[0149] Among them, k m =min(K(J)). For the operability of the allosteric form, the following formula is used to obtain the operability index. That is:

[0150]

[0151] According to the accessibility of the floating base assembly system, the working space of the cell robot is defined as:

[0152]

[0153] Determine the accessibility of the floating base assembly system, namely: There is P di ∈W RPO (i=1,2,…,n). For the accessibility evaluation of cell robots, the distance measure is defined, and the cell robot structure size is substituted to construct the accessibility evaluation function, namely:

[0154] G(P d ,q)=d(P d ,P r ),q=[q1 q2 … q4] T

[0155] By substituting the data of the two sets of configurations, we can get the G(P d ,q)=0, so they all meet the accessibility requirements. Then, according to the evaluation task of the floating base assembly system, the following optimization model is established. di ∈W TPO :

[0156] minimize G(P di ,q)

[0157] subject to:q imin ≤q i ≤q imax ,i=1,...,n

[0158] Substituting into the equation, we can get Max{Min G(P di ,q)|P di ∈W TPO}≤ε, that is, the cell robot has a task space W TPOreachable.

[0159] S106, based on the principle of minimum action, study the approximation law of the brachistocentre of the configuration of the cell robot-target combination. By constructing the action equation and using the gradient descent method to give the brachistocentre of the configuration of the combination, the minimum action path can be obtained to achieve the optimization of the configuration evaluation model.

[0160] According to the motion parameters and mass parameters of the cell robot, the kinetic energy of the unit and the assembly is calculated:

[0161]

[0162] Among them, m cell is the mass of the cell robot, r cell is its position vector.

[0163]

[0164] Among them, m target is the mass of the target assembly, r target is its position vector.

[0165] Calculate the potential energy of the floating base assembly system. In orbit near the earth, the gravitational potential energy of the floating base assembly system is:

[0166]

[0167] Where G is the gravitational constant, m e is the mass of the Earth, m c is the mass of the combined system, and r is the distance from the center of the earth.

[0168] The kinetic energy E v and potential energy E g The Lagrangian L is obtained by subtracting, that is:

[0169] L=E v -E g

[0170] Integrate the system Lagrangian L over time to obtain the action S, that is:

[0171]

[0172] The above Lagrange equation is used to solve the motion trajectory of the system. The motion equation is as follows:

[0173]

[0174] Among them, q i are generalized coordinates, is the generalized speed.

[0175] The gradient descent method is used to iteratively approximate the steepest descent line. The path is adjusted to minimize the action, making the path smooth and in line with physical constraints. Numerical simulation is used to verify the effectiveness of the path of this scheme, proving that its steepest descent line meets both the system dynamic and stability requirements.

[0176] For a given objective function f(θ), the update formula for gradient descent is:

[0177]

[0178] where θ λ is the parameter vector for the λth iteration, θ λ+1 is the parameter vector for the λ+1th iteration, η is the learning rate, is the objective function at θ λ The gradient at .

[0179] S107, based on the sequential quadratic programming method, a normalization and linearization method for the topological configuration evaluation model is given. The model evaluation value is obtained, compared with the evaluation index, and finally the model evaluation result is obtained. The iterative result in S106 is substituted into the evaluation model and normalized:

[0180]

[0181] Linearize the normalized model. Assume that the original nonlinear objective function is f(x), at the current iteration point x k Perform a first-order Taylor expansion at:

[0182]

[0183] in, is the objective function at x k The gradient at . Reconstruct the linearized constraint function, assuming that the original nonlinear constraint is g j (x)≤0, at the current iteration point x k Perform a first-order Taylor expansion at:

[0184]

[0185] in, is the constraint function at x k The gradient at . Perform sequential quadratic programming on the processed evaluation model. Select the initial point x0, calculate the initial objective function value f(x) and constraint g j (x0). Then iterate and calculate at the current iteration point x k At , construct and solve the quadratic programming subproblem:

[0186]

[0187]

[0188] Where d is the step vector, H k is a matrix of quadratic terms (which can be an approximation of the second-order derivative of the objective function).

[0189] Update the iteration point, the formula used is:

[0190] x k+1 =x k +α k d k

[0191] Among them, α k is the step size coefficient, usually determined by line search method. Output the optimized variable x * 、The optimal objective function value f(x * ) and the constraint value g j (x*), the obtained x * This is the model evaluation result. * Compare standard indicators. Figure 2 The evaluation result of the full envelope configuration shown is x * q , g j (x * q )=0.3471,f(x * q )=1.2863, Figure 3 The evaluation result of the envelope configuration of the point shown is x * d , g j (x * d )=0.6732,f(x * d )=0.8514, so the full envelope configuration is better than the point envelope configuration, and the full envelope configuration should be adopted when comparing the two.

[0192] The contents not described in detail in the specification of the present invention belong to the common knowledge of those skilled in the art.

[0193] Although the present invention has been disclosed as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solution of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

Claims

1. An evaluation method for reconstructing the topological configuration of a floating base assembly system, characterized in that: include: Step 1: Perform dynamic modeling on the assembly system to obtain the dynamic parameters of the assembly system, including stiffness, mass, and inertia; Step 2: Determine the parameters for evaluating the topological configuration of the system, including connection strength, topological stability, structural stiffness, mass distribution, and redundancy; Step 3: Analyze the mapping relationship of the floating base assembly system to obtain the mapping relationship between the dynamic parameters of the floating base assembly system and the topological configuration evaluation parameters of the assembly under different reconstruction conditions; Step 4: Construct constraint functions with the cell robot driving parameters, assembly system vibration parameters, assembly orbit parameters, and stability of the topological configuration reconstruction process as design variables; Step 5, using the mapping relationship and constraint function, determining a topological configuration evaluation model of the floating base assembly system; Step 6: By constructing the action equation and using the gradient descent method to give the steepest descent line of the assembly configuration, the minimum action path can be obtained to achieve the optimal configuration evaluation model; Step seven, normalize and linearize the configuration evaluation model, perform sequential quadratic programming on the processed configuration evaluation model, and obtain the configuration evaluation result.

2. The evaluation method for reconstructing the topological configuration of a floating base assembly system according to claim 1, characterized in that: In step 4, the cell robot driving parameters include: motor torque, motor speed, joint angle; the assembly system vibration parameters include: resonance frequency, vibration amplitude, damping ratio; the assembly orbit parameters include: orbit height, orbit inclination, orbit period; the stability of the topological configuration reconstruction process includes: structural deformation, stress distribution, and stability factor.

3. The evaluation method for reconstructing the topological configuration of a floating base assembly system according to claim 1, characterized in that: Step five includes: S51, conduct dexterity modeling analysis; obtain various dexterity measurement indicators through the Jacobian matrix of the cell robot, and solve the condition number k to obtain the ratio of the maximum singular value to the minimum singular value of the matrix; k(J)=α1 / α2 Where J is the Jacobian matrix, α1 and α2 are the maximum and minimum singular values ​​of J; S52, solving the minimum singular value to obtain the minimum workspace velocity generated by the unit joint velocity vector; S53, solving the inverse of the condition number to obtain the sensitivity of the velocity of the end effector to the joint velocity vector; S54, solve the operability metric index, and define the determinant of the product of the Jacobian matrix and its transpose as the operability metric ρ S55, conduct cell robot reachability analysis and define the cell robot’s workspace; S56, define the reachability description of the cellular robot; S57, define the evaluation task of cell robot reachability; S58, construct accessibility evaluation function; S59, establish an optimization model.

4. The evaluation method for reconstructing the topological configuration of a floating base assembly system according to claim 3, characterized in that: In S53, the minimum condition number k is used m The dexterity index D is defined by the reciprocal of Among them, k m =min(K(J)).

5. The evaluation method for reconstructing the topological configuration of a floating base assembly system according to claim 4, characterized in that: In S55, the workspace of the cell robot is defined as the set of all configurations of the end effector achieved by different joint rotation angles; if Q is the configuration space of the cell robot, SE(3) is the displacement and rotation angle of the cell robot, g ts :Q→SE(3) is a positive solution of the kinematic mapping, then the workspace W is defined as the set: Among them, φ is the joint rotation angle of the cell robot.

6. The evaluation method for reconstructing the topological configuration of a floating base assembly system according to claim 5, characterized in that: In S56, the accessibility of the cell robot is described as: If the given task is a task space W with pose requirements TPO = {P d ∈SE(3)}, where P d is the posture position required by the cell robot; for a given cell robot, its working space is W RPO Then: The accessibility evaluation problem is to judge W TPO Is it in the reachable space W? RPO Inside; Right now: There is P di ∈W RPO (i=1,2,…,n), where n is the number of joints of the floating base assembly system, i is the joint of the i-th cell robot, P di is the expected posture position of the i-th cell robot joint.

7. The evaluation method for reconstructing the topological configuration of a floating base assembly system according to claim 6, characterized in that: In S57, the evaluation task of the cell robot’s reachability is: Make P d With P r coincidence, where P r It is the posture position that the cell robot can reach in the floating base assembly system under the mission requirements; That is, P d With P r The distance measure d between p (P d ,P r )=0, the cell robot is considered to meet the accessibility requirements; set up R do ,R ro ∈SO(3), respectively representing the desired posture and reachable posture of the cell robot, P dp ,P rp ∈R 3 , respectively represent the desired position and reachable position of the cell robot; Then the distance measure is defined as: Where y is a constant related to the structural size of the cell robot.

8. The evaluation method for reconstructing the topological configuration of a floating base assembly system according to claim 7, characterized in that: In S58, a reachability evaluation function is constructed according to the evaluation task: G(P d ,q)=d(P d ,P r ),q=[q1 q2 … q4] T Where q is the quaternion of the cell robot joint. If G(P d ,q)=0, then the reachability requirement is met.

9. The evaluation method for reconstructing the topological configuration of a floating base assembly system according to claim 1, characterized in that: Step six includes: S61, establish the Lagrangian; S62, define action amount; S63, using the above Lagrange equation to solve the motion trajectory of the system; S64, using the gradient descent method, iteratively approximates the steepest descent line.

10. The evaluation method for reconstructing the topological configuration of a floating base assembly system according to claim 1, characterized in that: Step seven includes: S71, normalizing the evaluation model; S72, linearizing the normalized model; S73, performing sequential quadratic programming solution on the processed evaluation model; S74, outputting the optimized variables, the optimal objective function value and the constraint value, and the obtained variables are the model evaluation results; S75, performing standard index comparison on the obtained model evaluation results.

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