Robot flexible parameter modeling and identification method based on frequency domain test

Abstract

The invention belongs to the field of robot flexible parameter identification, and discloses a robot flexible parameter identification method and system based on frequency domain testing, which are used for modeling and parameter identification of flexible dynamic characteristics of a robot connecting rod and an overall system. A generalized Maxwell model (GMM) is adopted to perform modeling on the viscoelasticity characteristic of a single connecting rod, and a rigid-flexible coupling dynamic model with multiple connecting rods connected in series is obtained through derivation on the basis, so that the overall tail end dynamic response of the robot can be described. Input and output signals of the tail end of the robot are obtained through force hammer excitation and accelerometer response, and a frequency response function is obtained based on frequency domain processing. The flexible parameter identification process is realized by fitting a frequency domain transfer function obtained by mechanism modeling and a frequency response obtained by an experiment, and does not depend on large-scale simulation calculation and a large amount of experimental data. The modeling parameters can be adaptively adjusted in the fitting process, so that the identification result has stability and accuracy while keeping physical consistency.

Description

Technical Field

[0001] This invention belongs to the field of robot flexibility parameter identification, and more specifically, relates to a method for robot flexibility parameter identification based on frequency domain testing. Background Technology

[0002] As the application scope of industrial robots, service robots, and special-purpose robots continues to expand, the requirements for their operational accuracy and dynamic performance are constantly increasing. For robots with long cantilever arms, lightweight designs, or high-speed operations, their linkage and joint transmission systems often exhibit significant flexible characteristics, including elastic deformation, vibration modes, and damping effects. These flexible effects not only reduce end-effector positioning accuracy but may also induce resonance and structural fatigue, thereby affecting operational stability and system lifespan.

[0003] To effectively suppress the effects of flexibility and improve robot performance, accurately obtaining flexible dynamic parameters (including stiffness, damping, and equivalent mass) is a necessary prerequisite. These parameters are not only the foundation for establishing a rigid-flexible coupled dynamic model, but also the key basis for vibration suppression control, structural optimization design, and precision operation.

[0004] Currently, flexible robot modeling and parameter identification mainly rely on the Assumed Mode Method (AMM) and the Finite Element Method (FEM). AMM, based on continuum dynamics theory, approximates the flexible displacement distribution by selecting a finite number of shape functions and derives the rigid-flexible coupling dynamic model using the Lagrange equations. This method has relatively low computational cost and is convenient for controller design, but the model accuracy is limited by modal truncation, and high-frequency dynamic characteristics may be neglected. Furthermore, the selection of shape functions depends on boundary conditions and geometry, making modeling difficult and uncertain for robots with complex structures. FEM discretizes the structure into multiple finite elements and constructs the overall dynamic equations by assembling the element stiffness and mass matrices. FEM models have high accuracy and are suitable for complex geometries and non-uniform material distributions, but they have many degrees of freedom and high computational cost, making them unsuitable for real-time control and rapid parameter identification. Moreover, its accuracy is highly dependent on material and structural parameters, and there are often discrepancies between field-measured characteristics and theoretical predictions, requiring additional experimental correction.

[0005] Existing technology 1. Robot frequency domain model method with genetic algorithm parameter identification (KUKA KR10, MatlabSimscape environment)

[0006] This technology targets industrial robots, obtains the frequency response function through pulse hammer experiments, establishes a frequency domain dynamic model, uses a genetic algorithm for parameter identification, and verifies that the higher-dimensional model (24 parameters) has significantly improved accuracy in the frequency range compared to the simplified model (12 parameters).

[0007] Problems exist:

[0008] It only focuses on improving model accuracy and does not optimize for the computational complexity of real-time implementation on site;

[0009] Not robust enough to noise, genetic algorithms are difficult to compute quickly in real-time in real-world working environments.

[0010] Existing technology 2. Frequency domain gray box method for parameter identification of industrial multi-body flexible manipulators (Wernholt et al.)

[0011] This method employs frequency domain gray box identification technology, matching the nonparametric frequency response function with the parameterized model frequency response function, and achieving parameter identification by minimizing the error between the two. It also has high adaptability to nonlinear and multivariable chips.

[0012] Problems exist:

[0013] Busy with the design and optimization of frequency domain FRF estimation, sensitive to noise in the field environment;

[0014] The model is complex to construct and difficult to deploy quickly in the robot's field operation environment.

[0015] Existing technologies for identifying the flexible parameters of industrial robots often employ frequency response function matching and genetic algorithms or gray box model optimization strategies (such as the KUKA KR10 genetic algorithm method and the frequency domain gray box method proposed by Wernholt). These methods improve identification accuracy and model usability, but they are computationally complex, time-consuming in the identification process, and sensitive to noise, which is not conducive to rapid on-site deployment.

[0016] While the KUKA KR10 method improves model accuracy, it fails to optimize computational efficiency and noise resistance. The nonparametric FRF and error minimization methods used by Wernholt et al. are structurally rigorous, but rely on complex model construction and extensive experimental design, making them difficult to apply quickly in practical environments. Summary of the Invention

[0017] In response to existing technologies, the present invention proposes a method based on frequency domain testing combined with a generalized Maxwell model. By using equivalent mass concatenation GMM modeling, frequency domain impulse testing and PSO optimization identification strategies, it can not only ensure identification accuracy, but also significantly improve computational efficiency and applicability. It is particularly suitable for rapid identification of robot flexibility parameters in the field, and overcomes the shortcomings of existing technologies in terms of noise sensitivity, computational efficiency and field applicability.

[0018] This invention provides a method for identifying robot flexibility parameters based on frequency domain testing. Addressing the limitations of current mainstream methods that rely on time-domain response acquisition for flexibility parameter fitting, such as sensitivity to noise, computational complexity, and difficulty in rapid on-site implementation, this invention proposes a method combining frequency domain testing with a Generalized Maxwell Model (GMM) for robot flexibility modeling and parameter identification. This method significantly improves computational efficiency and applicability while maintaining identification accuracy, making it particularly suitable for implementation in real-world robot working environments. The specific implementation steps are as follows:

[0019] S1: Establish a dynamic model of a single link based on the generalized Maxwell model;

[0020] S2: Based on the generalized Maxwell model of a single link, establish a rigid-flexible coupling dynamic model of a multi-link robot;

[0021] S3: Frequency domain testing is performed using a force hammer and accelerometer to obtain the acceleration and force signals of the robot's end effector, calculate the frequency response function, and identify the flexibility parameters of each link based on the frequency response function.

[0022] Furthermore, the vibration at the end of a single link described in S1 can be equivalent to the flexibility of the link being represented by a generalized Maxwell model connected in series with the equivalent mass at the end on the same degree of freedom. The equivalent mass is used to characterize the momentum effect at the measuring point, and the GMM is used to characterize the frequency-dependent stiffness and damping of the structure.

[0023] A Generalized Maxwell Model (GMM) consists of a main spring and N Maxwell elements connected in parallel. Each Maxwell element consists of a spring and a damper connected in series. Let the input be the external force F(t) at the end point and the output be the displacement x(t) at the end point. Then, in the time domain, the constitutive equation of the GMM can be expressed as:

[0024]

[0025] Where k0 is the stiffness of the main spring (N / m), σ i (t) represents the stress contribution of the i-th Maxwell element, and N is the number of Maxwell elements.

[0026] For the i-th Maxwell cell, its time-domain equation is:

[0027]

[0028] Where, k i Let c be the spring stiffness of the i-th Maxwell element. i Let be the damping coefficient of the i-th Maxwell element. The first derivative of stress, It is the first derivative of the displacement.

[0029] Applying the Laplace transform to the above equation yields the equivalent stiffness of a single Maxwell element in the Laplace domain as follows: in, Let K be the relaxation time constant (s). The equivalent stiffness K of the entire GMM in the pull-like domain. GMM It can be represented as:

[0030]

[0031] The dynamic equation of the entire connecting rod in the tension domain can be written as:

[0032] ms 2 X(s)=F(s)-K GMM (s)X(s) (4)

[0033] Where F(s) is the input force signal, and X(s) is the displacement at the end of the link. Rearranging the above equation yields the displacement transfer function G for a single link. link (s) is:

[0034]

[0035] Where, m eq This refers to the equivalent mass acting at the end of the connecting rod.

[0036] Furthermore, the robot described in S2 has n series-connected rigid-flexible coupling links. In the local coordinate system of the links, only the flexibility in the y and z directions is considered (the other two directions perpendicular to the link axis), and the link axis is not compressed. The displacement δp at the end of the j-th link is... j for

[0037] δp j =[0,δ y ,δ z ] T (6)

[0038] Total displacement δp at the robot end effector ee The combined effect of the displacements at the ends of each link can be expressed as:

[0039]

[0040] in, This represents the rotational transformation from the local coordinates of segment j to the coordinates of the end point. Define the local compliance matrix for a single link. Its relationship with the force at the end of the connecting rod and the nodal displacement is as follows:

[0041]

[0042] in, Let be the y-direction deformation displacement at the end of the j-th link. Let be the z-direction deformation displacement at the end of the j-th link. Let be the y-direction force acting on the end of the j-th link. Let Z be the z-direction force acting on the end of the j-th link. Let be the equivalent stiffness of the GMM model in the y-direction at the end of the j-th link. Let be the equivalent stiffness of the GMM model at the end of the j-th link in the z-direction.

[0043] Define the embedding matrix The compliance of the link end is then mapped to a 3D compliance matrix in three-dimensional space. for:

[0044]

[0045] Let the homogeneous transformation from the local coordinates of segment j to the coordinates of the endpoint be: in This is a rotation transformation from the local coordinates of segment j to the coordinates of the end point. Let be the translation transformation from the local coordinates of segment j to the coordinates of the end point. Ignoring higher-order rotation terms caused by small deformations, the compliance matrix of the end point of the j-th link in the end point coordinate system is... for:

[0046]

[0047] Series structure subjected to force F at the same end ee Below, the displacement contributions of each segment are superimposed at the end, therefore the total compliance H flex (s) is the sum of the end flexibility of each segment:

[0048]

[0049] The equivalent mass matrix M at the end ee (q) is obtained from the attitude-dependent rigid body inertial mapping:

[0050]

[0051] Therefore, the dynamic equation at the end can be expressed as:

[0052]

[0053] Therefore, the force-displacement transfer function G at the ends of n connected links is... ee (s) can be expressed as:

[0054]

[0055] Furthermore, the frequency domain testing method described in S3 involves fixing an accelerometer to the robot's end effector and striking a designated point on the end effector perpendicularly / radially. The signal from the hammer is F(t), and the signal from the accelerometer is a(t). Using classical FRF estimation, the frequency response function of acceleration-force can be obtained:

[0056]

[0057] Among them, S aF (ω) is the cross spectrum of acceleration and force, S FF (ω) represents the force spectrum. The model predicts the frequency response function of acceleration-force. for

[0058]

[0059] Select multiple robot poses q (k) The frequency response function of the robot's acceleration-force under various postures was measured. Simultaneously, the predicted values ​​of the acceleration-force frequency response function under each pose are obtained based on the model. Where θ represents the GMM parameters included in the model, and the objective function J(θ) is constructed as follows:

[0060]

[0061] Here, Q represents the pose set, Ω represents the frequency point set, and w(ω) is the weight parameter, which is linked to the cross-correlation. θ can be obtained by solving the above objective function using the PSO algorithm.

[0062] Compared with the prior art, the robot flexibility parameter identification method based on frequency domain testing provided by the present invention has the following advantages:

[0063] 1. This invention models the flexibility of robot links by combining the generalized Maxwell model (GMM) with equivalent mass, which can take into account both the frequency-dependent characteristics of viscoelastic elements and the inertial effect of mechanical structures. Compared with traditional lumped parameter models, it has higher physical interpretability and applicability.

[0064] 2. Compared to the finite element method, which requires complex modeling and large-scale numerical calculations, this invention can complete the identification by relying only on a small amount of experimental data and the low-order parameter expression of GMM, which greatly reduces the modeling and calculation costs.

[0065] 3. The method of this invention is not only applicable to the identification of flexibility parameters of a single link, but can also be extended to multi-link connected robot systems. Furthermore, it can map the flexibility of a single link to the end-effector coordinate system through homogeneous transformation, thereby obtaining the dynamic characteristics of the entire end-effector. It has strong applicability.

[0066] 4. The experimental methods required for this invention are simple, requiring only conventional force hammers and accelerometers to complete the test, and it does not rely on the internal data of robot manufacturers, thus possessing strong engineering feasibility and promotional application value. Attached Figure Description

[0067] Figure 1 This is a flowchart of the method for establishing an envelope-type material removal prediction model driven by the implementation mechanism and data of this invention;

[0068] Figure 2 These are the modeling results of the time-domain vibration of a single link using the proposed method and the comparative method of this invention;

[0069] Figure 3 The diagram shows the modeling results of the time-domain vibration of the three-bar linkage using the proposed method and the comparative method of this invention.

[0070] Figure 4 This diagram illustrates the root mean square error optimization process during the identification of three-link dynamic parameters using PSO in the method proposed in this invention. Detailed Implementation

[0071] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0072] In the context of industrial applications, existing technologies face significant challenges in identifying robot flexibility parameters. Traditional identification methods based on time-domain response rely on the direct acquisition and fitting of displacement, velocity, or acceleration signals. This approach is often susceptible to noise interference when facing complex working conditions, leading to unstable parameter solutions. Furthermore, time-domain fitting typically involves the inversion and iterative calculation of nonlinear differential equations, resulting in high computational complexity. This makes it unsuitable for rapid modeling and online diagnostics in production environments, limiting the application potential of industrial robots in high-precision assembly, flexible manufacturing, and high-speed operation scenarios.

[0073] In multi-link robots, flexibility effects propagate and couple along the robotic arm. While existing gray-box modeling and genetic algorithm optimization methods can improve modeling accuracy, the model order is too high and the optimization process is slow. This makes it impossible for the system to provide real-time feedback when rapid changeover or online maintenance is required in actual production lines, and there is a time lag in flexibility compensation and trajectory correction. In addition, frequency domain gray-box models have strict requirements for experimental design. Once external shocks or changes in the measurement environment occur, the robustness of the model decreases significantly, resulting in inconsistent recognition results under different working conditions.

[0074] This method introduces a generalized Maxwell model, analytically transforming the linkage's flexibility characteristics into a frequency-dependent structure composed of a main spring and multiple Maxwell elements connected in parallel. It achieves integrated modeling with end-effector dynamics through equivalent mass. Unlike complex time-domain time-varying differential solutions, this model manifests as an algebraic combination of frequency-dependent stiffness and damping in the Laplace domain, significantly reducing computational complexity. By directly handling the force-displacement relationship in the frequency domain, it avoids noise amplification issues caused by time-domain signal integration, improving its anti-interference capability in production workshop environments.

[0075] In the testing phase, a transient impact is applied using a force hammer, and the end effector is acquired using an accelerometer, forming a frequency response function of acceleration and force. This process does not require long-term continuous excitation or rely on a complex multi-point measurement system, enabling rapid on-site experimental setup and data acquisition. The signal processing module obtains the experimental FRF by the ratio of the cross spectrum to the autospectrum, effectively avoiding time-domain filtering and computational errors. This solution provides on-site maintenance personnel with a low-cost, easily deployable, and flexible parameter testing method, significantly improving the maintainability of industrial robots.

[0076] During parameter optimization, an objective function based on the difference between the experimental free RF and the model-predicted free RF under multiple poses is constructed, and particle swarm optimization (PSO) is used for iterative optimization. Compared with traditional genetic algorithms, PSO has advantages in search speed and convergence stability, and can quickly obtain the global optimum or near-optimal solution under limited computing resources. This allows the robot to update its flexible characteristic parameters in a short time when switching tasks or adjusting processes, meeting the rapid response requirements in smart manufacturing scenarios.

[0077] The final identification system consists of a modeling module, a testing module, and an optimization module. The modeling module describes single-link and multi-link flexibility based on the Gaussian Model (GMM), the testing module enables rapid frequency domain excitation and signal acquisition in the field, and the optimization module completes parameter identification and correction. The synergistic effect of these three modules allows the system to achieve high-precision, low-latency modeling and identification of flexibility characteristics in industrial settings, providing fundamental support for high-dynamic precision control and flexibility compensation of robots. This overcomes the technical bottlenecks of existing technologies in industrial applications, such as noise sensitivity, computational complexity, and insufficient real-time performance.

[0078] Please see Figure 1 This invention provides a mechanism- and data-driven envelope-based material removal prediction model, and the specific model establishment method is as follows: Figure 1 As shown, it includes the following steps:

[0079] The specific implementation steps are as follows:

[0080] S1: Establish a dynamic model of a single link based on the generalized Maxwell model;

[0081] S2: Based on the generalized Maxwell model of a single link, establish a rigid-flexible coupling dynamic model of a multi-link robot;

[0082] S3: Frequency domain testing is performed using a force hammer and accelerometer to obtain the acceleration and force signals of the robot's end effector, calculate the frequency response function, and identify the flexibility parameters of each link based on the frequency response function.

[0083] Furthermore, the vibration at the end of a single link described in S1 can be equivalent to the flexibility of the link being represented by a generalized Maxwell model connected in series with the equivalent mass at the end on the same degree of freedom. The equivalent mass is used to characterize the momentum effect at the measuring point, and the GMM is used to characterize the frequency-dependent stiffness and damping of the structure.

[0084] A Generalized Maxwell Model (GMM) consists of a main spring and N Maxwell elements connected in parallel. Each Maxwell element consists of a spring and a damper connected in series. Let the input be the external force F(t) at the end point and the output be the displacement x(t) at the end point. Then, in the time domain, the constitutive equation of the GMM can be expressed as:

[0085]

[0086] Where k0 is the stiffness of the main spring (N / m), σ i (t) represents the stress contribution of the i-th Maxwell element, and N is the number of Maxwell elements.

[0087] For the i-th Maxwell cell, its time-domain equation is:

[0088]

[0089] Where, k i Let c be the spring stiffness of the i-th Maxwell element. i Let be the damping coefficient of the i-th Maxwell element. The first derivative of stress, It is the first derivative of the displacement.

[0090] Applying the Laplace transform to the above equation yields the equivalent stiffness of a single Maxwell element in the Laplace domain as follows: in, Let K be the relaxation time constant (s). The equivalent stiffness K of the entire GMM in the pull-like domain. GMM It can be represented as:

[0091]

[0092] The dynamic equation of the entire connecting rod in the tension domain can be written as:

[0093] ms 2 X(s)=F(s)-K GMM (s)X(s) (4)

[0094] Where F(s) is the input force signal, and X(s) is the displacement at the end of the link. Rearranging the above equation yields the displacement transfer function G for a single link. link (s) is:

[0095]

[0096] Where, m eq This refers to the equivalent mass acting at the end of the connecting rod.

[0097] Furthermore, the robot described in S2 has n series-connected rigid-flexible coupling links. In the local coordinate system of the links, only the flexibility in the y and z directions is considered (the other two directions perpendicular to the link axis), and the link axis is not compressed. The displacement δp at the end of the j-th link is... j for

[0098] δp j =[0,δ y ,δ z ] T (6)

[0099] Total displacement δp at the robot end effector ee The combined effect of the displacements at the ends of each link can be expressed as:

[0100]

[0101] in, This represents the rotational transformation from the local coordinates of segment j to the coordinates of the end point. Define the local compliance matrix for a single link. Its relationship with the force at the end of the connecting rod and the nodal displacement is as follows:

[0102]

[0103] in, Let be the y-direction deformation displacement at the end of the j-th link. Let be the z-direction deformation displacement at the end of the j-th link. Let be the y-direction force acting on the end of the j-th link. Let Z be the z-direction force acting on the end of the j-th link. Let be the equivalent stiffness of the GMM model in the y-direction at the end of the j-th link. Let be the equivalent stiffness of the GMM model at the end of the j-th link in the z-direction.

[0104] Define the embedding matrix The compliance of the link end is then mapped to a 3D compliance matrix in three-dimensional space. for:

[0105]

[0106] Let the homogeneous transformation from the local coordinates of segment j to the coordinates of the endpoint be: in This is a rotation transformation from the local coordinates of segment j to the coordinates of the end point. Let be the translation transformation from the local coordinates of segment j to the coordinates of the end point. Ignoring higher-order rotation terms caused by small deformations, the compliance matrix of the end point of the j-th link in the end point coordinate system is... for:

[0107]

[0108] Series structure subjected to force F at the same end ee Below, the displacement contributions of each segment are superimposed at the end, therefore the total compliance H flex (s) is the sum of the end flexibility of each segment:

[0109]

[0110] The equivalent mass matrix M at the end ee (q) is obtained from the attitude-dependent rigid body inertial mapping:

[0111]

[0112] Therefore, the dynamic equation at the end can be expressed as:

[0113]

[0114] Therefore, the force-displacement transfer function G at the ends of n connected links is... ee (s) can be expressed as:

[0115]

[0116] Furthermore, the frequency domain testing method described in S3 involves fixing an accelerometer to the robot's end effector and striking a designated point on the end effector perpendicularly / radially. The signal from the hammer is F(t), and the signal from the accelerometer is a(t). Using classical FRF estimation, the frequency response function of acceleration-force can be obtained:

[0117]

[0118] Among them, S aF (ω) is the cross spectrum of acceleration and force, S FF (ω) represents the force spectrum. The model predicts the frequency response function of acceleration-force. for

[0119]

[0120] Select multiple robot poses q (k) The frequency response function of the robot's acceleration-force under various postures was measured. Simultaneously, the predicted values ​​of the acceleration-force frequency response function under each pose are obtained based on the model. Where θ represents the GMM parameters included in the model, and the objective function J(θ) is constructed as follows:

[0121]

[0122] Here, Q represents the pose set, Ω represents the frequency point set, and w(ω) is the weight parameter, which is linked to the cross-correlation. θ can be obtained by solving the above objective function using the PSO algorithm.

[0123] Example 1

[0124] In this embodiment, a six-DOF articulated robot is selected, and its second joint link is modeled as a single link. An impact force is applied to the end of the link using a hammer, while an accelerometer is fixed to the end to collect acceleration and force signals. The frequency response function is obtained using frequency domain signal processing methods, and then combined with the structural form of the generalized Maxwell model, the end-effector flexibility is equivalent to a main spring and a parallel combination of multiple Maxwell elements, and connected in series with the equivalent mass of the end, thus realizing the modeling of the single-link dynamic characteristics.

[0125] like Figure 2 The equivalent stiffness and damping parameters identified by this method are input into the simulation model and compared with the measured frequency response. The results show that in the time domain response, the model's predicted curve and the experimental curve are in high agreement, with a mean square error of less than 5%, while the error of the traditional time domain identification method exceeds 15%. This verifies the significant advantages of this embodiment in improving identification accuracy and noise resistance.

[0126] Example 2

[0127] In this embodiment, a three-bar linkage robotic arm is modeled. First, a generalized Maxwell model of each link is established, and the corresponding local compliance matrix is ​​solved. Then, through rotation and homogeneous transformation matrices, the local compliance is mapped to the end-effector coordinate system, thereby obtaining the overall compliance matrix and the equivalent mass matrix. Finally, a transfer function model between the end-effector input force and displacement is constructed.

[0128] like Figure 3The model was validated under different robot postures. Experimental results show that regardless of whether the robotic arm is in a horizontally extended or vertically extended posture, the model's predicted end-effector displacement is highly consistent with the measured data, with an average error of less than 3%. This embodiment demonstrates that the method of the present invention can effectively solve the problems of complex superposition of flexible characteristics under multi-link coupling and the difficulty of rapid calculation by traditional methods.

[0129] Example 3

[0130] In this embodiment, a frequency domain testing device was designed, including a standard impact hammer, an integrated triaxial accelerometer, and a data acquisition module. During the test, the impact hammer acts perpendicularly on the robot's end effector. The acquired force and acceleration signals are processed by the signal processing module and then fed into the cross-spectrum and auto-spectrum calculation unit to obtain the experimental frequency response function.

[0131] Compared to long-time sampling schemes in the time domain, this device can complete the measurement of response characteristics across the entire frequency range under a single impact, reducing data acquisition time from several minutes to less than 5 seconds. Field tests show that the device can be quickly deployed in industrial production workshops and features ease of operation, low cost, and high precision.

[0132] Example 4 (corresponding to claims 8–9: parameter optimization method)

[0133] In this embodiment, an objective function is constructed, which consists of the sum of squared differences between the measured frequency response functions and the model-predicted frequency response functions under multiple robot postures, and weighted at different frequency points. The optimization algorithm employs particle swarm optimization, with parameters set to a swarm size of 50 and a maximum number of iterations of 200.

[0134] like Figure 4 Experimental results show that Particle Swarm Optimization (PSO) approaches the global optimum by the 50th iteration, demonstrating good parameter convergence stability. Compared with the genetic algorithm, PSO reduces computation time by approximately 40%, and the identified flexible parameters remain stable under different noise levels, validating the speed and robustness of this method.

[0135] Example 5

[0136] In this embodiment, an integrated identification system was developed, including a modeling module, a testing module, and an optimization module. The modeling module generates a flexible multi-link robot model based on the generalized Maxwell model, the testing module completes impact experiments and signal acquisition, and the optimization module calls the PSO algorithm to solve the objective function and output the flexibility parameters.

[0137] The system was validated on a typical six-degree-of-freedom robot. After modeling and testing, the system outputs end-effector flexibility parameters in just 120 seconds, reducing the trajectory tracking error from 0.8 mm to 0.6 mm. This example demonstrates the system's application potential in industrial assembly and precision machining scenarios.

[0138] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A robot flexible parameter identification method based on frequency domain test, characterized in that, The method comprises the following steps: First, a single-link dynamics model is established based on a generalized Maxwell model; Second, a robot rigid-flexible coupling dynamics model is established according to the single-link generalized Maxwell model; Third, a force hammer and an accelerometer are used to perform frequency domain testing, to obtain acceleration signals and force signals of the robot end, to calculate a frequency response function, and to identify flexible parameters of each link based on the frequency response function.

2. The method of claim 1, wherein, In the single-link dynamics model, flexibility of the link end is equivalent to the generalized Maxwell model and an end equivalent mass being connected in series in the same degree of freedom, wherein the generalized Maxwell model is composed of a main spring and a plurality of Maxwell units connected in parallel, and each Maxwell unit is composed of a spring and a damper connected in series.

3. The method according to claim 1 or 2, characterized in that, A displacement transfer function of the single link is equal to a ratio of displacement output to external force input, and the ratio is determined by the end equivalent mass and equivalent stiffness of the generalized Maxwell model, wherein the equivalent stiffness is a sum of the main spring stiffness and equivalent stiffness of each Maxwell unit.

4. A robot multi-link rigid-flexible coupling modeling method, characterized in that, The dynamics equation of the generalized Maxwell model of each link is mapped to the end coordinate system through a local flexibility matrix, to form a total flexibility matrix of the end and an end equivalent mass matrix, and to establish a transfer function relationship between end input force and displacement.

5. The method of claim 4, wherein, The local flexibility matrix of the single link is used to describe a relationship between deformation displacement of the end in y and z directions and external force, and flexibility coefficients are represented by equivalent stiffness of the generalized Maxwell model.

6. A frequency domain testing device for robot flexible parameter identification, characterized in that, The method comprises: a force hammer, used to apply an impact force at the robot end; an accelerometer, fixed to the robot end, used to collect acceleration signals; a signal processing module, used to calculate frequency response functions of acceleration and force and to compare and analyze the modeling results.

7. The apparatus of claim 6, wherein, The signal processing module is used to calculate a cross spectrum of acceleration and force, and to take a ratio of the cross spectrum to a self spectrum of force as the frequency response function.

8. A robot flexible parameter optimization identification method, characterized in that, A target function is constructed based on differences between measured frequency response functions and model predicted frequency response functions under a plurality of poses, and a particle swarm optimization algorithm is used to solve the target function, to obtain optimal parameters of the generalized Maxwell model.

9. The method of claim 8, wherein, The target function is a sum of squares of differences between measured frequency response functions and model predicted frequency response functions under different pose sets and frequency point sets, and is accumulated after being weighted according to a preset weight parameter.

10. A robot flexibility parameter identification system based on frequency domain testing, characterized by, The method comprises: a modeling module, used to establish dynamics equations of the single-link and multi-link generalized Maxwell models; a testing module, used to perform frequency domain experiments through the force hammer and the accelerometer and to collect frequency response functions; and an optimization module, used to identify and correct parameters of the generalized Maxwell model based on the frequency response functions.

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