Method for identifying dynamics parameters of multi-joint robot based on flexible skin coupling effect

Abstract

The application discloses a multi-joint robot dynamics parameter identification method based on flexible skin coupling effect, and belongs to the technical field of robot dynamics modeling and parameter identification. In view of the problem that the existing method ignores the flexible skin cross-joint coupling and nonlinear effect, leading to model inaccuracy and low control precision, the application first constructs a rigid skeleton dynamics model, superimposes a skin equivalent generalized moment to form an extended model, extracts independent base parameters, optimizes a design excitation trajectory, solves the base parameters by using a ridge regression, and combines a BPNN to compensate for residual errors to construct a hybrid identification model. The application can be applied to humanoid and service robot research and development, effectively improves motion control and collision detection precision, and is suitable for human-computer interaction scenes.

Description

Technical Field

[0001] This invention relates to the field of robot dynamics modeling and parameter identification technology, specifically to a method for identifying dynamic parameters of multi-joint robots based on the coupling effect of flexible skin. Background Technology

[0002] With the rapid development of humanoid robots, service robots, and biomimetic robot technologies, more and more robots are incorporating flexible skins, silicone overlays, or biomimetic soft tissue structures on the exterior of their rigid skeletons and joint actuators to enhance their biomimetic appearance, human-robot interaction safety, contact cushioning capabilities, and environmental adaptability. These flexible skins typically cover the robot's torso, limbs, and joint areas. During robot movement, they undergo complex deformations such as stretching, compression, shearing, and bending as the joints rotate, creating additional constraints and couplings with internal rigid links and adjacent structures.

[0003] Most existing methods for modeling and identifying the dynamics of multi-joint robots are based on the assumption of rigid bodies, typically treating the robot as composed of several ideal rigid links and joints, focusing on identifying parameters such as link mass, center of mass position, moment of inertia, and joint friction coefficient. In these methods, the influence of the robot's external flexible covering layer, soft tissue structure, or flexible skin on the system dynamics is often ignored, or only roughly handled by simple added mass, concentrated damping, or empirical compensation terms.

[0004] However, for multi-joint robots covered with flexible skins, the flexible skin is not simply a static additional layer; it generates significant additional dynamic effects during robot movement, mainly manifested in the following aspects:

[0005] Firstly, the flexible skin has elastic and viscoelastic characteristics, and during joint movement, it will generate additional restoring torque, additional damping torque and a certain hysteresis response as the joint displacement and velocity change.

[0006] Secondly, when flexible skin is continuously arranged across multiple joints or multiple rigid components, coupling will be formed between multiple degrees of freedom, so that the dynamic response of a certain joint is not only related to the state of the joint itself, but also to the position and velocity changes of adjacent joints.

[0007] Third, the actual mechanical response of flexible skin usually exhibits nonlinear and certain time-varying characteristics as attitude, velocity, contact state and material deformation change. Part of it can be described by an equivalent linear coupling model, while the other part belongs to unmodeled residuals that are difficult to accurately characterize with low-order analytical models.

[0008] Fourth, the influence of flexible skin on the overall inertial characteristics of the system is often mixed with rigid body inertial parameters, friction parameters and additional coupling parameters in actual identification. If not distinguished, it is easy to lead to unclear physical meaning of the identification results.

[0009] Due to the aforementioned factors, if traditional rigid body dynamics parameter identification methods are still used, it is easy for the identification results to deviate significantly from the actual system. Especially in multi-joint cooperative motion scenarios, models that do not consider the additional elasticity, additional damping, and cross-joint coupling effects of flexible skins are difficult to accurately reflect the actual dynamic response, thus affecting the accuracy and stability of tasks such as inverse dynamics calculation, feedforward compensation, trajectory tracking control, collision detection, and state estimation.

[0010] While some existing modeling methods for flexible structures can describe the deformation of flexible materials using finite element method, continuum mechanics, or high-dimensional elastic models, these methods are usually complex in modeling, have many parameters, and require a large amount of computation, making them unsuitable for direct application in online identification and control of multi-joint robot systems. At the same time, there is still a lack of a solution that balances modeling accuracy, identification feasibility, and engineering practicality in how to transform the continuum mechanics effects of flexible skin into a low-dimensional equivalent parametric model suitable for robot dynamics identification and achieve a unified expression with multi-joint rigid body dynamics models.

[0011] Therefore, there is an urgent need to propose a dynamic parameter identification method for multi-joint robots that can explicitly consider the coupling effect of flexible skin, so as to improve the robot dynamic model's ability to represent real physical systems and provide a more accurate model basis for subsequent motion control, force compensation, state prediction and structural design optimization. Summary of the Invention

[0012] To address the technical problem of insufficient accuracy in dynamic models caused by neglecting the cross-joint coupling effect of flexible skin in existing identification methods, this invention provides a method for identifying the dynamic parameters of multi-joint robots based on the coupling effect of flexible skin, including:

[0013] S1. Constructing the rigid skeleton dynamic model of the robot: Based on the mechanism configuration and linkage relationship of the multi-joint robot to be identified, establish dynamic equations that only include contributions from rigid components. The equations cover inertial forces, Coriolis forces and centrifugal forces, gravity and joint friction forces, serving as the basic modeling framework.

[0014] S2. Establish an equivalent dynamic model of the flexible skin: Based on the basic modeling framework established in S1, the flexible skin covering the robot surface is equivalent to m continuous flexible units. The additional generalized torque generated by the deformation of the flexible unit is calculated, and the additional torque term is superimposed into the basic modeling framework to form an extended dynamic model that includes the coupling effect of the flexible skin.

[0015] S3. Constructing a regression identification model: Based on the extended dynamic model, determine the set of parameters to be identified, including rigid link inertia parameters, joint friction parameters, and flexible skin physical parameters; eliminate linearly related terms in the set of parameters to be identified by orthogonal decomposition method, extract mutually independent basic parameter sets and their corresponding regression matrices, thereby transforming the dynamic model into a linear identification form;

[0016] S4. Generate and identify the excitation trajectory and collect experimental data: Based on the regression matrix, with the goal of optimizing the numerical conditions of the regression matrix, solve for the optimal excitation trajectory parameters and generate the optimal excitation trajectory that can fully stimulate the characteristics of each basic parameter; control the robot to execute the optimal excitation trajectory, and simultaneously collect joint position, joint velocity, joint acceleration and drive motor current data to form an experimental dataset.

[0017] S5. Execution Parameter Identification and Optimization Solution: Based on the experimental dataset, the data is filtered and preprocessed by differentiation to reconstruct the global regression matrix and torque vector; the basis parameter set is solved using the regularized least squares method to obtain the predicted torque of the physical model; the residual between the predicted torque and the actual collected torque is calculated, and the residual is compensated by learning using a neural network. The output of the physical model is superimposed with the compensation amount of the neural network to construct a hybrid dynamics model.

[0018] S6. Model Validation and Parameter Update: Validate the prediction accuracy of the hybrid power model using the test trajectory of the optimal excitation trajectory; when the validation error exceeds the preset threshold, adjust the excitation trajectory or the set of parameters to be identified based on the error analysis results, and repeat steps S4 to S6 until the model accuracy meets the requirements.

[0019] Furthermore, in S1, constructing the robot's rigid body skeleton dynamics model specifically includes:

[0020] Define the multi-joint robot to be identified as having n movable joints, and establish the generalized coordinates of the joints:

[0021]

[0022] Establishing generalized velocity of joints:

[0023]

[0024] Establish generalized acceleration of joints:

[0025]

[0026] Based on the generalized coordinates, velocities, and accelerations of the joints, a dynamic equation is established that includes only the contributions of rigid components:

[0027]

[0028] in, Represents the generalized coordinates of the joints. Represents the generalized velocity of the joint. This represents the generalized acceleration of the joint. This indicates the position of the nth joint. Represents the inertia matrix. Represents the Coriolis force and centrifugal force terms. Represents the gravity term. Indicates joint friction. This is the joint driving torque vector.

[0029] Furthermore, in S2, after the flexible skin is equivalent to m continuous flexible elements, the calculation of the deformation and additional generalized moment of each flexible element is also included:

[0030] Define the deformation of the j-th flexible element as:

[0031]

[0032] in, This represents the deformation of the j-th flexible element. Indicates the first The flexible unit is in its current posture The equivalent length, shear displacement, or combined deformation under these conditions; This indicates the joint configuration of a flexible skin in a natural, stress-free state.

[0033] The additional generalized torque is derived using the Lagrange equation:

[0034]

[0035] in, This represents the additional generalized moment vector exerted by the flexible skin on each joint of the robot, where m is the total number of flexible coupling elements. For the first The transpose of the equivalent Jacobian row vector of each flexible unit relative to the joint variables; For the first Equivalent stiffness parameters of each flexible element; For the first The equivalent damping parameters of each flexible element. For the j-th unit shape variable, Let be the deformation velocity of the j-th element.

[0036] Furthermore, in S3, the specific process of eliminating linearly correlated terms in the set of parameters to be identified using orthogonal decomposition includes:

[0037] Construct a standard regression matrix containing all sampling times. and parameter vector Establish equations ,in, It is the residual vector;

[0038] right Perform QR decomposition with column pivoting:

[0039]

[0040] in, For column permutation matrices, It is an orthogonal matrix. It is an upper triangular matrix;

[0041] The permuted matrix is ​​divided into independent columns based on its rank. and related columns ,satisfy Thus, the basis parameter vector is extracted. Transform the model into ,in, For the transformation matrix, As a basis parameter vector, For independent columns The corresponding standard parameter subset, For related columns The corresponding subset of standard parameters.

[0042] Furthermore, in S4, with the objective of optimizing the numerical conditions of the regression matrix, the optimal excitation trajectory parameters are solved, specifically including:

[0043] The trajectory of the i-th joint is constructed by combining an improved Fourier series with a quintic polynomial:

[0044]

[0045] in, Let be the trajectory of the i-th joint. These are Fourier series terms, used to provide rich frequency components and excite different dynamic parameters; The term is a fifth-order polynomial used to ensure that the trajectory satisfies the continuous constraints of position, velocity, and acceleration at the start and end times.

[0046] With the total regression matrix With minimizing the condition number as the core objective, a fitness function is constructed as follows:

[0047]

[0048] in, Representation matrix condition number; , , These represent the penalties for violations of constraints related to joint position, velocity, and acceleration, respectively. This represents an additional penalty term applied when the incentives in certain columns of the regression matrix are too weak. These are the weighting coefficients;

[0049] The particle swarm optimization algorithm is used to solve for the Fourier coefficients that minimize the fitness function J, thereby generating the optimal excitation trajectory.

[0050] Furthermore, in S5, the basis parameter set is solved using the regularized least squares method, specifically including:

[0051] Constructing the ridge regression objective function:

[0052]

[0053] in, For ridge regression estimates, Let be the basis parameter vector to be identified. For the global regression matrix, Let be the regularization coefficient, and take . ;

[0054] The predicted torque of the physical model is obtained by solving:

[0055]

[0056] in, Predict torque for physical models;

[0057] Calculate the physical model residuals:

[0058]

[0059] in, For physical model residuals, This is the global torque vector;

[0060] The residual is fitted using a BPNN neural network to obtain the residual compensation amount. The residual compensation from the neural network is superimposed with the predicted moment from the physical model to obtain the output of the hybrid model. .

[0061] The beneficial effects of this invention are:

[0062] (1) It can more accurately characterize the additional effects of flexible skin on robot dynamics:

[0063] This invention, based on the traditional multi-rigid-body dynamics model, introduces an equivalent additional generalized moment term from a flexible skin. This incorporates the equivalent stiffness effect, equivalent damping effect, and additional constraint effect on joint motion generated by the flexible skin into the dynamic identification model, thereby making the established dynamic model closer to the dynamic behavior of the real system. Compared to traditional methods that ignore the influence of the flexible skin or only use simple additional mass compensation, this invention can more accurately reflect the force characteristics and dynamic response of the robot during motion after being covered with a flexible skin.

[0064] (2) Improve the numerical stability and identifiability of dynamic parameter identification:

[0065] This invention does not directly rely on empirical trajectories for parameter identification. Instead, it constructs an excitation trajectory optimization mechanism aimed at minimizing the condition number of the total regression matrix. This mechanism combines improved Fourier series, fifth-order polynomial boundary constraints, and particle swarm optimization to generate an identification trajectory that satisfies joint position, velocity, and acceleration constraints and possesses high parameter excitation capability. This method effectively reduces the ill-conditioned nature of the regression matrix and enhances the excitation intensity of the regression terms corresponding to each basic parameter, thereby improving the numerical stability and identification accuracy of the dynamic parameter solution.

[0066] (3) It can suppress the influence of noise and ill-conditioned problems on the parameter solution results:

[0067] To address issues such as measurement noise, strong parameter correlation, and ill-conditioned regression matrices in real-world experimental data, this invention employs ridge regression to regularize the solution of basic parameters. Compared to ordinary least squares, ridge regression, by introducing a regularization term into the objective function, effectively reduces the instability caused by noise amplification and ill-conditioned matrices, improving the robustness and generalization ability of parameter estimation. This makes the obtained dynamic parameters more suitable for model building and control applications in real-world experimental environments.

[0068] (4) It can characterize the nonlinear residuals of the flexible skin and the system without modeling:

[0069] Building upon explicit dynamic modeling, this invention further constructs physical model residuals and employs BPNN to learn and compensate for these residuals, thereby establishing a hybrid dynamic identification model that combines a physical model with data-driven residual compensation. This approach not only preserves the mechanistic explanatory power of the equivalent models of rigid body dynamics and flexible skin, but also further fits the complex nonlinear effects of flexible skin, material hysteresis effects, local unmodeled couplings, and experimental perturbations—parts that are difficult to accurately describe using explicit analytical models. Therefore, it can significantly improve the overall model's prediction accuracy.

[0070] (5) Balancing the physical interpretability and engineering feasibility of the model:

[0071] This invention does not directly employ a high-dimensional finite element model or a complex continuum model to solve for the full extent of the flexible skin. Instead, it adopts a technical approach that combines equivalent generalized torque modeling, basic parameter identification, and residual compensation. This reduces modeling complexity and parameter solving difficulty while ensuring a certain level of physical interpretability. Furthermore, this method can directly utilize conventionally obtainable signals such as joint position and current for identification, making it easy to implement on practical multi-joint robot platforms and possessing strong engineering application value. Attached Figure Description

[0072] Figure 1 This is a flowchart of the method described in this invention. Detailed Implementation

[0073] The technical solution of the present invention will be further described below with reference to embodiments, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention. In the following embodiments, process equipment or devices not specifically specified are all conventional equipment or devices in the art. Unless specifically specified, the technical means used in the embodiments of the present invention are all conventional means well known to those skilled in the art.

[0074] Example 1, combined with Figure 1 This embodiment describes a method for identifying the dynamic parameters of a multi-joint robot based on the coupling effect of a flexible skin, including:

[0075] S1. Constructing the rigid skeleton dynamic model of the robot: Based on the mechanism configuration and linkage relationship of the multi-joint robot to be identified, establish dynamic equations that only include contributions from rigid components. The equations cover inertial forces, Coriolis forces and centrifugal forces, gravity and joint friction forces, serving as the basic modeling framework.

[0076] S2. Establish an equivalent dynamic model of the flexible skin: Based on the basic modeling framework established in S1, the flexible skin covering the robot surface is equivalent to m continuous flexible units. The additional generalized torque generated by the deformation of the flexible unit is calculated, and the additional torque term is superimposed into the basic modeling framework to form an extended dynamic model that includes the coupling effect of the flexible skin.

[0077] S3. Constructing a regression identification model: Based on the extended dynamic model, determine the set of parameters to be identified, including rigid link inertia parameters, joint friction parameters, and flexible skin physical parameters; eliminate linearly related terms in the set of parameters to be identified by orthogonal decomposition method, extract mutually independent basic parameter sets and their corresponding regression matrices, thereby transforming the dynamic model into a linear identification form;

[0078] S4. Generate and identify the excitation trajectory and collect experimental data: Based on the regression matrix, with the goal of optimizing the numerical conditions of the regression matrix, solve for the optimal excitation trajectory parameters and generate the optimal excitation trajectory that can fully stimulate the characteristics of each basic parameter; control the robot to execute the optimal excitation trajectory, and simultaneously collect joint position, joint velocity, joint acceleration and drive motor current data to form an experimental dataset.

[0079] S5. Execution Parameter Identification and Optimization Solution: Based on the experimental dataset, the data is filtered and preprocessed by differentiation to reconstruct the global regression matrix and torque vector; the basis parameter set is solved using the regularized least squares method to obtain the predicted torque of the physical model; the residual between the predicted torque and the actual collected torque is calculated, and the residual is compensated by learning using a neural network. The output of the physical model is superimposed with the compensation amount of the neural network to construct a hybrid dynamics model.

[0080] S6. Model Validation and Parameter Update: Validate the prediction accuracy of the hybrid power model using the test trajectory of the optimal excitation trajectory; when the validation error exceeds the preset threshold, adjust the excitation trajectory or the set of parameters to be identified based on the error analysis results, and repeat steps S4 to S6 until the model accuracy meets the requirements.

[0081] Specifically, this invention constructs extended dynamic equations based on rigid body dynamics models and equivalent generalized moment models of flexible skins. By combining basic parameter extraction, optimized excitation trajectory design, regularized parameter identification, and neural network residual compensation, a hybrid identification framework with both physical interpretability and high fitting ability is formed.

[0082] Furthermore, in S1, constructing the robot's rigid body skeleton dynamics model specifically includes:

[0083] Define the multi-joint robot to be identified as having n movable joints, and establish the generalized coordinates of the joints:

[0084]

[0085] Establishing generalized velocity of joints:

[0086]

[0087] Establish generalized acceleration of joints:

[0088]

[0089] Based on the generalized coordinates, velocities, and accelerations of the joints, a dynamic equation is established that includes only the contributions of rigid components:

[0090]

[0091] in, Represents the generalized coordinates of the joints. Represents the generalized velocity of the joint. This represents the generalized acceleration of the joint. This indicates the position of the nth joint. Represents the inertia matrix. Represents the Coriolis force and centrifugal force terms. Represents the gravity term. Indicates joint friction. This is the joint driving torque vector.

[0092] Specifically, this step aims to establish an ideal rigid body dynamics benchmark for the robot without skin. By defining generalized variables such as joint position, velocity, and acceleration, a standard dynamic equation containing inertial force, Coriolis force, gravity, and friction is constructed, providing a precise physical framework for the coupling effect of subsequent addition of flexible skin.

[0093] Furthermore, in S2, after the flexible skin is equivalent to m continuous flexible elements, the calculation of the deformation and additional generalized moment of each flexible element is also included:

[0094] Define the deformation of the j-th flexible element as:

[0095]

[0096] in, This represents the deformation of the j-th flexible element. Indicates the first The flexible unit is in its current posture The equivalent length, shear displacement, or combined deformation under these conditions; This indicates the joint configuration of a flexible skin in a natural, stress-free state.

[0097] The additional generalized torque is derived using the Lagrange equation:

[0098]

[0099] Among them, among them, This represents the additional generalized moment vector exerted by the flexible skin on each joint of the robot, where m is the total number of flexible coupling elements. For the first The transpose of the equivalent Jacobian row vector of each flexible unit relative to the joint variables; For the first Equivalent stiffness parameters of each flexible element; For the first The equivalent damping parameters of each flexible element. For the j-th unit shape variable, Let be the deformation velocity of the j-th element.

[0100] Specifically, the equivalent dynamic model of the flexible skin expresses the influence of the flexible skin as an additional generalized moment term, which is then superimposed on the robot's original rigid body dynamic equations to obtain an extended dynamic model;

[0101] 1) Definition of equivalent variables for flexible skin coupling unit

[0102] The flexible skin is divided along the robot's surface coverage area into... The equivalent flexible coupling unit, the first A flexible element spans one or more adjacent joint regions, and its deformation can be expressed as a function of the joint's generalized coordinates.

[0103] When the joint deviates from the reference configuration, the flexible element deforms at the following rate:

[0104]

[0105] in, For deformation speed, For the first The equivalent Jacobian row vector of each flexible unit relative to the joint variable.

[0106] 2) Potential energy function and dissipation function of flexible skin

[0107] If the flexible skin is approximated as a piecewise linear viscoelastic body, then the first... The elastic potential energy of a flexible unit can be expressed as:

[0108]

[0109] in, For the first The elastic potential energy of a flexible unit For the first The equivalent stiffness parameters of each flexible element. This is the squared term of the deformation variable.

[0110] The corresponding viscous dissipation function can be expressed as:

[0111]

[0112] in, Let be the viscous dissipation function of the j-th flexible skin equivalent coupling element. The square term of the deformation rate, For the first Equivalent damping parameters of each flexible element.

[0113] The total potential energy and total dissipation function for all flexible skin elements are as follows:

[0114]

[0115]

[0116] in, This represents the total potential energy corresponding to all flexible skin units. This represents the total dissipation corresponding to all flexible skin units;

[0117] 3) Obtain the additional generalized moment of the flexible skin from the Lagrange generalized force.

[0118] According to the definition of generalized force, the additional elastic generalized torque generated by the flexible skin on the joint space is:

[0119]

[0120] The additional damping torque generated by the flexible skin on the joint space is:

[0121]

[0122] Therefore, the total additional generalized torque of the flexible skin is:

[0123]

[0124] We can obtain:

[0125]

[0126] The additional torque of the flexible skin in the joint space is not determined by the state of a single joint, but is related to the joint variables spanned by the flexible unit. Therefore, it can show the cross-joint coupling effect caused by the flexible skin.

[0127] 4) Linearized matrix form under small deformation conditions

[0128] If the flexible skin is in a small deformation working range near the identified excitation trajectory, it can be referenced in the configuration. Nearby Perform a first-order approximation:

[0129]

[0130] Where linearization is performed near the natural configuration, we can take... It can be further approximated as a joint space matrix form:

[0131]

[0132] in,

[0133]

[0134]

[0135] These are the equivalent stiffness matrix and equivalent damping matrix of the flexible skin in the joint space, respectively.

[0136] Because some flexible elements span adjacent joints or even multiple joint regions, the matrix and It is generally not a diagonal matrix, but contains off-diagonal terms, that is:

[0137]

[0138] Among them, diagonal terms Characterizing the flexible skin on the first Local additional stiffness and damping of each joint; off-diagonal terms Characterizing the joint due to the continuous coverage of the flexible skin across the joint. With joints The coupling effect between them.

[0139] Furthermore, in S3, the specific process of eliminating linearly correlated terms in the set of parameters to be identified using orthogonal decomposition includes:

[0140] Construct a standard regression matrix containing all sampling times. and parameter vector Establish equations ,in, It is the residual vector;

[0141] right Perform QR decomposition with column pivoting:

[0142]

[0143] in, For column permutation matrices, It is an orthogonal matrix. It is an upper triangular matrix;

[0144] The permuted matrix is ​​divided into independent columns based on its rank. and related columns ,satisfy Thus, the basis parameter vector is extracted. Transform the model into ,in, For the transformation matrix, As a basis parameter vector, For independent columns The corresponding standard parameter subset, For related columns The corresponding subset of standard parameters.

[0145] Specifically, by expanding the joint space matrix to each joint, we can obtain the first... The additional torque of the flexible skin corresponding to each joint is:

[0146]

[0147] Therefore, the generalized torque applied to the flexible skin of all joints can be rearranged into a linear form with respect to the parameters:

[0148]

[0149] in, The equivalent parameter vector of the flexible skin can be written as:

[0150]

[0151] in, This is the regression matrix for flexible skin, whose elements are determined by joint displacement deviations. With joint velocity Combination and composition.

[0152] Furthermore, the overall extended dynamics model of the robot can be expressed as:

[0153]

[0154] in, Represents the rigid body inertia parameter. Indicates the friction parameter. This represents the coupling parameter of the flexible skin.

[0155] By combining them into a unified regression form, we can obtain

[0156]

[0157] For each sampling time Take the corresponding joint position ,speed acceleration Joint torque data And call the inverse dynamic regression matrix generation function to obtain the single-time regression matrix at that moment:

[0158]

[0159] The corresponding joint torque vector is All The single-time regression matrices of each sampled class are stacked row by row along the time dimension to construct the overall standard regression matrix:

[0160]

[0161] The extended dynamic model can then be written as:

[0162]

[0163] Because standard parameters have correlations or redundancies, The column vectors of the matrix are not all linearly independent, therefore the standard parameters generally cannot all be independently identified. What is truly identified are certain linear combinations of them, called basic parameters. Therefore, the overall standardized regression matrix... Perform QR decomposition with column pivoting:

[0164] according to Rank the column to identify independent and related columns. Divide the transformed column into two parts:

[0165] .

[0166] Furthermore, in S4, with the objective of optimizing the numerical conditions of the regression matrix, the optimal excitation trajectory parameters are solved, specifically including:

[0167] The trajectory of the i-th joint is constructed by combining an improved Fourier series with a quintic polynomial:

[0168]

[0169] in, Let be the trajectory of the i-th joint. These are Fourier series terms, used to provide rich frequency components and excite different dynamic parameters; The term is a fifth-order polynomial used to ensure that the trajectory satisfies the continuous constraints of position, velocity, and acceleration at the start and end times.

[0170] With the total regression matrix With minimizing the condition number as the core objective, a fitness function is constructed as follows:

[0171]

[0172] in, Representation matrix condition number; , , These represent the penalties for violations of constraints related to joint position, velocity, and acceleration, respectively. This represents an additional penalty term applied when the incentives in certain columns of the regression matrix are too weak. These are the weighting coefficients;

[0173] The particle swarm optimization algorithm is used to solve for the Fourier coefficients that minimize the fitness function J, thereby generating the optimal excitation trajectory.

[0174] Specifically, to improve the identifiability of dynamic parameters, this step, after constructing the extended dynamic model and determining the set of basic parameters, further designs the excitation trajectory for parameter identification. Unlike ordinary teaching trajectories or arbitrary reciprocating trajectories, the identification excitation trajectory used in this step is optimized with the goal of improving the numerical identifiability of the dynamic regression matrix. This ensures that, while satisfying the constraints of robot joint position, velocity, and acceleration, the regression terms corresponding to each basic parameter can be fully excited, thereby improving the accuracy and stability of subsequent parameter identification.

[0175] First, a mechanics model is established based on the robot's MDH parameters, and the angular constraint ranges for each joint are set. Then, the robot's structural parameters and neutral parameters are defined, and a set of initial postures within the allowable range of the joints is selected. The number of columns in the regression matrix is ​​calculated through a single test, thereby determining the number of basic parameters to be identified.

[0176] 1) Excitation trajectory parameterization method

[0177] The excitation trajectory is constructed using a parameterization method that combines an improved Fourier series with a fifth-degree polynomial.

[0178] No. The terms of the Fourier series can be written as:

[0179]

[0180] The corresponding velocities and accelerations are as follows:

[0181]

[0182]

[0183] in, The harmonic order; , For the fundamental frequency; and These are the Fourier coefficients to be optimized.

[0184] To ensure that the trajectory satisfies the following at the start and end points of the period:

[0185]

[0186] Therefore, a fifth-degree polynomial is introduced:

[0187]

[0188] Among them, polynomial coefficients The solution is obtained from the above boundary conditions. This method ensures that the identified trajectory has no abrupt changes during periodic transitions, which is beneficial for the actual robot movement due to additional impacts caused by boundary discontinuities, thus improving the identification effect.

[0189] 2) Optimize the design of the objective function

[0190] To ensure that the generated trajectory can fully excite the dynamic parameters, the trajectory coefficients are... and The optimization problem is constructed as an optimization problem with the objective of minimizing the condition number of the total regression matrix. The joint position, velocity, and acceleration are sampled at each time step within the entire sampling axis, and the single-time regression matrix is ​​calculated at each sampling time step. Then, stacking them along the time dimension forms the overall regression matrix:

[0191]

[0192] in, This represents the number of sampling points.

[0193] To improve the numerical stability of basis parameter identification, condition number As the main evaluation index of the objective function, the smaller the condition number, the less likely the regression matrix is ​​to be ill-conditioned, and the less sensitive the parameter identification is to noise and numerical errors; conversely, if the regression matrix is ​​ill-conditioned, the parameter identification is sensitive to noise and numerical errors, indicating that the basic parameters may be incorrectly solved.

[0194] To ensure that the trajectory meets the robot's actual joint constraints, position, velocity, and acceleration constraint penalty terms are added to the objective function. When a joint trajectory exceeds the upper or lower limit of the joint angle, a corresponding penalty function is introduced; when the maximum joint velocity exceeds a preset threshold, a velocity penalty term is introduced; when the maximum joint acceleration exceeds a preset threshold, an acceleration penalty term is introduced.

[0195] 3) Optimize algorithm implementation

[0196] Fourier coefficients of the parameters to be optimized using the particle swarm optimization algorithm and Joint optimization is performed. The particle swarm optimization algorithm uses the trajectory coefficient vector represented by each particle as the search object, and searches for the optimal fitness value by continuously updating the particle velocity and position.

[0197] Let the particle swarm size be Each particle corresponds to a parameter vector to be optimized, and its position is represented as:

[0198]

[0199] in, Indicates the first One particle; Indicates the current iteration number; Indicates the dimension of the optimization variable; Indicates the first The particle in the first The position vector at the next iteration.

[0200] Correspondingly, the first The velocity vector of each particle is represented as:

[0201]

[0202] Particle position vector The set of parameters that can be used to represent the excitation trajectory:

[0203]

[0204] in, Indicates the number of joints; Indicates the order of the Fourier series; and They represent the first The first joint The coefficients of the first harmonic.

[0205] The velocity of the particles in each iteration is updated according to the following formula:

[0206]

[0207] in, Inertial weight; For individual learning factors; For group learning factors; , For interval Random numbers; For the first The best position in the history of each particle; This represents the global optimal position of the current particle swarm.

[0208] Particle positions are corrected based on the updated velocity:

[0209]

[0210] Let the particle In the The fitness function value at the next iteration is If the current fitness is better than the particle's previous best position, then update the individual's best position:

[0211]

[0212] If there are instances in the current particle swarm that are better than the global optimum, then update the global optimum position:

[0213]

[0214] in, The fitness function;

[0215] To avoid premature convergence, the following improvement strategy was implemented:

[0216] 1) The inertia weight adaptively decreases with the number of iterations to balance global search capability and local convergence capability:

[0217]

[0218] in, This is the initial inertia weight; To terminate the inertia weight; This represents the maximum number of iterations.

[0219] 2) When the optimization results do not show significant improvement after multiple consecutive optimizations, some particles are re-randomized to improve population diversity;

[0220] 3) When the improvement in fitness of the most recent generations is less than a preset threshold, the early stopping condition is triggered to improve computational efficiency.

[0221] By setting the maximum number of iterations using the above method, and through algorithm optimization, the optimal excitation trajectory parameters that satisfy the robot's motion constraints and have superior recognition performance under the optimal adaptive degree function can be obtained. Subsequently, based on the optimized coefficients... Regenerate joint position trajectory , which serves as the target trajectory input during the actual machine experiment.

[0222] Furthermore, in S5, the basis parameter set is solved using the regularized least squares method, specifically including:

[0223] Constructing the ridge regression objective function:

[0224]

[0225] in, For ridge regression estimates, Let be the basis parameter vector to be identified. For the global regression matrix, Let be the regularization coefficient, and take . ;

[0226] The predicted torque of the physical model is obtained by solving:

[0227]

[0228] in, Predict torque for physical models;

[0229] Calculate the physical model residuals:

[0230]

[0231] in, For physical model residuals, This is the global torque vector;

[0232] The residual is fitted using a BPNN neural network to obtain the residual compensation amount. The residual compensation from the neural network is superimposed with the predicted moment from the physical model to obtain the output of the hybrid model. .

[0233] Specifically, the joint position trajectory As input to the joint motors of a multi-joint robot, the joint motor position and corresponding joint motor current data are collected at each moment.

[0234] After obtaining the identified excitation trajectory and completing the experimental data acquisition, the collected experimental samples are preprocessed in a unified manner, regression matrix is ​​constructed, basic parameters are solved, and residual compensation modeling is performed, thereby realizing the identification of dynamic parameters of multi-joint robot considering the coupling effect of flexible skin.

[0235] 1) Data processing:

[0236] To reduce the impact of sensor noise and acquisition errors on the identification results, the raw data is preprocessed:

[0237] a. Perform zero-bias correction on the joint current.

[0238] b. Low-pass filtering is applied to the joint position and current data. A fifth-order Butterworth low-pass filter is used to smooth the original position and current signals to suppress high-frequency noise.

[0239] c. Perform numerical differentiation on the filtered joint position sequence to obtain joint velocities and accelerations. Use the central difference method, calculating at the midpoints of the sequence and approximating at boundary points using forward or backward differences.

[0240] d. Convert the filtered joint current into an equivalent joint torque using the motor torque constant. .

[0241] 2) Construct the total regression matrix and the total moment vector:

[0242] After data preprocessing, the single-time standard regression matrix is ​​stacked row by row along the time dimension, i.e. (39), to form the total regression matrix. Correspondingly, the joint torque vectors at all times are also stacked in chronological order to form the total torque vector:

[0243]

[0244] For multiple sets of experimental data, the above construction should be completed within each set first, and then the data from each set should be combined. and Further splicing of the global regression matrix With global moment vector This is to improve the robustness and coverage of parameter estimation.

[0245] 3) Solving for the dynamic basis parameters based on ridge regression:

[0246] Given the constructed total regression matrix and total moment vector, a dynamic parameter estimation problem is established:

[0247]

[0248] in, Let be the basis parameter vector to be identified; This includes measurement errors and unmodeled terms.

[0249] Considering that the regression matrix may suffer from column correlation, noise amplification, or near-illness under actual experimental data conditions, ridge regression is used to solve for the parameters. The closed-form solution can be written as:

[0250]

[0251] 4) Physical model residual construction

[0252] After obtaining the basic physical model parameters, the identified parameters are used to calculate the predicted torque of the physical model;

[0253] Furthermore, the physical model residuals are calculated; these residuals include the portion not fully explained by the rigid body dynamics terms, friction terms, and the explicitly modeled linear coupling terms of the flexible skin, which typically correspond to factors such as the complex nonlinear effects of the flexible skin, material hysteresis, local unmodeled couplings, and experimental noise.

[0254] 5) Residual compensation modeling based on BPNN

[0255] To further improve the model's fitting ability and prediction accuracy, a backpropagation neural network (BPNN) is introduced to learn the residual terms based on the physical model obtained from ridge regression, thereby constructing a hybrid identification model of "physical model + data-driven residual compensation". In the actual implementation, an independent BPNN residual compensation network is established for each joint, and the input dimension, number of hidden layer neurons, output dimension, activation function, training algorithm, number of training epochs, target error, learning rate, and regularization parameters are configured individually for each joint. Each joint network adopts a 4-dimensional input, single-output structure, with the tansig activation function in the hidden layer and the purelin activation function in the output layer. The training algorithm is trainlm.

[0256] Using features related to joint dynamics as input to the neural network, it can be represented as:

[0257]

[0258] in, This represents a feature map consisting of joint position, velocity, acceleration, and combinations thereof. After extracting input features for each joint, the residual sequence for each joint is divided into a training set, a validation set, and a test set in a ratio of 0.7:0.15:0.15, and the corresponding BPNN network for each joint is trained.

[0259] Let the first The residual compensation network for each joint is as follows: Then its output can be expressed as

[0260]

[0261] The combination of residual compensation results for all joints is as follows:

[0262]

[0263] 6) Construct a hybrid identification model and complete the optimization solution.

[0264] After completing the BPNN training, the physical model output is superimposed with the neural network residual compensation to obtain the final hybrid model output.

Claims

1. A method for identifying the dynamic parameters of a multi-joint robot based on the coupling effect of flexible skin, characterized in that, include: S1. Constructing the rigid skeleton dynamic model of the robot: Based on the mechanism configuration and linkage relationship of the multi-joint robot to be identified, establish dynamic equations that only include contributions from rigid components. The equations cover inertial forces, Coriolis forces and centrifugal forces, gravity and joint friction forces, serving as the basic modeling framework. S2. Establish an equivalent dynamic model of the flexible skin: Based on the basic modeling framework established in S1, the flexible skin covering the robot surface is equivalent to m continuous flexible units. The additional generalized torque generated by the deformation of the flexible unit is calculated, and the additional torque term is superimposed into the basic modeling framework to form an extended dynamic model that includes the coupling effect of the flexible skin. S3. Constructing a regression identification model: Based on the extended dynamic model, determine the set of parameters to be identified, including rigid link inertia parameters, joint friction parameters, and flexible skin physical parameters; eliminate linearly related terms in the set of parameters to be identified by orthogonal decomposition method, extract mutually independent basic parameter sets and their corresponding regression matrices, thereby transforming the dynamic model into a linear identification form; S4. Generate and identify the excitation trajectory and collect experimental data: Based on the regression matrix, with the goal of optimizing the numerical conditions of the regression matrix, solve for the optimal excitation trajectory parameters and generate the optimal excitation trajectory that can fully stimulate the characteristics of each basic parameter; control the robot to execute the optimal excitation trajectory, and simultaneously collect joint position, joint velocity, joint acceleration and drive motor current data to form an experimental dataset. S5. Execution Parameter Identification and Optimization Solution: Based on the experimental dataset, the data is filtered and preprocessed by differentiation to reconstruct the global regression matrix and torque vector; the basis parameter set is solved using the regularized least squares method to obtain the predicted torque of the physical model; the residual between the predicted torque and the actual collected torque is calculated, and the residual is compensated by learning using a neural network. The output of the physical model is superimposed with the compensation amount of the neural network to construct a hybrid dynamics model. S6. Model Validation and Parameter Update: Validate the prediction accuracy of the hybrid power model using the test trajectory of the optimal excitation trajectory; when the validation error exceeds the preset threshold, adjust the excitation trajectory or the set of parameters to be identified based on the error analysis results, and repeat steps S4 to S6 until the model accuracy meets the requirements.

2. The method for identifying the dynamic parameters of a multi-joint robot based on the coupling effect of flexible skin according to claim 1, characterized in that, In S1, constructing the robot's rigid body skeleton dynamics model specifically includes: Define the multi-joint robot to be identified as having n movable joints, and establish the generalized coordinates of the joints: Establishing generalized velocity of joints: Establish generalized acceleration of joints: Based on the generalized coordinates, velocities, and accelerations of the joints, a dynamic equation is established that includes only the contributions of rigid components: in, Represents the generalized coordinates of the joints. Represents the generalized velocity of the joint. This represents the generalized acceleration of the joint. This indicates the position of the nth joint. Represents the inertia matrix. Represents the Coriolis force and centrifugal force terms. Represents the gravity term. Indicates joint friction. This is the joint driving torque vector.

3. The method for identifying the dynamic parameters of a multi-joint robot based on the coupling effect of flexible skin according to claim 2, characterized in that, In S2, after the flexible skin is equivalent to m continuous flexible elements, the calculation of the deformation and additional generalized moment of each flexible element is also included: Define the deformation of the j-th flexible element as: in, This represents the deformation of the j-th flexible element. Indicates the first The flexible unit is in its current posture The equivalent length, shear displacement, or combined deformation under these conditions; This indicates the joint configuration of a flexible skin in a natural, stress-free state. The additional generalized torque is derived using the Lagrange equation: in, This represents the additional generalized moment vector exerted by the flexible skin on each joint of the robot, where m is the total number of flexible coupling elements. For the first The transpose of the equivalent Jacobian row vector of each flexible unit relative to the joint variables; For the first Equivalent stiffness parameters of each flexible element; For the first The equivalent damping parameters of each flexible element. For the j-th unit shape variable, Let be the deformation velocity of the j-th element.

4. The method for identifying the dynamic parameters of a multi-joint robot based on the coupling effect of flexible skin according to claim 3, characterized in that, In S3, the specific process of eliminating linearly correlated terms in the set of parameters to be identified using orthogonal decomposition includes: Construct a standard regression matrix containing all sampling times. and parameter vector Establish equations ,in, The residual vector; right Perform QR decomposition with column pivoting: in, For column permutation matrices, It is an orthogonal matrix. It is an upper triangular matrix; The permuted matrix is ​​divided into independent columns based on its rank. and related columns ,satisfy Thus, the basis parameter vector is extracted. Transform the model into ,in, For the transformation matrix, As a basis parameter vector, For independent columns The corresponding standard parameter subset, For related columns The corresponding subset of standard parameters.

5. The method for identifying the dynamic parameters of a multi-joint robot based on the coupling effect of flexible skin according to claim 4, characterized in that, In S4, the goal is to optimize the numerical conditions of the regression matrix and solve for the optimal excitation trajectory parameters, specifically including: The trajectory of the i-th joint is constructed by combining an improved Fourier series with a quintic polynomial: in, Let be the trajectory of the i-th joint. These are Fourier series terms, used to provide rich frequency components and excite different dynamic parameters; The term is a fifth-order polynomial used to ensure that the trajectory satisfies the continuous constraints of position, velocity, and acceleration at the start and end times. With the total regression matrix With minimizing the condition number as the core objective, a fitness function is constructed as follows: in, Representation matrix condition number; , , These represent the penalties for violations of constraints related to joint position, velocity, and acceleration, respectively. This represents an additional penalty term applied when the incentives in certain columns of the regression matrix are too weak. These are the weighting coefficients; The particle swarm optimization algorithm is used to solve for the Fourier coefficients that minimize the fitness function J, thereby generating the optimal excitation trajectory.

6. The method for identifying the dynamic parameters of a multi-joint robot based on the coupling effect of flexible skin according to claim 5, characterized in that, In S5, the basis parameter set is solved using the regularized least squares method, specifically including: Constructing the ridge regression objective function: in, For ridge regression estimates, Let be the basis parameter vector to be identified. For the global regression matrix, Let be the regularization coefficient, and take . ; The predicted torque of the physical model is obtained by solving: in, Predict torque for physical models; Calculate the physical model residuals: in, For physical model residuals, This is the global torque vector; The residual is fitted using a BPNN neural network to obtain the residual compensation amount. The residual compensation from the neural network is superimposed with the predicted moment from the physical model to obtain the output of the hybrid model. .

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