A robot dynamics parameter dimension reduction identification method, system, device and medium

Abstract

The application provides a robot dynamics parameter dimension reduction identification method, system, device and medium, and belongs to the technical field of robot parameter identification, and comprises the following steps: a mapping matrix from a complete inertia parameter set to a base parameter set is established, and a robot joint torque linear regression model is established; a logarithmic Euclidean pullback metric matrix of the complete inertia parameter space is generated; an induced metric matrix from the complete inertia parameter to the base parameter set is generated; robot identification excitation trajectory data is acquired, and a joint torque regression model is stacked; an information matrix is normalized, and a dimension reduction parameter subspace is generated according to generalized information eigenvalues; the number of reserved directions of the dimension reduction parameter subspace is changed in turn, parameter identification and independent verification trajectory torque prediction are circularly executed for each candidate reserved dimension, the final reserved dimension is determined according to the root mean square error of the joint torque, a dimension-reduced robot dynamics parameter model is formed, and the model is used to calculate the predicted joint torque or the dynamics compensation joint torque.

Description

Technical Field

[0001] This invention belongs to the field of robot parameter identification technology, and in particular relates to a method, system, device and medium for dimensionality reduction identification of robot dynamic parameters. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] The dimension of the complete inertial parameters of a multi-link system increases rapidly with the number of links. Although the complete inertial parameters can be mapped to a minimum parameter set or a basic parameter set based on the column correlation of the observation matrix, the dimension of the basic parameter set remains high in multi-degree-of-freedom robots, and the finite-duration, spatially constrained excitation trajectory can usually only fully excite a portion of the parameter combinations.

[0004] Existing parameter dimensionality reduction methods often perform ordinary eigenvalue decomposition or singular value decomposition on the regression matrix, information matrix, and recursive least squares covariance matrix, and then retain some directions based on eigenvalue thresholds. When performing ordinary eigenvalue decomposition directly on the original parameter coordinates, the resulting modality ranking is easily affected by the choice of units and parameter scaling. Larger values ​​do not necessarily correspond to larger physical changes, and smaller values ​​do not necessarily correspond to parameter directions that can be discarded.

[0005] Log-Euclidean metrics on symmetric positive definite matrix manifolds can describe the intrinsic geometric relationships between the aforementioned parameters. Existing methods mainly use the log-Euclidean distance or its convex approximation as a regularization term in the parameter identification objective function to constrain the estimated value to be close to the prior value. However, they do not further explicitly convert this convex approximation into a pullback metric matrix in the inertial parameter space, geometrically normalize the information matrix, and determine the parameter combination subspace that should be retained.

[0006] Therefore, traditional robot dynamics parameter dimensionality reduction is affected by parameter dimensions and numerical scale; ordinary eigenvalue decomposition is difficult to interpret the physical meaning of retained or discarded directions; high-dimensional parameter sets are ill-conditioned and easily affected by noise; existing logarithmic Euclidean convex approximations are only used as regularization terms and not used to construct the geometric scale required for parameter dimensionality reduction. Summary of the Invention

[0007] To overcome the shortcomings of the prior art, the present invention provides a method, system, device and medium for dimensionality reduction identification of robot dynamic parameters. This method can unify the physical geometry of the link, the identifiable information of the data and the dimensionality reduction of the parameters, so that the comparison of parameter directions is based on the same local logarithmic Euclidean physical change scale, and the final retained dimension can be determined with quantifiable torque prediction error.

[0008] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions: Firstly, a method for dimensionality reduction identification of robot dynamic parameters is disclosed, including: For multi-link robots, a mapping matrix between the complete set of inertial parameters and the basic parameter set is established, and a linear regression model of joint torques is also established. Generate the log-Euclidean pullback metric matrix of the complete inertial parameter space; Using the mapping matrix from the generated complete inertial parameter set to the basis parameter set and the logarithmic Euclidean pullback metric matrix of the generated complete inertial parameter space, the induced metric matrix of the basis parameter set space is generated. Collect joint motion data during robot operation, stack and establish a linear regression model of joint torque, and construct an information matrix by combining joint torque noise information; use the induced metric matrix of the generated basis parameter set space to perform geometric normalization on the information matrix, and use the generalized information feature values ​​of the normalized information matrix to generate a dimension-reduced parameter subspace. Using the generated candidate dimensionality reduction parameter subspace, the generated stacked joint torque linear regression model is called to perform convex optimization on the dimensionality reduction coordinate increment and motor rotor inertia, so as to obtain the estimated values ​​of the basic parameter set and the estimated values ​​of the motor rotor inertia corresponding to each candidate retained dimension. The estimated values ​​of the basic parameter set and the estimated values ​​of the motor rotor inertia generated by each candidate retained dimension are substituted into the validation regression model to calculate the root mean square error of the joint torque corresponding to each candidate retained dimension. The final retained dimension and the corresponding estimated values ​​of the basic parameter set and the estimated values ​​of the motor rotor inertia are determined according to the rule of minimizing the validation error.

[0009] As a further technical solution, the process of establishing a linear regression model for joint torque is as follows: For robots with multiple joints, the mapping relationship between the complete set of inertial parameters and the set of basic parameters is obtained through numerical decomposition, the full-rank regression matrix is ​​obtained, and a linearized rigid body dynamics model under the full-rank regression matrix is ​​established. A linear regression model of joint torque is obtained by combining the linearized rigid body dynamics model and the motor inertia model.

[0010] As a further technical solution, the steps for generating the logarithmic Euclidean pullback metric matrix of the complete inertial parameter space are as follows: Definition of the first A physical consistency matrix is ​​commonly used in robots with multiple links; When the physical consistency matrix satisfies the basic physical constraints, the consistency matrix remains symmetric and positive definite. On a fourth-order symmetric and positive definite matrix manifold, the logarithmic Euclidean metric is used to describe the intrinsic physical changes between inertial parameters. At the reference point of the physical consistency matrix, a local quadratic approximation of the logarithmic Euclidean metric is established using the Fréchet derivative, thus obtaining the logarithmic Euclidean pullback metric matrix of the complete inertial parameter space.

[0011] As a further technical solution, the steps for establishing a local quadratic approximation of the logarithmic Euclidean metric are as follows: At the reference complete inertial parameters, perform eigenvalue decomposition on the reference physical consistency matrix; A first-order difference quotient matrix is ​​defined to describe the sensitivity to small changes in eigenvalues; Based on the eigenvalue decomposition of the reference physical consistency matrix and the first-order difference quotient matrix, the matrix logarithm is defined on the ... Fréchet derivative at the reference physical consistency matrix of each link; The response matrix and single-link pullback metric matrix are constructed based on the Fréchet derivative to measure the distance by which the change in the link's inertial parameters causes a change in the Log-Euclidean coordinate system. We obtain convex approximations and convex quadratic approximations based on logarithmic Euclidean metric; Will The metric matrices of each link are further assembled to obtain the logarithmic Euclidean pullback metric matrix of the complete inertial parameter space.

[0012] As a further technical solution, an induced metric matrix is ​​generated in the basis parameter set space, specifically as follows: Define the minimum local physical length of the base parameter increment; Based on the Log-Euclidean pullback metric in the complete inertial parameter space, the local physical scale is induced to the basic parameter space by solving the minimum physical change problem that satisfies the dynamic equivalence constraints, thereby obtaining a basic parameter metric matrix with the same dimension as the basic parameter regression matrix.

[0013] As a further technical solution, the information matrix is ​​geometrically normalized using the induced metric matrix of the generated basis parameter set space, specifically including: Construct a geometric whitening information matrix using the obtained induced metric matrix; After completing the physical scale normalization, the geometric whitening information matrix is ​​further decomposed to extract the main identifiable information directions under the unified local physical scale. The obtained feature directions are then mapped back to the primitive parameter space. The directions that can obtain more identifiable information under unit physical change are retained first, and the weakly identifiable directions are gradually discarded.

[0014] As a further technical solution, the estimated values ​​of the basic parameter set and the estimated values ​​of the motor rotor inertia corresponding to each candidate retained dimension are obtained, specifically including: Parameter identification is performed in the reduced-dimensional subspace: the space is updated by constraining the set of basis parameters to be identified based on the generated reduced-dimensional basis matrix; A semidefinite convex programming expression is constructed in the affine parameter subspace to solve for the increment of the parameter to be identified and the rotor inertia of the motor. After the solution is completed, the dimension-reduced coordinate increments are mapped back to the basic parameter space to obtain the estimated values ​​of the basic parameters and the estimated values ​​of the motor rotor inertia under the current retained dimension. Based on this, a dimension-reduced dynamic model is constructed for subsequent torque prediction and model verification.

[0015] As a further technical solution, parameter identification is performed iteratively according to the generated candidate retained dimension, and verification trajectories are calculated for those different from the identified trajectories; then, the 1st... The root mean square error of each joint and the root mean square error of the entire joint were verified; candidate dimensions were selected. The sum of the RMSEs of the full joint verification is used; the candidate dimension with the lowest sum of the RMSEs of the full joint verification is the final retained dimension, and the basic parameter estimates and motor rotor inertia estimates are obtained under this retained dimension.

[0016] Secondly, a robot dynamics parameter dimensionality reduction identification system is disclosed, including: The joint torque linear regression model construction module is configured to: establish a mapping matrix between the complete set of inertial parameters and the set of basic parameters for a multi-link robot, and establish a joint torque linear regression model; The log-Euclidean pullback metric matrix generation module is configured to generate a log-Euclidean pullback metric matrix for the complete inertial parameter space. The induced metric matrix module is configured to generate the induced metric matrix of the basis parameter set space using the generated mapping matrix from the complete inertial parameter set to the basis parameter set and the generated log-Euclidean pullback metric matrix of the complete inertial parameter space. The dimension reduction parameter subspace generation module is configured to: collect joint motion data during robot operation, stack and establish a linear regression model of joint torque and construct an information matrix by combining joint torque noise information; use the induced metric matrix of the generated basis parameter set space to perform geometric normalization on the information matrix, and use the generalized information feature values ​​of the normalized information matrix to generate a dimension reduction parameter subspace. The solution module is configured to: utilize the generated candidate dimensionality reduction parameter subspace, call the generated stacked joint torque linear regression model, perform convex optimization on the dimensionality reduction coordinate increment and motor rotor inertia, and obtain the estimated values ​​of the basic parameter set and the estimated values ​​of the motor rotor inertia corresponding to each candidate retained dimension; The parameter determination module is configured to: substitute the estimated values ​​of the basic parameter sets and the estimated values ​​of the motor rotor inertia generated by each candidate retained dimension into the validation regression model, calculate the root mean square error of the joint torque corresponding to each candidate retained dimension, and determine the final retained dimension and the corresponding estimated values ​​of the basic parameter sets and the estimated values ​​of the motor rotor inertia according to the rule of minimizing the validation error.

[0017] The above one or more technical solutions have the following beneficial effects: This invention establishes a linearized dynamic regression model for a robot. Using the physical consistency matrix corresponding to the prior complete inertial parameters as a reference, linearization is performed using the Fréchet derivative operator. The logarithmic Euclidean metric is locally convexly approximated as a pulled-back metric matrix in the complete inertial parameter set space, and a metric matrix under the basis parameter set is induced. The information matrix is ​​normalized using the metric matrix under the basis parameter set, and an identifiable parameter combination subspace is generated according to generalized eigenvalues. Inertial parameters are jointly estimated only within this subspace, and the retained dimension is determined iteratively using the RMSE verification of trajectory torque. This invention can reduce the influence of parameter dimensions and scale on modal ranking, and only requires updating a small number of dynamic parameters to further improve the accuracy of robot torque prediction, achieving the purpose of dimensionality reduction identification.

[0018] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0019] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0020] Figure 1 This is the overall flowchart of the robot dynamics parameter dimensionality reduction identification method based on logarithmic Euclidean pullback metric of the present invention; Figure 2 This is a flowchart illustrating the generation process of the linkage's complete inertial parameters, physical consistency matrix, matrix logarithm Fréchet derivative, and pull-back metric matrix in this invention. Figure 3 The curve showing the relationship between the reduced number of identification directions and the total RMSE of the verification trajectory torque in this embodiment of the invention is set with the RMSE of the minimum parameter set prior model as the reference horizontal line. Figure 4 This is a schematic diagram of the predicted torque verification of joint 1 in an embodiment of the present invention; Figure 5 This is a schematic diagram of the predicted torque verification of joint 2 in an embodiment of the present invention; Figure 6 This is a schematic diagram illustrating the verification of the predicted torque at joint 3 in an embodiment of the present invention; Figure 7 This is a schematic diagram of the verification of the predicted torque of joint 4 in an embodiment of the present invention; Figure 8 This is a schematic diagram illustrating the verification of the predicted torque of joint 5 in an embodiment of the present invention; Figure 9 This is a schematic diagram of the verification of the predicted torque of joint 6 in an embodiment of the present invention. Detailed Implementation

[0021] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0022] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations of the present invention.

[0023] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0024] Terminology Explanation: Robot dynamics parameters: A robot composed of multiple rigid links is typically described by 10 complete inertial parameters, including mass, first-order mass moment, and six independent components of the inertial tensor. The mass, center of mass, and inertial tensor of a robot link are not independent of each other; they jointly determine the symmetric positive definiteness of the physical consistency matrix. Different physical parameters have different dimensions and numerical scales. Reasonable and accurate robot dynamics parameters are the foundation for achieving high-precision torque prediction, feedforward compensation, collision detection, and model control.

[0025] Example 1 This embodiment discloses a method for dimensionality reduction identification of robot dynamic parameters, including: S1. A linearized robot dynamics model is established based on the recursive Newton-Euler method. A mapping operator between the complete set of inertial parameters and the basic parameter set is established. A linear regression model of joint torque is established based on the regression matrix of the basic parameter set, the regression matrix of the motor rotor inertia, and the friction torque term.

[0026] S2. Establish the robot physical consistency matrix, describe the logarithmic Euclidean metric based on the SPD manifold, and use the Fréchet derivative to approximate the local convexity of the logarithmic Euclidean distance as a Gram quadratic form of the complete inertial parameter increment, thereby generating the logarithmic Euclidean pullback metric matrix of the complete inertial parameter space.

[0027] S3 uses the linear mapping matrix from the complete inertial parameter set to the basis parameter set generated by S1 and the pull-back metric matrix of the complete inertial parameter space generated by S2 to generate the induced metric matrix of the basis parameter set space.

[0028] S4. Establish a finite Fourier series parameterized excitation trajectory. The robot executes the excitation trajectory to obtain the collected joint motion data. Stack the joint torque linear regression model established in S1 and construct an information matrix by combining the joint torque noise information. Use the basis parameter set space induced metric generated in S3 to perform geometric normalization on the information matrix. Use the generalized information feature values ​​of the normalized information matrix to generate a dimension-reduced parameter subspace.

[0029] S5 utilizes the candidate dimensionality reduction parameter subspace generated in S4, calls the stacked joint torque linear regression model generated in S4, and performs convex optimization to solve the dimensionality reduction coordinate increment and motor rotor inertia, obtaining the estimated values ​​of the basic parameter set and the estimated values ​​of the motor rotor inertia corresponding to each candidate retained dimension.

[0030] In step S6, the estimated values ​​of the basic parameter sets and the estimated values ​​of the motor rotor inertia generated from each candidate retained dimension in step S5 are substituted into the validation regression model to calculate the root mean square error of the joint torques corresponding to each candidate retained dimension. The final retained dimension and the corresponding estimated values ​​of the basic parameter sets and the estimated values ​​of the motor rotor inertia are determined according to the rule of minimizing validation error.

[0031] In one implementation example, step S1 specifically includes: establishing a linearized dynamic regression model for the robot.

[0032] For those with A robot with 1 joint can have its linearized rigid body dynamics model established using a recursive Newton-Euler method, i.e.: ; In the formula, These are the joint position, joint velocity, and joint acceleration vectors, respectively. This is the joint torque vector; The joint space inertia matrix; This is the matrix of Coriolis force and centripetal force coefficients; This is the term related to gravity. It is a non-full-rank regression matrix; For the reason The complete set of inertial parameters is formed by stacking the complete inertial parameters of each link in sequence. For the first The complete inertial parameters of the link are as follows: ; In the formula, For the diagonal component of the inertia tensor; The component of inertia; The first moment of mass; For the first The mass of each link; For the first The position of the center of mass of each link; equation This means that the first moment of the mass is equal to the product of the mass and the position vector of the centroid.

[0033] To obtain the full-rank regression matrix, a numerical decomposition method is used to obtain the mapping relationship between the complete set of inertial parameters and the basic parameter set, and a linearized rigid body dynamics model under the full-rank regression matrix is ​​established, namely: ; In the formula, It is a full-rank mapping matrix; A column vector of the base parameter set; is the full-rank regression matrix corresponding to the basis parameter set.

[0034] The robot joint torque model is obtained by combining the linearized dynamics model and the motor inertia model: ; In the formula, This is the rotor inertia regression matrix of the motor; This refers to the rotor inertia of the motor. Given the parameter vector of the friction model; This is the frictional torque calculated based on known friction model parameters.

[0035] In one implementation example, step S2 specifically includes: establishing a robot physical consistency matrix, describing the logarithmic Euclidean metric based on the SPD manifold, and using the Fréchet derivative to construct a locally convex approximation of the logarithmic Euclidean metric to generate a pullback metric matrix in the complete inertial parameter space.

[0036] Definition of the first A common physical consistency matrix for robots with multiple links is: ; In the formula, For the reason A defined fourth-order real symmetric physical consistency matrix; It is a third-order identity matrix; Represents the trace of a matrix; for The One component; Index of the inertial parameter components of a single link; For the first A fixed symmetric basis matrix; Represents partial derivatives; It represents the space of fourth-order real symmetric matrices.

[0037] The physical consistency matrix remains symmetric and positive definite when it satisfies the basic physical constraints. In a fourth-order symmetric positive definite matrix manifold The above relationship can be represented as In a fourth-order symmetric positive definite matrix manifold In this invention, the logarithmic Euclidean metric (LEM) is used to describe the intrinsic physical changes between inertial parameters, namely: ; In the formula, The Frobenius matrix norm derived from the inner product of Frobenius matrices; Let be any physical consistency matrix that satisfies the conditions; Represents the matrix logarithm operation; This represents a logarithmic Euclidean metric. Directly processing the matrix logarithm and logarithmic Euclidean distance during the identification and optimization process increases the nonlinear computational complexity. Therefore, this invention utilizes the Fréchet derivative at the reference point of the physically consistent matrix to establish a local quadratic approximation of the logarithmic Euclidean metric.

[0038] More specifically, this includes: First, when referring to complete inertial parameters Place, order The eigenvalues ​​of the reference physical consistency matrix can be decomposed as follows: ; In the formula, For the first Reference physical consistency matrix of each link; It is a matrix composed of orthogonal eigenvectors arranged column by column; For the first 1 eigenvalue, ; This indicates the construction of a diagonal matrix.

[0039] Next, a first-order difference quotient matrix is ​​defined to describe the sensitivity to small changes in eigenvalues: ; In the formula, It is a first-order difference quotient matrix; For its first Line 1 Column elements; For feature value index; Represents the natural logarithm operation.

[0040] Then, based on the eigenvalue decomposition of the reference physical consistency matrix and the first-order difference quotient matrix, the matrix logarithm... exist The Fréchet derivative at point F is defined as: ; In the formula, Let be any fourth-order real symmetric perturbation matrix; For the matrix logarithm in The Fréchet derivative operator at the location; This represents the Hadamard product.

[0041] Finally, based on the Fréchet derivative, a response matrix and a single-link pullback metric matrix are constructed to measure the distance of the change in the link's inertial parameters in Log-Euclidean coordinates, i.e.: ; In the formula, For the first Local matrix logarithmic response in each inertial parameter direction; For the first Logarithmic Euclidean pullback metric matrix of each link; for The Line 1 Column elements; Same type matrix and The Frobenius inner product. At this point, the convex approximation and the convex quadratic approximation based on the logarithmic Euclidean metric can be described as: ; In the formula, A local convex approximation for the LEM metric; This represents the increment of the complete inertial parameters. A locally convex quadratic approximation for the LEM metric. This convex quadratic approximation will... The Log-Euclidean geometry on the manifold maps back to the complete inertial parameter space, giving the parameter variations a physically consistent length definition. If we... The metric matrix of each link is further assembled into: ; In the formula, For the logarithmic Euclidean pullback metric matrix of the complete inertial parameter space; This indicates that a block diagonal matrix is ​​constructed sequentially. The distance in space for the complete inertial parameters has been redefined.

[0042] In one implementation example, a rigid link is used as an example. First, the ten-dimensional complete inertial parameter reference values ​​of the link are input. ,according to Obtain and calculate All eigenvalues. When the smallest eigenvalue is not greater than a preset positive number. When this occurs, it indicates that the reference parameters do not meet the preset strict physical consistency requirements, and it is necessary to change the reference parameters or project them onto a pseudo-inertial positive definite set; when Continue execution as needed.

[0043] Ten basis matrices Transform to In the characteristic coordinates: In the formula, This is the direction index for the complete inertial parameters of a single link; For the first A fixed basis matrix; For the reason An orthogonal matrix composed of the columns of the unit orthogonal eigenvectors; for exist The representation in the characteristic coordinate system. Calculate the difference quotient matrix based on the eigenvalues. and obtain ; In the formula, According to The first-order difference quotient matrix is ​​calculated from the four eigenvalues; For the first The response matrix of a basis matrix after the matrix logarithm Fréchet derivative mapping; left and right multiplication and This represents the transformation from characteristic coordinates back to the original coordinates. Each... Vectorized by column vectors, it consists of: ; In the formula, To make a fourth-order matrix The column vector is formed by connecting the first and last columns in sequence; This is the set of response matrices formed by arranging the vectorized results of the ten response matrices column-wise. Therefore, the pull-back metric of the i-th link can be directly calculated as: ; In the formula, Let be the logarithmic Euclidean local pullback metric matrix for this single link; Gram matrix is ​​the set of response matrices.

[0044] For a robot with multiple links, the above calculations are performed independently for each link, and the links are formed in a block-diagonal manner. The reference point can be set to fixed CAD parameters to keep the measurement constant throughout the offline identification process; alternatively, the latest parameters that have been smoothed and verified for physical consistency can be used to update the reference point during batch updates, and the measurement can be frozen between the two update times.

[0045] In one implementation example, step S3 specifically includes: The pullback metric of the complete inertial parameter space generated by S2 is induced into the basis parameter set space. The basis parameter set only specifies a linear combination of the complete inertial parameters and usually cannot uniquely recover the complete inertial parameters. To establish a local scale in the basis parameter space that is geometrically consistent with the Log-Euclidean of the complete inertial parameters, the minimum local physical length of the basis parameter increment is defined as: ; In the formula, For any set of basis parameters, increment; The increment of candidate complete inertial parameters to satisfy the mapping constraints; For incremental mapping constraints; The local logarithm of the candidate increment is the square of the Euclidean length. Indicated by To optimize the variables to their minimum values, we obtain the induced metric matrix of the basis parameter set space: ; In the formula, Let be the log-Euclidean induced metric matrix in the basis parameter set space. Since the minimum parameter mapping has a non-unique complete parameter representation, this invention is based on the Log-Euclidean pullback metric in the complete inertial parameter space. By solving the minimum physical change problem that satisfies the dynamic equivalence constraints, this local physical scale is induced to the basis parameter space, thereby obtaining a basis parameter metric matrix with the same dimension as the basis parameter regression matrix.

[0046] In one implementation example, step S4 specifically includes: Fourier series can represent continuous periodic signals using sine and cosine basis functions of different frequencies. Therefore, it has good smoothness, adjustable frequency characteristics, and is easy to differentiate, making it suitable as a robot excitation trajectory. ; in, This represents the position trajectory of the i-th joint. For trajectory bias term, Let be the kth harmonic coefficient. Harmonic coefficients This is the fundamental frequency.

[0047] Through optimization The excitation trajectory can be obtained, and then the robot control interface is used to execute the excitation trajectory to obtain the sampled and measured joint positions, joint velocities, joint accelerations, and joint torque vectors. and in By stacking the regression matrix generated by S1 at each sampling time point, the robot's identification model can be obtained: ; In the formula, For stacking The measured joint torque afterwards; For stacking The regression matrix of the subsequent basic parameter set; For stacking The motor inertia regression matrix; This refers to the rotor inertia of the motor. Given the parameter vector of the friction model; The stacking friction torque is calculated based on known friction model parameters.

[0048] Construct a log-Euclidean geometrically normalized information matrix and generate a parametric subspace. Regress the matrix based on the stacked basis parameter set. and joint torque noise covariance matrix Define the information matrix: ; In the formula, For information matrix; This is the symmetric positive definite covariance matrix of the stacked joint torque noise. However, the information matrix only reflects the sensitivity of the measurement data to the directions of the basis parameters, ignoring the physical scale of change corresponding to different parameter directions. Since the basis parameter space is inherited from the complete inertial parameter space, its Euclidean coordinates do not have a unified physical meaning. To eliminate this scale difference, this invention uses the induced metric matrix obtained in S3 to construct a geometric whitening information matrix: ; In the formula, To meet The symmetric inverse square root matrix, where for An identity matrix of order 1; For the geometrically whitened information matrix, this transformation maps the basis parameter space to a unit physical scale space, allowing the feature directions of the information matrix to be compared at a uniform local physical length. Therefore, The eigenvalues ​​no longer represent the amount of information brought about by the unit parameter change, but rather the identification information obtained by the unit Log-Euclidean physical change, thereby achieving the unity of physical geometry and data identifiability.

[0049] After physical scale normalization, the geometric whitening information matrix is ​​further decomposed to extract the main identifiable information directions under a unified local physical scale, and the obtained feature directions are mapped back to the primitive parameter space, i.e. In the formula, for The One unit orthogonal eigenvector; For the first A generalized information feature value; The first in the basis parameter set space A generalized feature direction; here For information modal indexing.

[0050] Equivalently satisfy In the formula Kronecker notation; equation Indicates each direction regarding Orthogonal unification. According to... Arrange the generalized feature directions from largest to smallest, and select the first... It consists of several directions. In the formula, To preserve the number of directions; For reduced-dimensional basis matrices; for An identity matrix of order 1; for The directional variance index is ,when season ,in For the first The theoretical variance index for each direction. Prioritize retaining directions that yield more identifiable information under unit physical changes, and gradually discard weakly identifiable directions to facilitate the subsequent construction of a dimensionality-reduced identification subspace.

[0051] In one implementation example, step S5 specifically includes: Parameter identification is performed in the reduced-dimensional subspace. Based on the reduced-dimensional basis matrix generated in step S4... The update space of the base parameter set to be identified is restricted to In the formula, These are the complete a priori values ​​of the inertial parameters; The prior values ​​of the basis parameter set; The increment of the parameter to be identified in the reduced-dimensional coordinates; The increment of the base parameter set is used; then, a semi-definite convex programming expression is constructed in the affine parameter subspace to solve for the increment of the parameter to be identified and the motor rotor inertia, i.e. ; In the formula, and These are the estimated values ​​of the dimension reduction coordinate increment and the motor rotor inertia, respectively. The stacking friction torque is calculated based on a known friction model. The vector L2 norm is used. After solving, the dimension-reduced coordinate increments are mapped back to the basis parameter space to obtain the estimated values ​​of the basis parameters and the estimated values ​​of the motor rotor inertia under the current retained dimension. Based on this, a dimension-reduced dynamic model is constructed for subsequent torque prediction and model verification.

[0052] The method of this invention can significantly reduce the number of identification variables, whereas previously all variables needed to be adjusted simultaneously. The basic parameters are now only adjusted for the ones selected earlier. One effective information direction.

[0053] In one implementation example, step S6 specifically includes: Determine the retained dimensionality and verify the dimensionality reduction effect. Follow the candidate retained dimensions generated in step S5. The parameter identification process is repeated, and a verification trajectory is calculated for trajectories that differ from the identified trajectory. ; In the formula, To preserve Stacked verification predictive torque in each direction; To verify the regression matrix of the stacked basis parameter set of the trajectory; To verify the stacked motor inertia regression matrix of the trajectory; Candidate dimension Basic parameter estimates under the given conditions; Candidate dimension The estimated value of the motor rotor inertia; To verify the number of sampling times, the number of sampling moments is then calculated. The root mean square error of each joint and the root mean square error of the entire joint were verified. ; In the formula, To verify the root mean square error; For joint indexing; and The first Predicted and measured joint torques at each verification sampling time; The sum of RMSEs is validated for all joints. Then, candidate dimensions are selected. The sum of RMSE for full joint verification : ; In the formula, To preserve the final dimension; This is the allowable error ratio; A temporary index for traversing candidate dimensions; To preserve The total validation error index in each direction. At this point, the candidate dimension with the lowest sum of all-joint validation RMSEs is the final retained dimension. This retained dimension is obtained. The estimated values ​​of the basic parameters and the estimated values ​​of the motor rotor inertia are obtained.

[0054] In one implementation example, an offline parameter dimensionality reduction identification method for an NB4 robot is disclosed. This embodiment uses a six-degree-of-freedom industrial robot.

[0055] 1. Data Preparation: The robot has six revolute joints, and the inertial parameters of these six links are used in the dynamics calculations. The complete inertial parameter set has a dimension of 60, the basis parameter set has a dimension of 36, and the mapping matrix satisfies... This is the mapping matrix that maps the robot from a 60-dimensional complete inertial parameter space to a 36-dimensional basis parameter set space.

[0056] The robot is controlled to perform Fourier series identification of the excitation trajectory, collecting joint positions, joint velocities, and joint torques, and then filtering the data to construct the regression matrix. Let the stacked basis parameter set regression matrix be denoted as... The motor inertia regression matrix is Stacking measurement torque .

[0057] Using a pre-identified nonlinear friction model, the frictional torques of the six joints are calculated based on the joint velocities at each sampling time, and then stacked as follows: Using complete CAD inertial parameters Generate minimum parameter prior ; In the formula, It is a priori column vector formed by the sequential stacking of the complete inertial parameters of the six links in CAD; These are the prior values ​​of the mapped base parameter set.

[0058] 2. Generate the minimum parameter logarithmic Euclidean induced metric.

[0059] The six links were generated according to Example 1. Pull back the metric matrix and construct... ; In the formula, For six The single-link pullback metric matrix is ​​constructed by dividing the entire inertial parameter space into blocks diagonally. Then, the induced metric matrix in the basis parameter set space is calculated. ; In the formula, For the parameters corresponding to the prior reference parameters The induced 36th order basis parameter set log-Euclidean metric matrix; To retrieve the inverse of the metric matrix for complete parameters. Perform symmetry and positive definiteness checks. If If the smallest eigenvalue is less than the numerical tolerance, then a diagonal regularization term sufficient to eliminate rounding error is added.

[0060] 3. Computational geometric normalized information modes.

[0061] With all torque channels having the same weight, the calculation... ; In the formula, This is the information matrix when the same weights are used in each torque channel in this embodiment; for The regression matrix of the stacked basis parameter set. Let ; Further calculation of the symmetric information matrix after geometric whitening and its feature decomposition ,then Arranged from largest to smallest, each Arranged in the same order. For all values ​​greater than the numerical tolerance... calculate .

[0062] The actual procedure in this embodiment can be As a representative threshold, it is used to observe whether the condition is met. The number of directions; among which, The value 17 is a threshold for the directional variance index; it is not a limitation of this invention. Modal directions are calculated in the minimum parameter space. , The unit eigenvector in the whitening coordinates Transform back to the original base parameter set coordinates.

[0063] 4. Decrease the parameter directions sequentially and perform convex optimization identification.

[0064] Let the number of reduction directions be The corresponding number of retained directions is For each ,Pick ; In the formula, The first sorted whitening coordinates A matrix composed of unit eigenvectors arranged column by column; Let be the dimension-reduced basis matrix in the coordinates of the original basis parameter set. Then solve the optimization equation. ; The objective function employing either the L2 norm or the squared L2 norm yields the same optimal solution. This can be obtained by calling the MOSEK solver within the CVX environment. .

[0065] 5. Cross-trajectory verification.

[0066] Control the robot to execute a cross-validation trajectory different from the identified trajectory, and construct... and And calculate the frictional torque based on the joint velocity of the verification trajectory. For each ,calculate: ; In the formula, To preserve Stacked predicted torque on the verification trajectory in each direction; To verify the regression matrix of the stacked basis parameter set of the trajectory; To verify the stacked motor inertia regression matrix of the trajectory; and These are the estimated values ​​of the basic parameter set and the estimated value of the motor rotor inertia under the current candidate dimension, respectively. To verify the stacking friction torque of the trajectory; To verify the number of trajectory sampling times, the torque vector is shaped as follows: The matrix. For the first... For each joint, calculate: ; After the loop ends, the horizontal axis represents the number of parameters reduced in different directions. Represented by the vertical axis This yields the RMSE trend curves for each direction of parameter reduction. It can also plot the RMSE lines for the CAD minimum parameter prior model or the unreduced identification model. If, after removing directions with large variance... The fact that the values ​​remain essentially unchanged indicates that these directions contribute little to the measurable torque in the verification task; further removal of these directions leads to... When the value increases significantly, it indicates that parameter combinations with effective predictive contributions are beginning to be discarded.

[0067] Ultimately, the maximum number of directions that can be reduced to satisfy the prediction error constraint can be selected: ; In the formula, This represents the maximum number of directions that can be reduced under error constraints. Indicates from candidates Take the maximum value from the set; the colon in the set indicates a candidate. The subsequent error conditions should be met; To reduce One direction, that is, to retain The sum of RMSE for verification in each direction; The percentage increase in allowable error relative to the reference value; This serves as a reference for verifying error metrics. The validation error can be taken from the unreduced model, the minimum validation error among all candidate models, or the pre-defined engineering allowable error.

[0068] like Figure 2As shown, this diagram illustrates the change in the total RMSE of joint torque prediction on the independent verification trajectory when the identification parameter directions are reduced sequentially according to the generalized information strength in an embodiment of the present invention. As the number of identification parameters reduced increases, the RMSE generally decreases in a stepwise manner, reaching its lowest point near the reduction of approximately 27 parameter directions. This indicates that prioritizing the removal of weakly identifiable parameter directions with large theoretical variance can improve the model's numerical stability and torque prediction generalization ability while reducing the identification dimensionality. When the number of parameter directions is further reduced, the RMSE rises rapidly, indicating that the main parameter directions closely related to torque prediction are beginning to be removed. When all identification directions are removed, the model degenerates to using only the minimum parameter set prior values, and its error returns to the prior baseline level shown by the red dashed line in the figure. Therefore, the final retained dimensionality can be determined based on the minimum verification RMSE or the allowable error threshold, thus balancing the degree of parameter dimensionality reduction with the torque prediction accuracy of the dynamic model.

[0069] like Figure 3 As shown, the example of this invention adopts the best dimensionality reduction result, that is, only 9 dynamic parameters are updated to obtain the joint torque prediction model of the robotic arm. The NRMSE error obtained by comparing the predicted test trajectory is within 5%, and the obtained joint torque prediction model has high accuracy. Figures 4-9 This is a comparison chart of the predicted torque, actual measured torque, and torque error of each joint in the dimension reduction identification model of this invention.

[0070] This example explicitly transforms the local convex approximation of the logarithmic Euclidean metric into the Gram pullback metric matrix in the complete inertial parameter space, and further induces it to the basis parameter set space, so that the mass, the first moment of mass, and the inertial tensor can be compared at a unified local physical scale.

[0071] In this example, the solution to the generalized eigenvalue problem of the information matrix relative to the log-Euclidean induced metric is achieved by selecting an identifiable combination of multiple original inertial parameters, rather than empirically deleting them based on the original parameter numbers. This reduces the impact of parameter dimensions, units, and numerical scales on the dimensionality reduction results.

[0072] This embodiment solves the parameter identification problem in a reduced-dimensional subspace, which can reduce the number of optimization variables, suppress the amplification of noise by weak excitation directions, improve the numerical instability caused by the ill-conditioned information matrix, and reduce the computational cost of parameter identification.

[0073] This example calculates the root mean square error of the joint-by-joint torque for each candidate dimension by independently verifying the trajectory, so that the retained dimension can be determined based on the actual torque prediction effect, avoiding reliance on a single feature value threshold.

[0074] Example 2 The purpose of this embodiment is to provide a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the above-described method.

[0075] Example 3 The purpose of this embodiment is to provide a computer-readable storage medium.

[0076] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, performs the steps of the above method.

[0077] Example 4 The purpose of this embodiment is to provide a robot dynamics parameter dimensionality reduction identification system, including: The joint torque linear regression model construction module is configured to: establish a mapping matrix between the complete set of inertial parameters and the set of basic parameters for a multi-link robot, and establish a joint torque linear regression model; The log-Euclidean pullback metric matrix generation module is configured to generate a log-Euclidean pullback metric matrix for the complete inertial parameter space. The induced metric matrix module is configured to generate the induced metric matrix of the basis parameter set space using the generated mapping matrix from the complete inertial parameter set to the basis parameter set and the generated log-Euclidean pullback metric matrix of the complete inertial parameter space. The dimension reduction parameter subspace generation module is configured to: collect joint motion data during robot operation, stack and establish a linear regression model of joint torque and construct an information matrix by combining joint torque noise information; use the induced metric matrix of the generated basis parameter set space to perform geometric normalization on the information matrix, and use the generalized information feature values ​​of the normalized information matrix to generate a dimension reduction parameter subspace. The solution module is configured to: utilize the generated candidate dimensionality reduction parameter subspace, call the generated stacked joint torque linear regression model, perform convex optimization on the dimensionality reduction coordinate increment and motor rotor inertia, and obtain the estimated values ​​of the basic parameter set and the estimated values ​​of the motor rotor inertia corresponding to each candidate retained dimension; The parameter determination module is configured to: substitute the estimated values ​​of the basic parameter sets and the estimated values ​​of the motor rotor inertia generated by each candidate retained dimension into the validation regression model, calculate the root mean square error of the joint torque corresponding to each candidate retained dimension, and determine the final retained dimension and the corresponding estimated values ​​of the basic parameter sets and the estimated values ​​of the motor rotor inertia according to the rule of minimizing the validation error.

[0078] Example 5 The purpose of this embodiment is to provide a computer program product containing instructions that, when run on a computer, causes the computer to perform the methods and functions involved in any of the embodiments described above.

[0079] The steps and methods involved in the apparatus of the above embodiments correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0080] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any particular combination of hardware and software.

[0081] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for dimensionality reduction identification of robot dynamic parameters, characterized in that, include: For multi-link robots, a mapping matrix between the complete set of inertial parameters and the basic parameter set is established, and a linear regression model of joint torques is also established. Generate the log-Euclidean pullback metric matrix of the complete inertial parameter space; Using the mapping matrix from the generated complete inertial parameter set to the basis parameter set and the logarithmic Euclidean pullback metric matrix of the generated complete inertial parameter space, the induced metric matrix of the basis parameter set space is generated. Collect joint motion data during robot operation, stack and establish a linear regression model of joint torque, and construct an information matrix by combining joint torque noise information; The information matrix is ​​geometrically normalized using the induced metric matrix of the generated basis parameter set space, and a dimension-reduced parameter subspace is generated using the generalized information eigenvalues ​​of the normalized information matrix. Using the generated candidate dimensionality reduction parameter subspace, the generated stacked joint torque linear regression model is called to perform convex optimization on the dimensionality reduction coordinate increment and motor rotor inertia, so as to obtain the estimated values ​​of the basic parameter set and the estimated values ​​of the motor rotor inertia corresponding to each candidate retained dimension. The estimated values ​​of the basic parameter set and the estimated values ​​of the motor rotor inertia generated by each candidate retained dimension are substituted into the validation regression model to calculate the root mean square error of the joint torque corresponding to each candidate retained dimension. The final retained dimension and the corresponding estimated values ​​of the basic parameter set and the estimated values ​​of the motor rotor inertia are determined according to the rule of minimizing the validation error.

2. The method for dimensionality reduction identification of robot dynamic parameters as described in claim 1, characterized in that, The process of establishing a linear regression model for joint torque is as follows: For robots with multiple joints, the mapping relationship between the complete set of inertial parameters and the set of basic parameters is obtained through numerical decomposition, the full-rank regression matrix is ​​obtained, and a linearized rigid body dynamics model under the full-rank regression matrix is ​​established. A linear regression model of joint torque is obtained by combining the linearized rigid body dynamics model and the motor inertia model.

3. The method for dimensionality reduction and identification of robot dynamic parameters as described in claim 1, characterized in that, The steps to generate the log-Euclidean pullback metric matrix of the complete inertial parameter space are as follows: Definition of the first A physical consistency matrix is ​​commonly used in robots with multiple links; When the physical consistency matrix satisfies the basic physical constraints, the consistency matrix remains symmetric and positive definite. On a fourth-order symmetric and positive definite matrix manifold, the logarithmic Euclidean metric is used to describe the intrinsic physical changes between inertial parameters. At the reference point of the physical consistency matrix, a local quadratic approximation of the logarithmic Euclidean metric is established using the Fréchet derivative, thus obtaining the logarithmic Euclidean pullback metric matrix of the complete inertial parameter space.

4. The robot dynamics parameter dimensionality reduction identification method as described in claim 3, characterized in that, The steps to establish a local quadratic approximation of the logarithmic Euclidean metric are as follows: At the reference complete inertial parameters, perform eigenvalue decomposition on the reference physical consistency matrix; A first-order difference quotient matrix is ​​defined to describe the sensitivity to small changes in eigenvalues; Based on the eigenvalue decomposition of the reference physical consistency matrix and the first-order difference quotient matrix, the matrix logarithm is defined on the ... Fréchet derivative at the reference physical consistency matrix of each link; The response matrix and single-link pullback metric matrix are constructed based on the Fréchet derivative to measure the distance by which the change in the link's inertial parameters causes a change in the Log-Euclidean coordinate system. We obtain convex approximations and convex quadratic approximations based on logarithmic Euclidean metric; Will The metric matrices of each link are further assembled to obtain the logarithmic Euclidean pullback metric matrix of the complete inertial parameter space.

5. The method for dimensionality reduction identification of robot dynamic parameters as described in claim 1, characterized in that, The induced metric matrix for generating the basis parameter set space is as follows: Define the minimum local physical length of the base parameter increment; Based on the Log-Euclidean pullback metric in the complete inertial parameter space, the local physical scale is induced to the basic parameter space by solving the minimum physical change problem that satisfies the dynamic equivalence constraints, thereby obtaining a basic parameter metric matrix with the same dimension as the basic parameter regression matrix.

6. The method for dimensionality reduction identification of robot dynamic parameters as described in claim 1, characterized in that, The estimated values ​​of the basic parameter set and the estimated value of the motor rotor inertia corresponding to each candidate retained dimension are obtained, specifically including: Parameter identification is performed in the reduced-dimensional subspace: the space is updated by constraining the set of basis parameters to be identified based on the generated reduced-dimensional basis matrix; Construct a semidefinite convex programming expression in the affine parameter subspace to solve for the increment of the parameter to be identified and the rotor inertia of the motor. After the solution is completed, the dimension-reduced coordinate increments are mapped back to the basic parameter space to obtain the estimated values ​​of the basic parameters and the estimated values ​​of the motor rotor inertia under the current retained dimension. Based on this, a dimension-reduced dynamic model is constructed for subsequent torque prediction and model verification.

7. A robot dynamics parameter dimensionality reduction identification system, characterized in that, include: The joint torque linear regression model construction module is configured to: establish a mapping matrix between the complete set of inertial parameters and the set of basic parameters for a multi-link robot, and establish a joint torque linear regression model; The log-Euclidean pullback metric matrix generation module is configured to generate a log-Euclidean pullback metric matrix for the complete inertial parameter space. The induced metric matrix module is configured to generate the induced metric matrix of the basis parameter set space using the generated mapping matrix from the complete inertial parameter set to the basis parameter set and the generated log-Euclidean pullback metric matrix of the complete inertial parameter space. The dimension reduction parameter subspace generation module is configured to: collect joint motion data during robot operation, stack and establish a linear regression model of joint torque and construct an information matrix by combining joint torque noise information; use the induced metric matrix of the generated basis parameter set space to perform geometric normalization on the information matrix, and use the generalized information feature values ​​of the normalized information matrix to generate a dimension reduction parameter subspace. The solution module is configured to: utilize the generated candidate dimensionality reduction parameter subspace, call the generated stacked joint torque linear regression model, perform convex optimization on the dimensionality reduction coordinate increment and motor rotor inertia, and obtain the estimated values ​​of the basic parameter set and the estimated values ​​of the motor rotor inertia corresponding to each candidate retained dimension; The parameter determination module is configured to: substitute the estimated values ​​of the basic parameter sets and the estimated values ​​of the motor rotor inertia generated by each candidate retained dimension into the validation regression model, calculate the root mean square error of the joint torque corresponding to each candidate retained dimension, and determine the final retained dimension and the corresponding estimated values ​​of the basic parameter sets and the estimated values ​​of the motor rotor inertia according to the rule of minimizing the validation error.

8. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 6.

9. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method described in any one of claims 1-6.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it performs the steps of the method described in any one of claims 1-6 above.

Images