A dual sparse efficient identification method and system for robot dynamics parameters

Abstract

The application belongs to the technical field of robot dynamics parameter identification, and discloses a double sparse efficient identification method and system for robot dynamics parameters. The method comprises the following steps: S1, collecting joint positions, joint speeds, joint torques and joint accelerations of a robot to be processed at each time; S2, constructing an implicit dynamics equation of the joint torque by taking the joint torque as a target; S3, constructing a base function database, evaluating the importance of each base function in the base function database, thereby completing the first sparse of the base function; and performing sparsification on the coefficient matrix to make some elements in the coefficient matrix 0, thereby completing the second sparse of the base function, determining the base function and the coefficient matrix, and realizing the acquisition of an explicit dynamics equation of the joint torque. Through the application, the technical problems of complex theoretical modeling or low interpretability of a black box model in the prior art are solved.

Description

Technical Field

[0001] This invention belongs to the technical field of robot dynamics parameter identification, and more specifically, relates to a dual sparse and efficient identification method and system for robot dynamics parameters. Background Technology

[0002] Robots have low body stiffness, making it difficult to precisely control machining trajectories. Furthermore, excessive cutting forces can easily cause vibrations, reducing machining quality. Dynamic parameters are crucial for describing a robot's motion and mechanical characteristics. Accurately identifying these parameters can reduce system errors, enabling precise motion and force control, improving the robot's positioning and tracking accuracy, and allowing it to perform highly precise operations such as grinding, milling, and welding.

[0003] Generally, the equations of motion for robots are derived using traditional Newton-Euler and Euler-Lagrange methods. Applying these methods to multi-degree-of-freedom robots is extremely complex and requires many assumptions based on idealized conditions. Furthermore, nonlinear characteristics present in real-world robots, such as joint friction, are often difficult to model, leading to modeling errors. Accurate parameter identification is based on theoretical models, and these nonlinear factors also limit the accuracy of parameter identification.

[0004] Data-driven modeling methods infer system dynamics from collected data, avoiding complex mathematical derivations and modeling processes, as well as modeling errors caused by idealized assumptions, and have been widely applied and developed. In recent years, Gaussian processes, compressed sensing, and neural networks have been applied to the nonlinear identification of fluid systems to discover the relationship between inputs and outputs. These trained neural networks can solve supervised learning tasks while obeying physical laws described by nonlinear partial differential equations. However, neural networks are black-box models and cannot provide a physical explanation for the established relationship between inputs and outputs.

[0005] Therefore, there is an urgent need for a data-driven method to obtain high-precision dynamic parameters of serial robots in a short time. Summary of the Invention

[0006] To address the above-mentioned deficiencies or improvement needs of existing technologies, this invention provides a dual sparse and efficient identification method and system for robot dynamic parameters, solving the technical problems of complex theoretical modeling or low interpretability of black-box models, which are easy to calculate.

[0007] To achieve the above objectives, according to one aspect of the present invention, a dual sparse and efficient identification method for robot dynamic parameters is provided, the method comprising the following steps:

[0008] S1 collects motion data of the robot at various moments during its movement, including joint position, joint velocity, joint torque, and joint acceleration.

[0009] S2 takes the joint torque as the target and constructs an implicit dynamic equation in which the joint torque is equal to the product of the coefficient matrix and the unknown function, wherein the unknown function is a functional relationship between the joint position, joint velocity and joint acceleration and the basis function;

[0010] S3 For the basis functions, construct a basis function database, evaluate the importance of each basis function in the database, and discard those whose importance does not meet the preset importance conditions, thereby completing the first layer of sparsity of the basis functions; sparsify the coefficient matrix so that some elements in the coefficient matrix are 0, thereby completing the second layer of sparsity of the basis functions, thereby determining the basis functions and coefficient matrix, and realizing the explicit mechanical equation of the joint torque.

[0011] More preferably, in step S3, the basis function database is configured according to the following expression:

[0012]

[0013] Where Θ(X) is the basis function library, It is a k-th order polynomial, X is a basis function, and P is a polynomial of order k. k It is the series of basis functions.

[0014] More preferably, in step S2, the joint torque is fitted using a random forest model, where the input features of the model are the columns of the basis function library, and the output features are the joint torque.

[0015] More preferably, in step S3, the evaluation of importance is performed according to the following steps:

[0016] S31 uses each basis function in Θ(X) as a random forest model h t The random forest model h is trained by taking input x as x and outputting joint torque as y. t (x);

[0017] S32 assigns a number to each basis function, inputs the collected motion data at different times into each basis function, calculates the basis function values ​​at different times, and thus forms a matrix X of basis function values ​​at different times. m×n Where m is the total number of time steps, n is the total number of basis functions, and X... m×n As input to the random forest model, the generalization performance score(D) of the random forest model is calculated.

[0018] S33 will use matrix Xm×n The order of the i-th column in the matrix is ​​shuffled to obtain the shuffled matrix X′. m×n , with X′ m×n As input to the random forest model, the generalization performance score(D) of the random forest model is calculated. (P) ), where i is the number of the basis function;

[0019] S34 utilizes the score(D) and score(D) (p) Calculate the importance score for the i-th column, calculate the importance scores for all columns, and thus obtain the importance scores for all basis functions.

[0020] S35 sorts all basis functions by importance scores, plots Elbow curves, calculates the rate of change at each point, and discards basis functions that do not meet the preset importance criteria.

[0021] More preferably, in step S32, the score(D) is calculated according to the following method:

[0022]

[0023] The importance score is calculated according to the following formula:

[0024] importance(i)=score(D)-score(D (p) )

[0025] Where y is the true value of the output feature, i.e. the true value of the joint torque, x is the input feature, i.e. the basis function, H(x) is the predicted value of the model, and D is the original dataset.

[0026] More preferably, in step S33, the rate of change of each point is calculated according to the following formula:

[0027]

[0028] Among them, the features are sorted from most important to least important, and importance(i) and importance(i+1) represent the difference in importance between the i-th and i+1-th features, respectively. i It describes the speed at which importance changes.

[0029] More preferably, in step S33, the preset importance condition is performed as follows: if |k i |<10 -5 If the first point is m, then for all points i = 1 to m, we have |k i |>=10 -5 We retain the first m features, which are the m basis functions ranked first in importance.

[0030] More preferably, the second sparsity is performed according to the following method:

[0031] First, let the coefficient matrix be Ξ=(Θ T Θ) -1 Θ T Γ, where Θ(X) represents the basis function library, Γ represents the joint torque, and Ξ represents the coefficient matrix.

[0032] Secondly, set the threshold to η. For any Ξ(i) in the matrix, if |Ξ(i)| < η, then let Ξ(i) = 0 to obtain Ξ′(i). Iterate and perform least squares solution until convergence.

[0033] More preferably, in step S2, the implicit dynamic equations are performed according to the following relationships:

[0034] sym(Γ)=sym(Θ(X))Ξ

[0035] Where sym(Γ) represents the symbolic expression of the joint torque composed of symbolic variables such as [τ1 τ2 τ3], and sym(Θ(X)) represents the symbolic expression of the joint torque composed of symbolic variables such as [τ1 τ2 τ3]. A symbolic basis function library consisting of symbolic variables, where Ξ represents the coefficient matrix.

[0036] According to another aspect of the present invention, a dual sparse high-efficiency identification system for robot dynamic parameters is provided, characterized in that it includes a processor for executing the dual sparse high-efficiency identification method for robot dynamic parameters described above.

[0037] In summary, the technical solutions conceived by this invention have the following beneficial effects compared with the prior art:

[0038] 1. This invention can identify the robot's dynamic formula using only the raw data of a single robot trajectory run and a single program. Traditional dynamic parameter identification requires cumbersome steps such as theoretical modeling and solving for the minimum parameter set, which requires a lot of learning and reference and takes a long time to prepare. However, the dual sparse method of this invention can complete the identification by running only one program, with a total running time of less than 10 seconds.

[0039] 2. Traditional modeling methods require a certain mathematical derivation process and have high requirements for theoretical level; while existing deep learning algorithms only consider black box models of mapping relationships and cannot obtain mechanism knowledge that conforms to physical laws. The method provided by this invention combines prior knowledge in the selection of basis function library, making the algorithm's calculations reasonable and avoiding tedious theoretical derivation. It is a gray box model with partial interpretability.

[0040] 3. Compared with deep learning methods that involve a large amount of work, such as building neural networks and adjusting network parameters, the first layer of the dual sparsity identification method provided in this invention only uses the scoring algorithm in random forest, and the second layer of sparsity uses the sequential threshold least squares method, which is an iterative operation of the least squares algorithm with threshold constraints. Both are simple and common algorithms, making the method more accessible.

[0041] 4. In terms of identification accuracy, this dual sparse and efficient identification method also achieves more accurate results than traditional identification methods. After a series of cumbersome steps, the error percentage of traditional dynamic parameter identification methods is usually around 10%, while the error percentage of this method is only around 5%. While saving computation time, it obtains more accurate identification results. Attached Figure Description

[0042] Figure 1 This is a flowchart of a data-driven method for efficient identification of dual sparse robot dynamic parameters according to a preferred embodiment of the present invention.

[0043] Figure 2 This is a robot model diagram of a preferred embodiment of the present invention;

[0044] Figure 3 This is a robot running trajectory for identification in a preferred embodiment of the present invention;

[0045] Figure 4 The following is the importance ranking result of the feature items in the basis function library of the joint dynamics of each preferred embodiment of the present invention, wherein (a) is the elbow curve of joint 1, (b) is the elbow curve of joint 2, and (c) is the elbow curve of joint 3.

[0046] Figure 5 This is the change of the basis function library in the preferred embodiment of the present invention when performing double sparsity optimization; wherein, (a) is the basis function library before sparsification, (b) is the basis function library after the first sparsification, (c) is the basis function library after the first sparsification and rearrangement, so that the non-zero terms are arranged in a concentrated manner, and (d) is the basis function library after the second sparsification.

[0047] Figure 6 This is a comparison of the identification effect of the method with the traditional minimum identification method in a preferred embodiment of the present invention. Figures (a), (b), and (c) are comparison figures of the torque calculated by the double sparsity method, the torque calculated by the least squares method, and the actual torque of joints 1, 2, and 3, respectively. Figure (d) is a comparison figure of the error of the torque calculated by the double sparsity method for joint 3 and the error of the torque calculated by the least squares method.

[0048] Figure 7This is a comparison diagram of the identification time of a preferred embodiment of the present invention and the time required by conventional identification methods. In all the figures, the same reference numerals are used to denote the same elements or structures, wherein: 1-joint 1, 2-joint 2, 3-joint 3. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0050] A method for rapid prediction of machining errors of thin-walled parts under multiple working conditions includes the following steps:

[0051] S1. Obtain the joint motion dataset

[0052] The robot is driven to move along a specific trajectory, and data such as joint position, joint velocity, and joint torque at each point are collected. The joint acceleration is then calculated from these data, which together form the original training data. The dataset is then smoothed and filtered.

[0053] The specific sub-steps are as follows:

[0054] S1.1 Plan a motion trajectory for the robot so that the trajectory covers the entire working area of ​​the robot as much as possible, and so that each joint is fully excited.

[0055] S1.2. Program the trajectory and have the robot execute the program to collect the joint angles q and joint velocities at each point during the motion. Joint torque τ data.

[0056] S1.3, regarding joint velocity The joint acceleration is obtained by difference. And on The joint torque τ data is also filtered and smoothed.

[0057] S2. Constructing a robot dynamics basis function library

[0058] The dynamic parameters of the first three joints of a six-DOF robot are much larger than those of the other three joints. To simplify the calculation, the dynamics of joints 1-3 of the robot are analyzed. Based on common sense about dynamics, a series of simple basis functions are selected as columns of the parameter matrix to form a basis function library to be screened, and the corresponding coefficient matrix is ​​obtained.

[0059] The base function library is constructed as follows:

[0060] S2.1 Construct a dynamic system of the following form:

[0061]

[0062] vector The function f(x(t)) represents the state of the system at time t, and the function f(x(t)) represents the dynamic constraints that define the system's equations of motion.

[0063] S2.2, set t1, t2, ... t m The joint data obtained at each time step are arranged into a matrix:

[0064]

[0065] Construct a basis function library Θ(X), where each column of Θ(X) is a nonlinear function related to X, consisting of a constant term and a polynomial.

[0066]

[0067] Let Θ(X) represent a k-th order polynomial, and each column Θ(X) represents a candidate function.

[0068] S2.3. Only a few terms in the basis function library Θ(X) are active. The state of each term can be observed through the coefficient matrix, i.e.:

[0069] Γ=Θ(X)Ξ

[0070] in l is the number of samples sampled over time. m is the number of candidate functions, and the sparse matrix Ξ can be represented as:

[0071]

[0072] S3. Perform first-stage sparsity on the basis functions based on feature importance index.

[0073] Using joint torque as the target value, the importance of each function in the basis function library obtained by S2 is evaluated, and basis functions with less impact on the result are discarded, thus completing the first layer of sparsity of the basis function library.

[0074] The specific sub-steps are as follows:

[0075] S3.1 Using a random forest model to fit the joint torques

[0076] The model's input features x are the columns of Θ(X), and the output features y are the joint torques, i.e., using multiple... The sum is used to fit the joint torque τ(q), and through this step, the trained model h is obtained. t (x).

[0077] S3.2 Evaluate the importance of input features

[0078] When calculating the importance of the i-th feature, the i-th feature of the N samples is reordered randomly, and the initial feature i is denoted as x. n,i The reordered feature sequence becomes x′ n,i Calculate the importance of the model prediction at this point, i.e.:

[0079]

[0080] Where D is the original data used in S3.1, D (p) It is Chinese x n,i Use x′ n,i The data after the replacement.

[0081] The score(D) is calculated using "out-of-package estimation." Each random forest base learner uses only a subset of samples for computation, while the remaining samples are used to estimate the model's generalization performance. Let D... t Let ht(x) represent the actual training sample set used by ht(x), and let H(x) represent the out-of-bag prediction for sample x, that is, the prediction on x by only considering the base learners that were not trained on x, as follows:

[0082]

[0083] Where Ι(·) is an indicator function, taking values ​​of 1 and 0 when · is true and false, respectively. Calculation yields:

[0084]

[0085] score(D (p) The calculation is similar.

[0086] S3.3 Filter features based on importance

[0087] Since importance(i) represents the importance of the i-th column, we can filter and retain the more important items based on the results. Sorting by importance from highest to lowest, the distribution of importance(i) (i = 1, ..., N) usually follows an elbow curve, i.e., the rate of change k at each point is calculated. i hour:

[0088]

[0089] Let |k i |<10 -5 If the first point is m, it means that the changes in the Nm points after point m have little effect on the joint torque, so the first m features are retained.

[0090] S4. Secondary sparsity of function libraries based on sparse regression methods

[0091] A sequential threshold least squares method is used to constrain the coefficient matrix corresponding to the basis function library, so that the coefficients of some basis functions are 0, thereby completing the second sparsity of the basis function library.

[0092] S5. Calculate the robot's inverse dynamics equations

[0093] By multiplying the final symbolic basis function library with the coefficient matrix, the explicit robot dynamics equations can be obtained.

[0094] The coefficient matrix sparsity is achieved using the sequential threshold least squares algorithm. The specific method is as follows:

[0095] The solution method for the coefficient matrix Ξ is as follows:

[0096]

[0097] Set the threshold to η. For any Ξ(i) in the matrix, if |Ξ(i)| < η, then let Ξ(i) = 0 to obtain Ξ′(i). Iterate through the least squares solution until convergence.

[0098] Solving for the explicit dynamic expressions of a robot joint requires symbolic mathematical solutions, the specific methods of which are as follows:

[0099] Will Defined as a symbol, Θ(X) is expressed as the symbol matrix sym(Θ(X)), which is multiplied by the obtained sparse coefficient matrix Ξ to obtain:

[0100] sym(Γ)=sym(Θ(X))Ξ

[0101] At this point, if the corresponding coefficient in Ξ is 0, then the corresponding symbol term will not appear in sym(Γ), thus obtaining the explicit expression of robot dynamics and completing the identification of unknown dynamic parameters.

[0102] The following is a specific application example of the present invention, and its main process is as follows: Figure 1 As shown, it includes the following steps:

[0103] S1. Obtain the joint motion dataset

[0104] This embodiment identifies the Staubli TX2-90L robot. The dynamic parameters of the first three joints of the six-DOF robot are much larger than those of the other three joints. To simplify the calculation, only the dynamics of joints 1-3 are analyzed. A schematic diagram of the first three joints of the robot is shown below. Figure 2 As shown.

[0105] S1.1 Planning the robot's motion trajectory

[0106] Plan a trajectory that allows the robot to traverse its own workspace. To ensure the robot's joints are fully energized and to prevent collisions with other objects in space, the joint angles are set to (-180, 180), (-20, 50), and (-20, 60), respectively, with maximum joint angular velocities of [missing values]. The maximum joint angular accelerations are respectively With this constraint in mind, a feasible robot trajectory can be obtained using a genetic algorithm, and its position in the robot's workspace is as follows: Figure 3 As shown. It should be noted that since the trajectory is not unique, it can be generated multiple times, and trajectories with abrupt changes in the robot's joint angular velocity and angular acceleration should be avoided as much as possible.

[0107] S1.2 Robot joint motion data acquisition

[0108] Motion program instructions were written in the robot's SRS software, and the parameters to be collected were written to make the robot run the trajectory program and acquire joint data. A total of 3496 points were obtained. The motion data of these points includes the joint angular position q and velocity of the robot during movement. Both the joint torque τ and the torque τ can be read directly.

[0109] S1.3 Construction of the original dataset

[0110] Because q is needed at the same time, As the input to the inverse dynamics, therefore by The robot's joint acceleration is obtained by difference. However, due to the joint angular velocity... The torque τ itself contains significant noise, therefore smoothing filtering is required. Similarly, It is by The result obtained by difference also requires analysis of acceleration. Filtering is performed to reduce the impact of noise during the identification process.

[0111] S2. Constructing a robot dynamics basis function library

[0112] S2.1 Constructing a dynamic system

[0113] The joint torque τ can be written as the product of the parameter matrix and the coefficient matrix, i.e.

[0114] Γ=Θ(X)Ξ

[0115] in

[0116]

[0117] Θ(X) is the parameter matrix, and Ξ is the corresponding coefficient matrix.

[0118] S2.2 Calculate the basis function library

[0119] A parameter matrix Θ(X) is formed by assembling a set of candidate nonlinear function classes. Θ(X) is then called a basis function library, and each column of Θ(X) consists of the values ​​of the basis functions. The form of Θ(X) is as follows:

[0120]

[0121] This represents a polynomial of order k. In this instance, k = 3 is used, meaning the polynomial is at most third order. Substitute the variables into the relevant variables. Θ(X) can be specifically written as:

[0122]

[0123] Θ(X) is constructed based on the original data, with 3496 rows corresponding to the number of samples. All terms in the unsparsed basis function library are non-zero, such as... Figure 5 As shown in (a).

[0124] S3. Perform first-stage sparsity on the basis functions based on feature importance index.

[0125] S3.1. Fit the joint torque using a random forest model.

[0126] The basis function values ​​in each column of Θ(X) are used as input features of the random forest model, and each column of the joint torque Γ is used as the output feature, i.e.:

[0127] x1:D1=Θ1(X)→y1:τ1

[0128] x2:D2=Θ2(X)→y2:τ2

[0129] x3:D3=Θ3(X)→y3:τ3

[0130] The model is fitted based on this mapping relationship.

[0131] S3.2, Evaluation of Feature Importance

[0132] The generalization accuracy of the model is calculated using out-of-package estimation, which involves re-randomly sorting the i-th feature of N samples. Let the dataset be D at this point. (p) Let its generalization accuracy be denoted as score(D). (p) The higher the change compared to score(D), the greater the importance of the feature.

[0133] Sort the features according to their importance, and label them as 'Feature 1', 'Feature 2', ..., 'Feature N' from highest to lowest importance. Figure 4In the figure, (a), (b) and (c) are the elbow curves of joint 1, joint 2 and joint 3, respectively. It can be seen that for each joint, the trend of the importance of each feature changes in the shape of an elbow curve. That is, there is a certain elbow point m. The rate of change of the function value of each point before m is large, while the degree of change of each point after m is very small and gradually stabilizes, retaining the first m features.

[0134] like Figure 5 The x-axis represents the rows of the matrix, and the y-axis represents the columns. If there is a point at (x, y), then the function term at that point is not zero. Figure 5 (c) is to Figure 5 The result of arranging all non-zero terms in (b) in a set manner. Figure 5 The basis function libraries of (c) and (b) are actually equivalent, as can be seen. Figure 5 Compared to (a), the basis function library is more sparse.

[0135] S4. Secondary sparsity of function libraries based on sparse regression methods

[0136] This step achieves sparsity for the coefficient matrix Ξ. The coefficient matrix Ξ is obtained by performing least-squares calculations based on the joint moment matrix Γ and the function library Θ(X). For Ξ, a coefficient threshold η is set, i.e., for any term Ξ(i) in Ξ:

[0137] If Ξ(i) < η, then Ξ(i) = 0

[0138] The term corresponding to Ξ(i) = 0 is Θ(i) in the basis function library. Then, Θ(X) is used to remove the corresponding i-th term to obtain the new basis function library Θ. * (X), recalculate Ξ′:

[0139]

[0140] The coefficient matrix Ξ′ is constrained based on the coefficient threshold η, and this process is repeated iteratively until convergence. The final basis function library is as follows: Figure 5 As shown in (d), the base function library and Figure 5 It is even more sparse than (c).

[0141] S5, Calculating the inverse dynamics formula of a robot

[0142] Symbolizing the variables, that is, the variables of each joint Defined as a symbolic variable, the basis function library Θ(X) becomes a symbolic matrix. Combining this with the calculation of Ξ using the least squares method, the explicit expression for τ can be obtained:

[0143]

[0144]

[0145]

[0146] Therefore, the torque of each joint of the robot can be obtained directly from the joint data. Figure 6 (a), (b), and (c) are graphs comparing the torque values ​​calculated by the double sparsity method with the actual torque and the torque calculated by the least squares method for joints 1, 2, and 3, respectively. Figure 6 Figure (d) is a comparison of the calculation errors of the third joint torque using the double sparse method and the least squares method. It can be seen that the torque value calculated by this identification method has a higher degree of agreement with the measured value and a smaller absolute deviation. Because the error is extremely small when using the double sparse method to identify the third joint, from... Figure 6 (c) is difficult to distinguish, therefore in Figure 6 In section (d), the calculation errors of the third joint of the two methods are compared, and it can be seen that the error of this method is smaller. The calculated absolute error RMSE is shown in Table 1. The verification results show that the double sparsity method has higher calculation accuracy compared with the traditional identification method.

[0147] Table 1 Comparison of Calculation Errors

[0148]

[0149] like Figure 7 As shown, although all methods require steps such as calculating the excitation trajectory, collecting experimental data, and calculating the identification results, the traditional dynamic identification method involves cumbersome theoretical model derivation and minimum parameter set calculation, which is time-consuming and laborious. The proposed dual sparse and efficient identification method eliminates the derivation steps and can obtain the identification results through the constructed algorithm in just 0.2s, saving the time required for parameter identification.

[0150] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for efficient dual-sparse identification of robot dynamic parameters, characterized in that, The method includes the following steps: S1 collects motion data of the robot at various moments during its movement, including joint position, joint velocity, joint torque, and joint acceleration. S2 takes the joint torque as the target and constructs an implicit dynamic equation in which the joint torque is equal to the product of the coefficient matrix and the unknown function, wherein the unknown function is a functional relationship between the joint position, joint velocity and joint acceleration and the basis function; S3 For the basis functions, construct a basis function database, evaluate the importance of each basis function in the database, and discard those whose importance does not meet the preset importance conditions, thereby completing the first layer of sparsity of the basis functions; sparsify the coefficient matrix so that some elements in the coefficient matrix are 0, thereby completing the second layer of sparsity of the basis functions, thereby determining the basis functions and coefficient matrix, and realizing the explicit mechanical equation of the joint torque.

2. The method for efficient dual-sparse identification of robot dynamic parameters as described in claim 1, characterized in that, In step S3, the basis function database is configured according to the following expression: in, It is a base function library. yes k A polynomial of order P, where X is a basis function. k It is the series of basis functions.

3. The method for efficient identification of dual sparse robot dynamic parameters as described in claim 2, characterized in that, In step S2, the joint torque is fitted using a random forest model. The input features of the model are the columns of the basis function library, and the output features are the joint torque.

4. The method for efficient identification of dual sparse robot dynamic parameters as described in claim 3, characterized in that, In step S3, the importance is evaluated according to the following steps: S31 will Each basis function in the random forest model is used as a basis function. Input With joint torque as output In this way, the random forest model is trained. ; S32 Numbers each basis function, inputs the collected motion data at different times into each basis function to calculate the basis function values ​​at different times, thus forming a matrix X of basis function values ​​at different times. m n Where m is the total number of time steps, n is the total number of basis functions, and X... m n The generalization performance of the random forest model is calculated by using it as input. ; S33 will use matrix X m n The order of the i-th column in the matrix is ​​shuffled to obtain the shuffled matrix X. m n , with X m n The generalization performance of the random forest model is calculated by using it as input. , where i is the number of the basis function; S34 Utilizing the and Calculate the importance score for the i-th column, and calculate the importance scores for all columns to obtain the importance scores for all basis functions. S35 sorts all basis functions by importance scores, plots an elbow curve, calculates the rate of change at each point, and discards basis functions that do not meet the preset importance criteria.

5. The method for efficient dual-sparse identification of robot dynamic parameters as described in claim 4, characterized in that, In step S32, the Calculate using the following method: The importance score is calculated according to the following formula: Where y is the true value of the output feature, i.e., the true value of the joint torque; x is the input feature, i.e., the basis function. These are the model's predicted values. This is the original dataset.

6. The method for efficient identification of dual sparse robot dynamic parameters as described in claim 4, characterized in that, In step S33, the rate of change of each point is calculated according to the following formula: Among them, the features are sorted from most important to least important. , They represent the first The importance difference of each feature It describes the speed at which importance changes.

7. The method for efficient dual-sparse identification of robot dynamic parameters as described in claim 4, characterized in that, In step S33, the preset importance condition is performed as follows: If The first point is For All have , keep before m One feature, namely, those ranked higher in importance. One basis function.

8. The method for efficient identification of dual sparse robot dynamic parameters as described in claim 1, characterized in that, The second layer of sparsity is performed as follows: First, set the coefficient matrix. ,in, Represents the base function library, Indicates joint torque. Represents the coefficient matrix; Secondly, set the threshold to For any matrix ,like Then let ,get The least squares solution is performed iteratively until convergence.

9. The method for efficient identification of dual sparse robot dynamic parameters as described in claim 1, characterized in that, In step S2, the implicit dynamic equations are performed according to the following relationships: in, A symbolic expression representing joint torque. Indicates by The symbolic base function library constituted This represents the coefficient matrix.

10. A dual sparse high-efficiency identification system for robot dynamic parameters, characterized in that, Includes a processor for executing the dual sparse efficient identification method for robot dynamic parameters as described in any one of claims 1-9.

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