Dynamic modeling method, device and electronic equipment based on residual compensation

Abstract

The present invention provides a dynamic modeling method, device and electronic device based on residual compensation, which is based on the obtained mechanical arm joint information and adopts iterative reweighted least squares method to realize parameter estimation of minimum inertia parameter set to determine the preliminary dynamic identification model. According to the preliminary dynamic identification model, the mechanical arm is made to track the preset trajectory to obtain the residual torque data set and joint information. Based on the residual torque data set and joint information, a dynamic residual model is constructed by adopting nonlinear dynamic sparse identification method. The final dynamic model is obtained by combining the preliminary dynamic identification model and the dynamic residual model. In this scheme, the iterative reweighted least squares method is used to realize parameter identification, which reduces the influence of numerical magnitude difference and outlier value of each joint torque of the mechanical arm, improves the accuracy of the dynamic identification model, and combines the dynamic residual model constructed based on the nonlinear dynamic sparse identification method for compensation, thereby improving the accuracy of the final dynamic model.

Description

Technical Field

[0001] The present invention relates to the field of robotics technology, and in particular to a dynamics modeling method, device and electronic equipment based on residual compensation. Background Art

[0002] The dynamic model of collaborative robots is widely used in tasks such as collision detection, teaching dragging, and torque control. Its accuracy is crucial to the effective implementation of the above functions. The establishment of existing dynamic models can be divided into the following two steps: Step 1. Establishment of model structure; Step 2. Acquisition of model parameters. Step 1 can be achieved through methods such as Lagrangian or Newton-Euler. In step 2, there are three main existing methods: Computer Aided Design (CAD) method; physical experiment method (also known as disassembly measurement method); overall identification method.

[0003] The CAD method requires a CAD model of the robot and calculates the inertia parameters through software. However, due to assembly errors and other issues, there will be deviations between the theoretical and actual values ​​of the inertia parameters. At the same time, the CAD method cannot quantify the nonlinear effects such as friction and flexibility in the robot, which have a great impact on the accuracy of the model. The physical experiment method requires the design of identification experiments for different parameters, and requires precise sensors and external measuring instruments. The implementation process is relatively cumbersome and the identification effect depends on the quality of the experimental design. The overall identification method linearly parameterizes the dynamic model structure, and then makes the robot track the designed excitation trajectory and collects time series data of motion and torque. Then, all parameters in the dynamic model structure are identified through the parameter estimation algorithm. It does not require the design of separate experiments for different parameters, and the identified parameters are more accurate.

[0004] The improvement of the accuracy of the kinetic model has a significant impact on the various functional effects that rely on the model. Therefore, how to obtain a higher-precision kinetic model has long been an important topic in the field of research and application, and has received extensive attention from researchers.

[0005] The robot arm has a variety of complex dynamic characteristics, including strong nonlinear effects such as friction, flexibility, hysteresis and motion errors. When performing dynamic modeling, it is crucial to fully consider these effects for the accuracy of the model. However, in the existing overall identification method modeling process, simplifications are usually made, such as approximating the nonlinear friction effect as a linear model of Coulomb plus viscous friction, and ignoring nonlinear effects such as joint flexibility, hysteresis and motion errors. Although this simplification improves the feasibility of modeling, it also causes the existence of unmodeled items in the dynamic model, resulting in a decrease in the accuracy of the model.

[0006] In addition, parameter identification is often required in the process of building a dynamic model, which places high demands on the quality of sensor sampling data. However, sensor measurement noise is unavoidable and is prone to outliers. At the same time, there is a large numerical difference in the torque of the front three joints of the robot arm compared to the rear three joints. The overall identification method usually uses the least squares (LS) to achieve parameter identification, and LS can only minimize the root mean square error (RMSE) in a statistical sense, which may affect the parameter accuracy of the dynamic model.

[0007] When the load at the end of the robot arm changes, or when parts wear out and age due to frequent use and long equipment life, the parameters of the dynamic model will change and the mismatch with the real parameters will increase. These changes further reduce the accuracy of the established dynamic model. Summary of the invention

[0008] The purpose of the embodiments of the present invention is to provide a dynamic modeling method, device and electronic device based on residual compensation, so as to improve the accuracy of the dynamic model.

[0009] In a first aspect, the present invention provides a dynamic modeling method based on residual compensation, the method comprising:

[0010] Construct a preliminary dynamic identification model containing the minimum inertial parameter set to be identified;

[0011] Acquire joint information of the robot arm, and perform parameter estimation on the minimum inertia parameter set to be identified based on the joint information and using iterative reweighted least squares method to determine the preliminary dynamic identification model;

[0012] According to the preliminary dynamics identification model, the robot arm is made to track a preset trajectory to obtain a residual torque data set and joint information;

[0013] Based on the residual torque data set and joint information, a dynamic residual model is constructed using a nonlinear dynamic sparse identification method;

[0014] The final kinetic model is obtained by combining the preliminary kinetic identification model and the kinetic residual model.

[0015] In an optional embodiment, the step of obtaining joint information of the robotic arm includes:

[0016] Designing an excitation trajectory, and optimizing the excitation trajectory;

[0017] The robot arm is controlled to track the optimized excitation trajectory, and the joint information of the robot arm is collected during the tracking process.

[0018] In an optional implementation, the step of optimizing the excitation trajectory includes:

[0019] A parameterized model of the excitation trajectory is constructed based on a finite Fourier series to characterize the corresponding relationship between the information of each joint of the robotic arm, wherein the decision variables of the excitation trajectory include an angular position offset, an amplitude of a sine function, and an amplitude of a cosine function;

[0020] Based on the robot arm workspace limitation, start-stop limitation and joint angle threshold limitation, a nonlinear optimization model for the decision variables is constructed;

[0021] Iteratively optimizing the nonlinear optimization model, and determining optimized decision variables based on the optimized nonlinear optimization model and the corresponding relationship;

[0022] The optimized incentive trajectory is obtained according to the optimized decision variables.

[0023] In an optional embodiment, the step of collecting various information of the robot arm during the tracking process includes:

[0024] Collecting the joint angular position, joint angular velocity and joint torque of each joint of the robotic arm during the tracking process;

[0025] Performing filtering processing on the joint angular position and the joint angular velocity based on a zero-phase Butterworth low-pass filter;

[0026] The joint angular acceleration is obtained by using the second-order central difference, forward difference and backward difference methods on the filtered joint angular velocity;

[0027] The joint torque is filtered based on a robust local weighted smoothing method.

[0028] In an optional embodiment, the step of estimating parameters of the minimum inertia parameter set to be identified based on the joint information and using iterative reweighted least squares method comprises:

[0029] Based on the preprocessed joint angular position, angular velocity, angular acceleration and motor output torque, the initial value of the minimum inertia parameter set is obtained by the least square method;

[0030] Obtaining an initial torque error vector based on the initial value of the minimum inertia parameter set obtained and the preliminary dynamic identification model;

[0031] Construct a weighting matrix based on the current moment error vector;

[0032] Adding the weighted matrix to the representation of the preliminary dynamic identification model, and using the weighted least square method to perform parameter estimation on the minimum inertia parameter set in the representation;

[0033] When the termination condition is reached, the termination condition is that the set number of iterations or the maximum value of the parameter change is less than the set threshold, the iteration is terminated and the identification value of the final minimum inertia parameter set is output. If the termination condition is not reached, the torque error vector is updated and the weighted least squares solution is iteratively calculated.

[0034] In an optional embodiment, after the step of determining the preliminary kinetic identification model, the method further comprises a step of verifying the preliminary kinetic identification model, which step comprises:

[0035] The robot arm is made to track an excitation trajectory based on finite Fourier series optimization or an arbitrary PTP trajectory, and the actual value of the joint torque during the tracking process is collected;

[0036] The theoretical value of the joint torque is calculated based on the preliminary dynamic identification model;

[0037] Based on the actual value of the joint torque and the theoretical value of the joint torque, an evaluation index value is calculated according to the set evaluation index, and verification of the preliminary dynamics identification model is achieved based on the evaluation index value.

[0038] In an optional embodiment, the step of constructing a dynamic residual model using a nonlinear dynamic sparse identification method based on the residual moment data set and the joint information includes:

[0039] The dynamic residual model is parameterized as a set of candidate functions characterized by joint information;

[0040] Constructing a sparse regression model based on the residual moment data set, the dynamic mapping result obtained by the preliminary dynamic identification model, and the candidate function set;

[0041] The sparse regression model is solved based on the sequential threshold least squares method, and the dynamic residual model is determined based on the candidate function set obtained by the solution.

[0042] In an optional embodiment, the step of parameterizing the dynamic residual model into a set of candidate functions represented by joint information comprises:

[0043] Based on the joint information, a constant term, a polynomial term, a sine function term and a cosine function term are obtained;

[0044] Construct a candidate function according to the constant term, the polynomial term, the sine function term and the cosine function term;

[0045] The dynamic residual model is constructed as a parameterized model characterized by a candidate function set consisting of multiple candidate functions.

[0046] In a second aspect, the present invention provides a dynamic modeling device based on residual compensation, the device comprising:

[0047] A first building module is used to build a preliminary dynamic identification model including a minimum inertial parameter set to be identified;

[0048] An estimation module, used for obtaining joint information of the robot arm, and performing parameter estimation on the minimum inertia parameter set to be identified based on the joint information and using an iterative reweighted least square method to determine the preliminary dynamic identification model;

[0049] An information acquisition module, used for preliminarily identifying a model according to the dynamics, and making the robot arm track a preset trajectory to obtain a residual torque data set and joint information;

[0050] A second construction module is used to construct a dynamic residual model based on the residual moment data set and joint information by adopting a nonlinear dynamic sparse identification method;

[0051] The model acquisition module is used to combine the preliminary dynamics identification model and the dynamics residual model to obtain the final dynamics model.

[0052] In a third aspect, the present invention provides an electronic device, comprising a memory and a processor, wherein the memory stores a computer program executable on the processor, and when the processor executes the computer program, the steps of the method described in any one of the aforementioned implementation modes are implemented.

[0053] The present invention provides a dynamic modeling method, device and electronic device based on residual compensation. By constructing a preliminary dynamic identification model containing a minimum inertia parameter set to be identified, after obtaining the joint information of the robot arm, the parameters are estimated based on the joint information and the iterative reweighted least squares method to determine the preliminary dynamic identification model. According to the preliminary dynamic identification model, the robot arm is made to track a preset trajectory to obtain a residual torque data set and joint information. Based on the residual torque data set and the joint information, a nonlinear dynamic sparse identification method is used to construct a dynamic residual model. The final dynamic model is obtained by combining the preliminary dynamic identification model and the dynamic residual model. In this solution, the iterative reweighted least squares method is used to realize parameter identification, which reduces the influence of numerical magnitude differences and outliers between the joints of the robot arm, improves the accuracy of the dynamic identification model, and is combined with the dynamic residual model constructed based on the nonlinear dynamic sparse identification method for compensation, thereby improving the accuracy of the final dynamic model. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments of the present invention are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0055] Figure 1 A flow chart of a dynamic modeling method based on residual compensation provided by an embodiment of the present invention;

[0056] Figure 2 for Figure 1 A flowchart of the sub-steps included in S12;

[0057] Figure 3 for Figure 2 A flowchart of the sub-steps included in S121;

[0058] Figure 4 for Figure 2 A flowchart of the sub-steps included in S122;

[0059] Figure 5 for Figure 1 Another flow chart of the sub-steps included in S12;

[0060] Figure 6 A flow chart of a verification method in a dynamic modeling method based on residual compensation provided in an embodiment of the present invention;

[0061] Figure 7 for Figure 1 A flowchart of the sub-steps included in S14;

[0062] Figure 8 for Figure 7 A flowchart of the sub-steps included in S141;

[0063] Fig. 9 A functional module block diagram of a dynamic modeling device based on residual compensation provided by an embodiment of the present invention;

[0064] Fig.10 This is a structural block diagram of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0065] The technical solutions in the embodiments of the present invention will be described below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0066] See also Figure 1, which is a flow chart of a dynamic modeling method based on residual compensation provided by an embodiment of the present invention, the dynamic modeling method based on residual compensation can be performed by a dynamic modeling device based on residual compensation, the dynamic modeling device based on residual compensation can be implemented by software and / or hardware, and can be configured in an electronic device, the electronic device can be a computer device, a server, a programmable logic controller, etc. The detailed steps of the dynamic modeling method based on residual compensation are introduced as follows.

[0067] S11, constructing a preliminary dynamic identification model including a minimum inertial parameter set to be identified.

[0068] S12, obtaining joint information of the robot arm, and performing parameter estimation on the minimum inertia parameter set to be identified based on the joint information and using an iterative reweighted least squares method to determine the preliminary dynamic identification model.

[0069] S13, preliminarily identifying the model based on the dynamics, and making the robot arm track a preset trajectory to obtain a residual torque data set and joint information.

[0070] S14, based on the residual torque data set and the joint information, a nonlinear dynamics sparse identification method is used to construct a dynamics residual model.

[0071] S15, combining the preliminary kinetic identification model and the kinetic residual model to obtain a final kinetic model.

[0072] The robot arm targeted by this embodiment can be but not limited to a six-joint robot arm. The overall idea of ​​the dynamic modeling method based on residual compensation provided by this embodiment is to first construct a preliminary dynamic identification model, which includes a minimum inertia parameter set to be identified. Therefore, it is necessary to perform parameter identification on the minimum inertia parameter set to determine the preliminary dynamic identification model. The method used for parameter identification is iterative reweighted least squares (IRLS), which considers a weighting matrix based on LS, and the weighting matrix is ​​composed of a moment error vector.

[0073] After the preliminary dynamics identification model is determined, the dynamics residual model needs to be determined. In this embodiment, the dynamics residual model is constructed by using the sparse identification of nonlinear dynamics (SINDy).

[0074] Finally, the dynamic residual model can be used to perform residual compensation on the basis of the preliminary dynamic identification model, so as to finally determine the dynamic model.

[0075] In this embodiment, in the step of constructing a preliminary dynamic identification model including a minimum inertial parameter set to be identified, linear parameterization of the dynamic model can be implemented based on SymPyBotics to construct the preliminary dynamic identification model. SymPyBotics is an open source Python library that is implemented based on SymPy (a symbolic mathematics library for Python) and can be used for symbolic derivation of robot kinematics and dynamics.

[0076] In this embodiment, the Coulomb-plus-viscosity linear friction model and the motor moment of inertia of each joint are considered in the modeling process. The minimum inertia parameter set is a vector containing multiple parameters, for example, it can contain 54 parameters. The form of the linear parameterized dynamic preliminary identification model can be shown as follows:

[0077] (1)

[0078] in, (In the six-joint scenario) are joint angular position, angular velocity and angular acceleration; is the regression matrix composed of measurable parameters; is the minimum inertial parameter set to be identified; is the measurable joint torque (i.e., the motor equivalent output torque, which is linearly mapped by the motor winding current in the present invention, as shown in the following formula).

[0079] (2)

[0080] In the formula, is the reduction ratio corresponding to each joint; is the motor torque coefficient corresponding to each joint; is the motor winding current.

[0081] On the basis of constructing the above preliminary dynamic identification model, it is necessary to identify the minimum inertia parameter set. Parameter estimation can be performed based on the obtained joint information of the robot arm and using IRLS.

[0082] Specifically, see Figure 2 In this embodiment, the step of obtaining the joint information of the robot arm can be implemented in the following manner:

[0083] S121, designing an excitation trajectory and optimizing the excitation trajectory.

[0084] S122, controlling the robotic arm to track the optimized excitation trajectory, and collecting information of each joint of the robotic arm during the tracking process.

[0085] In this embodiment, the excitation trajectory needs to be able to activate the dynamic characteristics of each joint of the robot arm as much as possible. Figure 3 , the optimization of the excitation trajectory can be achieved by:

[0086] S1211, constructing a parameterized model of the excitation trajectory based on a finite Fourier series to characterize the corresponding relationship with the information of each joint of the robotic arm, wherein the decision variables of the excitation trajectory include an angular position offset, an amplitude of a sine function, and an amplitude of a cosine function.

[0087] S1212: Based on the robot arm workspace limitation, start / stop limitation, and joint angle threshold limitation, a nonlinear optimization model for the decision variables is constructed.

[0088] S1213, iteratively optimizing the nonlinear optimization model, and determining optimized decision variables based on the optimized nonlinear optimization model and the corresponding relationship.

[0089] S1214, obtaining an optimized incentive trajectory according to the optimized decision variables.

[0090] In this embodiment, the parameterization of the excitation trajectory is achieved based on the finite Fourier series in the following manner to obtain a parameterized model:

[0091] (3)

[0092] In the formula, t represents time; the finite Fourier series is composed of the order Definition, represented by sin and cos functions, l Indicates the specified order , the angular frequency multiples of the sin function and cos function; is the angular position offset; is the fundamental frequency, and the excitation frequency The relationship is: ; is the order of the Fourier series; and are the amplitudes of the sine and cosine functions respectively.

[0093] The design of the excitation trajectory needs to ensure continuous excitation of the dynamic characteristics of the system of interest. For a nonlinear system such as a robotic arm, the requirement of large amplitude distribution should be met, that is, the range of motion of the robotic arm should be as large as possible. Therefore, it is necessary to optimize the parameters of the corresponding relationship between the above-mentioned characterization of the information of each joint of the robotic arm and the trajectory information. Among them, and is specified in advance, then the decision variables to be optimized in the incentive trajectory are trajectory information, including: , and Therefore, the number of decision variables to be optimized is .

[0094] In order to ensure that the robot arm can safely track the excitation trajectory, it is necessary to meet the robot arm workspace restrictions, start-stop restrictions and joint angle threshold restrictions. Among them, the start-stop restrictions include start-stop angle position, speed and acceleration restrictions, and the joint angle restrictions include joint angle position, speed and acceleration threshold restrictions. Therefore, in this embodiment, based on the constraints such as the robot arm workspace restrictions and start-stop restrictions, a nonlinear optimization problem as shown below is constructed:

[0095] (4)

[0096] In the formula, is the regression matrix condition number; and are the lower and upper limits of joint angular position, joint angular velocity and joint angular acceleration respectively; is the initial angular position of the joint; and They are the starting time and the ending time within a single excitation trajectory cycle respectively; is the Cartesian space position of the robot after forward kinematics calculation under the excitation trajectory, It is the working space of the robot arm.

[0097] In this embodiment, the nonlinear optimization problem constructed above is solved iteratively. During the solution process, a smaller excitation frequency can be set and the parallel computing of MATLAB can be used to speed up the iteration. Based on the joint information obtained in each round of iteration, combined with the corresponding relationship between the joint information and the trajectory information, the optimized trajectory information can be obtained. In this way, when the iteration termination condition is met, the final optimized trajectory information can be obtained, and then the final optimized excitation trajectory is determined. The excitation trajectory is the excitation trajectory of each joint of the robot arm, that is, the robot arm can control the operation of each joint according to the excitation trajectory.

[0098] In this embodiment, the URDF file of the robot arm can also be introduced to realize the feasibility verification of the excitation trajectory (body and environment collision analysis).

[0099] After obtaining the optimized excitation trajectory, the robot arm can be controlled to track the optimized excitation trajectory. Specifically, the excitation trajectory can be sent to each joint of the robot arm according to the control cycle, and the tracking can be achieved through servo control, and the information of each joint of the robot arm during the tracking process can be collected. Figure 4 In this embodiment, joint information can be collected in the following ways:

[0100] S1221, collecting the joint angular position, joint angular velocity and joint torque of each joint of the robot arm during the tracking process.

[0101] S1222, filtering the joint angular position and the joint angular velocity based on a zero-phase Butterworth low-pass filter.

[0102] S1223, the joint angular velocity after filtering is subjected to second-order central difference, forward difference and backward difference methods to obtain the joint angular acceleration.

[0103] S1224, filtering the joint torque based on a robust local weighted smoothing method.

[0104] In this embodiment, the joint angle position, joint angle velocity and motor winding current of each joint of the robot arm can be collected in real time during the tracking process. Based on the motor winding current, motor torque coefficient and joint reduction ratio and according to formula (2), the joint torque of each joint can be calculated.

[0105] For the joint angle position and joint angle velocity, a zero-phase Butterworth low-pass filter can be used for filtering. For the joint torque, a robust locally weighted scatterplot smoothing (RLOESS) method can be used for filtering.

[0106] In order to obtain the joint angular acceleration, the filtered joint angular velocity can be subjected to second-order central difference. At the same time, the missing values ​​corresponding to the start and stop moments of the joint can be calculated by forward and backward difference methods. The difference formula involved is as follows:

[0107] (5)

[0108] (6)

[0109] (7)

[0110] In the formula, for relative to In this example, To control the cycle, is the current sampling time, Represents the angular velocity mapping. At this time, the regression matrix in equation (1) can be constructed from the preprocessed data: and joint torque .

[0111] Based on the above, please refer to Figure 5 Based on the joint information obtained above, IRLS is used to estimate the minimum inertia parameter set to be identified. This can be achieved in the following ways:

[0112] S123, based on the preprocessed joint angle position, angular velocity, angular acceleration and motor output torque, an initial value of a minimum inertia parameter set is obtained by a least squares method.

[0113] S124, obtaining an initial torque error vector based on the obtained initial value of the minimum inertia parameter set and the preliminary dynamic identification model.

[0114] S125, constructing a weighting matrix according to the current torque error vector.

[0115] S126, adding the weighted matrix to the representation of the preliminary dynamic identification model, and using the weighted least square method to perform parameter estimation on the minimum inertia parameter set in the representation.

[0116] S127, if the termination condition is met, the termination condition is that the set number of iterations or the maximum value of the parameter change is less than the set threshold, then the iteration is terminated and the identification value of the final minimum inertia parameter set is output.

[0117] S128: If the termination condition is not met, the moment error vector is updated and the weighted least square solution is iteratively calculated. That is, the process returns to the above step S125 to iteratively calculate the weighted least square solution.

[0118] In this embodiment, the preliminary dynamic identification model described in formula (1) is expanded according to the time series to obtain the following form:

[0119] (8)

[0120] In the formula, is the regression matrix in The specific value of each sampling moment; is the total number of sampling moments. The matrix operation involved in the above formula is: , which is an overdetermined set of equations. Therefore, the minimum inertia parameter set to be identified can be obtained by LS solution: :

[0121] (9)

[0122] However, there is a large difference in the magnitude of the torque between the front three joints and the rear three joints of the robot arm, and outliers are likely to exist in the sampled data. The minimum inertia parameter set obtained by parameter estimation using formula (9) is In the above figure, the identification accuracy of the last three joints is poor. Moreover, LS can only minimize RMSE in a statistical sense. The identification results obtained have no substantial connection with the actual physical parameters and are sensitive to measurement noise, so the results are not accurate enough.

[0123] Based on this, in this embodiment, a logistic function with a normalization effect is introduced to achieve weighting, thereby reducing the impact of numerical magnitude and outliers. The weighting function is shown in formula (10):

[0124] (10)

[0125] In the formula, is the torque error vector, and its initial value is shown in formula (11); the Logistic function is an S-shaped function from 0 to 1.

[0126] (11)

[0127] The moment error vector described by equations (10) and (11) can form a weighted matrix , so as to realize the normalization of the data at each moment:

[0128] (12)

[0129] The above formula means that based on the motor output torque And the joint torque based on the dynamic preliminary identification model Get the torque error vector , and then the weighting matrix is ​​obtained based on the moment error vector according to formula (12).

[0130] The weighted least squares solution can be obtained from formula (12): On this basis, the weighted matrix is ​​added to the representation of the preliminary dynamic identification model to obtain the representation shown below. On this basis, IRLS updates Implement parameter identification.

[0131] (13)

[0132] Based on the minimum inertial parameter set obtained by identification, the final preliminary dynamic identification model can be determined. On this basis, please refer to Figure 6 In this embodiment, the preliminary dynamic identification model can also be verified, which can be achieved in the following ways:

[0133] S21, enabling the robot arm to track the excitation trajectory based on finite Fourier series optimization or an arbitrary PTP trajectory, and collecting the actual value of the joint torque during the tracking process.

[0134] S22, calculating and obtaining a theoretical value of the joint torque based on the preliminary dynamics identification model.

[0135] S23, based on the actual value of the joint torque and the theoretical value of the joint torque, and in accordance with the set evaluation index, an evaluation index value is calculated, and based on the evaluation index value, the preliminary dynamics identification model is verified.

[0136] In this embodiment, the preliminary dynamic identification model is verified to evaluate the accuracy of the identification result. Another excitation trajectory based on finite Fourier series optimization or an arbitrary PTP trajectory can be selected to control the robot to run according to the trajectory, and the joint torque during the operation of the robot is obtained as the actual value of the joint torque.

[0137] In addition, based on the dynamic preliminary identification model determined above, and in combination with the preprocessed joint angular position, joint angular velocity, joint angular acceleration and its minimum inertia parameter set, the joint torque is calculated according to the dynamic preliminary identification model as the theoretical value of the joint torque.

[0138] The actual value of the joint torque is compared with the theoretical value of the joint torque to achieve verification. In this embodiment, an evaluation index can be set, for example, RMSE and determination coefficient (R-Square, R 2 ) as evaluation indicators:

[0139] (14)

[0140] (15)

[0141] In the formula, is the first Theoretical value of joint torque at sampling moment; For the robot arm The actual value of the joint torque at the sampling moment.

[0142] The evaluation index value is calculated according to the set evaluation index, and the verification result of the preliminary kinetic identification model is obtained based on the evaluation index value. For example, when the evaluation index value meets the preset threshold, it can be determined that the preliminary kinetic identification model has been verified. Otherwise, it is determined that the preliminary kinetic identification model has not been verified, and the identification work needs to be redone.

[0143] After the preliminary kinetic identification model is constructed in the above manner and verified, the following kinetic residual model is constructed.

[0144] In this embodiment, based on the above-obtained preliminary dynamics identification model and the robot arm tracking the preset trajectory, the residual torque data set and joint information are obtained, wherein the residual torque data set refers to the residual torque data expanded in time series, and the residual torque data is obtained by subtracting the joint torque obtained based on the preliminary dynamics identification model and the actual joint torque of the collected robot arm. The joint information refers to the joint angular position, joint angular velocity and joint angular acceleration of the robot arm in the process of tracking the preset trajectory.

[0145] On this basis, see Figure 7 , a dynamic residual model can be constructed based on the residual moment dataset and joint information using SINDy in the following manner:

[0146] S141, parameterize the dynamic residual model into a set of candidate functions characterized by joint information.

[0147] S142, constructing a sparse regression model for the residual moment data set, the dynamic mapping result obtained by the preliminary dynamic identification model, and the candidate function set.

[0148] S143, solving the sparse regression model based on the sequential threshold least squares method, and determining the dynamic residual model based on the candidate function set obtained by the solution.

[0149] In this embodiment, a dynamic residual model is constructed based on SINDy. The inverse dynamics model of the robot arm can be described as:

[0150] (16)

[0151] In the formula, is the mapping relationship of the real inverse dynamics of the robot; are the parameters of the real inverse dynamics of the robot; are the joint angular position, joint angular velocity and joint angular acceleration respectively.

[0152] Equation (16) can also be described as the initial dynamics identification model obtained by the overall identification method superimposed on the unknown dynamics (i.e., the dynamics residual model):

[0153] (17)

[0154] In the formula, is the preliminary identification model of dynamics obtained by the overall identification method; To preliminarily identify the parameters of the model for dynamics; is the unknown residual dynamics; are the parameters of the residual dynamics.

[0155] The residual dynamics in Equation (17) can be approximated by a data-driven gray-box modeling method (i.e., SINDy). Compared with black-box modeling methods such as neural networks, SINDy requires less data and has certain robustness and physical interpretability. At the same time, it is more likely to achieve online approximation of residual dynamics. The principle of SINDy approximating residual dynamics is as follows:

[0156] (18)

[0157] In the formula, time is ignored for the sake of simplicity. ; is used to construct the residual dynamics Item candidate function; is the residual dynamics used to approximate the first joint No. The coefficients of the candidate functions; is the dynamic residual model of the first joint obtained by SINDy.

[0158] SINDy is based on the following assumptions: The governing equations of most nonlinear dynamic systems is determined by only a few important terms. Therefore, is a sparse vector.

[0159] In formula (18), The candidate functions form a candidate function library:

[0160] (19)

[0161] See also Figure 8 In this embodiment, the candidate functions constitute a candidate function set, and the candidate function set is constructed as follows:

[0162] S1411, obtaining a constant term, a polynomial term, a sine function term and a cosine function term based on the joint information.

[0163] S1412, constructing a candidate function according to the constant term, the polynomial term, the sine function term and the cosine function term.

[0164] S1413, constructing the dynamic residual model as a parameterized model represented by a candidate function set consisting of multiple candidate functions.

[0165] The selection of candidate functions is very flexible, and physical prior knowledge of the system can be incorporated to improve the accuracy of identification. If no prior knowledge is available, the candidate function can be composed of constant terms, polynomial terms, and trigonometric terms, as shown below:

[0166] (20)

[0167] In the formula, represents a constant term; Represented by The second-order polynomial is constructed. Similarly, the subscript P in the formula represents the order of the polynomial term; and Respectively represented by The sine function terms and the remainder function terms are formed.

[0168] In this way, the dynamic residual model can be constructed as a candidate function set consisting of multiple candidate functions after sparse processing. The corresponding time series data on both sides of formula (18) are collected and a sparse regression problem is constructed.

[0169] Then, the SINDy kinetic residual model can be obtained by solving the problem using the sequential threshold least squares method. At this time, equation (18) can be expressed in the following matrix form:

[0170] (twenty one)

[0171] In the formula, Represents the matrix formed by substituting the time series data represented by joint information into the candidate function set; Represents the sparse coefficient matrix of the candidate function set to be identified.

[0172] Finally, the solution of Eq. (21) is formulated as a sparse regression problem:

[0173] (twenty two)

[0174] In the formula, for The penalty term plays a role in sparseening the coefficients; is the regularization parameter used to adjust The penalty strength of the penalty term. The solution to the sparse regression problem uses the sequential threshold least squares method.

[0175] In this embodiment, the kinetic residual model can be determined based on the above method. Based on this, the kinetic residual model can be superimposed on the preliminary kinetic identification model to obtain the final kinetic model, which is in the following form:

[0176] (twenty three)

[0177] in, is the preliminary identification model of dynamics obtained by the overall identification method; is the above-mentioned dynamic residual model, The approximate form of For real dynamics.

[0178] In the dynamic modeling method based on residual compensation provided in this embodiment, when optimizing the excitation trajectory, a method using MATLAB parallel computing is proposed to improve the timeliness of the optimization process. At the same time, the constraints of the workspace are incorporated into the optimization problem and a collision analysis is performed on the optimized excitation trajectory, thereby improving the feasibility of the trajectory. In fact, the optimization of the excitation trajectory is easy to implement in the offline stage, but most of the optimized trajectories cannot be run in an actual robotic arm. From the survey, the existing references that use the overall identification method to implement dynamic modeling have not considered the timeliness and feasibility of excitation trajectory optimization.

[0179] From the actual test results, the optimization method of the excitation trajectory provided in this embodiment is basically consistent with the trajectory condition number generated by the existing mainstream method, and the feasibility of the generated excitation trajectory is greatly improved.

[0180] In addition, compared with the existing mainstream overall identification method based on LS to achieve parameter estimation, in this embodiment, the IRLS method based on the Logistic weighted function can reduce the impact of the magnitude of the torque of the front 3 joints and the rear 3 joints of the manipulator and the outliers in the sampling data, and can improve the parameter identification accuracy of the rear 3 joints. Finally, the accuracy of the preliminary dynamic identification model can be improved, thereby improving the effect of related functions that rely on the development of the dynamic model. The comparison of the prediction effect of RMSE and R2 of the preliminary dynamic identification model obtained based on LS and IRLS under two excitation trajectories is shown in Table 1. It can be seen from the table that on the verification excitation trajectory (corresponding to 2), the performance improvement (RMSE angle) of each joint of the IRLS-based identification model over that of LS is: 11.63%; 7.37%; 12.44%; 36.88%; 42.83%; 50.01%.

[0181] Table 1 Comparison data table

[0182]

[0183] In this embodiment, a method for constructing a dynamic residual model based on SINDy is proposed to compensate for the residual between the predicted torque and the actual torque in the preliminary dynamic identification model. SINDy is a gray box modeling method and can be used as a universal approximator, so it can be used to approximate the unmodeled items and parameter mismatch items in the dynamic model. A parameterized dynamic residual model can be obtained by SINDy, and the amount of data required is less than that of black box modeling methods such as neural networks, and online identification can be achieved. From the test results, within the range of the training data provided, SINDy can compensate for the dynamic residual well, and it can be used to improve the accuracy of the dynamic model for the robotic arm operating in fixed working conditions.

[0184] In summary, the dynamic modeling method based on residual compensation provided in this embodiment uses MATLAB parallel computing to improve the timeliness of the excitation trajectory optimization process, and performs collision analysis between the body and the environment based on URDF on the optimized excitation trajectory, thereby improving the feasibility of the trajectory.

[0185] In addition, an IRLS parameter identification method based on the Logistic weighted function was designed. This scheme reduces the influence of the magnitude of the torque of the front three joints and the back three joints of the manipulator and the outliers of the sampling data through the Logistic function, and improves the accuracy of the dynamic identification model.

[0186] Furthermore, a method for constructing a dynamic residual model based on SINDy is proposed. This scheme uses the SINDy gray-box modeling method to approximate the residual dynamics caused by unmodeled items and parameter mismatches, which can improve the accuracy of the dynamic model of the manipulator under fixed working conditions.

[0187] Based on the same inventive concept, please refer to Fig. 9 , an embodiment of the present invention further provides a functional module schematic diagram of a dynamic modeling device based on residual compensation. This embodiment can divide the functional modules of the dynamic modeling device based on residual compensation according to the above method embodiment. For example, each functional module can be divided according to each function, or two or more functions can be integrated into one processing module. The above integrated module can be implemented in the form of hardware or in the form of software functional modules. It should be noted that the division of modules in the embodiment of the present invention is schematic, which is only a logical functional division, and there may be other division methods in actual implementation.

[0188] For example, when each functional module is divided into corresponding functional modules, Fig. 9 The kinetic modeling device based on residual compensation shown is only a schematic diagram of the device. The kinetic modeling device based on residual compensation may include a first construction module, an estimation module, an information acquisition module, a second construction module and a model acquisition module. The functions of each functional module of the kinetic modeling device based on residual compensation are described in detail below.

[0189] A first building module is used to build a preliminary dynamic identification model including a minimum inertial parameter set to be identified;

[0190] An estimation module, used for obtaining joint information of the robot arm, and performing parameter estimation on the minimum inertia parameter set to be identified based on the joint information and using an iterative reweighted least square method to determine the preliminary dynamic identification model;

[0191] An information acquisition module, used for preliminarily identifying a model according to the dynamics, and making the robot arm track a preset trajectory to obtain a residual torque data set and joint information;

[0192] A second construction module is used to construct a dynamic residual model based on the residual moment data set and joint information by adopting a nonlinear dynamic sparse identification method;

[0193] The model acquisition module is used to combine the preliminary dynamics identification model and the dynamics residual model to obtain the final dynamics model.

[0194] It can be understood that the above-mentioned first building module, estimation module, information acquisition module, second building module and model acquisition module can be used to execute the above-mentioned S11 to S15. The detailed implementation method of the first building module, estimation module, information acquisition module, second building module and model acquisition module can refer to the relevant contents of the above-mentioned S11 to S15.

[0195] In a possible implementation, the estimation module may be used to:

[0196] Designing an excitation trajectory, and optimizing the excitation trajectory;

[0197] The robot arm is controlled to track the optimized excitation trajectory, and the joint information of the robot arm is collected during the tracking process.

[0198] In a possible implementation, the estimation module is specifically used for:

[0199] A parameterized model of the excitation trajectory is constructed based on a finite Fourier series to characterize the corresponding relationship between the information of each joint of the robotic arm, wherein the decision variables of the excitation trajectory include an angular position offset, an amplitude of a sine function, and an amplitude of a cosine function;

[0200] Based on the robot arm workspace limitation, start-stop limitation and joint angle threshold limitation, a nonlinear optimization model for the decision variables is constructed;

[0201] Iteratively optimizing the nonlinear optimization model, and determining optimized decision variables based on the optimized nonlinear optimization model and the corresponding relationship;

[0202] The optimized incentive trajectory is obtained according to the optimized decision variables.

[0203] In a possible implementation, the estimation module is specifically used for:

[0204] Collecting the joint angular position, joint angular velocity and joint torque of each joint of the robotic arm during the tracking process;

[0205] Performing filtering processing on the joint angular position and the joint angular velocity based on a zero-phase Butterworth low-pass filter;

[0206] The joint angular acceleration is obtained by using the second-order central difference, forward difference and backward difference methods on the filtered joint angular velocity;

[0207] The joint torque is filtered based on a robust local weighted smoothing method.

[0208] In a possible implementation, the estimation module may also be used for:

[0209] Based on the preprocessed joint angular position, angular velocity, angular acceleration and motor output torque, the initial value of the minimum inertia parameter set is obtained by the least square method;

[0210] Obtaining an initial torque error vector based on the initial value of the minimum inertia parameter set obtained and the preliminary dynamic identification model;

[0211] Construct a weighting matrix based on the current moment error vector;

[0212] Adding the weighted matrix to the representation of the preliminary dynamic identification model, and using the weighted least square method to perform parameter estimation on the minimum inertia parameter set in the representation;

[0213] When the termination condition is reached, the termination condition is that the set number of iterations or the maximum value of the parameter change is less than the set threshold, the iteration is terminated and the identification value of the final minimum inertia parameter set is output. If the termination condition is not reached, the torque error vector is updated and the weighted least squares solution is iteratively calculated.

[0214] In a possible implementation, the residual compensation-based dynamic modeling device further includes a verification module, which can be used to:

[0215] The robot arm is instructed to track an excitation trajectory based on finite Fourier series optimization or an arbitrary PTP trajectory, and actual values ​​of joint torques are collected during the tracking process; theoretical values ​​of joint torques are calculated based on the preliminary dynamics identification model;

[0216] Based on the actual value of the joint torque and the theoretical value of the joint torque, an evaluation index value is calculated according to the set evaluation index, and verification of the preliminary dynamics identification model is achieved based on the evaluation index value.

[0217] In a possible implementation, the second building block may be used to:

[0218] The dynamic residual model is parameterized as a set of candidate functions characterized by joint information;

[0219] Constructing a sparse regression model based on the residual moment data set, the dynamic mapping result obtained by the preliminary dynamic identification model, and the candidate function set;

[0220] The sparse regression model is solved based on the sequential threshold least squares method, and the dynamic residual model is determined based on the candidate function set obtained by the solution.

[0221] In a possible implementation, the second building block may be used to:

[0222] Based on the joint information, a constant term, a polynomial term, a sine function term and a cosine function term are obtained;

[0223] Construct a candidate function according to the constant term, the polynomial term, the sine function term and the cosine function term;

[0224] The dynamic residual model is constructed as a parameterized model characterized by a candidate function set consisting of multiple candidate functions.

[0225] See also Fig.10 , is a block diagram of an electronic device provided in an embodiment of the present invention, the electronic device may be a computer device, etc., and the electronic device includes a memory, a processor, and a communication module. The memory, the processor, and the communication module are electrically connected to each other directly or indirectly to achieve data transmission or interaction. For example, these components can be electrically connected to each other via one or more communication buses or signal lines.

[0226] The memory is used to store computer programs or data. The memory can be, but is not limited to, random access memory (RAM), read only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), etc.

[0227] The processor is used to read / write data or programs stored in the memory, and execute the dynamic modeling method based on residual compensation provided by any embodiment of the present invention.

[0228] The communication module is used to establish a communication connection between the electronic device and other communication terminals through the network, and is used to send and receive data through the network.

[0229] It should be understood that Fig.10The structure shown is only a schematic diagram of the structure of the electronic device. The electronic device may also include Fig.10 More or fewer components as shown, or with Fig.10 Different configurations are shown.

[0230] Furthermore, an embodiment of the present invention also provides a computer-readable storage medium, which stores machine-executable instructions. When the machine-executable instructions are executed, the dynamic modeling method based on residual compensation provided in the above embodiment is implemented.

[0231] Specifically, the computer-readable storage medium can be a general storage medium, such as a mobile disk, a hard disk, etc. When the computer program on the computer-readable storage medium is executed, the above-mentioned dynamic modeling method based on residual compensation can be executed. Regarding the process involved when the computer-readable storage medium and its executable instructions are executed, reference can be made to the relevant description in the above-mentioned method embodiment, which will not be described in detail here.

[0232] In summary, the dynamic modeling method, device and electronic device based on residual compensation provided by the embodiments of the present invention construct a preliminary dynamic identification model containing the minimum inertia parameter set to be identified, obtain the joint information of the robotic arm, and then perform parameter estimation based on the joint information and the iterative reweighted least squares method to determine the preliminary dynamic identification model. According to the preliminary dynamic identification model and by making the robotic arm track the preset trajectory, the residual torque data set and joint information are obtained, and the dynamic residual model is constructed based on the residual torque data set and joint information and the nonlinear dynamic sparse identification method. The final dynamic model is obtained by combining the preliminary dynamic identification model and the dynamic residual model. In this solution, the iterative reweighted least squares method is used to realize parameter identification, which reduces the influence of the numerical magnitude difference and outlier value between the joints of the robotic arm, improves the accuracy of the dynamic identification model, and is combined with the dynamic residual model constructed based on the nonlinear dynamic sparse identification method for compensation, thereby improving the accuracy of the final dynamic model.

[0233] In the embodiments provided by the present invention, it should be understood that the disclosed devices and methods can be implemented in other ways. The device embodiments described above are only schematic. For example, the division of the units is only a logical function division. There may be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some communication interfaces, and the indirect coupling or communication connection of devices or units can be electrical, mechanical or other forms.

[0234] In addition, the units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0235] Furthermore, the functional modules in the various embodiments of the present invention may be integrated together to form an independent part, or each module may exist independently, or two or more modules may be integrated to form an independent part.

[0236] It should be noted that if the function is implemented in the form of a software function module and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, server, or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM), random access memory (RAM), disk or optical disk, etc., various media that can store program codes.

[0237] In this document, relational terms such as first and second, etc. are used merely to distinguish one entity or operation from another entity or operation, but do not necessarily require or imply any such actual relationship or order between these entities or operations.

[0238] The above description is only an embodiment of the present invention and is not intended to limit the protection scope of the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A dynamic modeling method based on residual compensation, characterized in that: The method comprises: Construct a preliminary dynamic identification model containing the minimum inertial parameter set to be identified; Acquire joint information of the robot arm, and perform parameter estimation on the minimum inertia parameter set to be identified based on the joint information and using iterative reweighted least squares method to determine the preliminary dynamic identification model; According to the preliminary dynamics identification model, the robot arm is made to track a preset trajectory to obtain a residual torque data set and joint information; Based on the residual torque data set and joint information, a dynamic residual model is constructed using a nonlinear dynamic sparse identification method; Combining the preliminary kinetic identification model and the kinetic residual model to obtain a final kinetic model; The step of constructing a dynamic residual model based on the residual moment data set and joint information and using a nonlinear dynamic sparse identification method comprises: The dynamic residual model is parameterized into a candidate function set represented by joint information; a sparse regression model is constructed for the residual torque data set, the dynamic mapping results obtained by the preliminary dynamic identification model, and the candidate function set; the sparse regression model is solved based on the sequential threshold least squares method, and the dynamic residual model is determined based on the candidate function set obtained by the solution.

2. The dynamic modeling method based on residual compensation according to claim 1 is characterized in that: The step of obtaining the joint information of the robotic arm comprises: Designing an excitation trajectory, and optimizing the excitation trajectory; The robot arm is controlled to track the optimized excitation trajectory, and the joint information of the robot arm is collected during the tracking process.

3. The dynamic modeling method based on residual compensation according to claim 2 is characterized in that: The step of optimizing the excitation trajectory comprises: A parameterized model of the excitation trajectory is constructed based on a finite Fourier series to characterize the corresponding relationship between the information of each joint of the robotic arm, wherein the decision variables of the excitation trajectory include an angular position offset, an amplitude of a sine function, and an amplitude of a cosine function; Based on the robot arm workspace limitation, start-stop limitation and joint angle threshold limitation, a nonlinear optimization model for the decision variables is constructed; Iteratively optimizing the nonlinear optimization model, and determining optimized decision variables based on the optimized nonlinear optimization model and the corresponding relationship; The optimized incentive trajectory is obtained according to the optimized decision variables.

4. The dynamic modeling method based on residual compensation according to claim 2 is characterized in that: The step of collecting various information of the robot arm during the tracking process includes: Collecting the joint angular position, joint angular velocity and joint torque of each joint of the robotic arm during the tracking process; Performing filtering processing on the joint angular position and the joint angular velocity based on a zero-phase Butterworth low-pass filter; The joint angular acceleration is obtained by using the second-order central difference, forward difference and backward difference methods on the filtered joint angular velocity; The joint torque is filtered based on a robust local weighted smoothing method.

5. The dynamic modeling method based on residual compensation according to claim 1 is characterized in that: The step of estimating parameters of the minimum inertia parameter set to be identified based on the joint information and using iterative reweighted least squares method comprises: Based on the preprocessed joint angular position, angular velocity, angular acceleration and motor output torque, the initial value of the minimum inertia parameter set is obtained by the least square method; Obtaining an initial torque error vector based on the initial value of the minimum inertia parameter set obtained and the preliminary dynamic identification model; Construct a weighting matrix based on the current moment error vector; Adding the weighted matrix to the representation of the preliminary dynamic identification model, and using the weighted least square method to perform parameter estimation on the minimum inertia parameter set in the representation; When the termination condition is reached, the termination condition is that the set number of iterations or the maximum value of the parameter change is less than the set threshold, the iteration is terminated and the identification value of the final minimum inertia parameter set is output. If the termination condition is not reached, the torque error vector is updated and the weighted least squares solution is iteratively calculated.

6. The dynamic modeling method based on residual compensation according to claim 1 is characterized in that: After the step of determining the preliminary kinetic identification model, the method further comprises the step of verifying the preliminary kinetic identification model, which step comprises: The robot arm is made to track an excitation trajectory based on finite Fourier series optimization or an arbitrary PTP trajectory, and the actual value of the joint torque during the tracking process is collected; The theoretical value of the joint torque is calculated based on the preliminary dynamic identification model; Based on the actual value of the joint torque and the theoretical value of the joint torque, an evaluation index value is calculated according to the set evaluation index, and verification of the preliminary dynamics identification model is achieved based on the evaluation index value.

7. The dynamic modeling method based on residual compensation according to claim 1 is characterized in that: The step of parameterizing the dynamic residual model into a set of candidate functions represented by joint information comprises: Based on the joint information, a constant term, a polynomial term, a sine function term and a cosine function term are obtained; Construct a candidate function according to the constant term, the polynomial term, the sine function term and the cosine function term; The dynamic residual model is constructed as a parameterized model characterized by a candidate function set consisting of multiple candidate functions.

8. A dynamic modeling device based on residual compensation, characterized in that: The device is used to implement the dynamic modeling method based on residual compensation according to any one of claims 1 to 7, comprising: A first building module is used to build a preliminary dynamic identification model including a minimum inertial parameter set to be identified; An estimation module, used for obtaining joint information of the robot arm, and performing parameter estimation on the minimum inertia parameter set to be identified based on the joint information and using an iterative reweighted least square method to determine the preliminary dynamic identification model; An information acquisition module, used for preliminarily identifying a model according to the dynamics, and making the robot arm track a preset trajectory to obtain a residual torque data set and joint information; A second construction module is used to construct a dynamic residual model based on the residual moment data set and joint information by adopting a nonlinear dynamic sparse identification method; The model acquisition module is used to combine the preliminary dynamics identification model and the dynamics residual model to obtain the final dynamics model.

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program that can be run on the processor, characterized in that: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

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