Mechanical arm model parameter identification method and system based on deep learning

Abstract

The invention relates to a mechanical arm model parameter identification method and system based on deep learning, and the method comprises the following steps: 1, converting a parameter identification problem of a space mechanical arm kinetic equation into a deep learning parameter identification problem, and designing a feedforward network approximate mass matrix; step 2, constructing a loss function to optimize a model parameter deep learning process of a mechanical arm kinetic equation; 3, realizing structure description of a network layer in deep learning; 4, performing fractional order optimization on the triangular matrix obtained in the step 1, and designing an activation function for the deep learning part; and 5, evaluating the performance of the deep learning algorithm on the mechanical arm parameter identification problem. According to the method, a system identification parameter set is simplified, and the number of identification parameters is reduced, so that the convergence speed of deep learning training is improved, the learning efficiency is enhanced, the high efficiency and precision of an algorithm are ensured, and the identification precision and generalization ability are improved.

Description

Technical Field

[0001] The present invention belongs to the fields of robotic arm dynamics, parameter identification, and intelligent learning, and particularly relates to a robotic arm model parameter identification method and system based on deep learning. Background Art

[0002] In the space environment, the reliability and stability of a space robotic arm are of great significance. The errors in the robotic arm model structure and sensor sampling errors are key interference factors affecting the design and implementation of control algorithms. In the space robotic arm control system, the sources of model structure errors are complex and many errors are difficult to effectively eliminate in practical applications. For example, as the execution time of space missions increases and the spacecraft fuel is consumed, the structure of the space robotic arm including the base may change, which not only affects the economy and operational performance of space mission execution but also poses a threat to the safety of the space robotic arm. These errors significantly affect the precise manipulation ability of the space robotic arm and pose a potential threat to the execution safety of space station maintenance, compliant capture, and other space missions. Traditional space robotic arm parameter identification methods often have high computational complexity, lack real-time performance and means for dealing with non-linear models, and are also relatively weak in data noise processing and environmental adaptation.

[0003] In recent years, deep learning algorithms have made significant progress in the field of robotics, demonstrating the powerful application potential of intelligent algorithms in this field and providing new ideas for the parameter identification of space robotic arm systems. Through large-scale data learning and feature extraction, deep learning can effectively overcome the limitations of traditional identification methods in high-dimensional system spaces. Compared with traditional control algorithms, deep learning shows more efficient capabilities in dealing with non-linear dynamic models and high-dimensional data, can effectively reduce the dependence on robotic arm model information, and efficiently utilize real-time data during task execution. Therefore, data-driven intelligent model identification methods have broad application prospects in the field of space robotic arms. However, single deep learning methods still have limitations and face several challenges in the parameter identification of space robotic arm models. Deep learning usually requires a large amount of computing resources and time, especially in complex systems such as space robotic arms. In addition, deep learning models lack physical interpretability of robotic arm models and are difficult to provide good generalization ability when facing data-driven identification tasks.

[0004] Although traditional parameter identification methods can reduce model errors through error source analysis and control strategy design, they still face problems such as high computational complexity and poor adaptability. Although existing deep learning-based parameter identification methods have strong data processing capabilities, their training process has a high time cost and the prediction performance and success rate need to be improved, and the identification accuracy and generalization ability have not been fully guaranteed. Therefore, there are still many challenges in the model parameter identification of space robotic arms in the prior art.

[0005] Based on this, taking the space manipulator system as the research background and analysis framework, there is an urgent need for a manipulator model parameter identification method and system based on deep learning, which indirectly identifies the system model parameters through deep learning and the characteristics of the manipulator system, overcoming the problem of insufficient identification accuracy of traditional deep learning. Summary of the Invention

[0006] In order to solve the problems of high complexity and poor adaptability of traditional identification methods, as well as the decline in efficiency and accuracy caused by excessive identification parameters in deep learning, the present invention proposes a manipulator model parameter identification method and system based on deep learning.

[0007] The present invention relates to a manipulator model parameter identification method based on deep learning, including the following steps:

[0008] Step 1: Convert the parameter identification problem of the space manipulator dynamics equation into a deep learning parameter identification problem, and design a feedforward network to approximate the mass matrix;

[0009] Step 2: Construct a loss function to optimize the deep learning process of the model parameters of the manipulator dynamics equation;

[0010] Step 3: Implement the structural description of the network layer in deep learning;

[0011] Step 4: Optimize the triangular matrix obtained in Step 1 by fractional order, and design an activation function for the deep learning part;

[0012] Step 5: Evaluate the performance of the deep learning algorithm in the manipulator parameter identification problem.

[0013] Further, in Step 1, the space manipulator dynamics equation is decomposed into the following form:

[0014]

[0015] where τ is the manipulator torque information, D(q) is its mass matrix, is the Coriolis force and centrifugal force matrix, are respectively the joint angle, angular velocity and angular acceleration of the manipulator;

[0016] The parameter identification problem of the manipulator dynamics equation is converted into a deep learning parameter identification problem by decomposing the mass matrix D(q) in the form of a positive definite symmetric matrix into the product of a triangular matrix L and its transpose;

[0017] Approximate the mass matrix by designing a feedforward network:

[0018]

[0019] where, represents an approximation of the mass matrix D(q), where φ are the network parameters, is an approximation of the original triangular matrix.

[0020] Furthermore, in step two, for the deep learning parameter identification problem proposed in step one, the loss function is constructed as follows:

[0021]

[0022] where φ * are the optimized parameters of φ; is the independent variable φ that minimizes the Loss function, that is, the parameter value φ needs to be found to minimize the value of the loss function Loss; the inverse approximation function is obtained from the function that maps the robotic arm dynamics function back to joint positions, velocities, and accelerations;

[0023] In the loss function, the inverse approximation function has the specific form:

[0024]

[0025] The function is described as a forward model and is expressed as follows:

[0026]

[0027] Furthermore, in step three, the differential form of the mass matrix D(q) is calculated as follows:

[0028]

[0029] The differential form of the triangular matrix L in the neural network is calculated as follows:

[0030]

[0031] where W i represents the node weight matrix, and b i represents the node bias vector;

[0032] For a given input d i-1 , the output d i of the i-th network layer is expressed as d i = f i (W i T d i-1 + b i ), where f i is a non-linear activation function, and the structure of the network layer in this deep learning algorithm is described as:

[0033]

[0034] Further, in step four, design the triangular matrix L and perform fractional-order optimization:

[0035]

[0036] where l d is a diagonal matrix, l t is a strictly lower triangular matrix, γ is an adjustable parameter, D is a fractional-order differential operator, α and β are adjustable fractional-order operators, L d and L t represent the fractional-ordered diagonal matrix and the strictly lower triangular matrix representation symbols.

[0037] Further, in step four, design the activation function σ′(x) of deep learning as:

[0038]

[0039] where η is an adjustable parameter, x is an independent variable, k1 and k0 are hyperparameters for biasing the activation function, and the function exp represents the natural exponential function.

[0040] Further, in step five, use the mean square error MSE as the core evaluation index for evaluating the network performance, define the mean square error of torque as an evaluation criterion for deep learning, and use τ MSE to represent it; at the same time, define the mean square error of energy as another evaluation criterion for deep learning, and use E MSE to represent it.

[0041] Further, in step five, design the calculation methods for the mean square error of energy and the mean square error of torque as follows:

[0042] E MSE = ∑(dEdt - dEdt real ) 2

[0043] τ MSE = ∑(τ cal - τ real ) 2 (11)

[0044] where τ cal is the fitted value calculated from the deep learning result, τ real is the true value filtered in the dataset, and dEdt are calculated from the training result, and dEdt real represents the true value of this calculation result in the dataset,

[0045] The present invention also relates to a system for a method of identifying parameters of a robotic arm model based on deep learning, the system including a computer module for running the method of identifying parameters of the robotic arm model based on deep learning.

[0046] Beneficial effects

[0047] Aiming at the problem of uncertainty of the robotic arm model, the present invention proposes a method and system for identifying parameters of a robotic arm model based on deep learning. According to the physical characteristics of the robotic arm dynamics equation, using the property that the mass matrix is symmetric positive definite, it is decomposed into the product of a triangular matrix and its transpose, and the indirect identification of the system model parameters is completed through deep learning. This method simplifies the system identification parameter set, reduces the number of identified parameters, thereby improving the convergence speed of deep learning training and enhancing the learning efficiency, ensuring the high efficiency and accuracy of the algorithm. This method overcomes the problem of insufficient identification accuracy of traditional deep learning and improves the identification accuracy and generalization ability.

[0048] In the deep learning process of the present invention, a fractional-order operator and an activation function are introduced, improving the learning accuracy of the model. The fractional-order operator is used to optimize the triangular matrix, and more adjustable parameters are used to adjust this data-driven parameter identification algorithm. The activation function proposed by the present invention has stronger non-linear characteristics, enabling the deep neural network to generate specific sequence characteristics, and more refined adjustments can be made when passed to the next layer, so that the network generates hierarchical sequence information, which is particularly suitable for parameter identification of strong non-linear robotic arm dynamics models. Description of the drawings

[0049] Figure 1 Schematic diagram of the robotic arm neural network structure of the present invention;

[0050] Figure 2 Schematic diagram of the deep learning robotic arm dynamics network of the present invention;

[0051] Figure 3 Schematic diagram of the application system for identifying parameters of the deep learning robotic arm dynamics of the present invention;

[0052] Figure 4 System flow chart of the system for the method of identifying parameters of a robotic arm model based on deep learning of the present invention;

[0053] Figure 5a For the data-driven model prediction of the present invention Schematic diagram of the effect with the matrix element being 1;

[0054] Figure 5b For the data-driven model prediction of the present invention Schematic diagram of the effect with the matrix element being 2;

[0055] Figure 6a For the data-driven model prediction of the present invention Schematic diagram of the effect when the matrix element is 1;

[0056] Figure 6b For the prediction of the data-driven model of the present invention Schematic diagram of the effect when the matrix element is 2;

[0057] Figure 7a Schematic diagram of the effect when the matrix element of G predicted by the data-driven model of the present invention is 1;

[0058] Figure 7b Schematic diagram of the effect when the matrix element of G predicted by the data-driven model of the present invention is 2;

[0059] Figure 8a Schematic diagram of the effect when the matrix element of τ predicted by the data-driven model of the present invention is 1;

[0060] Figure 8b Schematic diagram of the effect when the matrix element of τ predicted by the data-driven model of the present invention is 2. Detailed implementation manners

[0061] The following is a specific description of this implementation manner in combination with Figure 1 to 8.

[0062] The present invention relates to a method for identifying the parameters of a robotic arm model based on deep learning, including the following steps:

[0063] Step 1: Convert the parameter identification problem of the spatial robotic arm dynamics equation into a deep learning parameter identification problem, and design a feedforward network to approximate the mass matrix.

[0064] Decompose the spatial robotic arm dynamics equation into the following form:

[0065]

[0066] where τ is the robotic arm torque information, D(q) is its mass matrix, is the Coriolis force and centrifugal force matrix, are respectively the rotation angle, angular velocity and angular acceleration of the robotic arm joints;

[0067] Therefore, the parameter identification problem of the robotic arm dynamics equation can be solved by a deep learning parameter identification problem, that is, decompose the positive definite symmetric matrix form of the mass matrix D(q) into the product of a triangular matrix L and its transpose, and then complete the parameter identification of the dynamics equation composed of the triangular matrix L and its derivative through deep learning;

[0068] By using the deep learning method to approximate the parameters of the robotic arm dynamics equation, the network structure diagram is as Figure 1As shown, a feedforward network is designed to approximate the mass matrix. After its decomposition into the triangular matrix L correlation function, the neural network expression is as follows:

[0069]

[0070] Wherein, represents the approximation of the mass matrix D(q), φ is the network parameter, is the approximation of the original triangular matrix, which does not depend on the velocity and acceleration information of the robotic arm joints, and and

[0071] have no direct functional relationship. During the deep learning process, their operation processes are independent, thus not affecting the network learning ability.

[0072] Step 2: Construct a loss function to optimize the model parameters of the robotic arm dynamics equation in the deep learning process.

[0073] For the deep learning parameter identification problem proposed in Step 1, construct the following loss function:

[0074]

[0075] Wherein, φ * is the parameter after optimizing φ; is the independent variable φ that minimizes the Loss function, that is, it is necessary to find the parameter value φ to minimize the value of the loss function Loss; the inverse approximation function is obtained from the function that maps the robotic arm dynamics function back to the joint position, velocity, and acceleration.

[0076] This loss function is used to optimize the model parameters and improve the prediction accuracy. Its main role is to make the predicted output of the model close to the actual target value by adjusting the parameters of the model, and to improve the model generalization ability through loss function regularization. By monitoring the change of the loss function, the training process of the model can be effectively evaluated and adjusted.

[0077] In the loss function, the inverse approximation function is described by using the robotic arm dynamics equation, and the specific form is:

[0078]

[0079] This equation is used for the backpropagation calculation of the neural network. For the specific schematic diagram of the neural network structure, see Figure 2 .

[0080] For the obtained backpropagation function to is re-described as a forward model, and the specific form is as follows:

[0081]

[0082] Step 3. Implement the structural description of the network layer in deep learning.

[0083] In the process of parameter identification of the deep learning of the manipulator dynamics model, the differential form of the mass matrix D(q) is calculated as follows:

[0084]

[0085] The differential form of the triangular matrix L in the neural network is calculated as follows:

[0086]

[0087] Inside the specific network layer of this neural network, each network layer i consists of a linear transformation and a non-linear activation function, where W i represents the node weight matrix, and b i represents the node bias vector. For a given input d i-1 , the output d i of the i-th network layer is expressed as d i = f i (W i T d i-1 + b i ), where f i is the non-linear activation function. In this training process, the weight matrix W i and the bias vector b i are adjusted through an optimization algorithm to minimize the prediction error of the network. The triangular matrix L can be deduced backward through the chain rule. The propagation process of the network layer of this deep learning method can be described by the following formula:

[0088]

[0089] Among them, the triangular matrix L can be deduced by the chain rule. In the actual calculation process, the update of these parameters is completed through the backpropagation algorithm. Once these parameters complete the numerical calculation after training, they will remain unchanged in the test or deployment phase, so they are called time-invariant parameters. The flowchart of the manipulator dynamics model parameter identification system based on deep learning proposed by the present invention is as Figure 3 shown.

[0090] Step 4. Perform fractional-order optimization on the triangular matrix obtained in Step 1 and design an activation function for the deep learning part.

[0091] Design the triangular matrix L and perform fractional-order optimization:

[0092]

[0093] where $l$ d is a diagonal matrix, $l$ t is a strictly lower triangular matrix, $\gamma$ is an adjustable parameter, $D$ is a fractional differential operator, $\alpha$ and $\beta$ are adjustable fractional order operators, $L$ d and $L$ t represent the fractional diagonal matrix and the strictly lower triangular matrix representation symbols;

[0094] Design the activation function $\sigma'(x)$ of deep learning as:

[0095]

[0096] where $\eta$ is an adjustable parameter, $x$ is the independent variable, $k_1$ and $k_0$ are hyperparameters for biasing the activation function, and the function $\exp$ represents the natural exponential function; this activation function can significantly improve the expression ability and flexibility of the model, has strong non - linear characteristics, and can generate sequence features layer by layer. By introducing non - linear transformation, the multi - layer neural network can construct a highly complex decision boundary, improve the accuracy of model learning, and is suitable for the robotic arm model with strong non - linear characteristics.

[0097] Step Five: Evaluate the performance of the deep - learning algorithm in the robotic arm parameter identification problem.

[0098] Adopt the Mean Squared Error (MSE) as one of the core evaluation indicators for evaluating the network performance. MSE is a commonly used regression loss function, which calculates the evaluation criterion by calculating the average of the squared differences between the predicted value and the true value, and has the characteristics of intuitiveness, small computational complexity, and easy to understand. The mean squared error MSE, as a key indicator for evaluating the performance of the learning network, measures the accuracy of the network by calculating the average squared error between the predicted value and the true value.

[0099] Define the mean squared error of torque as an evaluation criterion for deep learning, denoted by $\tau$ MSE ; at the same time, define the Energy Mean Squared Error (EMSE) of energy as another evaluation criterion for deep learning, denoted by $E$ MSE . Among these two indicators, the mean squared error of torque measures the deviation degree of the output torque of the dynamic equation of the final result identified by the algorithm, and the energy mean squared error can measure the energy consumption of the identified model when the robotic arm is performing tasks.

[0100] Combining the mean squared error of torque, the mean squared error of energy, and the unit calculation time of deep learning, the performance and performance of this deep - learning model in robotic arm parameter identification can be evaluated from different dimensions, providing effective guidance for the training and optimization of the model. The calculation methods of the mean squared error of energy and the mean squared error of torque are designed as follows:

[0101]

[0102] Among them, τ cal is the fitting value calculated from the deep learning result, and τ real is the true value after filtering in the dataset. and dEdt are calculated from the training result, and dEdt real represents the true value of this calculation result in the dataset.

[0103] The algorithm system flow chart of the present invention is as Figure 4 shown.

[0104] The present invention also relates to a system for identifying the parameters of a robotic arm model based on deep learning, and the system includes a computer module for running the method for identifying the parameters of the robotic arm model based on deep learning.

[0105] Embodiment

[0106] According to the specific implementation manner, the algorithm of the present invention is trained and tested in a simulation environment. To verify the effectiveness of the algorithm, the prediction results of the data-driven model are compared, and the algorithm metrics are compared and evaluated.

[0107] Step 1: Convert the parameter identification problem of the spatial robotic arm dynamics equation into a deep learning parameter identification problem, and design a feed-forward network to approximate the mass matrix;

[0108] The spatial robotic arm dynamics equation is decomposed into the following form:

[0109]

[0110] Among them, τ is the robotic arm torque information, D(q) is its mass matrix, is the Coriolis force and centrifugal force matrix, are respectively the joint angle, angular velocity and angular acceleration of the robotic arm;

[0111] Converting the parameter identification problem of the robotic arm dynamics equation into a deep learning parameter identification problem is to decompose the mass matrix D(q) in the form of a positive definite symmetric matrix into the product of a triangular matrix L and its transpose;

[0112] Approximate the mass matrix by designing a feed-forward network:

[0113]

[0114] Among them, represents the approximation of the mass matrix D(q), φ is the network parameter, is the approximation of the original triangular matrix.

[0115] Step 2: Construct a loss function to optimize the model parameters in the deep learning process of the robotic arm dynamics equation;

[0116] For the deep learning parameter identification problem proposed in Step 1, construct the following loss function:

[0117]

[0118] where φ * is the optimized parameter of φ; is the independent variable φ that minimizes the Loss function, that is, it is necessary to find the parameter value φ to minimize the value of the loss function Loss; the inverse approximation function is obtained from the function that maps the robotic arm dynamics function back to joint position, velocity, and acceleration;

[0119] The inverse approximation function in the loss function The specific form is:

[0120]

[0121] Describe the function as a forward model, which is expressed as follows:

[0122]

[0123] Step 3: Implement the structural description of the network layer in deep learning;

[0124] In the deep learning parameter identification process of this robotic arm dynamics model, the differential form of the mass matrix D(q) is calculated as follows:

[0125]

[0126] The differential form of the triangular matrix L in the neural network is calculated as follows:

[0127]

[0128] Inside the specific network layer of this neural network, each network layer i consists of a linear transformation and a non-linear activation function, where W i represents the node weight matrix, and b i represents the node bias vector. For a given input d i-1 , the output d i of the i-th network layer is expressed as d i = f i (W i T d i-1 + b i ), where f iis a non-linear activation function. During this training process, the weight matrix W is adjusted through an optimization algorithm i and the bias vector b i to minimize the prediction error of the network. Through the chain rule, the triangular matrix L can be deduced backwards. The propagation process of the network layer in this deep learning method can be described by the following formula:

[0129]

[0130] where the triangular matrix L can be deduced by the chain rule. In the actual calculation process, the update of these parameters is completed through the backpropagation algorithm. Once these parameters complete the numerical calculation after training, they will remain unchanged during the testing or deployment phase, so they are called time-invariant parameters. The flow chart of the robotic arm dynamics model parameter identification system based on deep learning proposed by the present invention is as Figure 3 shown

[0131] Step 4: Perform fractional-order optimization on the triangular matrix obtained in Step 1, and design an activation function for the deep learning part;

[0132] Design the triangular matrix L and perform fractional-order optimization:

[0133]

[0134] where l d is a diagonal matrix, l t is a strictly lower triangular matrix, γ is an adjustable parameter, D is a fractional-order differential operator, α and β are adjustable fractional-order operators, L d and L t represent the fractional-ordered diagonal matrix and the strictly lower triangular matrix representation symbols;

[0135] In this embodiment, γ = 0.92, α = 0.7, and β = 0.9.

[0136] Design an activation function to enhance the non-linear mapping ability. The activation function proposed by the present invention is:

[0137]

[0138] where η is an adjustable parameter, x is the independent variable, and the function exp represents the natural exponential function. k1 and k0 are hyperparameters used to bias the activation function. η is 20, k0 is 0.1, and k1 is 1. This activation function can significantly improve the expression ability and flexibility of the model, has strong non-linear characteristics, and can generate sequence features layer by layer. By introducing non-linear transformation, the multi-layer neural network can construct a highly complex decision boundary, improve the accuracy of model learning, and is applicable to the robotic arm model with strong non-linear characteristics.

[0139] During the deep learning training process, it is necessary to select the angle, speed, acceleration, and torque information of the physical two-link space manipulator to form a data set, constituting 17 data sets. Among them, 16 are used for training, and 1 is used for data fitting analysis to train the results.

[0140] To verify the designed activation function and the effectiveness of the deep learning identification algorithm proposed in this patent, experiments are also designed to compare the performance with other common activation functions (such as Softplus, ReLU, linear activation functions, etc.) and the standard Feed-Forward Neural Network (FFNN). Under the same model, the improved Softplus activation function performs better than other activation functions, and the comparison results are shown in Table 1.

[0141] Table 1 Comparison of activation function effects

[0142] Activation function or algorithm Mean square error of torque Mean square error of energy Unit calculation time (s / Hz) Improved Softplus 1.138·10^-2 2.285·10^-2 6.465·10^-4 / 1187.6 Softplus 5.932·10^-2 7.690·10^-1 7.473·10^-4 / 1436.1 ReLU 6.122·10^-2 1.619 7.846·10^-4 / 1473.9 Linear activation function 5.356·10^-1 1.174 7.291·10^-4 / 1256.2

[0143] Through the comparison of the data in Table 1, the improved Softplus activation function shows lower index errors within similar calculation cycles, indicating its better performance. Nonlinear activation functions help alleviate the problems of gradient disappearance and gradient explosion, making the deep learning model easier to train and converge.

[0144] Step 5: Evaluate the performance of the deep learning algorithm in the problem of manipulator parameter identification.

[0145] The Mean Squared Error (MSE) is used as one of the core evaluation indicators to evaluate the network performance. MSE is a commonly used regression loss function, which calculates the evaluation standard by calculating the average of the squared differences between the predicted values and the true values, and has the characteristics of intuitiveness, small computational complexity, and easy to understand. The mean squared error MSE is used as a key indicator to evaluate the performance of the learning network, and it measures the accuracy of the network by calculating the average squared error between the predicted values and the true values.

[0146] Define the mean squared error of torque as an evaluation criterion for deep learning, denoted by τ MSE ; at the same time, define the mean squared error of energy as another evaluation criterion for deep learning, denoted by E MSE . Among these two indicators, the mean squared error of torque measures the deviation degree of the output torque of the dynamics equation of the final result identified by the algorithm, and the mean squared error of energy can measure the energy consumption of the identification model when the manipulator performs tasks.

[0147] Combining the mean square error of torque, the mean square error of energy, and the deep learning unit calculation time, the performance and performance of the deep learning model in the robotic arm parameter identification can be evaluated from different dimensions, providing effective guidance for the training and optimization of the model. The calculation methods for the mean square error of energy and the mean square error of torque are designed as follows:

[0148]

[0149] where τ cal is the fitted value calculated from the deep learning result, and τ real is the true value filtered in the dataset. and dEdt are calculated from the training results. dEdt real represents the true value of the calculation result in the dataset.

[0150] The algorithm system flow chart of the present invention is as shown in Figure 4 shown.

[0151] By calculating the energy error of the robotic arm and avoiding system instability caused by over-driving, the performance of the deep learning model in the robotic arm parameter identification can be more comprehensively evaluated in different dimensions, providing effective guidance for the training and optimization of the model, which is of great significance for ensuring the stable movement of the robotic arm and preventing over-driving.

[0152] For generality analysis, a deep learning network containing the parameter ζ is added in the training process of the present invention to identify the parameter of the mass matrix G. To facilitate the comparison of the parameter matrices of the robotic arm dynamics system, the robotic arm mass matrix, the Coriolis force and centrifugal force matrix, and the combination of joint velocity and acceleration are selected in the designed comparative experiment for G and the output torque as the final comparison indicators. After the training is completed, the comparison results of the prediction samples are shown in Figures 6, 7, and 8. The subscript est in the figure is the predicted value, which is used for comparison with the true value represented by the subscript d.

[0153] The comparison of the identification results shows that in the dynamic prediction model of the robotic arm, the prediction error of the product of the mass matrix and the joint acceleration is between 0.28 Nm and 0.41 Nm ( Figure 5a and 5b) The prediction errors of the Coriolis force and the centrifugal force multiplied by the joint velocity are from 0.23 Nm to 0.11 Nm, the prediction error of the output torque is within 0.42 Nm to 0.51 Nm, and the prediction error of the mass matrix term G is within 0.009 Nm to 0.04 Nm. This indicates that the data-driven deep learning identification method proposed in this patent can identify the parameters of the robotic arm dynamics model with high precision. Considering factors such as the universality of the robotic arm model, the deep learning method constructed in this comparative experiment includes a network for identifying the mass matrix term G, but it is generally a linear network and is independent and does not affect the learning network for data-driven identification of the triangular matrix L of the main body of the robotic arm dynamics model. Analyzing the simulation experiment, the following conclusions can be drawn: In the spatial robotic arm model sampled on the air-bearing platform, the algorithm proposed in this patent can successfully identify that the mass matrix term G of the robotic arm is close to the zero matrix, further demonstrating the innovation of the model-driven robotic arm deep learning parameter identification algorithm proposed in this patent.

[0154] To further verify the effectiveness of the algorithm proposed in this patent, a comparative experiment was conducted using an unoptimized deep learning parameter identification algorithm and a traditional feedforward neural network, with the mean squared error and sampling time efficiency as the main evaluation indicators. Table 2 summarizes the comparison results:

[0155] Table 2 Summary Evaluation Comparison Table of Algorithm Metrics.

[0156] List of algorithms Mean square error of torque Mean square error of energy Unit calculation time (s / Hz) Method proposed in this patent 1.138·10^-2 2.285·10^-2 6.465·10^-4 / 1187.6 Triangular matrix identification method 1.189·10^-2 2.088·10^-1 8.855·10^-4 / 1022.8 Triangular matrix identification without filtering 9.570·10^-1 3.462·10^1 7.228·10^-4 / 1245.3 Linear activation function 6.693·10^2 2.456·10^2 7.125·10^-4 / 1257.7

[0157] Analyzing the comparison results shows that compared with traditional deep learning and deep learning algorithms based on the triangular matrix of robotic arm dynamics, the data-driven robotic arm dynamics parameter identification method proposed in this patent exhibits significant advantages in terms of identification accuracy under similar training speeds and the same dataset conditions. On the premise of ensuring the consistency of the sample size, the deep learning parameter identification method proposed in this invention is superior to other comparison methods in terms of both the mean squared error and the robotic arm energy error indicators. Compared with the feedforward neural network, the method proposed in this invention solves the problem of the dataset tending to overfit and shows smaller errors and higher stability in terms of error tracking ability.

[0158] The above content of this invention is only the preferred embodiment of this invention and is not used to limit the implementation of this invention. Those of ordinary skill in the art can easily make corresponding adaptations or modifications according to the main concept and spirit of this invention. Therefore, the protection scope of this invention should be subject to the protection scope required by the claims.

Claims

1. A method for identifying the parameters of a robotic arm model based on deep learning, characterized in that It includes the following steps: Step 1: Transform the parameter identification problem of the space manipulator dynamics equation into a deep learning parameter identification problem, and design a feedforward network to approximate the mass matrix; Step 2: Construct a loss function to optimize the deep learning process of the model parameters of the manipulator dynamics equation; Step 3: Implement the structural description of the network layer in deep learning; Step 4: Perform fractional-order optimization on the triangular matrix obtained in Step 1, and design an activation function for the deep learning part; Step 5: Evaluate the performance of the deep learning algorithm in the manipulator parameter identification problem.

2. The method for identifying the parameters of the robotic arm model based on deep learning according to claim 1, wherein, In Step 1, the space manipulator dynamics equation is decomposed into the following form: where τ is the manipulator torque information, D(q) is its mass matrix, is the Coriolis and centrifugal force matrix, q, are respectively the rotation angle, angular velocity and angular acceleration of the manipulator joints; The transformation of the parameter identification problem of the manipulator dynamics equation into a deep learning parameter identification problem is to decompose the mass matrix D(q) in the form of a positive definite symmetric matrix into the product of a triangular matrix L and its transpose; Approximate the mass matrix by designing a feedforward network: Among them, represents an approximation of the mass matrix D(q), and φ are the network parameters, is an approximation of the original triangular matrix.

3. The method for identifying the parameters of the robotic arm model based on deep learning according to claim 1, wherein In Step 2, for the deep learning parameter identification problem proposed in Step 1, construct the following loss function: Among them, φ * is the parameter after φ optimization; is the independent variable φ that minimizes the Loss function, that is, it is necessary to find the parameter value φ to minimize the value of the loss function Loss; the inverse approximation function is obtained from the function that maps the manipulator dynamics function back to the joint position, velocity, and acceleration; Inverse approximation function in the loss function The specific form is as follows: The function is described as a forward model as follows:

4. The method for identifying the parameters of the robotic arm model based on deep learning according to claim 1, wherein In Step 3, the differential form of the mass matrix D(q) is calculated as follows: The differential form of the triangular matrix L in the neural network is calculated as follows: Among them, W i represents the node weight matrix, and b i represents the node bias vector; For a given input d i-1 , the output d i of the i-th network layer is expressed as d i = f i (W i T d i-1 + b i ), where f i is a non-linear activation function, and the structure of the network layer in this deep learning algorithm is described as:

5. The method for identifying the parameters of the robotic arm model based on deep learning according to claim 1, characterized in that, In Step 4, design the triangular matrix L and perform fractional-order optimization: Among them, l d is a diagonal matrix, l t is a strictly lower triangular matrix, γ is an adjustable parameter, D is a fractional differential operator, α and β are adjustable fractional operators, L d and L t represent the fractionalized diagonal matrix and the strictly lower triangular matrix representation symbols.

6. The method for identifying the parameters of the robotic arm model based on deep learning according to claim 5, wherein In Step 4, design the activation function σ′(x) of deep learning as: where η is an adjustable parameter, x is an independent variable, k1 and k0 are hyperparameters for biasing the activation function, and the function exp represents the natural exponential function.

7. The method for identifying the parameters of the robotic arm model based on deep learning according to claim 6, wherein In step five, the mean square error (MSE) is used as the core evaluation index for assessing the network performance. The mean square error of torque is defined as an evaluation criterion for deep learning, denoted by τ MSE ; meanwhile, the mean square error of energy is defined as another evaluation criterion for deep learning, denoted by E MSE for representation.

8. The method for identifying the model parameters of a manipulator based on deep learning according to claim 7, wherein In Step 5, design the calculation methods for the mean square error of energy and the mean square error of torque as follows: Among them, τ cal is the fitted value calculated from the deep learning result, and τ real is the true value after filtering in the dataset. and dEdt are calculated from the training result, and dEdt real represents the true value of this calculation result in the dataset.

9. A system for implementing the method for identifying the model parameters of a manipulator based on deep learning according to any one of claims 1 to 8, the system including a computer module for running the method for identifying the model parameters of a manipulator based on deep learning.

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