Mechanical arm dynamic model construction method based on physical information and knowledge inspiration

Abstract

The invention relates to a mechanical arm dynamic model construction method based on physical information and knowledge inspiration, and the method comprises the steps: through a physical information knowledge base, a model internal structure priori framework, a data set, a neural network, a loss function and other module components, constructing a mechanical arm dynamic model in a structured and modularized neural network learning architecture; physical information and knowledge are integrated into a network topology structure and a calculation process to serve as model prior, and dependence on data is greatly reduced. A plurality of sub-neural networks are used for fitting unknown functions in the model, network trainable parameters are optimized and iterated on the basis of an easily obtained sampling data set and an optimized loss function, and a forward model and a reverse model can be obtained at the same time. The method inherits the strong expression ability of the neural network, the form is more universal, standardized and modularized, any rigid body system dynamic model with complete constraints can be learned, the physical rationality is ensured, and the method has the advantages of being small in modeling difficulty, explainable, high in precision, not prone to overfitting, high in training speed and the like.

Description

Technical Field

[0001] The present invention belongs to the field of robotics technology, and in particular relates to a method for constructing a mechanical arm dynamics model based on physical information and knowledge inspiration. Background Art

[0002] The rigid body system dynamics model is the basis for application scenarios such as system simulation verification and structural design optimization, motion control and trajectory optimization, fault diagnosis and maintenance. There are three main methods for establishing the rigid body system dynamics model: model engineering, data-driven system parameter identification, and neural network model learning:

[0003] 1) Model engineering requires the use of simulation software or physical measurements of the system's physical parameters such as mass, center of gravity, length, active force, dissipated force, etc. (physical measurements are more accurate because they contain deviations caused by the manufacturing process), and then use Newtonian mechanics, Lagrangian mechanics or Hamiltonian mechanics and the known prior structure of the system to derive and solve the rigid body dynamics equations. This method, at the cost of high-cost precise measurements and expert engineering efforts, can produce accurate forward and inverse models at the same time, but does not include situations where the physical mechanisms such as contact friction and multi-phase change interactions are not yet fully understood (or the generated model has large deviations from these situations), and the model is only applicable to the specific system derived.

[0004] 2) Data-driven system parameter identification is to learn model parameters from observation data rather than measurements, and it also requires the derivation of motion equations; assumptions or prior knowledge about the forces acting on the system in model engineering can be used to reduce the parameters that need to be learned. This type of method is much easier to model than model engineering, but it also requires the collection of good data to identify system parameters. In addition, the method has limited expressive power. For example, linear regression can only infer linear combinations of system parameters and cannot be used for closed-loop system dynamics.

[0005] 3) Neural network model learning (usually black box) does not require any knowledge about the system. This type of method uses an arbitrary function approximator - a neural network, such as a deep learning network, to optimize model parameters to fit a large amount of observational data. Only forward or inverse models can be obtained, which is not easy to integrate with existing control frameworks such as feedback linearization. The learned model has a good prediction effect on the training data (and its distribution), but its extrapolation and generalization ability is not as good as the model engineering method, and there is an overfitting (or large variance) problem; since it does not rely on the rigid body dynamics assumption, it can learn systems including contact.

[0006] Although the neural network (black box) model learning method has strong expressive power, it overemphasizes and relies on data and ignores the use of physical information and prior knowledge. For example, in the actual application of robot system dynamics modeling, a large amount of data is not feasible or economical, and instead it is often necessary to perform robust extrapolation from fewer samples (usually collected online in real time). Therefore, the existing technology has the following disadvantages in constructing rigid body system dynamics models: high cost of model construction, only applicable to the specific system derived, limited expressive power, overfitting of neural network models, ignoring the use of physical information and prior knowledge, and requiring a large amount of data training. Summary of the invention

[0007] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a method for constructing a robot arm dynamics model based on physical information and knowledge inspiration.

[0008] The purpose of the present invention can be achieved by the following technical solutions:

[0009] The present invention provides a method for constructing a mechanical arm dynamics model based on physical information and knowledge inspiration, and particularly relates to a learning architecture, module components and calculation process of a multi-degree-of-freedom mechanical arm dynamics forward and inverse model. The method comprises the following steps: using Lagrangian mechanics as the prior framework of the mechanical arm dynamics model, embedding the Euler-Lagrangian formula into the neural network learning architecture as the Lagrangian network, decomposing the generalized force into a dissipative force model in the form of a control affine, fitting the dissipative force model in the form of a control affine with a neural network, obtaining a forward model and an inverse model, defining the forward model residual as a loss function, obtaining a sampling data set through the angle and speed sensors deployed in each driver of the mechanical arm, optimizing and iteratively solving the trainable parameters of the neural network using the sampling data set and the loss function, and obtaining the optimized forward model and inverse model.

[0010] Furthermore, the Euler-Lagrange formula is:

[0011]

[0012] Where q is the generalized coordinate, is the generalized speed, is the generalized acceleration, L is the Lagrangian, P is the generalized force, M(q) is the inertia matrix, G(q) is the gravity term, C represents the force generated by the centripetal force and the Coriolis force, and L is the Lagrangian, which is the generalized coordinate q and the generalized velocity The function of L Lagrangian is:

[0013]

[0014] in, represents kinetic energy, V(q) represents potential energy; where M(q) is the inertia matrix which is symmetric and positive definite.

[0015] Furthermore, the Euler-Lagrange formula is embedded in the neural network learning architecture as a Lagrangian network, specifically using two sub-neural networks to approximate the unknown functions M(q) and G(q) in the model, and using the lower triangular matrix L(q) to represent M, M(q) and G(q) as follows:

[0016]

[0017] in, represents the estimator, θ and φ are the neural network weight parameters representing kinetic energy and potential energy.

[0018] Furthermore, the generalized force is decomposed into a dissipative force model of a control affine form, and the dissipative force model is:

[0019]

[0020] Among them, u is the control input, which is mapped into the corresponding generalized force through the input Jacobian matrix B(q), For other dissipative forces.

[0021] Furthermore, the use of a neural network to fit the dissipative force model of the affine form specifically includes: using two sub-neural networks to fit the Jacobian matrix B(q) in the dissipative force model with other dissipative forces Recorded as ω,ψ are generalized dissipative forces.

[0022] Furthermore, the forward model f is:

[0023]

[0024] The inverse model f -1 It is expressed as an estimator using the Euler-Lagrange formula.

[0025] Furthermore, the loss function may be:

[0026]

[0027] Among them, θ and φ are the neural network weight parameters representing kinetic energy and potential energy, ω and ψ are generalized dissipative forces, and θ, φω and ψ are learned using the observed time series results of generalized quantities as the data set. is the Mahalanobis norm, is the diagonal covariance matrix of the generalized acceleration.

[0028] Furthermore, the loss function may also be:

[0029]

[0030] in and It is obtained by solving the forward model f using the 4th-order Runge-Kutta method using a sampled data set.

[0031] Furthermore, the sampled data set includes generalized displacement and generalized velocity, which are obtained by sampling at time intervals using angle and speed sensors deployed on each driver of the robotic arm. The generalized displacement and generalized velocity are the angle and speed of each driving motor of the robotic arm.

[0032] Furthermore, the sampled data set and the loss function are used to optimize and iteratively solve the trainable parameters of the neural network, wherein the neural network includes a Lagrangian network and a dissipative force network, the Lagrangian network includes two sub-neural networks, the two sub-neural networks approximate the unknown functions M(q) and G(q) in the model, and the dissipative force network includes two sub-neural networks, the two sub-neural networks fit the Jacobian matrix B(q) in the dissipative force model and other dissipative force The dissipative force network can also continue to integrate prior knowledge of friction forces such as Coulomb friction and viscous friction to further constrain the dissipative force of the constructed robotic arm dynamics model.

[0033] Compared with the prior art, the present invention has the following advantages:

[0034] (1) The present invention uses physical information and knowledge to learn a discrete-time model of rigid body system dynamics based on a specific system state input sampling data set. The physical information and knowledge here are all physical principles and basic assumptions in the field of system dynamics, rather than specialized knowledge or expert experience about the modeled system, thereby greatly reducing the difficulty of modeling. Using the Euler-Lagrange formula as the prior framework of the internal structure of the dynamic model and integrating prior knowledge such as dissipative forces in the form of control affines, this method can decouple the forces generated by the Coriolis effect, potential field, control input, and dissipative sources, overcome the difficulties of high-cost precise measurement and high-cost expert engineering efforts in model engineering, greatly reduce dependence on data, and can better achieve a balance between calculation accuracy and calculation efficiency and model bias and model variance.

[0035] (2) The present invention is more universal, standardized, and modular in the neural network architecture and training process, inheriting the strong expressive ability of neural networks. It can learn any rigid body system dynamics model with complete constraints, including tree-shaped and closed-loop kinematics without being limited to multi-degree-of-freedom robotic arms, solving the problem of limited expressive ability of model engineering and system parameter identification methods, and ensuring physical rationality.

[0036] (3) The present invention is interpretable and weakly supervised. It can be trained with online samples collected in real time or offline data, has high data utilization, fast training speed, and can realize online learning. It is more robust and not prone to overfitting. Under the same data conditions, the model deviation of the black-box neural network model learning method is smaller than that of the black-box neural network model learning method by only using the physical information of the Euler-Lagrange formula as the intrinsic structure prior framework. It can also generate high-precision forward and inverse models at the same time, which is also not available in black-box neural network model learning.

[0037] (4) The present invention takes advantage of the integration of physical information and knowledge-inspired and discrete data-driven neural networks. In a structured and modular neural network learning architecture, physical information and knowledge are integrated into the network topology and computational process as model priors, which greatly reduces the dependence on data and can better achieve a balance between computational accuracy and efficiency and between model bias and variance. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 This is the overall architecture diagram of the present invention. DETAILED DESCRIPTION

[0039] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0040] Embodiment 1:

[0041] like Figure 1 As shown: In this embodiment, Lagrangian mechanics is used as the prior framework of the internal structure of the system dynamics model. More specifically, the Euler-Lagrangian formula with non-conservative forces and generalized coordinates is preferred. The Lagrangian quantity L used to describe the complete dynamics of a given system is the generalized coordinate q and the generalized velocity The function is usually chosen

[0042]

[0043] In the formula, represents kinetic energy, V(q) represents potential energy; where M(q) needs to be a symmetric and positive definite mass (inertia) matrix to ensure that non-zero velocities produce positive kinetic energy.

[0044] Using the calculus of variations, we can obtain the Euler-Lagrange formula

[0045]

[0046] Where P is the generalized force. Substituting into equation (1) and the conservative force G(q) = dV / dq, we get the second-order ordinary differential equation (ODE), namely the Euler-Lagrange formula:

[0047]

[0048] Where C represents the force generated by the centripetal force and the Coriolis force, and Using equation (2), any multi-rigid body mechanical system with complete constraints can be described, such as coupled pendulums, multi-DOF manipulators, parallel robots, etc.

[0049] In the present invention, the Euler-Lagrange formula is embedded into the (deep) neural network learning architecture, that is, physical information is encoded in the network topology, which not only ensures physical rationality - following the laws of physics (Lagrangian mechanics in this case) and the principle of conservation of energy, but also integrates available prior knowledge, which is generally physical principles and basic assumptions in the field of system dynamics rather than specific domain expertise or expert experience. Physical information and knowledge inspiration and data-driven neural networks (universal function approximators) complement each other and bring out the best in each other, thus bringing into play the integrated advantages of the two.

[0050] Several sub-neural networks are used to fit the unknown functions in the model (such as mass inertia matrix, conservative force, dissipative force, etc.), and the network trainable parameters are optimized and iteratively solved using sampling data sets (such as system state input data) and loss functions, so that forward and inverse models can be obtained at the same time.

[0051] Specifically, two sub-neural networks (Lagrangian networks) are used to approximate the unknown functions M(q) and G(q) in the model. By taking advantage of the symmetry of M and using the lower triangular matrix L(q) to represent M, the number of parameters can be reduced by half. Then,

[0052]

[0053] In the formula, represents the estimator, θ and φ are the corresponding neural network weight parameters. Here, it is necessary to ensure the symmetry and positive definiteness of M: ① Positive definiteness (i.e. ) ensures that M is reversible, and the resulting model can be used as a forward model. ② By expressing the matrix M as the product of a lower triangular matrix L (this condition only guarantees its symmetry and positive semi-determinism) and adding a non-negative linear offset ò to the diagonal elements, that is, M(q)=L(q)L(q) T+òI, which can ensure that M is positive definite for all generalized coordinate configurations. ③However, this parameterization method may be disadvantageous in numerical solution because the diagonals of all inputs for random weights are close to ò, which is harmful to the forward model. The inversion of small eigenvalues ​​of M will lead to the amplification of the control torque. Therefore, further, it can be achieved by inverting the diagonal l diag Before nonlinearization (non-diagonal elements use linear activation), add an offset constant α, that is, l diag =σ(l diag +α)+ò, the nonlinear activation σ can be preferably ReLu or Softplus, thus ensuring positive diagonals and positive eigenvalues. This transformation is not necessary to obtain a good model, but it balances the forward and inverse model losses.

[0054] The generalized force P is further decomposed into a dissipative force model that controls the affine form:

[0055]

[0056] In the formula, the control input u is mapped into the corresponding generalized force through the input Jacobian matrix B(q), while other dissipative forces are given by The generalized force in the control affine form is easy to use for feedback linearization control technology. Inverting B(q) will produce a linear control law. It is not difficult to find that F and B in equation (4) are similar to M and G in equation (2), and can also be fitted by two sub-neural networks (dissipative force networks), which are recorded as

[0057] Here, the generalized force utilizes prior knowledge, that is, it is decomposed into a control affine form and then fitted as an unknown function using a sub-neural network. It can also be input as sampling data through actual measurements without utilizing any physical information (of course, this will introduce more precise measurement work). It can also continue to integrate prior knowledge of friction such as Coulomb friction and viscous friction to further constrain the dissipative force of the modeled rigid body system.

[0058] At this point, it is not difficult to get the forward model f as

[0059]

[0060] Similarly, the inverse model f -1 It can be expressed as an estimate using formula (2).

[0061] The neural network parameters θ, φ representing kinetic and potential energy and ω, ψ representing generalized dissipative forces are learned using the observed time series results of generalized quantities as a dataset. The key to learning network parameters through optimization methods is to find the right loss function. Directly, the loss function can be chosen to minimize the residual of the Euler-Lagrange differential equation. For example, the loss function using the forward model residual is

[0062]

[0063] In the formula, is the Mahalanobis norm, is the diagonal covariance matrix of the generalized acceleration. Using the covariance is helpful for loss normalization because the magnitude of the residuals may vary between different generalized coordinate degrees of freedom. The loss function can also use the residuals of the forward model and the inverse model.

[0064] However, in practice, given a sampled discrete-time data set of system state changes

[0065]

[0066] Among them, q k , is the generalized displacement and generalized velocity at time t, u k is the driving control input at time t, q′ k , is the generalized displacement and velocity at time t′=t+Δt. Since it is digital sampling, Δt is constant here; N is the number of configuration points. The following loss function is usually preferred

[0067]

[0068] In the formula, and It is obtained by solving equation (5) using the fourth-order Runge-Kutta (RK4) method using the sample data set D. The advantages of using equation (7) instead of equation (6) are: 1) First, the acceleration It is often not measured directly, but estimated by finite difference approximation in practice, which amplifies the high-frequency noise in the data sample; while equation (7) does not require estimation As the regression target. 2) Secondly, it has been observed that minimizing the prediction error: Equation (7) is a better metric for optimizing the parameters of the dynamic model than aligning the acceleration predicted by the model with the acceleration estimated in the data: Equation (6). The disadvantage is that the computational effort of Equation (7) is a constant factor times that of Equation (6).

[0069] 4th-order Runge-Kutta method (RK4) prediction and The specific scheme is as follows: First, define the system state quantity Accordingly here, Calculate according to formula (5). Then the standard integral of RK4 is

[0070]

[0071] In addition, since the Lagrangian is not unique, adding a regularization term in the form of weight decay helps to obtain a unique solution. The Euler-Lagrange equation is invariant to linear transformations: if α is non-zero, L′=αL+β can still solve the original equation. Therefore, an additional weight regularization / penalty function term can be added to the original loss function, that is,

[0072]

[0073] In the formula, represents the loss function, Ω is the L of the neural network parameters 2 Norm.

[0074] Embodiment 2:

[0075] The parts not mentioned in this embodiment are the same as those in Embodiment 1.

[0076] The method of the present invention mainly involves a data set, a physical information knowledge base, a priori framework of the intrinsic structure of the dynamic model, and a neural network for fitting unknown functions in the model, including Lagrangian subnetworks and dissipative force subnetworks, as well as module components such as loss functions.

[0077] First, for a 6-DOF robot, q = [q 1 ,q 2 ,…,q 6 ]; the system state required in data set D The u used as the control input can be obtained by sampling at equal time intervals using sensors deployed on the robot arm when the robot arm executes the nominal trajectory. The method requires a small amount of data to train the neural network and has a high data utilization rate. It can be trained online with samples collected in real time or trained as an offline data set. Therefore, the data in the data set D can be provided to the required modules or components such as the neural network, the model's internal structure framework, and the loss function in an online or offline manner.

[0078] The physical information knowledge base is a module that stores and schedules the physical information or prior knowledge required by other module components. The physical information knowledge generally refers to the physical principles and basic assumptions in the field of system dynamics rather than specific domain expertise or expert experience, which greatly reduces the difficulty of modeling and makes this method widely applicable. Combined with the strong fitting ability of neural networks, it can learn any rigid body system dynamics model with complete constraints. Specifically:

[0079] In terms of the internal structure of the dynamic model, Lagrangian mechanics is used as the prior physical information of the internal structure of the learned model, that is, the Euler-Lagrangian formula with non-conservative forces and generalized coordinates is preferred, so that the system dynamics equation (2) can be obtained and the forward model f and the inverse model f can be easily derived.-1 The Hamiltonian mechanics principle can also be used. The advantage of Hamiltonian mechanics is that the inverse matrix can be obtained directly, and the disadvantage is that the momentum is difficult to observe directly.

[0080] In this embodiment, the generalized force utilizes prior knowledge, that is, it is decomposed into the control affine form (4), and the dissipative force sub-neural network is used to fit the unknown function. It can also be used as sampling data input through actual measurement without using any physical information (of course, this will introduce more precise measurement work). It can also continue to integrate prior knowledge of friction such as Coulomb friction and viscous friction to further constrain the dissipative force of the modeled rigid body system.

[0081] In terms of neural network topology, (1) this embodiment uses two sub-neural networks (i.e., Lagrangian networks) to approximate the unknown functions M(q) and G(q) in the model; it is also possible to choose to share some network parameters between the two sub-networks, because M and G follow the same physical principles (Lagrangian mechanics) and physical manifestations (both depend on q). (2) M is symmetric and positive definite: ① Positive definiteness (i.e., ) ensures that M is reversible, and the obtained model can be used as a forward model; ② Express the matrix M as the product of a lower triangular matrix L(q) (guaranteeing symmetry and reducing the number of parameters by half), and add a non-negative linear offset ò to the diagonal elements, that is, M = LL T +òI, ensuring the positive definiteness of M for all generalized coordinate configurations; ③ Preferably, further ensuring that M has positive diagonals and positive eigenvalues, by nonlinearizing the diagonal l diag And add a shift constant α, that is, l diag =σ(l diag +α)+ò to achieve the nonlinear activation σ, ReLu or Softplus can be preferred (non-diagonal elements use linear activation). (3) The generalized force P that controls the affine form also requires two sub-neural networks That is, the dissipative force network) to fit.

[0082] In the definition of the loss function, (1) directly, we can choose to minimize the residual of the Euler-Lagrange differential equation, such as the loss function of the forward model residual as shown in Equation (6), which is to align the acceleration predicted by the model with the acceleration estimated in the data. It is often not measured directly, but estimated by finite difference approximation in practice, which amplifies the high-frequency noise present in the data sample. (2) Preferably, the generalized coordinates and generalized velocities are aligned, that is, equation (7), which is a better indicator for the optimization of dynamic model parameters. and It is obtained by solving equation (5) based on the sampled data set D using the 4th-order Runge-Kutta method. (3) In addition, weight regularization or penalty function terms can be added to the above loss function, which helps to obtain a unique solution and improve the optimization iteration efficiency.

[0083] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of various equivalent modifications or substitutions within the technical scope disclosed by the present invention, and these modifications or substitutions should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A method for constructing a robot arm dynamics model based on physical information and knowledge inspiration, characterized in that: The following steps are involved: Lagrangian mechanics is used as the prior framework of the robot arm dynamics model, the Euler-Lagrangian formula is embedded in the neural network learning architecture as the Lagrangian network, the generalized force is decomposed into a dissipative force model in the control affine form, and the neural network is used to fit the dissipative force model in the control affine form to obtain the forward model and the inverse model. The forward model residual is defined as the loss function, and the sampling data set is obtained by deploying the angle and speed sensors of each drive of the robot arm. The sampling data set and the loss function are used to iteratively optimize the trainable parameters of the neural network to obtain the optimized forward model and inverse model.

2. A method for constructing a mechanical arm dynamics model based on physical information and knowledge inspiration according to claim 1, characterized in that: The Euler-Lagrange formula is: Among them, q is the generalized coordinate, is the generalized speed, is the generalized acceleration, L is the Lagrangian, P is the generalized force, M(q) is the inertia matrix, G(q) is the gravity term, C represents the force generated by the centripetal force and the Coriolis force, and L is the Lagrangian, which is the generalized coordinate q and the generalized velocity The function of L Lagrangian is: in, represents kinetic energy, V(q) represents potential energy; where M(q) is the inertia matrix which is symmetric and positive definite.

3. A method for constructing a mechanical arm dynamics model based on physical information and knowledge inspiration according to claim 1 or 2, characterized in that: The Euler-Lagrange formula is embedded in the neural network learning architecture as a Lagrangian network, specifically using two sub-neural networks to approximate the unknown functions M(q) and G(q) in the model, and using the lower triangular matrix L(q) to represent M, where M(q) and G(q) are: in, represents the estimator, θ and φ are the neural network weight parameters representing kinetic energy and potential energy.

4. The method for constructing a mechanical arm dynamics model based on physical information and knowledge inspiration according to claim 1, characterized in that: The generalized force is decomposed into a dissipative force model of a control affine form, and its dissipative force model is: Among them, u is the control input, which is mapped into the corresponding generalized force through the input Jacobian matrix B(q), For other dissipative forces.

5. A method for constructing a mechanical arm dynamics model based on physical information and knowledge inspiration according to claim 1 or 4, characterized in that: The method of using a neural network to fit the dissipative force model of the affine form specifically includes: using two sub-neural networks to fit the Jacobian matrix B(q) in the dissipative force model with other dissipative forces Recorded as ω,ψ are generalized dissipative forces.

6. The method for constructing a mechanical arm dynamics model based on physical information and knowledge inspiration according to claim 1, characterized in that: The forward model f is: The inverse model f -1 It is expressed as an estimator using the Euler-Lagrange formula.

7. The method for constructing a mechanical arm dynamics model based on physical information and knowledge inspiration according to claim 1, characterized in that: The loss function can be: Among them, θ and φ are the neural network weight parameters representing kinetic energy and potential energy, ω and ψ are generalized dissipative forces, and θ, φω and ψ are learned using the observed time series results of generalized quantities as the data set. is the Mahalanobis norm, is the diagonal covariance matrix of the generalized acceleration.

8. The method for constructing a mechanical arm dynamics model based on physical information and knowledge inspiration according to claim 1, characterized in that: The loss function can also be: in and It is obtained by solving the forward model f using the 4th-order Runge-Kutta method using a sampled data set.

9. The method for constructing a mechanical arm dynamics model based on physical information and knowledge inspiration according to claim 1, characterized in that: The sampled data set includes generalized displacement and generalized velocity, which are obtained by sampling at time intervals such as the rotation angle and rotation speed sensors deployed on each driver of the robotic arm. The generalized displacement and generalized velocity are the rotation angle and rotation speed of each drive motor of the robotic arm.

10. The method for constructing a mechanical arm dynamics model based on physical information and knowledge inspiration according to claim 1, characterized in that: The method uses a sampling data set and a loss function to optimize and iteratively solve the trainable parameters of the neural network, wherein the neural network includes a Lagrangian network and a dissipative force network, the Lagrangian network includes two sub-neural networks, the two sub-neural networks approximate unknown functions M(q) and G(q) in the model, and the dissipative force network includes two sub-neural networks, the two sub-neural networks fit the Jacobian matrix B(q) in the dissipative force model and other dissipative force The dissipative force network can also continue to integrate prior knowledge of friction forces such as Coulomb friction and viscous friction to further constrain the dissipative force of the constructed robotic arm dynamics model.

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