Construction method of robot dynamics physical information prediction neural network based on motor and external force coupling

Abstract

The application discloses a robot dynamics physical information prediction neural network construction method based on motor and external force coupling and relates to the technical field of robots. The method comprises the following steps: embedding a motor dynamics equation into a DeLaN network, establishing an explicit dynamics mapping relationship between system motion states and motor currents by mapping between motor currents and joint torques; introducing an external force term by fitting a Jacobian matrix and constructing an approximate mapping of the Jacobian matrix by using a data-driven method; and constructing an initial model, obtaining an inverse dynamics model of a mechanical arm after motor dynamics and external force modeling are incorporated into the initial model. Compared with the most advanced method, the application has higher modeling accuracy and generalization ability and better control performance. The innovative scheme provides solid technical support for realizing real-time and accurate control in the field of robots.

Description

Technical Field

[0001] This invention relates to the field of robotics, and more specifically to a method for constructing a neural network for predicting robot dynamics physical information based on the coupling of motors and external forces. Background Technology

[0002] With the development of industrial automation and intelligent technologies, robotic arms are widely used in complex environments such as parts assembly, medical operations, and human-machine interaction. External forces in interactive scenarios can significantly alter the dynamic characteristics of a system; therefore, high-precision dynamic modeling in complex dynamic environments is crucial for achieving precise control of robotic arms.

[0003] Traditional modeling methods are mainly based on physical principles (such as the Lagrange method and the Newton-Euler method) to derive dynamic equations. They rely on precise physical parameters and complex formula derivations, and contain a lot of simplification and linearization, making it difficult to describe complex nonlinear external forces.

[0004] In recent years, purely data-driven methods have been widely used in dynamic modeling. This approach does not rely on physical parameters, learning the system's dynamics directly from data, and performs exceptionally well in handling complex nonlinear scenarios. However, the black-box nature of this method prevents the capture of the underlying physical structure, limiting the ability to gain a deep understanding of the system and interpret the results. Overfitting and poor physical interpretability also hinder its integration with classical control frameworks.

[0005] To overcome the limitations of purely data-driven methods, Physical Information Neural Networks (PINNs), which combine physical principles with data-driven approaches, are increasingly being used for robot dynamics modeling. PINNs embed fundamental physical principles as constraints into the neural network's architecture and training, allowing the network to naturally follow physical laws during the learning process. For example, Deep Lagrangian Networks (DeLaNs) embed Lagrangian mechanics into the network, maintaining the symmetry and positive definiteness of the inertia matrix during learning. This not only effectively learns the system's dynamic equations but also ensures physical interpretability. Due to the conservative nature of Lagrangian mechanics, DeLaNs cannot model complex, non-conservative forces such as friction and external forces.

[0006] To address the limitations of DeLaN in modeling non-conservative forces, current research incorporates friction models into the system's dynamics and adds dissipative force networks to handle friction, achieving better modeling results in friction scenarios. However, for external contact forces, current attempts to embed contact forces into physical information neural networks are typically targeted at specific scenarios with restrictive assumptions, thus lacking broad applicability. Other research introduces feedforward neural networks (FFNNs) on top of the DeLaN model, which can learn all uncertainties that DeLaN cannot describe. However, due to the black-box nature of FFNNs, the learned uncertainties lack physical interpretability, and their outputs may violate known physical laws. Furthermore, many robotic arms lack joint torque sensors, making it impossible to obtain accurate joint torque data. Summary of the Invention

[0007] In view of this, this invention provides a method for constructing a predictive neural network for robot dynamics based on the coupling of motor and external force. It integrates motor dynamics and external force modeling into a Deep Lagrange Network (DeLaN) framework; establishes an explicit dynamic mapping relationship between the system motion state and motor current to compensate for the lack of joint torque data; and proposes two methods for fitting the Jacobian matrix estimation method by introducing external force terms, thereby constructing two dynamic models based on PINNs. Experiments on different robotic arms show that the proposed models can achieve high-precision torque estimation under external disturbances without the need for joint torque sensors. Compared with existing state-of-the-art methods, it has higher modeling accuracy and generalization ability, as well as superior control performance. This innovative approach provides solid technical support for achieving real-time and accurate control in the field of robotics.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] A method for constructing a robot dynamics physical information prediction neural network based on the coupling of motor and external force includes the following steps:

[0010] The motor dynamics equations are embedded into the DeLaN network, and an explicit dynamic mapping relationship between the system motion state and the motor current is established by mapping the motor current and the joint torque.

[0011] An external force term is introduced by fitting the Jacobian matrix, and an approximate mapping of the Jacobian matrix is ​​constructed using a data-driven method.

[0012] An initial model is constructed, and after incorporating motor dynamics and external force modeling into the initial model, the inverse dynamics model of the robotic arm is obtained.

[0013] Optionally, the expression for the inverse dynamics model of the robotic arm is as follows:

[0014]

[0015] The network input is the joint angle q of the robotic arm and the joint angular velocity. Joint angular acceleration and the terminal six-dimensional force F ext The output is the motor current i, where The matrix representing centrifugal force and Coriolis force.

[0016] g(q) represents the gravity vector, H(q) is the mass matrix, τ represents the generalized force acting on the system's generalized coordinate q, i is the motor current, r is the reduction ratio, and k t τ is the motor torque constant. F For frictional torque, τ ext As an external force, the inverse dynamics model introduces a mapping relationship between the joint torque τ and the motor current i, and finally establishes a dynamic mapping relationship between the system motion state and the motor current.

[0017] Optionally, the dynamics of a DC motor are described by the following equations:

[0018] τ=rk t i;

[0019] Where τ is the joint torque, i is the motor current, and k t denoted as the motor torque constant, and r as the reduction ratio.

[0020] Optionally, the joint friction torque is:

[0021]

[0022] Wherein, the constant ε is a smoothing parameter set empirically to 10⁻³, r is the deceleration ratio, and k v It is the coefficient of friction. The joint angular velocity; the coulomb term T when power flows from the motor to the load. c The value is When the power directions are opposite, the Coulomb term T c The value is

[0023] Optionally, the formula for the external force term is described as follows:

[0024] τ ext =J T (q)F ext ;

[0025] τ ext For external torque; F ext Let J(q) be the external force or torque of the end effector, and J(q) be the Jacobian matrix of the robotic arm.

[0026] Optionally, the Jacobian matrix can be fitted using the direct Jacobian, as follows:

[0027] The robot's configuration is determined by its rigid links and joint angles. Through forward kinematics, the joint angle q is converted into the end effector's pose x, i.e., x = f(q). The end effector pose x describes the spatial configuration of the robot's end effector in the task space, consisting of a position vector and attitude parameters. The forward kinematics model is obtained by a chain multiplication of a series of homogeneous transformation matrices, representing the transformation from the base coordinate system to the end effector coordinate system. To analyze the relationship between the end effector velocity and the joint velocities, a Jacobian matrix is ​​introduced, defined as:

[0028]

[0029] in For joint velocity, Let the end-effector velocity be defined as the Jacobian matrix, establishing a differential mapping relationship between the joint space and the task space. Therefore, the direct Jacobian method directly learns the mapping relationship between the end-effector velocity and the joint velocity. The network input is the joint angle q, and the output is the Jacobian matrix J(q). The loss function is designed as follows:

[0030]

[0031] Where N represents the number of training samples. The actual measured end velocity. The terminal velocity predicted by the model is calculated as follows:

[0032]

[0033] in, This represents the Jacobian matrix of the network prediction.

[0034] Optionally, the Jacobian matrix can be obtained using kinematic differential methods, as follows: First, the system's kinematic behavior is learned, and a forward kinematic model is fitted, i.e., the mapping relationship between joint angles and end-effector pose, x = f(q), to capture the global nonlinearity of kinematics and cover the entire workspace; the partial derivatives of the forward kinematic model f(q) with respect to q are calculated to obtain the system's Jacobian matrix:

[0035]

[0036] The network takes a joint angle q as input and outputs the end effector pose x. It is trained using supervised learning, and the loss function is designed to predict the end effector pose. With respect to the actual end effector pose Mean square error between:

[0037]

[0038] Optionally, the network parameter structure of the initial model is described as follows:

[0039]

[0040] θ, φ, and ψ represent the weight parameters that the network needs to train to learn the mass matrix H(q), potential energy V(q), and Jacobian matrix J(q), respectively. Parameter k represents the parameters that the motor dynamics model needs to learn, including the reduction ratio r and the motor torque constant k. t Coulomb term T c and friction coefficient k v .

[0041] As can be seen from the above technical solution, compared with the prior art, this invention provides a method for constructing a robot dynamics physical information prediction neural network based on the coupling of motor and external force, effectively solving the limitations of physical information neural networks in modeling non-conservative forces (especially complex external force fields) and the problem of missing joint torque data in actual robot systems. Motor dynamics and external force modeling are integrated into a deep Lagrangian network framework. An explicit dynamic mapping relationship between the system motion state and motor current is established to compensate for the lack of joint torque data. Two methods are proposed to fit the Jacobian matrix estimation method by introducing external force terms, thereby constructing two dynamic models based on PINNs. Experiments on different robotic arms show that the proposed models can achieve high-precision torque estimation under external disturbances without the need for joint torque sensors. Compared with the state-of-the-art methods, it has higher modeling accuracy and generalization ability, as well as better control performance. The model exhibits the following core advantages in dynamic modeling experiments:

[0042] 1. Extremely high modeling accuracy: Thanks to explicit external force modeling, the two proposed models demonstrate excellent modeling performance under various complex external force scenarios, with an average R0 in multiple scenarios. 2 The accuracy reached above 0.953, with an average improvement of 55.34% in modeling accuracy compared to the DeLaN model and 17.23% compared to DeLaN-FFNN.

[0043] 2. Excellent generalization ability: Generalization experiments under unseen external forces show that the two proposed models have better generalization ability than DeLaN and DeLaN-FFNN. In particular, as the external force increases further, the degradation is significantly better than other advanced methods. Even when the external force reaches 20 times, R can still be guaranteed. 2 It is above 0.85.

[0044] 3. Excellent control performance: Model-based inverse dynamics control experiments show that both proposed models can achieve good trajectory tracking under external disturbances. The RMSE of trajectory tracking for each joint is less than 0.8, which is better than other advanced methods, demonstrating superior control performance.

[0045] This innovative solution provides solid technical support for achieving real-time and precise control in the field of robotics. Attached Figure Description

[0046] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0047] Figure 1 This is a schematic diagram of the network model of the present invention. Detailed Implementation

[0048] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0049] To address the limitations of physical information neural networks in non-conservative force modeling and the lack of joint torque data in practical robot systems, this invention integrates motor dynamics and external force modeling into a deep Lagrangian network framework, proposing two dynamic models based on PINNs.

[0050] For robotic arms without joint torque sensors, the motor dynamics equations are embedded into the DeLaN network. By incorporating the mapping between motor current and joint torque into the training process, an explicit dynamic mapping relationship between the system motion state and motor current is finally established, achieving high-fidelity dynamic modeling under the condition of no torque sensor.

[0051] To address the limitations of DeLaN in external force modeling, two methods for fitting the Jacobian matrix are proposed to introduce external force terms. The first method directly learns the mapping relationship between end-effector velocity and joint velocity, called direct Jacobian. The second method first learns the system's kinematic behavior, and then obtains the Jacobian matrix by differential analysis of the learned positive kinematic model, called kinematic differentiation. The training process implicitly satisfies kinematic geometric constraints, resulting in stronger physical consistency and interpretability.

[0052] Multiple dynamic modeling experiments were conducted on the UR5 and UR10e six-DOF manipulators under various external force scenarios. The results show that the proposed two models outperform other state-of-the-art methods in terms of modeling accuracy, generalization ability, and control performance. This verifies the effectiveness of introducing motor dynamics and external force modeling, and demonstrates that implicitly satisfying geometric constraints through learning kinematic behavior improves physical consistency and interpretability, further enhancing model performance.

[0053] The dynamic modeling method based on physical information neural networks proposed in this invention has both high real-time performance and high precision, is fully applicable to robot control, and can operate stably in complex external force environments, providing important technical support for the intelligent control of robots.

[0054] This invention discloses a method for constructing a neural network for predicting robot dynamics physical information based on the coupling of motor and external force, comprising the following steps:

[0055] The motor dynamics equations are embedded into the DeLaN network, and an explicit dynamic mapping relationship between the system motion state and the motor current is established by mapping the motor current and the joint torque.

[0056] An external force term is introduced by fitting the Jacobian matrix, and an approximate mapping of the Jacobian matrix is ​​constructed using a data-driven method.

[0057] An initial model is constructed, and after incorporating motor dynamics and external force modeling into the initial model, the inverse dynamics model of the robotic arm is obtained.

[0058] Specifically, it includes the following:

[0059] Many robotic arms lack joint torque sensors, making it impossible to obtain accurate torque data. Therefore, a dynamic modeling approach for joint motors is proposed. The dynamics of a typical DC motor with a harmonic reducer are described by the following equations:

[0060] τ=rk t i;

[0061] Where τ is the joint torque, i is the motor current, and k t Let be the motor torque constant, and r be the reduction ratio. The UR10e robotic arm has a high reduction ratio and uses harmonic drive, resulting in low mechanical efficiency and a large proportion of friction effect. Therefore, selecting a suitable friction model is important.

[0062] In the UR10e robotic arm, due to the low friction in the well-designed and maintained brushless motor, the system's friction is primarily due to harmonic drive. Therefore, the friction model used in the paper for the UR5e robotic arm is adopted here, as it shares a similar motor structure with the UR10e. It assumes that the frictional torque consists of a "standard" frictional torque and an asymmetric, smooth Coulomb frictional torque. The frictional torque on the j-th motor side is described by the following formula:

[0063]

[0064] The constant ε is a smoothing parameter set empirically to 10⁻³. When power flows from the motor to the load, the coulomb term T... c The value is When the power directions are opposite, the Coulomb term T c The value is k is the angular velocity of the motor. v It is the coefficient of friction.

[0065] Since the friction of the UR10e robotic arm is mainly generated by harmonic drive, and the motor angular velocity is... Given the joint angular velocity, the joint friction torque is:

[0066]

[0067] The motor actuator model is incorporated into a deep Lagrangian model, including the reduction ratio r and the motor torque constant k. t Coulomb term T c and friction coefficient k v As a method for learning network weights, end-to-end training is used to jointly optimize the model and parameters, ultimately establishing a dynamic mapping relationship between the system's motion state and the motor current. Unlike traditional parameter identification, these parameters are not calibrated through offline experiments, but rather dynamically adapted as part of the modeling framework.

[0068] When robots perform tasks such as grasping, assembly, and surgery, the robot's end effector needs to come into contact with the object, generating external contact forces. Accurate modeling of these external contact forces is crucial for improving robot performance and safety. The formula for the external torque is described below:

[0069] τ ext =J T (q)F ext ;

[0070] τ ext It is the external torque, which is the torque acting on each joint of the robotic arm. F extIt refers to the external force or torque of the end effector, measured by a six-dimensional force sensor at the end effector, including three-dimensional external force (F). x ,F y ,F z ) and three-dimensional external torque (M) x M y M z J(q) is the Jacobian matrix of the robotic arm, which represents the external force F acting on the end effector. ext Torque τ converted to joint space ext Since robot manufacturers do not disclose various parameters of their robots, the exact Jacobian matrix is ​​often difficult to obtain. Therefore, a data-driven approach is used to construct an approximate mapping of the Jacobian matrix, and two different methods are proposed to fit the Jacobian matrix.

[0071] (1) Direct Jacobi

[0072] The robot's configuration is determined by its rigid links and joint angles. Through forward kinematics, the joint angle q can be converted into the end effector's pose x, i.e., x = f(q). The end effector pose x describes the spatial configuration of the robot's end effector in the task space, typically consisting of a position vector and attitude parameters. The forward kinematics model is obtained by chaining a series of homogeneous transformation matrices, representing the transformation from the base coordinate system to the end effector coordinate system. To analyze the relationship between the end effector velocity and joint velocities, the Jacobian matrix is ​​introduced, defined as:

[0073]

[0074] in For joint velocity, Let the end-effector velocity be defined as the Jacobian matrix, establishing a differential mapping relationship between the joint space and the task space. Therefore, the direct Jacobian method directly learns the mapping relationship between the end-effector velocity and the joint velocity. The network input is the joint angle q, and the output is the Jacobian matrix J(q). The loss function is designed as follows:

[0075]

[0076] Where N represents the number of training samples. The actual measured end velocity. The terminal velocity predicted by the model is calculated as follows:

[0077]

[0078] in This represents the Jacobian matrix of the network prediction. The neural Jacobian method directly learns the differential mapping between joint health and the task space, essentially fitting a local linearization of a chain structure with data, and cannot globally model nonlinear kinematics. If the data only covers a local workspace, significant prediction bias may occur in untrained areas, and data noise and overfitting may violate the kinematic geometry constraints of the robotic arm.

[0079] (2) Kinematic differential

[0080] The kinematic differential method first learns the system's kinematic behavior, fitting a forward kinematic model, i.e., the mapping relationship between joint angles and end-effector pose, x = f(q). This captures the global nonlinearity of kinematics and covers the entire workspace. Then, by calculating the partial derivatives of the forward kinematic model f(q) with respect to q, the Jacobian matrix of the system is obtained.

[0081]

[0082] The network takes a joint angle q as input and outputs the end effector pose x. It is trained using supervised learning, and the loss function is designed to predict the end effector pose. With respect to the actual end effector pose Mean square error between:

[0083]

[0084] The forward kinematics model is essentially a chain rule for the transformation of the robotic arm's link coordinate system. During the learning process, because the model itself is constrained by the robotic arm's geometry (such as the orthogonality of the rotation matrix and the invariance of link lengths), the network implicitly satisfies these geometric constraints during training. These constraints are represented as the analytic derivative of f(q), and each partial derivative in the Jacobian matrix element is a factor. The geometric constraints of the robotic arm's linkage structure are inherited, which makes the learned Jacobian matrix highly physically consistent.

[0085] Each element in the Jacobian matrix has a clear kinematic interpretation, intuitively explaining the specific contribution of joint angle changes to the position and attitude changes of the end effector. It directly reflects the spatial coupling relationship of the robotic arm configuration parameters and has high physical interpretability. This method yields a Jacobian matrix with high physical consistency and interpretability, perfectly integrating external force modeling into PINN.

[0086] The specific network parameter structure of the model is described below:

[0087]

[0088] θ, φ, and ψ represent the weight parameters that the network needs to train to learn the mass matrix H(q), potential energy V(q), and Jacobian matrix J(q), respectively. Parameter k represents the parameters that the motor dynamics model needs to learn, including the reduction ratio r and the motor torque constant k. t Coulomb term T c and friction coefficient k v The inverse dynamics model of the robotic arm can be represented as:

[0089]

[0090] The training process learns not only system dynamics but also the Jacobian matrix. Therefore, to prevent the learning of system dynamics from being neglected due to the dominance of the Jacobian matrix during training, an additional penalty term λ is introduced. The optimization objective of DeLaN-MKF is defined as follows:

[0091]

[0092] The optimization objective of DeLaN-MJF is defined as follows:

[0093]

[0094] The ultimate goal is to learn the dynamics of the system. Therefore, when optimizing the model, it is necessary to balance the loss of dynamics and Jacobian matrix as much as possible, and ensure that the system dynamics are learned to the maximum extent while learning an accurate Jacobian matrix.

[0095] By incorporating motor dynamics modeling and external force modeling into the model, the inverse dynamics model of the robotic arm is finally obtained:

[0096]

[0097] The network structures of DeLaN-MJF and DeLaN-MKF are as follows: Figure 1 As shown, the network input is the robot arm joint angle q and the joint angular velocity. Joint angular acceleration and the terminal six-dimensional force F ext The output is the motor current i.

[0098] The orange part represents the structure of DeLaN, which parameterizes the mass matrix H(q) and potential energy V(q) to learn the conservative forces of the system, while decomposing the mass matrix H(q) into a lower triangular matrix to ensure its symmetry and positive definiteness.

[0099] The blue section represents external force modeling, where forces in the task space are mapped to the joint space using the Jacobian transpose. Two neural network methods are used to fit the system's Jacobian matrix: DeLaN-MKF, based on an analytical kinematic approach, first learns the system's forward kinematic model and then differentiates it to obtain the Jacobian matrix J(q). The DeLaN-MJF model, based on a direct Jacobian method, directly learns the differential mapping between the joint space and task space to fit the Jacobian matrix J(q).

[0100] The purple section represents the motor dynamics modeling. By introducing a mapping relationship between joint torque τ and motor current i, a dynamic mapping relationship between the system motion state and motor current is ultimately established, compensating for the lack of joint torque sensors. Since joint friction accounts for a significant portion of actual robotic arm joints, a joint friction modeling component is also included.

[0101] The green portion represents the loss functions of the two models, where the loss function for DeLaN-MKF is defined as: in This represents the motor current predicted by the model. The loss function of DeLaN-MJF is defined as... Both models' loss functions include the overall model's dynamic loss and the Jacobian matrix loss. λ is used to balance the proportion of these two losses in the total loss value.

[0102] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0103] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for constructing a neural network for predicting the physical information of robot dynamics based on the coupling of motor and external force, characterized in that, Includes the following steps: The motor dynamics equations are embedded into the DeLaN network, and an explicit dynamic mapping relationship between the system motion state and the motor current is established by mapping the motor current and the joint torque. An external force term is introduced by fitting the Jacobian matrix, and an approximate mapping of the Jacobian matrix is ​​constructed using a data-driven method. An initial model is constructed, and after incorporating motor dynamics and external force modeling into the initial model, the inverse dynamics model of the robotic arm is obtained.

2. The method for constructing a robot dynamics physical information prediction neural network based on the coupling of motor and external force as described in claim 1, characterized in that, The expression for the inverse dynamics model of the robotic arm is as follows: The network input is the joint angle q of the robotic arm and the joint angular velocity. Joint angular acceleration and the terminal six-dimensional force F ext The output is the motor current i, where The matrix represents the centrifugal force and the Coriolis force, g(q) represents the gravity vector, H(q) is the mass matrix, τ represents the generalized force acting on the system's generalized coordinate q, i is the motor current, r is the reduction ratio, and k t τ is the motor torque constant. F For frictional torque, τ ext As an external force, the inverse dynamics model introduces a mapping relationship between the joint torque τ and the motor current i, and finally establishes a dynamic mapping relationship between the system motion state and the motor current.

3. The method for constructing a robot dynamics physical information prediction neural network based on the coupling of motor and external force as described in claim 1, characterized in that, The dynamics of a DC motor are described by the following equations: τ=rk t i; Where τ is the joint torque, i is the motor current, and k t denoted as the motor torque constant, and r as the reduction ratio.

4. The method for constructing a robot dynamics physical information prediction neural network based on the coupling of motor and external force as described in claim 3, characterized in that, The joint friction torque is: Wherein, the constant ε is a smoothing parameter set empirically to 10⁻³, r is the deceleration ratio, and k v It is the coefficient of friction. The joint angular velocity; the coulomb term T when power flows from the motor to the load. c The value is When the power directions are opposite, the Coulomb term T c The value is 5. The method for constructing a robot dynamics physical information prediction neural network based on the coupling of motor and external force according to claim 1, characterized in that, The formula for the external force term is described as follows: τ ext =J T (q)F ext ; τ ext For external torque; F ext Let J(q) be the external force or torque of the end effector, and J(q) be the Jacobian matrix of the robotic arm.

6. The method for constructing a robot dynamics physical information prediction neural network based on the coupling of motor and external force as described in claim 5, characterized in that, The Jacobian matrix is ​​fitted using the direct Jacobian method, as follows: The robot's configuration is determined by its rigid links and joint angles. Through forward kinematics, the joint angle q is converted into the end effector's pose x, i.e., x = f(q). The end effector pose x describes the spatial configuration of the robot's end effector in the task space, consisting of a position vector and attitude parameters. The forward kinematics model is obtained by a chain multiplication of a series of homogeneous transformation matrices, representing the transformation from the base coordinate system to the end effector coordinate system. To analyze the relationship between the end effector velocity and the joint velocities, a Jacobian matrix is ​​introduced, defined as: in For joint velocity, Let the end-effector velocity be defined as the Jacobian matrix, establishing a differential mapping relationship between the joint space and the task space. Therefore, the direct Jacobian method directly learns the mapping relationship between the end-effector velocity and the joint velocity. The network input is the joint angle q, and the output is the Jacobian matrix J(q). The loss function is designed as follows: Where N represents the number of training samples. The actual measured end velocity. The terminal velocity predicted by the model is calculated as follows: in, This represents the Jacobian matrix of the network prediction.

7. The method for constructing a robot dynamics physical information prediction neural network based on the coupling of motor and external force according to claim 5, characterized in that, The Jacobian matrix is ​​obtained using kinematic differential methods, as follows: First, the system's kinematic behavior is learned, and a forward kinematic model is fitted, i.e., the mapping relationship between joint angles and end-effector pose, x = f(q), to capture the global nonlinearity of kinematics and cover the entire workspace. The partial derivatives of the forward kinematic model f(q) with respect to q are calculated to obtain the system's Jacobian matrix. The network takes a joint angle q as input and outputs the end effector pose x. It is trained using supervised learning, and the loss function is designed to predict the end effector pose. With the actual end effector pose Mean square error between:

8. The method for constructing a robot dynamics physical information prediction neural network based on the coupling of motor and external force according to claim 1, characterized in that, The network parameter structure of the initial model is described as follows: θ, φ, and ψ represent the weight parameters that the network needs to train to learn the mass matrix H(q), potential energy V(q), and Jacobian matrix J(q), respectively. Parameter k represents the parameters that the motor dynamics model needs to learn, including the reduction ratio r and the motor torque constant k. t Coulomb term T c and friction coefficient k v .

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