A method for detecting the terminal force of flexible joint robots based on neural network momentum observer

Abstract

This invention discloses a method for detecting the end effector force of a flexible joint robot based on a neural network momentum observer. The method includes: establishing a dynamic mathematical model of the flexible joint robot; establishing a momentum equation for the robot system under unconstrained free motion; constructing a momentum equation for the robot's interaction with the environment, incorporating system uncertainties; determining a momentum observer to estimate the perturbation torque under unconstrained free motion; approximating the dynamic model of the perturbation torque of the robot system based on a neural network method; and determining a neural network-based momentum observer to estimate the external torque when the robot contacts the environment. This method for detecting the end effector force of a flexible joint robot based on a neural network momentum observer combines a system dynamics model with neural network technology, improving the accuracy of end effector force detection and enhancing the robot's adaptability and safety during interaction with the environment.

Description

Technical Field

[0001] This invention belongs to the field of robot control technology, specifically relating to a method for detecting the end effector force of a flexible joint robot based on a neural network momentum observer. Background Technology

[0002] In today's rapidly developing robotics technology, flexible joint robots, due to their lightweight design and high flexibility, have become important tools for performing complex tasks. They are widely used in industrial manufacturing, medical rehabilitation, service robots, and other fields, and can operate flexibly in confined or complex environments. However, the inherent characteristics of flexible joint robots, such as the flexibility and nonlinearity of their structure, make the accurate detection of end-effector forces a challenging task.

[0003] Traditional force detection methods primarily rely on force / torque sensors mounted on the robot's end effector. While this method is direct and relatively simple, it also has several significant drawbacks. First, sensor installation increases the robot's hardware cost and system complexity. Second, the weight and size of the sensor can affect the robot's dynamic performance and operational flexibility. Furthermore, the sensor's measurement accuracy and durability can be affected by the external environment. Summary of the Invention

[0004] This invention provides a method for detecting the end effector force of a flexible joint robot based on a neural network momentum observer to solve the aforementioned technical problems. Specifically, the technical solution is as follows:

[0005] A method for detecting the end effector force of a flexible joint robot based on a neural network momentum observer includes:

[0006] S1: Establish a dynamic mathematical model for the flexible joint robot;

[0007] S2: Based on the system dynamics model, establish the momentum equation for the robot system under unconstrained free motion;

[0008] S3: In light of the uncertainties of the robot system, establish a system dynamics model for the interaction between the robot and the environment, and construct momentum equations for the interaction process between the robot and the environment that include system uncertainties;

[0009] S4: Determine the momentum observer to estimate the perturbation torque under unconstrained free motion;

[0010] S5: A dynamic model of the disturbance torque of a robot system based on a neural network method;

[0011] S6: Determine a momentum observer based on a neural network to estimate the external torque when the robot comes into contact with the environment.

[0012] Furthermore, in step S1, considering the viscous friction terms on the joint motor side and the link side and neglecting the external forces interacting with the environment, the dynamic model of the flexible joint robot can be expressed as:

[0013]

[0014] in,

[0015] τ J =K s (q-θ)#(3)

[0016] τ J ∈R 6 Represents the elastic force transmitted through the joint, q∈R 6 and θ∈R 6 These indicate the joint positions at the connecting end and the motor end, respectively. and τ represents the friction term at the connection end and the motor end, respectively. m ∈R 6 K represents the torque signal of the motor. s ∈R 6×6 and D s ∈R 6×6 It is a diagonal matrix representing the stiffness and damping coefficients of the joint, M(q)∈R 6×6 Represents the mass matrix, Let G(q) ∈ R represent the Coriolis force matrix. 6 Let I(θ) ∈ R represent the gravity vector. 6×6 The inertia matrix is ​​the motor side.

[0017] From the matrix From the properties of skew-symmetric matrices, we can derive:

[0018]

[0019] Assume M(q), G(q) and The parameters are known, but due to mechanical structure errors, these parameters may be inaccurate; they are treated as parameter perturbations. The specific friction model is also unknown; the influence of friction and parameter perturbations on the system is also considered as system disturbance torque. Therefore, the robot's link-side model can be re-expressed as:

[0020]

[0021] Where τ δ ∈R 6 This represents the system's disturbance torque.

[0022] Further, in step S2, the total energy of the robot, E, is defined as the sum of its kinetic energy T and gravitational potential energy U:

[0023]

[0024] in Based on (1) and (4), we can obtain:

[0025]

[0026] Therefore, the generalized momentum of a robot can be defined as:

[0027]

[0028] Based on (1) and (4), the time derivative of momentum p can be obtained as:

[0029]

[0030] This formula describes the change of generalized momentum over time, including the effects of internal and external disturbances to the system.

[0031] Furthermore, in step S3, the environmental force can be expressed as:

[0032] F e =K e (x e -x)=J -T (q)τ ex #(10)

[0033] Where x e K is the location vector of the environment. e ∈R 6×6 F represents the diagonal stiffness matrix of the environment. e ∈R 6 This represents the external force vector, which can be estimated using a momentum observer;

[0034] Considering the system disturbance torque and external torque, the link-side model of the robot can be described as follows:

[0035]

[0036] Where τ ex ∈R 6 equals J T (q)F e ∈R 6 F e ∈R 6 It is an external force. According to formulas (4) and (10), we can obtain The time derivative is:

[0037]

[0038] Further, in step S4, based on equation (11), the momentum observer of the robot in its unconstrained free motion state is defined as:

[0039]

[0040] Where, r δ (t c )∈R 6 It is the current time t c down r δ The observation results of (t), r δ (0) = 0, K I ∈R 6×6 It is a diagonal matrix, p(t) c ) indicates at time t c ≥0 generalized momentum of the robot;

[0041] Substituting equations (5) and (9) into equation (12) to obtain their time derivatives, the dynamics of the linear and decoupled residuals can be expressed as:

[0042]

[0043] Its Laplace transform is:

[0044]

[0045] Where, r δ，j τ δ，j and K I，j They represent r respectively δ , τ δ and K I The diagonal element, j, represents the corresponding joint, under ideal conditions:

[0046]

[0047] Furthermore, in step S5, a neural network method is used to approximate the perturbation dynamics of the system, and the observed perturbation torque is used as the target for training the neural network, τ. δ The approximation result can be expressed as:

[0048]

[0049] in, The value estimated using a neural network method can be represented as:

[0050]

[0051] Among them, f NN (·) represents the mapping of the neural network. This represents a very small, acceptable error that satisfies... in It is a predefined, very small constant.

[0052] Furthermore, in (18), the input to the neural network is The output is

[0053] The subscript indicates the corresponding joint;

[0054] The specific steps for data acquisition and disturbance moment modeling are as follows:

[0055] (1) Data acquisition process under free and unconstrained motion: Allow the robot end effector to move freely along an appropriate excitation trajectory, i.e., external torque τ ex =0, and at the same time, data is obtained through the momentum observer equation (13), including joint position q and joint velocity. and the observed residual r δ These data are recorded in time series format to facilitate neural network training;

[0056] (2) Modeling of disturbance moment: A feedforward neural network is used to model the residual value r observed through equation (13). δ Perform approximations until the following condition is met:

[0057]

[0058] During training, mean squared error is chosen as the loss function, which is defined as follows:

[0059]

[0060] Where Θ represents the weights of the neural network, r i δ (k+j) represents the true state value of sample i.

[0061] Let j represent the predicted value of sample i. In the formula, j = 1, 2, ..., N, where N is the length of the time series.

[0062] i = 1, 2, ..., M, where M represents the number of training set sample sequences.

[0063] Furthermore, the feedforward neural network is represented as:

[0064]

[0065] in k represents the k-th time step, and Ψ(·) represents the ReLU activation function.

[0066] W I ∈R12×16 and W o ∈R 16×6 β represents the weight matrices of the hidden layer and the output layer, respectively; i ∈R 16 and β o ∈R 6 These represent the bias vectors of the hidden layer and the output layer, respectively.

[0067] Furthermore, the value estimated through step S5 will be... Applied to (13), the expression for estimating external torque using a neural network-based momentum observer is:

[0068]

[0069] Where, r ex (t c ) represents the current time t c The observed external torque.

[0070] The advantage of this invention lies in the provision of a force detection method for the end effector of a flexible joint robot based on a neural network momentum observer. By combining a system dynamics model with neural network technology, it aims to improve the accuracy and real-time performance of force detection. The neural network momentum observer can effectively estimate the momentum change of the system, thereby inferring the force acting on the robot's end effector. This method not only improves the accuracy of end effector force detection but also enhances the robot's adaptability and safety when interacting with the environment. Attached Figure Description

[0071] 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 some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0072] Figure 1 This is a flowchart of the end-effector force detection method for flexible joint robots based on a neural network momentum observer proposed in this invention;

[0073] Figure 2 A schematic diagram illustrating the interaction between the flexible joint robot used in this invention and its environment;

[0074] Figure 3 This is a schematic diagram of the two-layer feedforward neural network used in this invention.

[0075] Figure 4 This is a diagram showing the training loss and validation loss of a neural network, an application example of this invention.

[0076] Figure 5 This is a graph showing the test data results of the neural network after training, as an application example of the present invention.

[0077] Figure 6 This is a test error graph of the neural network after training, as an application example of the present invention.

[0078] Figure 7 This is a diagram showing the external force results estimated using a neural network observer in an application example of the present invention. Detailed Implementation

[0079] Embodiments of the present invention are described in detail below. Examples of these embodiments are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0080] like Figure 1 The figure shown is a method for detecting the end effector force of a flexible joint robot based on a neural network momentum observer, comprising:

[0081] Step S1: Establish a dynamic mathematical model for the flexible joint robot.

[0082] In step S1, for a 6-DOF serial robot arm with flexible joints, considering the viscous friction terms on the joint motor side and the link side and neglecting the external forces interacting with the robot and the environment, the dynamic model of the flexible joint robot can be expressed as:

[0083]

[0084] in,

[0085] τ J =K s (q-θ)#(3)

[0086] τ J ∈R 6 Represents the elastic force transmitted through the joint, q∈R 6 and θ∈R 6 These indicate the joint positions at the connecting end and the motor end, respectively. and τ represents the friction term at the connection end and the motor end, respectively. m ∈R 6 K represents the torque signal of the motor. s ∈R 6×6 and D s ∈R 6×6 It is a diagonal matrix representing the stiffness and damping coefficients of the joint, M(q)∈R 6×6 Represents the mass matrix, Let G(q) ∈ R represent the Coriolis force matrix. 6 Let I(θ) represent the gravitational vector, then I(θ) = R 6×6 This is the inertia matrix on the motor side.

[0087] An absolute position sensor is installed between the motor side and the connection side to detect the position and velocity at both ends of the elastic element. This allows for the measurement of the deformation of the joint's elastic element, which can then be used to calculate the joint output torque. Therefore, considering only equation (1), the measured joint torque can be used as a substitute for the torque command in the rigid body model. Specifically, by replacing τ with... It can achieve properties similar to those of rigid robots.

[0088] From the matrix From the properties of skew-symmetric matrices, we can derive:

[0089]

[0090] In this application, we assume M(q), G(q) and The parameters are known, but due to mechanical structure errors, these parameters may be inaccurate; they are treated as parameter perturbations. The specific friction model is also unknown; considering the effects of friction and parameter perturbations on the system as system disturbance torques, the robot's link-side model can then be redefined as:

[0091]

[0092] Where τ δ ∈R 6 It represents the disturbance torque of a system, such as the frictional force and parameter disturbance of an unknown system.

[0093] Step S2: Based on the system dynamics model, establish the momentum equation for the robot system under unconstrained free motion.

[0094] In step S2, let the total energy of the robot be E, defined as the sum of its kinetic energy T and gravitational potential energy U:

[0095]

[0096] in Based on (1) and (4), we can obtain:

[0097]

[0098] This indicates an energy balance in the system. Therefore, the robot's generalized momentum can be defined as:

[0099]

[0100] Based on (1) and (4), the time derivative of momentum p can be obtained as:

[0101]

[0102] This formula describes the change of generalized momentum over time, including the effects of internal and external disturbances within the system. In this case, the change in generalized momentum is affected not only by the joint torque τ, but also by the system disturbance torque τ. δ In addition, we need to consider the effects of Coriolis force and gravity. Thus, by measuring joint torques and combining them with the momentum balance equations, we can estimate the forces generated during the robot's interaction with the environment.

[0103] Step S3: In light of the uncertainties of the robot system, establish a system dynamics model for the robot's interaction with the environment, and construct momentum equations for the robot's interaction with the environment that incorporate system uncertainties.

[0104] In step S3, as Figure 2 This demonstrates a model of interaction between a flexible joint robot and its environment. Figure 2 In this system, springs and dampers are mainly composed of reducers and joint elastic elements.

[0105] In practical applications, robot systems exhibit various uncertainties and errors, including mechanical structure errors, unknown frictional characteristics, and manufacturing and assembly errors. These uncertainties affect the accuracy and stability of robot control. When the robot comes into contact with its environment, the stiffness and damping characteristics of the environment also influence the system. The environment is typically represented as a second-order mass-spring-damped system; in this invention, for ease of analysis, the environment is simplified to a single spring model. Specifically, the environmental forces can be expressed as:

[0106] F e =K e (x e -x)=J -T (q)τ ex #(10)

[0107] Where x e K is the location vector of the environment. e ∈R 6×6 F represents the diagonal stiffness matrix of the environment. e ∈R 6 This represents the external force vector, which can be estimated using a momentum observer.

[0108] Considering the system disturbance torque and external torque, the link-side model of the robot can be described as follows:

[0109]

[0110] Where τex ∈R 6 equals J T (q)F e ∈R 6 F e ∈R 6 It is an external force. According to formulas (4) and (10), we can obtain The time derivative is:

[0111]

[0112] Based on the principle of robot momentum, a momentum observer can be designed to estimate the perturbation forces during unconstrained robot motion. However, if this observer is used to estimate the external forces when the robot comes into contact with its environment, the estimated forces will include perturbation terms, affecting the accuracy of force detection and reducing its precision. Therefore, without addressing the impact of perturbation forces, the observer cannot be directly used to estimate external forces. Thus, the key challenge of this task lies in how to eliminate the influence of these perturbation terms on the observer.

[0113] Step S4: Determine the momentum observer estimate of the disturbance torque under unconstrained free motion.

[0114] In step S4, based on equation (11), the momentum observer of the robot in its unconstrained free motion state is defined as:

[0115]

[0116] Where, r δ (t c )∈R 6 It is the current time t c down r δ The observation results of (t), r δ (0) = 0, K I ∈R 6×6 It is a diagonal matrix, p(t) c ) indicates at time t c The generalized momentum of the robot is ≥0. It is worth noting that the vector r... δ (t) can be measured The joint torque τ(t) is calculated through the iterative process of equation (12) without the need for the inverse operation of the inertia matrix.

[0117] Substituting equations (5) and (9) into equation (12) to obtain their time derivatives, the dynamics of the linear and decoupled residuals can be expressed as:

[0118]

[0119] Its Laplace transform is:

[0120]

[0121] Where, r δ，j τ δ，j and K I，j They represent r respectively δ , τ δ and K I The diagonal elements, j, represent the corresponding joints. Furthermore, these six decoupled transfer functions have the same gain. Under ideal conditions:

[0122]

[0123] This effectively means the gain should be as large as possible. However, this observer cannot be used directly to estimate external forces; if used in this way, the estimated external forces will include perturbation torques, thus affecting the accuracy of the estimation. Therefore, perturbation torques must be identified and incorporated into the observer to eliminate their influence.

[0124] Step S5: Approximate the dynamic model of the disturbance torque of the robot system based on the neural network method.

[0125] In step S5, given that a multilayer neural network can approximate any continuous nonlinear function with arbitrarily high precision, a neural network method can be used to approximate the system's perturbation dynamics, and the observed perturbation torque can be used as the target for training the neural network. Therefore, τ δ The approximation result can be expressed as:

[0126]

[0127] in, The value estimated using a neural network method can be represented as:

[0128]

[0129] Among them, f NN (·) represents the mapping of the neural network. This represents a very small, acceptable error that satisfies... in It is a predefined, very small constant.

[0130] In (18), the input to the neural network is The output is The subscript indicates the corresponding joint.

[0131] The specific steps for data acquisition and disturbance moment modeling are as follows:

[0132] (1) Data acquisition process under free and unconstrained motion: Allow the robot end effector to move freely along an appropriate excitation trajectory, i.e., external torque τ ex =0, and at the same time, data is obtained through the momentum observer equation (13), including joint position q and joint velocity. and the observed residual r δ These data are recorded in time series format to facilitate neural network training. In this way, the dynamic characteristics of the robot system under conditions without external disturbances can be captured, providing fundamental data support for subsequent approximation using neural networks and estimation of disturbance torques.

[0133] (2) Modeling of disturbance moment: A feedforward neural network is used to model the residual value r observed through equation (13). δ Perform approximations until the following condition is met:

[0134]

[0135] During training, mean squared error is chosen as the loss function, which is defined as follows:

[0136]

[0137] Where Θ represents the weights of the neural network, r i δ (k+j) represents the true state value of sample i. Let j represent the predicted value of sample i. In the formula, j = 1, 2, ..., N, where N is the length of the time series, and i = 1, 2, ..., M, where M represents the number of training set sample sequences.

[0138] In the embodiments of this application, such as Figure 3 As shown, the feedforward neural network is approximated using a two-layer feedforward neural network with 16 hidden neurons. The feedforward neural network can be represented as:

[0139]

[0140] in k represents the k-th time step, Ψ(·) represents the ReLU activation function, and W I ∈R 12×16 and W o ∈R 16×6 β represents the weight matrices of the hidden layer and the output layer, respectively. i ∈R 16 and β o ∈R 6 These represent the bias vectors of the hidden layer and the output layer, respectively.

[0141] Step S6: Determine the momentum observer based on the neural network to estimate the external torque when the robot comes into contact with the environment.

[0142] Based on equation (11), the external torque can be expressed as:

[0143]

[0144] Obviously, if the disturbance torque τ δ The unknown will greatly affect the accuracy of external force estimation. Therefore, we cannot directly use motion observers to estimate external forces.

[0145] Previously discussed methods include using an observer to estimate the disturbance torque while employing a neural network (NN) to approximate the disturbance dynamics model. Once the disturbance model is established using the NN method, it can be integrated into the observer to estimate external torques during robot-environment interactions. This integration leverages the neural network's ability to approximate disturbance dynamics, combined with the observer's feedback mechanism, to achieve real-time estimation of external disturbance torques, thereby improving the system's adaptability and control accuracy in complex environments.

[0146] As discussed in S4, the perturbation torque is approximated using a neural network (NN) method. Once the NN is trained, the predicted torque... This can be applied to equation (13). Specifically, the value estimated through step S5 will be used. Applied to (13), the expression for estimating external torque using a neural network-based momentum observer is:

[0147]

[0148] Where, r ex (t c ) represents the current time t c The observed external torque.

[0149] Therefore, the external force estimated in Cartesian space is:

[0150]

[0151] This method can effectively estimate the external forces acting on a robot when it interacts with its environment, thereby improving the system's control accuracy and responsiveness.

[0152] In this example, the implementation is divided into two phases. The initial phase involves the robotic arm moving freely and without constraints. In this phase, a force observer defined by equation (13) is used to estimate the perturbation force, without considering the uncertainty of the system. The estimated force is then compared with the actual force. In the case of free and unconstrained motion, the external force should ideally be zero, and deviations from zero are attributed to the presence of uncertain perturbations. To facilitate the training of the neural network, the end effector is guided to move along various periodic trajectories, thereby generating the necessary dataset.

[0153] In the subsequent stage, a neural network is used to approximate the uncertainty of the system. The trained neural network is then integrated into the observer, forming a neural network-based observer described by equation (23). This neural network observer is then applied to estimate the external forces during free motion, aiming to verify the effectiveness of the proposed method. It is expected that the estimated external forces should be close to zero, thus verifying the feasibility of the method.

[0154] Data sampling and training process: To reduce the impact of uncertainty, a series of free and unconstrained experiments were conducted to generate data for offline training, where the observer parameters were set as follows: K I =diag(20, 20, 20, 20, 20, 20). For a specific point-to-point trajectory, 10 different motion trajectories were created. This method allows the robot to run at different speeds, thereby capturing the effects of speed-related factors such as friction and Coriolis forces. The dataset consists of 100 sample sequences, each consisting of a pair of data x. N r δ (k)}∈R 18 Composition, in which r represents the input to the neural network. δ (k)∈R 6 This indicates the corresponding output.

[0155] During training, 70% of the data is used for training, 20% for validation, and 10% for testing. The loss is as follows: Figure 4 As shown, the neural network converged after 450 iterations. The mean squared errors (MSEs) of the training loss and validation loss were 0.0262 Nm and 0.0267 Nm, respectively.

[0156] Training and experimental results: The trained neural network model was integrated into an observer defined by equation (23) to estimate the external forces acting on the system. During free and unconstrained motion, the estimated external forces should ideally be close to zero when no external forces are acting. If the estimate from the neural network-based observer is close to zero, this demonstrates the effectiveness of the proposed method.

[0157] The main focus of the training results is joint torque, which is then converted into a Cartesian force representation. In this invention, only linear forces are considered, and rotational torque is ignored. Figure 5-6 The training results of the neural network on a test data sequence are shown. The trained neural network provides relatively accurate estimates, and its mean absolute error (MAE) and MSE values ​​are listed in Table 1.

[0158] Table 1 Test Data MSE and MAE

[0159] Parameter (Nm) X Y Z MAE 0.131 0.105 0.038 MSE 0.027 0.017 0.028

[0160] After integrating the trained neural network into the observer, the results of the free motion experiment are as follows: Figure 7 As shown in the figure, the external force estimated using the neural network observer is approximately zero, with an error range of [-1.2, 1.2] Nm. Considering the use of highly flexible electrical components to estimate the external force, this level of accuracy is considered satisfactory. The MAE and MSE of the baseline momentum observer and the neural network-based momentum observer are recorded in Table 2. The examples demonstrate that the method proposed in this invention is effective in mitigating the effects of system uncertainties and improving the accuracy of external estimation.

[0161] Table 2. External force MAE and MSE of the benchmark method and the NMO proposed in this application.

[0162] MAE X Y Z MSE X Y Z benchmark 1.71 1.49 0.30 benchmark 3.34 2.29 0.11 NMO 0.29 0.25 0.07 NMO 0.13 0.19 0.01

[0163] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the above embodiments do not limit the present invention in any way, and all technical solutions obtained by equivalent substitution or equivalent transformation fall within the protection scope of the present invention.

Claims

1. A method for detecting the end effector force of a flexible joint robot based on a neural network momentum observer, characterized in that, include: S1: Establish a dynamic mathematical model for the flexible joint robot; S2: Based on the system dynamics model, establish the momentum equation for the robot system under unconstrained free motion; S3: In light of the uncertainties of the robot system, establish a system dynamics model for the interaction between the robot and the environment, and construct momentum equations for the interaction process between the robot and the environment that include system uncertainties; S4: Determine the momentum observer to estimate the perturbation torque under unconstrained free motion; S5: A dynamic model of the disturbance torque of a robot system based on a neural network method; S6: Determine a momentum observer based on a neural network to estimate the external torque when the robot comes into contact with the environment; In step S1, considering the viscous friction terms on the joint motor side and the link side and neglecting the external forces interacting with the robot's environment, the dynamic model of the flexible joint robot can be expressed as: in, t J =K s (q-θ) (3) τ J ∈R 6 Represents the elastic force transmitted through the joint, q∈R 6 and θ∈R 6 These indicate the joint positions at the connecting end and the motor end, respectively. and τ represents the friction term at the connection end and the motor end, respectively. m ∈R 6 K represents the torque signal of the motor. s ∈R 6×6 and D s ∈R 6×6 It is a diagonal matrix representing the stiffness and damping coefficients of the joint, M(q)∈R 6 ×6 Represents the mass matrix, Let G(q) ∈ R represent the Coriolis force matrix. 6 Let I(θ) ∈ R represent the gravity vector. 6×6 The inertia matrix is ​​the motor side. From the matrix From the properties of skew-symmetric matrices, we can derive: Assume M(q), G(q) and The parameters are known, but due to mechanical structure errors, these parameters may be inaccurate; they are treated as parameter perturbations. The specific friction model is also unknown; the influence of friction and parameter perturbations on the system is also considered as system disturbance torque. Therefore, the robot's link-side model can be re-expressed as: Where τ δ ∈R 6 Indicates the system disturbance torque; Environmental forces can be expressed as: F e =K e (x e -x)=J -T (q)τ ex (10) Where x e K is the location vector of the environment. e ∈R 6×6 F represents the diagonal stiffness matrix of the environment. e ∈R 6 This represents the external force vector, which can be estimated using a momentum observer; Considering the system disturbance torque and external torque, the link-side model of the robot can be described as follows: Where τ ex ∈R 6 equals J T (q)F e ∈R 6 F e ∈R 6 It is an external force. According to formulas (4) and (10), we can obtain The time derivative is: In step S4, based on equation (11), the momentum observer of the robot in its unconstrained free motion state is defined as: Where, r δ (t c )∈R 6 It is the current time t c down r δ The observation results of (t), r δ (0) = 0, K I ∈R 6×6 It is a diagonal matrix, p(t) c ) indicates at time t c ≥0 generalized momentum of the robot; In step S5, a neural network method is used to approximate the perturbation dynamics of the system, and the observed perturbation torque is used as the target for training the neural network, τ. δ The approximation result can be expressed as: in, The value estimated using a neural network method can be represented as: Among them, f NN (·) represents the mapping of the neural network. This represents a very small, acceptable error that satisfies... in It is a predefined, very small constant.

2. The method for detecting the end effector force of a flexible joint robot based on a neural network momentum observer according to claim 1, characterized in that, In step S2, the total energy of the robot is defined as E, which is the sum of its kinetic energy T and gravitational potential energy U: in Based on (1) and (4), we can obtain: Therefore, the generalized momentum of a robot can be defined as: Based on (1) and (4), the time derivative of momentum p can be obtained as: This formula describes the change of generalized momentum over time, including the effects of internal and external disturbances to the system.

3. The method for detecting the end effector force of a flexible joint robot based on a neural network momentum observer according to claim 2, characterized in that, Substituting equations (5) and (9) into equation (12) to obtain their time derivatives, the dynamics of the linear and decoupled residuals can be expressed as: Its Laplace transform is: Where, r δ，j τ δ，j and K I，j They represent r respectively δ , τ δ and K I The diagonal element, j, represents the corresponding joint, under ideal conditions:

4. The method for detecting the end effector force of a flexible joint robot based on a neural network momentum observer according to claim 3, characterized in that, In (18), the input to the neural network is The output is The subscript indicates the corresponding joint; The specific steps for data acquisition and disturbance moment modeling are as follows: (1) Data acquisition process under free and unconstrained motion: Allow the robot end effector to move freely along an appropriate excitation trajectory, i.e., external torque τ ex =0, and at the same time, data is obtained through the momentum observer equation (13), including joint position q and joint velocity. and the observed residual r δ These data are recorded in time series format to facilitate neural network training; (2) Modeling of disturbance moment: A feedforward neural network is used to model the residual value r observed through equation (13). δ Perform approximations until the following condition is met: During training, mean squared error is chosen as the loss function, which is defined as follows: Where Θ represents the weights of the neural network, This represents the true state value of sample i. Let j represent the predicted value of sample i. In the formula, j = 1, 2, ..., N, where N is the length of the time series, and i = 1, 2, ..., M, where M represents the number of training set sample sequences.

5. The method for detecting the end effector force of a flexible joint robot based on a neural network momentum observer according to claim 4, characterized in that, The feedforward neural network is represented as: in k represents the k-th time step, Ψ(·) represents the ReLU activation function, and W1∈R 12×16 and W0∈R 16×6 β represents the weight matrices of the hidden layer and the output layer, respectively; i ∈R 16 and β0∈R 6 These represent the bias vectors of the hidden layer and the output layer, respectively.

6. The method for detecting the end effector force of a flexible joint robot based on a neural network momentum observer according to claim 3, characterized in that, The estimate obtained through step S5 Applied to (13), the expression for estimating external torque using a neural network-based momentum observer is: Where, r ex (t c ) represents the current time t c The observed external torque.

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