Method and device for constructing feedforward torque model coupled with spanwise driven joint

Abstract

The application provides a construction method and device of a feedforward torque model of a coupling span driven joint, and the method comprises the following steps: constructing an initial dynamics equation of each joint according to a steel wire rope torque between coupling span driven joints of a target object, an effective torque of each joint of the target object, and a motor torque corresponding to each joint; establishing a friction force model of each joint according to an actual speed of each joint and an actual friction force of each joint, and constructing a gravity model of each joint according to a low-speed reciprocating motion state quantity of each joint; constructing a target feedforward torque model of each joint according to the initial dynamics equation of each joint, the friction force model of each joint, the gravity model of each joint, and an optimal trajectory, wherein the target feedforward torque model comprises an observation matrix and a minimum parameter inertia set; and controlling the motion of each joint in the target object based on the target feedforward torque model of each joint. The accuracy of tendon coupling span driven joint parameter identification is improved.

Description

Technical Field

[0001] This application relates to the field of model building technology, and more specifically, to a method and apparatus for constructing a feedforward torque model of a coupled span drive joint. Background Technology

[0002] With the rapid development of robotics technology, especially the continuous progress in the fields of bionic robots, flexible robots, and humanoid robots, tendon-coupled span-driven joints have gradually become important actuators for achieving complex motion control due to their advantages such as high dexterity, lightweight, and humanoid structure. However, since tendon transmission systems are essentially flexible transmission mechanisms, their dynamic behavior exhibits significant nonlinearity and strong coupling characteristics, posing a severe challenge to high-precision torque modeling and control.

[0003] In existing technologies, dynamic modeling methods for robotic arms or joints mainly rely on Lagrange equations or the Newton-Euler method to construct theoretical models, and then combine these with parameter identification techniques to obtain a minimum set of inertial parameters. These methods are relatively mature in rigid linkage robots, but they exhibit significant limitations when dealing with tendon-driven systems. Models constructed using existing methods cannot achieve accurate control of tendon-coupled span-driven joints. Therefore, a new method for constructing feedforward torque models is urgently needed. Summary of the Invention

[0004] The purpose of this application is to address the shortcomings of the prior art by providing a method and apparatus for constructing a feedforward torque model of a coupled span drive joint, thereby improving the accuracy of constructing the feedforward torque model of the coupled span drive joint.

[0005] To achieve the above objectives, the technical solutions adopted in the embodiments of this application are as follows: In a first aspect, embodiments of this application provide a method for constructing a feedforward torque model of a coupled span-driven joint, the method comprising: Based on the wire rope torque between the coupled span drive joints of the target object, the effective torque of each joint of the target object, and the motor torque corresponding to each joint, the initial dynamic equations of each joint are constructed. The friction model of each joint is established based on the actual speed and actual friction force of each joint, and the gravity model of each joint is constructed based on the low-speed reciprocating motion state variables of each joint. Based on the initial dynamic equations of each joint, the friction model of each joint, the gravity model of each joint, and the optimal trajectory, a target feedforward torque model for each joint is constructed. The target feedforward torque model includes the observation matrix and the minimum parameter inertia set. The motion of each joint in the target object is controlled based on the target feedforward torque model of each joint.

[0006] Secondly, embodiments of this application also provide a device for constructing a feedforward torque model of a coupled span-driven joint, the device comprising: The first construction module is used to construct the initial dynamic equations of each joint based on the wire rope torque between the coupled span drive joints of the target object, the effective torque of each joint of the target object, and the motor torque corresponding to each joint. The second construction module is used to establish the friction force model of each joint based on the actual speed and actual friction force of each joint, and to establish the gravity model of each joint based on the low-speed reciprocating motion state variables of each joint. The third construction module is used to construct the target feedforward torque model of each joint based on the initial dynamic equations of each joint, the friction force model of each joint, the gravity model of each joint, and the optimal trajectory. The target feedforward torque model includes the observation matrix and the minimum parameter inertia set. The control module is used to control the movement of each joint in the target object based on the target feedforward torque model of each joint.

[0007] Thirdly, embodiments of this application also provide an electronic device, including: a processor, a memory, and a bus. The memory stores program instructions executable by the processor. When the application runs, the processor communicates with the memory via the bus, and the processor executes the program instructions to perform the steps of the method for constructing the feedforward torque model of the coupled span drive joint described in the first aspect.

[0008] Fourthly, embodiments of this application also provide a computer-readable storage medium storing a computer program, which is read and executes the steps of the method for constructing the feedforward torque model of the coupled span drive joint described in the first aspect.

[0009] The beneficial effects of this application are: This application provides a method and apparatus for constructing a feedforward torque model for a coupled span-driven joint. The method involves constructing initial dynamic equations for each joint based on the wire rope torque between the coupled span-driven joints of the target object, the effective torque of each joint, and the corresponding motor torque. Frictional force models for each joint are established based on their actual speed and frictional force, and gravity models are constructed based on their low-speed reciprocating motion states. Target feedforward torque models for each joint are constructed based on the initial dynamic equations, frictional force models, gravity models, and optimal trajectories. These target feedforward torque models include an observation matrix and a minimum parameter inertia set. The motion of each joint in the target object is controlled based on these target feedforward torque models. This data-driven approach addresses the problem of high-precision identification of frictional force models in complex tendon-coupled span-driven joints. By excluding the influence of nonlinear friction and gravity, and considering flexible transmission, the method improves the expressive power of the dynamic model and enhances the accuracy of parameter identification for tendon-coupled span-driven joints. Attached Figure Description

[0010] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0011] Figure 1 A flowchart illustrating a method for constructing a feedforward torque model of a coupled span-driven joint, as provided in an embodiment of this application; Figure 2 A flowchart illustrating the construction method of the feedforward torque model of the second coupled span drive joint provided in the embodiments of this application; Figure 3 A flowchart illustrating the method for constructing the feedforward torque model of the third coupled span drive joint provided in this application embodiment; Figure 4 A flowchart illustrating the method for constructing the feedforward torque model of the fourth coupled span drive joint provided in this application embodiment; Figure 5 A flowchart illustrating the method for constructing the feedforward torque model of the fifth coupled span drive joint provided in this application embodiment; Figure 6 This is a schematic diagram illustrating the convergence process of neural network model training provided in an embodiment of this application. Figure 7 A schematic diagram of a friction model provided in an embodiment of this application; Figure 8This is a schematic diagram of interactive force data collected by a force sensor, provided in an embodiment of this application. Figure 9 A comparative diagram of the verification results of a gravity model provided in an embodiment of this application; Figure 10 A comparative diagram illustrating the verification results of a target feedforward moment model provided in an embodiment of this application; Figure 11 A schematic diagram of an apparatus for constructing a feedforward torque model of a coupled span drive joint, as provided in an embodiment of this application; Figure 12 This is a structural block diagram of an electronic device provided in an embodiment of this application. Detailed Implementation

[0012] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. It should be understood that the accompanying drawings in this application are for illustrative and descriptive purposes only and are not intended to limit the scope of protection of this application. Furthermore, it should be understood that the schematic drawings are not drawn to scale. The flowcharts used in this application illustrate operations implemented according to some embodiments of this application. It should be understood that the operations in the flowcharts may not be implemented in sequence, and steps without logical contextual relationships may be reversed or implemented simultaneously. In addition, those skilled in the art, guided by the content of this application, may add one or more other operations to the flowcharts, or remove one or more operations from the flowcharts.

[0013] Furthermore, the described embodiments are merely some, not all, of the embodiments of this application. The components of the embodiments of this application described and illustrated herein can typically be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0014] It should be noted that the term "comprising" will be used in the embodiments of this application to indicate the presence of the features declared thereafter, but does not exclude the addition of other features.

[0015] Optionally, the method for constructing the feedforward torque model of the coupled span drive joint provided in this application embodiment can be applied to an electronic device, such as a mobile phone, tablet computer, laptop computer, PDA, desktop computer, or other terminal device with computing power and display function, or it can be a server. Specifically, it can be applied to applications in terminal devices, such as mobile phone applications (APP) and computer application systems.

[0016] Figure 1 This is a flowchart illustrating a method for constructing a feedforward torque model of a coupled span drive joint, as provided in an embodiment of this application. The execution subject of this method is as described above: electronic device. Figure 1 As shown, the method includes: S101. Based on the wire rope torque between the coupled span drive joints of the target object, the effective torque of each joint of the target object, and the motor torque corresponding to each joint, construct the initial dynamic equations of each joint.

[0017] The initial dynamic equations constructed are dynamic equations that include the characterization of tendon mechanical flexible coupling behavior, and these initial dynamic equations include frictional torque and gravitational torque.

[0018] The target object can be a biomimetic robot or a humanoid robot, etc. The target object may include three joints: one independent joint and two coupled span-driven joints. The two coupled span-driven joints are connected by a steel cable. For example, joint 1 is the independent joint of the target object, and joints 2 and 3 are coupled span-driven joints on the target object. Joint 1 is driven by motor 1, and joints 2 and 3 are driven by motors 2 and 3 simultaneously. The motor torque corresponding to joint 2 refers to the motor torque of motor 2, and the motor torque corresponding to joint 3 refers to the motor torque of motor 3.

[0019] The expression for the wire rope torque is as follows: Formula (I). The wire rope torque in Formula (I) is a matrix composed of the wire rope torques of each joint in the two coupled span drive joints.

[0020] Formula (1) in, For the torque of the wire rope, This represents the rotation angle of the joint. Let be the angular velocity of the joint. The rotation angle of the motor in the joint. The radius of the driving wheel, The radius of the drive wheel, For tendon stiffness coefficient, This represents the tendon damping coefficient.

[0021] The expression for the effective torque of each joint is shown in Formula (II) below. The effective torque in Formula (II) is a matrix composed of the effective torques of all joints.

[0022]

[0023] in, For effective torque, Here is the mass matrix of the link. Here is the matrix of centrifugal force and Coriolis force of the connecting rod. Let be the gravity vector matrix of the link. Let be the friction force matrix of the joint.

[0024] The expression for the motor torque corresponding to each joint is shown in Formula (III) below. The motor torque in Formula (III) is a matrix composed of the motor torques corresponding to all joints.

[0025] Formula (3) in, The moment of inertia matrix of the motor, Let be the damping coefficient matrix of the motor. This is the transmission ratio matrix of the motor. This is the friction force matrix of the motor. This refers to the motor torque.

[0026] S102. Establish friction models for each joint based on the speed and friction of each joint, and construct gravity models for each joint based on the low-speed reciprocating motion state variables of each joint.

[0027] Specifically, the frictional force model of tendon-driven joints can be obtained through neural network data driving, and the gravity model of each joint can be identified using regression model.

[0028] Optionally, considering that each joint has significant nonlinear friction characteristics during low-speed movement, directly using an idealized linear model would lead to large dynamic modeling errors. Therefore, a friction force model for each joint is constructed by collecting the speed of each joint at different movement stages and the friction force at each speed.

[0029] The low-speed reciprocating motion of each joint can refer to the small-amplitude reciprocating motion performed by each joint in a state of low speed and near zero acceleration. At this time, the inertial force and centrifugal force can be ignored. Therefore, the gravity model of each joint can be constructed based on the motion state variables of each joint in this state.

[0030] S103. Based on the initial dynamic equations of each joint, the friction model of each joint, the gravity model of each joint, and the optimal trajectory, construct the target feedforward torque model of each joint, and control the motion of each joint in the target object based on the target feedforward torque model of each joint.

[0031] The target feedforward moment model includes the observation matrix and the minimum parameter inertial set.

[0032] Optionally, since the initial dynamic equations include the effects of friction and gravity, these effects are removed from the initial dynamic equations. The minimum parameter inertia set in the target feedforward torque model is then solved based on the remaining inertial force, Coriolis force, and centrifugal force models. After obtaining the target feedforward torque model for each joint, the motion of each joint can be controlled based on this model. The obtained minimum parameter inertia set includes identification parameters for tendon elasticity; therefore, the target feedforward torque model takes into account the influence of tendon elasticity on joint motion, making the control of joint motion based on the obtained target feedforward torque model more precise.

[0033] Optionally, after obtaining the target feedforward torque model, a model that does not include tendon elasticity identification parameters can be used to compare with the target feedforward torque model in this embodiment to verify the accuracy of the target feedforward torque model in this embodiment.

[0034] In this embodiment, initial dynamic equations for each joint are constructed based on the wire rope torque between the coupled span-driven joints of the target object, the effective torque of each joint, and the corresponding motor torque. Frictional force models for each joint are established based on their actual speed and frictional force, and gravity models are constructed based on their low-speed reciprocating motion states. Target feedforward torque models for each joint are constructed based on their initial dynamic equations, frictional force models, gravity models, and optimal trajectories. These target feedforward torque models include observation matrices and a minimum parameter inertia set. The motion of each joint in the target object is controlled based on these target feedforward torque models. This data-driven approach solves the problem of high-precision identification of frictional force models in complex tendon-coupled span-driven joints. By excluding the influence of nonlinear friction and gravity, and considering flexible transmission, the expressive power of the dynamic model is improved, thus enhancing the accuracy of parameter identification for tendon-coupled span-driven joints.

[0035] Figure 2 A flowchart illustrating the method for constructing the feedforward torque model of the second coupled span drive joint provided in this application embodiment is shown below. Figure 2As shown, in S101 above, the initial dynamic equations for each joint are constructed based on the wire rope torque between the coupled span drive joints of the target object, the effective torque of each joint of the target object, and the motor torque corresponding to each joint. This can include: S201. Determine the link matrix information corresponding to the joint based on the wire rope torque between the coupled span drive joints and the effective torque of the joints.

[0036] The link matrix information includes the link mass matrix. Centrifugal force and Coriolis force matrix of connecting rod and the link gravity vector matrix .

[0037] Specifically, the link matrix information of the joints can be calculated based on formulas (I) and (II) above. The rotation angle, angular velocity, motor rotation angle, and effective torque of each joint can be collected, and these parameters can be substituted into formulas (I) and (II) to calculate the link mass matrix. Centrifugal force and Coriolis force matrix of connecting rod and the link gravity vector matrix Among them, the link mass matrix Centrifugal force and Coriolis force matrix of connecting rod and the link gravity vector matrix Each parameter can contain k rows of parameters, where the k-th row represents the matrix of the k-th joint. For example, the mass matrix of a link. The parameters in the k-th row represent the link mass matrix of the k-th joint.

[0038] S202. Based on the link matrix information corresponding to the joint, the friction force of the joint, the motor friction force corresponding to the joint, the motor torque corresponding to the joint, and the motor matrix information corresponding to the joint, construct the initial dynamic equation of the joint.

[0039] The motor matrix information includes the motor's moment of inertia matrix, damping coefficient matrix, and transmission ratio matrix.

[0040] Specifically, the initial dynamic equations for each joint can be obtained by combining equations (ii) and (iii) above. Specifically, the initial dynamic equation for joint 1 is shown in equation (iv) below.

[0041] Formula (IV) in, Link mass matrix The first line of parameters, The matrix of centrifugal force and Coriolis force of the connecting rod The first line of parameters, The gravity vector matrix of the connecting rod The first line of parameters, Let the frictional torque be that of joint 1. For motor torque 1, The moment of inertia matrix of motor 1, Here is the damping coefficient matrix for motor 1. Let be the transmission ratio matrix of motor 1. Here is the friction force matrix for motor 1. For joint angle, Joint angular velocity, Joint angular acceleration, The angular velocity of the motor is 1. Let 1 be the angular acceleration of the motor.

[0042] The initial dynamic equation of joint 2 is shown in Formula (V) below.

[0043] Formula (5) in, Link mass matrix The second line of parameters, The matrix of centrifugal force and Coriolis force of the connecting rod The second line of parameters, The gravity vector matrix of the connecting rod The second line of parameters, The frictional torque of joint 2, For motor torque 2, The moment of inertia matrix of motor 2, Here is the damping coefficient matrix for motor 2. This is the transmission ratio matrix for motor 2. Here is the friction force matrix for motor 2. For joint angle, Joint angular velocity, Joint angular acceleration, The angular velocity of the motor is 2. The angular acceleration of the motor is 2. For motor torque 3, The moment of inertia matrix of motor 3, Here is the damping coefficient matrix for motor 3. This is the transmission ratio matrix for motor 3. Here is the friction force matrix for motor 3. For joint angle, Joint angular velocity, Joint angular acceleration, The angular velocity of the motor is 3. The acceleration is the angular velocity of the motor.

[0044] The initial dynamic equation of joint 3 is shown in the following formula (VI).

[0045] Formula (VI) in, Link mass matrix The third line of parameters, The matrix of centrifugal force and Coriolis force of the connecting rod The third line of parameters, The gravity vector matrix of the connecting rod The third line of parameters, Let be the frictional torque of joint 3. For motor torque 2, The moment of inertia matrix of motor 2, Here is the damping coefficient matrix for motor 2. This is the transmission ratio matrix for motor 2. Here is the friction force matrix for motor 2. For joint angle, Joint angular velocity, Joint angular acceleration, The angular velocity of the motor is 2. The angular acceleration of the motor is 2. For motor torque 3, The moment of inertia matrix of motor 3, Here is the damping coefficient matrix for motor 3. This is the transmission ratio matrix for motor 3. Here is the friction force matrix for motor 3. For joint angle, Joint angular velocity, Joint angular acceleration, The angular velocity of the motor is 3. The acceleration is the angular velocity of the motor.

[0046] In this embodiment, the wire rope torque is taken into account when calculating the mass matrix, centrifugal force and Coriolis force matrix, and gravity matrix, that is, the flexibility factor of the coupled span drive joint is taken into account, so as to make the calculation results more accurate, and thus make the initial dynamic equation constructed based on the mass matrix, centrifugal force and Coriolis force matrix, and gravity matrix with consideration of the wire rope torque more accurate.

[0047] Figure 3 A flowchart illustrating the method for constructing the feedforward torque model of the third coupled span drive joint provided in this application embodiment is shown below. Figure 3 As shown, the friction force model of each joint established in S102 above based on the actual speed and actual friction force of each joint may include: S301. Generate the velocity matrix of each joint based on the actual velocity of each joint, input the velocity matrix of each joint into the neural network model corresponding to each joint, and obtain the friction information output by the neural network model corresponding to each joint.

[0048] The neural network model includes a first neural network model and a second neural network model, wherein the input layer of the first neural network model and the input layer of the second neural network model have different model parameters.

[0049] Specifically, the inputs to the neural network model are the velocities of joint 1 and the coupled joints. The velocities of joint 1, joint 2, and joint 3 can form a velocity matrix. The output of the neural network is the frictional torque of joint 1 and the coupled joints. The two hidden layer nodes use the Sigmoid function as their activation function.

[0050] S302. Based on the velocity matrix of each joint and the friction information output by the neural network model corresponding to each joint, determine the weight matrix and bias matrix of the hidden layer of the first neural network model and the hidden layer of the second neural network model, and construct the friction model based on the weight matrix and bias matrix.

[0051] Specifically, the friction force model expression is as shown in the following formula (VII).

[0052] Formula (VII) in, Frictional force at each joint; The velocity matrix is ​​input to the network; [The result is...] Let be the weight matrix of the hidden layer of the first neural network model, be the weight matrix of the hidden layer of the second neural network model, be the bias matrix of the first neural network model, and be the bias matrix of the second neural network model. This is the activation function.

[0053] Figure 4 A flowchart illustrating the method for constructing the feedforward torque model of the fourth coupled span-driven joint provided in this application embodiment is shown below. Figure 4 As shown, the gravity model of each joint constructed in S102 based on the low-speed reciprocating motion state variables of each joint may include: S401. Control the joint to reciprocate at low speed, and collect first state data and second state data with the same position, opposite speed and zero acceleration.

[0054] The first state data and the second state data satisfy the conditions of the following formula (viii).

[0055] Formula (8) in, The rotation angle of the joint in the first state data. Let be the angular velocity of the joint in the first state. The rotational angular acceleration of the joint in the first state data. The rotation angle of the joint in the second state data. The rotational angular velocity of the joint in the second state data. This represents the angular acceleration of the joint in the second state data.

[0056] S402. Add the effective joint torques corresponding to the first state data and the effective joint torques corresponding to the second state data to obtain the initial gravitational torque of the joint, and linearize the initial gravitational torque to obtain the gravity model of the joint.

[0057] Specifically, based on the above formulas (ii) and (viii), the effective torque of the joint corresponding to the first state data and the effective torque of the joint corresponding to the second state data can be added together to obtain the initial gravitational torque of the joint as shown in the following formula (ix).

[0058] Formula (8) in, The effective joint torque corresponding to the first state data. This represents the effective joint torque corresponding to the second state data.

[0059] Since each joint operates at an extremely low speed, there is no Coriolis force. Furthermore, because the speed is so small, the centripetal force of each joint can be neglected. Therefore, equation (8) can be simplified to the right side containing only the gravitational torque. That is, the simplified equation (8) is... The gravitational torque of joint 1 is approximated as 0. The gravitational torques of joint 2 and joint 3 are linearized to obtain the gravitational model of the joint as shown in the following formula (IX).

[0060] Formula (IX) in, The gravitational torque of joint 2, Let be the gravitational torque of joint 3. Let x be the distance from the center of mass of all members after link 2 to the origin of the link coordinate system 2 in the x-direction. This represents the distance in the x-direction from the center of mass of all members after link 2 to the origin of the link coordinate system 3; Let be the distance in the y-direction from the center of mass of all members after link 2 to the origin of the link coordinate system 2. Let be the distance in the y-direction from the center of mass of all members after link 2 to the origin of the link coordinate system 3. = , = , = , = .

[0061] Figure 5 A flowchart illustrating the method for constructing the feedforward torque model of the fifth coupled span drive joint provided in this application embodiment is shown below. Figure 5 As shown in S103, based on the initial dynamic equations of each joint, the friction model of each joint, the gravity model of each joint, and the optimal trajectory, a target feedforward torque model for each joint is constructed, which may include: S501. Subtract the friction model and gravity model of each joint from the initial dynamic equations of each joint to obtain the intermediate dynamic equations of each joint.

[0062] In the intermediate dynamic equations, the joint matrix after removing the friction and gravity models is equal to the product of the observation matrix and the minimum parameter inertial set.

[0063] Specifically, after subtracting the friction model and gravity model of the joint from the above formulas (iv) to (vi), the intermediate dynamic equations obtained from formulas (iv) to (vi) after subtracting the friction model and gravity model of the joint are as follows: Formula (x).

[0064] Formula (10) In the formula, The observation matrix, also commonly referred to as the regression matrix, has dimensions of 1. ; The joint torque after removing friction and gravitational components, with dimension 1. ; For the residual vector, This is the minimum parameter inertia set. At this point, the parameters in the minimum parameter inertia set of the intermediate dynamic equations are unknown parameters.

[0065] S502. Each joint performs multiple movements based on the optimal trajectory, and collects multiple sets of motion state information and motion motor torque.

[0066] Specifically, after obtaining the optimal trajectory of the target object, each joint is made to move at different times based on the optimal trajectory. Each time it moves, a set of motion state information and motion motor torque can be collected. Each set of motion state information includes the rotation angle, rotational angular velocity and rotational angular acceleration of the three joints, the rotation angle, rotational angular velocity and rotational angular acceleration of the motor corresponding to each joint, and the motion motor torque obtained for each movement.

[0067] S503. Based on multiple sets of motion state information, multiple sets of motion motor torques, and intermediate dynamic equations, determine the parameter values ​​of each parameter in the minimum parameter inertia set in the target feedforward torque model, and construct the target feedforward torque model for each joint.

[0068] Optionally, based on multiple sets of motion state information, multiple sets of motion motor torques, and intermediate dynamic equations, a preset method is used to determine the values ​​of each parameter in the minimum parameter inertia set in the target feedforward torque model. After determining the values ​​of each parameter in the minimum parameter inertia set, the values ​​of each parameter in the minimum parameter inertia set are substituted into the above formula (x) to obtain the target feedforward torque model.

[0069] Optionally, S503 above, determining the parameter values ​​of the minimum parameter inertia set in the target feedforward torque model based on multiple sets of motion state information, multiple sets of motion motor torques, and intermediate dynamic equations, may include: Substituting multiple sets of motion state information into the observation matrix of the intermediate dynamic equation, and substituting multiple sets of motor torque, friction torque, and gravitational torque into the joint matrix of the intermediate dynamic equation, the parameter values ​​of the minimum parameter inertia set in the intermediate dynamic equation are obtained. Among them, the friction torque of each set of motion is obtained based on the aforementioned formula (VII) and the motion parameters of the joint, and the gravitational torque of each set of motion is obtained based on the aforementioned formula (IX) and the motion parameters of the joint.

[0070] Specifically, multiple sets of motion state information are substituted into the observation matrix in the intermediate dynamic equation, and multiple sets of motor torque, friction torque and gravity torque are substituted into the joint matrix in the intermediate dynamic equation. Then, the observation matrix and torque vector obtained at each sampling time are stacked to form an overdetermined equation set, as shown in the following formula (XI).

[0071] Formula (XI) in, The torque of the m-th motor is... Let m be the frictional torque of the group. The m-th group of gravitational moments The motion state information of group m. It is the minimum parameter inertial set.

[0072] By using the standard least squares estimation method to identify the parameters of the stacked matrix, the estimated value of the minimum inertia parameter can be obtained: .

[0073] The final set of minimum inertial parameters .

[0074] in These are the identification parameters added after the tendon elastic deformation treatment.

[0075] Optionally, the process of determining the optimal trajectory includes: Obtain the state parameters of each joint at multiple time points, based on the objective function. Given the preset constraints and the state parameters, solve... The optimal trajectory is obtained, wherein, For the first Joints in finite Fourier series The coefficient of the cosine term, For the first Joints in finite Fourier series The coefficient of the sine term; For joints The fifth degree polynomial of the th Term coefficient, For the fundamental frequency, The number of harmonics, The total duration of the trajectory. These are variables calculated based on the sampling time.

[0076] in, The condition number measures the ill-conditioned nature of a matrix. It is the norm of the matrix inverse multiplied by the norm of the matrix itself. The 2-norm is called the spectral condition number. In parameter identification, this manifests as the increased influence of noise from joint and motor state measurements on the solution. Therefore, the condition number of the observation matrix should be as small as possible. The expression is as follows: .

[0077] The preset constraints are as follows (Formula XII).

[0078] Formula (12) in, They represent the first Each joint in time The angle, angular velocity, and angular acceleration at any given moment. They represent the first The maximum angle, maximum angular velocity, and maximum angular acceleration of each joint; and These represent the start and end times of the motion, respectively.

[0079] in, To ensure that the quintic polynomial terms have the same periodicity as the finite Fourier series, Where n is the current period of the Fourier series, specifically, . This ensures that the fifth-order polynomial terms also have the same period as the finite Fourier series, maintaining their inherent advantages. Simultaneously, the fifth-order polynomial and its first and second-order derivatives can be used to ensure that the excitation trajectory satisfies the boundary conditions: the initial and final positions of the trajectory are consistent with the structural design range, and the initial and final velocities and accelerations of the trajectory are zero. Each link can satisfy all six fifth-order polynomial coefficients through six boundary conditions. Using finite Fourier series coefficients , This indicates that the only variables remaining to be optimized are the coefficients of a finite Fourier series. To fully stimulate the parameters to be identified, while limiting the upper limits of output and input errors (i.e., reducing noise interference with identification), the condition number of the observation matrix is ​​used as the objective function. Considering the constraints of structure and motion space, the range of motion, velocity, and acceleration of each joint are set as inequality constraints for optimization to ensure that each joint operates within a reasonable range.

[0080] The design concept for the joint motion trajectory is as follows: A finite Fourier series combined with a fifth-order polynomial is used for the excitation trajectory design. The finite Fourier series is composed of sinusoidal signals, thus its velocity and acceleration expressions can be directly derived, reducing the noise impact of differential operations. Furthermore, due to the periodicity of the Fourier series, multiple repetitive trajectories can be executed during the experiment. The signal-to-noise ratio can be improved by averaging the results, enhancing the stability and accuracy of the measurement data. Simultaneously, introducing a fifth-order polynomial to replace the constant term in the finite Fourier series helps smooth the first and second derivatives of the trajectory, preventing vibration or jitter in the robotic arm when executing this excitation trajectory, thereby ensuring a smooth and stable trajectory. This not only improves signal continuity but also significantly reduces the impact of vibration on data acquisition accuracy, enhancing the system's response stability and robustness.

[0081] The following are example experimental data provided in this application.

[0082] For example, training data for the neural network needs to be collected first. In the experiment, multiple sets of trapezoidal velocity trajectories were planned for the three joints, with the speed of the uniform velocity segment of each trajectory increasing sequentially from 0.1 to 3 rad / s. Joint 1 is only affected by friction during uniform motion. The speed value of the uniform velocity segment was increased from the lowest speed of 0.1 rad / s to the highest speed of 3 rad / s in increments of 0.1 rad / s. The average value of the joint torque collected during the uniform velocity segment was taken as the friction value corresponding to that speed. Since the coupled joint is affected by both gravity and friction during constant speed motion, the coupled joint was placed horizontally to avoid the influence of gravity on the dynamic characteristics. In the coupled joint experiment, the speed value of the constant velocity segment of joint 2 was initially kept at the lowest speed value of 0.1 rad / s, while the speed value of the constant velocity segment of joint 3 was gradually increased from 0.1 rad / s to 3 rad / s, with each increment being 0.1 rad / s. Then, the constant velocity segment velocity value of joint 2 was increased by 0.1 rad / s, and the same process was repeated for the constant velocity segment of joint 3. Finally, the velocities of both joints were increased from 0.1 rad / s to 3 rad / s to obtain the velocity combinations of all coupled joints. The average value of the joint torque values ​​collected in each constant velocity segment is the friction force value corresponding to the coupled joint at different velocities. The neural network friction model was built using a Python 3.70 script based on the TensorFlow 2.9.1 framework. The datasets for joint 1 and coupled joints contained 1200, 2500, and 2500 samples, respectively. Before model training and testing, the input dataset was read and split into training and testing sets in an 8:2 ratio. All input variables in the training and validation sets were normalized to eliminate the bias of each input vector due to different scales. During the training phase, the batch size was set to 16. The learning rate and number of iterations were set to 0.005 and 1100, respectively. AdamW was set as the optimizer, and mean squared error (MSE) was selected as the loss function to guide model training. The model was trained for 1100 epochs, with validation performed after each epoch. The convergence process of the neural network model training is shown in Figure 6. Table 1 summarizes the specific training results, including the mean squared error (MSE), mean absolute error (MAE), and R-squared index on the validation set. The mean squared errors for the three joints reached 0.008 Nm, 0.048 Nm, and 0.12 Nm, respectively, and the mean absolute errors reached 0.051 Nm, 0.157 Nm, and 0.184 Nm, respectively, demonstrating good convergence results.

[0083] Table 1 Network training results

[0084] The friction model obtained through training is shown in Figure 7. The model shows that the trained friction model fits the training data very well. To verify the accuracy of the neural network friction model, a friction compensation experiment was designed. A handle was connected to cause the joint to reciprocate at a low speed along the axis. An ATI six-dimensional force sensor was used to detect the human-machine interaction force, thereby evaluating the model's accuracy. Friction compensation adopted feedforward control. In each control cycle, the controller collected the joint encoder speed in real time, inputting it into the friction model to calculate the compensation torque. After transmission ratio conversion, it was issued as a motor torque command. To eliminate the influence of gravity, the coupled joint was placed horizontally, and the friction compensation effect was tested under low-speed dragging. Comparative experiments were conducted under conditions with and without neural network compensation. The interaction force data collected by the force sensor is shown in Figure 7. Figure 8 As shown in Table 2, the peak difference (PP) and standard deviation (SD) of the experimental curves for different joints are shown in Table 2. From the frictional force experimental results of a single joint, it can be seen that the dragging interaction force during the uniform motion phase is almost 0 N, indicating that the neural network frictional force model has high accuracy. For joints 1, 2, and 3, the maximum time delay of the compensation error introduced by static friction at the start of motion or reversal reaches 0.33 s, 0.31 s, and 0.45 s, respectively. The introduced frictional force compensation error leads to a large dragging interaction torque value at the start or reversal, thus resulting in a poorer frictional force compensation effect at the start or reversal. From the comprehensive verification experimental results of the coupled joint frictional force model, it can be seen that the peak difference in the uncompensated case is 4.5 times and 6.32 times that of the compensated case in the x and y directions, respectively, and the standard deviation in the x and y directions is 5.6 times and 7.41 times that of the compensated case, respectively, indicating that the frictional force compensation result is good. After applying feedforward frictional force compensation, the drag resistance of the coupled joint is significantly lower.

[0085] Table 2 Experimental results of friction forces at different joints

[0086] For example, in this embodiment, to eliminate the interference of inertial force and centrifugal force on the identification process, the elbow joint is locked. A set of low-speed trapezoidal velocity curves is run for the shoulder joint extension / flexion degrees of freedom to ensure joint stability during identification. Joint torques and corresponding state data are extracted from the uniform velocity segment, and sampling points with the same position but opposite velocities are selected; their torque values ​​are then converted into gravity data. Based on this, the position data of joints 2 and 3 are filtered, substituted into the observation matrix, and fitted using the least squares method. The final identified gravity torque parameters are detailed in Table 3. To verify the accuracy of the gravity identification model, another set of low-speed trapezoidal velocity curves is run for the shoulder joint extension / flexion degrees of freedom. The actual gravity value of the joint is then compared with the model-predicted torque calculated using the gravity parameters. The verification results are shown in Figure 9. The root mean square error (RMSE) of the shoulder joint extension / flexion degree of freedom and the elbow joint extension / flexion degree of freedom modeling and identification were 0.072 Nm and 0.0585 Nm, respectively, indicating that the identified gravity model has high accuracy.

[0087] Table 3 Gravity parameter identification results

[0088] For example, in this embodiment, the optimized excitation trajectory is run continuously and repeatedly three times to collect motor position, torque data, and joint magnetic encoder position data. First, the raw data is averaged to obtain single-cycle data, thereby reducing the influence of random noise. Then, the torque data and position data are low-pass filtered respectively. Joint velocity, acceleration, motor velocity, and acceleration are obtained by continuous difference of theoretical position data to avoid the noise influence of difference. First, the least squares method is used to identify the parameters of the inertial force, Coriolis force, and centrifugal force models that include tendon elasticity terms. Then, the inertial force, Coriolis force, and centrifugal force models that do not include tendon elasticity terms are identified for comparative analysis. The number of parameters identified for the model that includes tendon elasticity terms is 21, and the number of parameters identified for the model that does not include tendon elasticity terms is 15. The specific identification results are shown in Table 4. Figure 10 This diagram illustrates the comparison of verification results for a target feedforward torque model provided in this application embodiment. The verification trajectory in Figure 10(a) is run to compare the actual torque collected by the motor with the torque predicted by the model, thereby verifying the accuracy of the identification model for inertial force, Coriolis force, and centrifugal force. The verification results are as follows: Figure 10 (b) Figure 10 (c) Figure 10 As shown in (d) in the table. Table 5 shows the root mean square error of the joint moment residuals with and without consideration of tendon elasticity.

[0089] Table 4 Model Identification Results

[0090] Table 5. Root mean square error of residuals for different joint moments

[0091] The identification results show that, without considering the influence of tendons, the root mean square errors (RMSE) for the three joint models are 0.5635 Nm, 0.8552 Nm, and 0.9277 Nm, respectively. After considering the influence of tendons, the RMSE for the three joint models decreases to 0.2155 Nm, 0.2468 Nm, and 0.2120 Nm, respectively, indicating that the proposed method can improve the accuracy of model estimation. The ratio of the RMSE value to the joint torque range for all three joints is less than 10%, indicating that the identified inertial force, Coriolis force, and centrifugal force models have high accuracy.

[0092] Figure 11 A schematic diagram of an apparatus for constructing a feedforward torque model of a coupled span drive joint, as provided in an embodiment of this application, is shown below. Figure 11 As shown, the device includes: The first construction module 601 is used to construct the initial dynamic equations of each joint based on the wire rope torque between the coupled span drive joints of the target object, the effective torque of each joint of the target object, and the motor torque corresponding to each joint. The second construction module 602 is used to establish the friction force model of each joint based on the actual speed and actual friction force of each joint, and to establish the gravity model of each joint based on the low-speed reciprocating motion state of each joint. The third construction module 603 is used to construct the target feedforward torque model of each joint based on the initial dynamic equation of each joint, the friction force model of each joint, the gravity model of each joint, and the optimal trajectory. The target feedforward torque model includes the observation matrix and the minimum parameter inertia set. The control module 604 is used to control the movement of each joint in the target object based on the target feedforward torque model of each joint.

[0093] Optionally, the first construction module 601 is specifically used for: Based on the wire rope torque between the coupled span drive joints and the effective torque of the joints, the link matrix information corresponding to the joints is determined. The link matrix information includes the link mass matrix, the link centrifugal force and Coriolis force matrix, and the link gravity vector matrix. Based on the link matrix information corresponding to the joint, the friction force of the joint, the motor friction force corresponding to the joint, the motor torque corresponding to the joint, and the motor matrix information corresponding to the joint, the initial dynamic equation of the joint is constructed. The motor matrix information includes the rotational inertia matrix of the motor, the damping coefficient matrix of the motor, and the transmission ratio matrix of the motor.

[0094] Optionally, the second building module 602 is specifically used for: Generate the velocity matrix of each joint based on the actual velocity of each joint; The velocity matrix of each joint is input into the neural network model corresponding to each joint to obtain the friction information output by the neural network model corresponding to each joint. The neural network model includes a first neural network model and a second neural network model, and the input layer of the first neural network model and the input layer of the second neural network model have different model parameters. Based on the velocity matrix of each joint and the friction information output by the neural network model corresponding to each joint, the weight matrix and bias matrix of the hidden layer of the first neural network model and the hidden layer of the second neural network model are determined. The friction force model is constructed based on the weight matrix and the bias matrix.

[0095] Optionally, the second building module 602 is specifically used for: Control the joint to reciprocate at low speed, and collect first state data and second state data with the same position, opposite speed and zero acceleration; The effective joint torque corresponding to the first state data and the effective joint torque corresponding to the second state data are added together to obtain the initial gravitational torque of the joint. The initial gravitational torque is then linearized to obtain the gravity model of the joint.

[0096] Optionally, the third building module is specifically used for: Subtracting the friction model and gravity model of each joint from the initial dynamic equation of each joint yields the intermediate dynamic equation of each joint. In the intermediate dynamic equation, the joint matrix after removing the friction and gravity models is equal to the product of the observation matrix and the minimum parameter inertia set. Each joint performs multiple movements based on the optimal trajectory, and collects multiple sets of motion state information and motion motor torque; Based on the multiple sets of motion state information, multiple sets of motion motor torques, and the intermediate dynamic equations, the parameter values ​​of each parameter in the minimum parameter inertia set in the target feedforward torque model are determined, and the target feedforward torque model of each joint is constructed.

[0097] Optionally, the third building module 603 is specifically used for: Substitute the multiple sets of motion state information into the observation matrix of the intermediate dynamic equation, and substitute the multiple sets of motion motor torques, the friction force model, and the gravity model into the joint matrix of the intermediate dynamic equation to obtain the parameter values ​​of each parameter in the minimum parameter inertia set of the intermediate dynamic equation.

[0098] Optionally, the process of determining the optimal trajectory includes: Obtain the state parameters of each joint at multiple time points; Based on the objective function Given the preset constraints and the state parameters, solve... The optimal trajectory is obtained, wherein, For the first Joints in finite Fourier series The coefficient of the cosine term, For the first Joints in finite Fourier series The coefficient of the sine term; For joints The fifth degree polynomial of the th Term coefficient, For the fundamental frequency, The number of harmonics, The total duration of the trajectory. These are variables calculated based on the sampling time.

[0099] Figure 12 This is a structural block diagram of an electronic device 700 provided in an embodiment of this application. (See diagram below.) Figure 12 As shown, the electronic device may include: a processor 701 and a memory 702.

[0100] Optionally, a bus 703 may also be included, wherein the memory 702 is used to store machine-readable instructions executable by the processor 701. When the electronic device 700 is running, the processor 701 communicates with the memory 702 via the bus 703, and the processor 701 executes the machine-readable instructions to perform the method steps in the above method embodiments.

[0101] This application also provides a computer-readable storage medium storing a computer program, which, when run by a processor, executes the method steps in the above-described embodiment of the method for constructing the feedforward torque model of the coupled span drive joint.

[0102] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems and devices described above can be referred to the corresponding processes in the method embodiments, and will not be repeated here. In the several embodiments provided in this application, it should be understood that the disclosed systems, devices, and methods can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. Furthermore, multiple modules or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the displayed or discussed mutual coupling or direct coupling or communication connection can be through some communication interfaces; the indirect coupling or communication connection of devices or modules can be electrical, mechanical, or other forms.

[0103] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. If the functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes: USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, optical disks, and other media capable of storing program code.

[0104] The above are merely specific embodiments of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for constructing a feedforward torque model of a coupled span-driven joint, characterized in that, The method includes: Based on the wire rope torque between the coupled span drive joints of the target object, the effective torque of each joint of the target object, and the motor torque corresponding to each joint, the initial dynamic equations of each joint are constructed. The friction model of each joint is established based on the actual speed and actual friction force of each joint, and the gravity model of each joint is constructed based on the low-speed reciprocating motion state variables of each joint. Based on the initial dynamic equations of each joint, the friction model of each joint, the gravity model of each joint, and the optimal trajectory, a target feedforward torque model for each joint is constructed. The target feedforward torque model includes the observation matrix and the minimum parameter inertia set. The motion of each joint in the target object is controlled based on the target feedforward torque model of each joint.

2. The method for constructing the feedforward torque model of the coupled span-driven joint according to claim 1, characterized in that, The initial dynamic equations for each joint are constructed based on the wire rope torque between the coupled span drive joints, the effective torque of each joint, and the corresponding motor torque of each joint, including: Based on the wire rope torque between the coupled span drive joints and the effective torque of the joints, the link matrix information corresponding to the joints is determined. The link matrix information includes the link mass matrix, the link centrifugal force and Coriolis force matrix, and the link gravity vector matrix. Based on the link matrix information corresponding to the joint, the friction force of the joint, the motor friction force corresponding to the joint, the motor torque corresponding to the joint, and the motor matrix information corresponding to the joint, the initial dynamic equation of the joint is constructed. The motor matrix information includes the rotational inertia matrix of the motor, the damping coefficient matrix of the motor, and the transmission ratio matrix of the motor.

3. The method for constructing the feedforward torque model of the coupled span-driven joint according to claim 1, characterized in that, The step of establishing a friction force model for each joint based on the actual speed and actual friction torque of each joint includes: Generate the velocity matrix of each joint based on the actual velocity of each joint; The velocity matrix of each joint is input into the neural network model corresponding to each joint to obtain the friction information output by the neural network model corresponding to each joint. The neural network model includes a first neural network model and a second neural network model, and the input layer of the first neural network model and the input layer of the second neural network model have different model parameters. Based on the velocity matrix of each joint and the friction information output by the neural network model corresponding to each joint, the weight matrix and bias matrix of the hidden layer of the first neural network model and the hidden layer of the second neural network model are determined. The friction force model is constructed based on the weight matrix and the bias matrix.

4. The method for constructing the feedforward torque model of the coupled span-driven joint according to claim 1, characterized in that, The construction of the gravity model for each joint based on the low-speed reciprocating motion state variables of each joint includes: Control the joint to reciprocate at low speed, and collect first state data and second state data with the same position, opposite speed and zero acceleration; The effective joint torque corresponding to the first state data and the effective joint torque corresponding to the second state data are added together to obtain the initial gravitational torque of the joint. The initial gravitational torque is then linearized to obtain the gravity model of the joint.

5. The method for constructing the feedforward torque model of the coupled span-driven joint according to claim 1, characterized in that, The process involves constructing a target feedforward torque model for each joint based on its initial dynamic equations, friction model, gravity model, and optimal trajectory. This includes: Subtracting the friction model and gravity model of each joint from the initial dynamic equation of each joint yields the intermediate dynamic equation of each joint. In the intermediate dynamic equation, the joint matrix after removing the friction and gravity models is equal to the product of the observation matrix and the minimum parameter inertia set. Each joint performs multiple movements based on the optimal trajectory, and collects multiple sets of motion state information and motion motor torque; Based on the multiple sets of motion state information, multiple sets of motion motor torques, and the intermediate dynamic equations, the parameter values ​​of each parameter in the minimum parameter inertia set in the target feedforward torque model are determined, and the target feedforward torque model of each joint is constructed.

6. The method for constructing the feedforward torque model of the coupled span-driven joint according to claim 5, characterized in that, The step of determining the parameter values ​​of the minimum parameter inertia set in the target feedforward torque model based on the multiple sets of motion state information, multiple sets of motion motor torques, and the intermediate dynamic equations includes: Substitute the multiple sets of motion state information into the observation matrix of the intermediate dynamic equation, and substitute the multiple sets of motion motor torques, the friction force model, and the gravity model into the joint matrix of the intermediate dynamic equation to obtain the parameter values ​​of each parameter in the minimum parameter inertia set of the intermediate dynamic equation.

7. The method for constructing the feedforward torque model of the coupled span-driven joint according to claim 1, characterized in that, The process of determining the optimal trajectory includes: Obtain the state parameters of each joint at multiple time points; Based on the objective function Given the preset constraints and the state parameters, solve... The optimal trajectory is obtained, wherein, For the first Joints in finite Fourier series The coefficient of the cosine term, For the first Joints in finite Fourier series The coefficient of the sine term; For joints The fifth degree polynomial of the th Term coefficient, For the fundamental frequency, The number of harmonics, The total duration of the trajectory, These are variables calculated based on the sampling time.

8. A device for constructing a feedforward torque model of a coupled span-driven joint, characterized in that, include: The first construction module is used to construct the initial dynamic equations of each joint based on the wire rope torque between the coupled span drive joints of the target object, the effective torque of each joint of the target object, and the motor torque corresponding to each joint. The second construction module is used to establish the friction force model of each joint based on the actual speed and actual friction force of each joint, and to establish the gravity model of each joint based on the low-speed reciprocating motion state variables of each joint. The third construction module is used to construct the target feedforward torque model of each joint based on the initial dynamic equations of each joint, the friction force model of each joint, the gravity model of each joint, and the optimal trajectory. The target feedforward torque model includes the observation matrix and the minimum parameter inertia set. The control module is used to control the movement of each joint in the target object based on the target feedforward torque model of each joint.

9. An electronic device, characterized in that, It includes a memory and a processor, the memory storing a computer program executable by the processor, and the processor executing the computer program to implement the steps of the method for constructing the feedforward torque model of the coupled span drive joint as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, performs the steps of the method for constructing a feedforward torque model of a coupled span-driven joint as described in any one of claims 1-7.

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