A robot driving control method, device, equipment and storage medium

Abstract

The application provides a robot driving control method, device, equipment and storage medium, comprising: calculating a tracking error according to a desired trajectory and an actual running trajectory corresponding to each joint of a current time of a linkage robot; calculating the tracking error by using a sliding mode control algorithm to obtain a first input torque of the current time; taking an actual input torque of a previous time and the actual running trajectory as inputs of a dynamic neural network to predict an unknown torque in a robot dynamics model at the current time, and taking the predicted unknown torque as a second input torque of the current time; determining an actual input torque of the current time according to the first input torque and the second input torque, and controlling the linkage robot to move according to the actual input torque of the current time; and solving the problem of stability and accuracy decline of the linkage robot caused by various uncertain factors in the prior art.

Description

Technical Field

[0001] This application relates to the field of robot control research, and in particular to a robot drive control method, device, equipment and storage medium. Background Technology

[0002] Due to their unique operability and flexibility, robots have been widely used in industrial assembly, machine welding, safety and explosion protection, and engineering machinery. For different task modes, different spatial motion trajectory planning is required for linkage robots to achieve precise positioning or tracking. Therefore, precise, fast, and efficient control of the actuators of linkage robots is particularly important. The spatial trajectory tracking control problem of linkage robots is to make the position, velocity, angular displacement, and other state information of the links track a given desired trajectory by giving the driving torque between each link. However, due to the inherent structural uncertainties, non-structural uncertainties, and environmental uncertainties in robot modeling, the stability and accuracy of the robot will decrease, ultimately leading to a significant deviation between the robot's trajectory and the desired trajectory. Summary of the Invention

[0003] This application provides a robot drive control method, apparatus, device, and storage medium to solve the problem of decreased stability and accuracy of linkage robots in the prior art due to various uncertainties.

[0004] In a first aspect, this application provides a robot drive control method, including:

[0005] The tracking error is calculated based on the expected trajectory and actual running trajectory of each joint of the linkage robot at the current moment.

[0006] The tracking error is calculated using a sliding mode control algorithm to obtain the first input torque at the current moment;

[0007] The actual input torque and the actual running trajectory of the previous moment are used as inputs to the dynamic neural network to predict the unknown torque in the robot dynamics model at the current moment, and the predicted unknown torque is used as the second input torque at the current moment.

[0008] Based on the first input torque and the second input torque, the actual input torque at the current moment is determined, and the linkage robot is controlled to move according to the actual input torque at the current moment.

[0009] In one or more possible embodiments, the step of using the actual input torque and the actual running trajectory from the previous moment as inputs to a dynamic neural network to predict the unknown torque in the robot's dynamics model at the current moment, and using the predicted unknown torque as the second input torque at the current moment, includes:

[0010] The input vector Z is used as the input to the dynamic neural network; wherein, the input vector Z includes the system state, the tracking error, and the actual input torque at the previous moment; the system state is used to characterize the actual running trajectory at the current moment;

[0011] The input vector Z is nonlinearly transformed by the weights and hidden layer activation functions of a dynamic neural network to obtain an approximate output of the unknown torque, and the approximate output is used as the second input torque at the current moment; wherein the approximate output includes an approximation error, and the approximation error is not greater than a preset value.

[0012] In one or more possible embodiments, the method further includes updating the weights of the dynamic neural network according to a preset update rate, the update rate being related to the tracking error and the actual input torque at the previous moment.

[0013] In one or more possible embodiments, the preset update rate is calculated according to the following formula:

[0014]

[0015] in, This indicates the preset update rate. The gain is the diagonal matrix gain, and j represents the number of hidden layer nodes. Let represent the hidden layer activation function, and s be the sliding mode surface vector constructed based on the tracking error. Represents the weights of a dynamic neural network. This represents the positive constant damping coefficient.

[0016] In one or more possible embodiments, the step of using a sliding mode control algorithm to calculate the tracking error and obtain the first input torque at the current moment includes:

[0017] The filtering error is determined based on the tracking error and its derivative.

[0018] A non-singular terminal sliding surface is constructed based on the filtered error signal; wherein, the non-singular terminal sliding surface is used to characterize the degree of deviation between the expected trajectory and the actual running trajectory of the linkage robot;

[0019] Based on the filtered error signal and the non-singular terminal sliding surface, the first input torque at the current moment is calculated using the following formula:

[0020]

[0021] in, This represents the first input torque at the current moment. and A constant greater than 0, For filtering error, Represents discontinuous symbolic functions; Represents the sliding mode surface vector of a non-singular terminal. and A constant greater than 0 The range is .

[0022] Secondly, this application provides a robot drive control device, comprising:

[0023] The error determination module is used to calculate the tracking error based on the expected trajectory and actual running trajectory of each joint of the linkage robot at the current moment.

[0024] The first input torque determination module is used to calculate the tracking error using a sliding mode control algorithm to obtain the first input torque at the current moment;

[0025] The second input torque determination module is used to use the actual input torque and the actual running trajectory of the previous moment as inputs to the dynamic neural network, predict the unknown torque in the robot dynamics model at the current moment, and use the predicted unknown torque as the second input torque at the current moment.

[0026] The drive module is used to determine the actual input torque at the current moment based on the first input torque and the second input torque, and to control the linkage robot to move based on the actual input torque at the current moment.

[0027] In one or more possible embodiments, the second input torque determination module is specifically used for:

[0028] The input vector Z is used as the input to the dynamic neural network; wherein, the input vector Z includes the system state, the tracking error, and the actual input torque at the previous moment; the system state is used to characterize the actual running trajectory at the current moment;

[0029] The input vector Z is nonlinearly transformed by the weights and hidden layer activation functions of a dynamic neural network to obtain an approximate output of the unknown torque, and the approximate output is used as the second input torque at the current moment; wherein the approximate output includes an approximation error, and the approximation error is not greater than a preset value.

[0030] In one or more possible embodiments, a weight update module is further included, which is used to update the weights of the dynamic neural network according to a preset update rate, the update rate being related to the tracking error and the actual input torque at the previous moment.

[0031] In one or more possible embodiments, the weight update module is specifically used for:

[0032] The preset update rate is calculated using the following formula:

[0033]

[0034] in, This indicates the preset update rate. The gain is the diagonal matrix gain, and j represents the number of hidden layer nodes. Let represent the hidden layer activation function, and s be the sliding mode surface vector constructed based on the tracking error. Represents the weights of a dynamic neural network. This represents the positive constant damping coefficient.

[0035] In one or more possible embodiments, the first input torque determining module is specifically used for:

[0036] The filtering error is determined based on the tracking error and its derivative.

[0037] A non-singular terminal sliding surface is constructed based on the filtered error signal; wherein, the non-singular terminal sliding surface is used to characterize the degree of deviation between the expected trajectory and the actual running trajectory of the linkage robot;

[0038] Based on the filtered error signal and the non-singular terminal sliding surface, the first input torque at the current moment is calculated using the following formula:

[0039]

[0040] in, This represents the first input torque at the current moment. and A constant greater than 0, For filtering error, Represents discontinuous symbolic functions; Represents the sliding mode surface vector of a non-singular terminal. and A constant greater than 0 The range is .

[0041] Thirdly, this application provides an electronic device, comprising: at least one processor, and a memory communicatively connected to said at least one processor, wherein:

[0042] The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the method as described in any of the first aspects.

[0043] Fourthly, this application provides a computer-readable medium storing computer-executable instructions for performing any of the methods described in the first aspect.

[0044] The robot drive control method, apparatus, device, and storage medium provided in this application can solve the problem of decreased stability and accuracy of linkage robots in the prior art due to various uncertainties. Attached Figure Description

[0045] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application, and do not constitute an undue limitation of this application.

[0046] Figure 1 This is a block diagram of a controller design method based on a mechanistic model, provided according to an embodiment.

[0047] Figure 2 This is a block diagram of a controller design method based on a local data model according to an embodiment;

[0048] Figure 3 This is a flowchart of a robot drive control method provided according to an embodiment;

[0049] Figure 4 This is a robust robot control architecture based on data-driven and structure-adaptive principles, provided according to an embodiment.

[0050] Figure 5 This is a system architecture diagram provided according to an embodiment;

[0051] Figure 6 This is a graph showing the given trajectory, actual trajectory, and tracking trajectory error of a link 1 according to an embodiment.

[0052] Figure 7 This is a graph showing the given trajectory, actual trajectory, and tracking trajectory error of a link 2 according to an embodiment.

[0053] Figure 8 This is a control input curve diagram of link 1 and link 2 according to an embodiment;

[0054] Figure 9 This is a prediction curve of the corresponding uncertainty factors for link 1 and link 2 according to an embodiment;

[0055] Figure 10 This is a schematic diagram of a robot drive control device according to an embodiment;

[0056] Figure 11This is a schematic diagram of an electronic device according to an embodiment;

[0057] Figure 12 This is a schematic diagram of a computer-readable storage medium provided according to an embodiment. Detailed Implementation

[0058] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0059] It should be noted that the terms "first," "second," etc., used in the specification, claims, and accompanying drawings of this disclosure are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this disclosure described herein can be implemented in orders other than those illustrated or described herein. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this disclosure. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this disclosure as detailed in the appended claims.

[0060] Furthermore, in the description of the embodiments of this application, unless otherwise stated, " / " means "or". For example, A / B can mean A or B. The "and / or" in the text is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can mean: A exists alone, A and B exist simultaneously, and B exists alone. In addition, in the description of the embodiments of this application, "multiple" means two or more.

[0061] Currently, most control methods for linear and nonlinear systems are based on models. If the mathematical model of the controlled system cannot be accurately obtained, it often leads to decreased control accuracy, deterioration of dynamic performance, and even system instability, making it difficult to achieve the expected control objectives.

[0062] The term "mechanism" refers to the process of establishing a mathematical model of a system through theoretical derivation, starting from its physical laws, kinematics, and dynamics principles. For example, for a mechanical system, its equations of motion can be constructed based on Newton's laws or Lagrange's equations; for a circuit system, its state equations can be established based on Kirchhoff's laws. This mechanism-based modeling approach has clear physical meaning, but its practical application is often limited by the complexity and uncertainty of the system.

[0063] Current controller design mainly follows three approaches: First, the controller is designed entirely based on a mechanistic model, with its structure and parameters derived from the theoretical model, such as... Figure 1 As shown; secondly, for systems with inaccurate mechanistic models and significant uncertainties, controller design can introduce data-driven or model-free methods for compensation within the mechanistic framework; thirdly, for systems with complex models, high orders, and strong nonlinearity, a controller design approach based on local data models can be adopted to reduce dependence on a globally accurate model, as shown in the following examples. Figure 2 As shown. The so-called "mechanism" refers to the process of establishing a mathematical model of a system through theoretical derivation, starting from the physical laws, kinematics, and dynamics principles of the system. For example, for a mechanical system, its equations of motion can be constructed based on Newton's laws or Lagrange's equations; for a circuit system, its state equations can be established based on Kirchhoff's laws. This mechanism-based modeling method has clear physical meaning, but in practical applications it is often limited by the complexity and uncertainty of the system.

[0064] With industrial development, increased production scale, higher equipment integration, and increasingly complex technological demands, establishing accurate mathematical models of systems has become extremely difficult. This is especially true for robotic systems, whose modeling process inevitably faces various uncertainties: structural uncertainties determined by their own properties and difficult to accurately estimate during motion; non-structural uncertainties caused by measurement errors, parameter perturbations, internal friction, and unmodeled higher-order dynamics; and environmental uncertainties from external disturbances (such as wind speed, temperature and humidity, and gravity changes). These factors make accurate robot modeling particularly difficult, thus posing a significant challenge to the design of high-precision, highly robust controllers. Furthermore, the effectiveness and accuracy of the robot's control and actuation methods largely determine the system's tracking performance. Existing control and actuation methods suffer from the following problems:

[0065] (1) Robot modeling inevitably involves structural uncertainty, non-structural uncertainty, and environmental uncertainty. This uncertainty makes it impossible to accurately model the robot, resulting in significant steady-state errors or even instability in practical applications of control methods based on accurate models.

[0066] (2) Robots are sensitive to changes in their own state and have high requirements for real-time performance. Therefore, there are strict requirements for the real-time performance and engineering implementation of control algorithms. However, existing high-precision control algorithms often have a heavy computational burden and are difficult to balance real-time performance and control accuracy.

[0067] (3) The robot control system is a complex system, which is affected by uncertain time-varying factors, internal friction, parameter perturbation, external environmental interference and gravity field. A reasonable controller is designed to ensure the stability of the system.

[0068] (4) The multi-morphic nature of robot tasks and how to design a stable controller that is not affected by structural changes are urgent problems to be solved.

[0069] (5) Existing parameter adaptive methods excel in fast response and real-time control, but have limited adaptability to environmental changes.

[0070] Due to their unique operability and flexibility, robots have been widely used in industrial assembly, machine welding, safety explosion protection, engineering machinery and other fields. For different task modes, it is necessary to plan the spatial motion trajectory of the linkage robot in order to achieve precise positioning or tracking. Therefore, it is particularly important to control the actuator of the linkage robot accurately, quickly and efficiently. The spatial trajectory tracking control problem of the linkage robot is to make the position, velocity, angular displacement and other state information of the linkage track the given desired trajectory by giving the driving torque between each link.

[0071] For ease of understanding, the terms used in the embodiments of this invention are explained below:

[0072] Data-driven control refers to a control theory and method that designs controllers without relying on a precise mechanistic model of the controlled object. It utilizes online or offline I / O data of the controlled system, along with knowledge derived from data processing, to design the controller, achieving convergence, stability, and robustness under certain assumptions. Essentially, the unknown parts of the model are equivalent to a dynamic linearized model, which is then used to approximate the unknown parts of the system. Its main advantages are that the controller design does not require precise knowledge of the system's mechanistic model, only the system's I / O data; it also does not require prior system training, enabling adaptive structural control, and is suitable for complex or difficult-to-model industrial systems.

[0073] Sliding mode variable structure control is a type of nonlinear controller with strong robustness and high fault tolerance to various uncertainties in the system. When the model and parameters of the controlled object vary within a certain range, a good control effect can be achieved by designing a sliding mode controller, meaning it has good fault tolerance to changes in system parameters, model uncertainties, and external disturbances. Currently, chattering elimination is one of the main research directions in sliding mode control. Time lag, sign function switching, and system inertia are all causes of system chattering. Sign function switching is also a major cause of system singularity. These causes not only increase system energy consumption and reduce the lifespan of actuators, but also easily excite unmodeled dynamics in the system, affecting the system control quality.

[0074] Finite-time stability is a core research direction in control theory. It requires that the state variables of a system converge precisely to zero after a finite time under specific initial conditions, rather than the infinite-time convergence of traditional asymptotic stability. Compared with traditional asymptotic stability (which only converges when time approaches infinity), finite-time stability has a faster convergence speed and stronger disturbance rejection performance, making it an important goal for high-precision and high-dynamic control systems.

[0075] Dynamic neural networks are a type of neural network with adaptive structure. This means that the network can automatically adjust its structure according to changes in input data or task requirements. This capability gives the network greater flexibility and efficiency when handling complex and variable tasks. Traditional neural networks typically require manual adjustment of hyperparameters and maintaining a fixed network structure during training, while dynamic neural networks can automatically optimize these parameters through real-time learning and feedback mechanisms, making them more advantageous when dealing with dynamic and changing tasks.

[0076] Adaptive structure: With the increasing complexity of data and the uncertainty of the environment, traditional fixed-structure models are difficult to cope with diverse needs. Adaptive structure improves flexibility and robustness by dynamically adjusting the model architecture. Adaptive structure refers to the ability of a system or model to adjust its own structure according to changes in the environment or input data. This ability enables the system to dynamically optimize performance and adapt to different scenarios.

[0077] Time axis synchronization strategy: Considering the lag in data transmission and control timing, and simulating the time delay phenomenon of biological neural networks, this invention adopts an adaptive approach to handle the time delay problem, thereby maintaining time axis synchronization. By monitoring system performance indicators (such as error and delay) in real time, the control law is dynamically adjusted to change the network dynamic characteristics and achieve the synchronization goal. Time axis synchronization control refers to ensuring the time coordination between different parts of the network or between different networks, so as to correctly process time-series data or achieve stable control of dynamic systems.

[0078] With the current development of industry, production scale, equipment manufacturing, and technological requirements have become very complex, making the establishment of precise mathematical models of systems seem impractical. However, system input / output (I / O) data is available. Therefore, this application is data-driven, utilizing observable I / O data to construct a direct description of the system's dynamic characteristics, thereby eliminating the reliance on precise analytical models. This application addresses the control problem of robots by providing a robot drive control method. It uses a dynamic neural network to predict unknown torques caused by uncertainties in the system model, i.e., to obtain a mathematical model of the unknown parts of the robot system. This achieves robust tracking control with online learning and adaptive capabilities, independent of precise dynamic models. A detailed flowchart is shown below. Figure 3 As shown, it includes:

[0079] Step 301: Calculate the tracking error based on the expected trajectory and actual running trajectory of each joint of the linkage robot at the current moment;

[0080] In one or more possible embodiments, a preset rotation angle is given for each joint of the linkage robot. Where i represents the nth joint and qi represents the given value of the rotation angle of the i-th joint; then, the actual rotation angle of each joint is measured by a sensor. This yields the actual measured value; for ease of subsequent calculations, we define... Let be the reference trajectory of the system, and satisfy . , , , If the actual running trajectory of the robot is given, then the tracking error can be defined by formula (1):

[0081] (1)

[0082] in, Let i be 1, 2, 3..., where i is a positive integer. The number of joints in this system (linkage robot) is the number of i.

[0083] Step 302: The tracking error is calculated using a sliding mode control algorithm to obtain the first input torque at the current moment;

[0084] In one or more possible embodiments, the robot model is divided into a local mechanistic model and a completely unknown mathematical model. The unknown mathematical model includes: internal and external disturbances of the structure, unknown gravity, mutual friction of the actuators, etc. The unknown mathematical model cannot be accurately measured and quantified, but the local mechanistic model can be obtained by the Lagrangian mechanistic modeling method; Formula (2) is the rigid body model of the linkage robot:

[0085] (2)

[0086] in, Here is the system inertia matrix. For Coriolis matrix, It is the gravity vector. The friction force vector. External disturbances in the geodetic coordinate system It is a constant matrix. To control the input torque, For system status, Represents the number of joints / links, i.e., the system order. These are joint angular displacement, angular velocity, and angular acceleration, respectively, all of which are system state vectors;

[0087] The rigid body model of the linkage robot has the following properties:

[0088] Property 1: The inertia matrix is ​​positive definite and symmetric, and satisfies: in, and It is an unknown positive constant.

[0089] Property Two: , where ζ represents an arbitrary, non-zero n-dimensional real column vector; Let denote the Euclidean norm of vector ζ.

[0090] In one or more possible embodiments, a filtering error is calculated based on the tracking error, specifically using the following formula: the filtering error is determined based on the tracking error and its derivative.

[0091] (3)

[0092] in, , , The symbols are diagonal matrix symbols, and, according to the structure of equation (3), and They have the same convergence.

[0093] In one or more possible embodiments, a non-singular terminal sliding surface is constructed based on the filtered error signal; wherein, the non-singular terminal sliding surface is used to characterize the deviation between the desired trajectory and the actual running trajectory of the linkage robot; the specific formula for the non-singular terminal sliding surface is as follows:

[0094] (4)

[0095] in, and If the value is greater than 0, the r-filter error signal is greater than 1, and sign( ) represents a symbolic function.

[0096] In one or more possible embodiments, formula (2) is modified to obtain formula (5):

[0097] (5)

[0098] From the properties of the rigid body model, we can see that... If it is positive definite, symmetric, and bounded, then It is also positive definite and bounded, so we can obtain formula (6).

[0099] (6)

[0100] in, It is a constant invertible diagonal matrix. It is unknown;

[0101] Formula (6) will The decomposition is into a constant diagonal matrix A and an unknown term Δm, mainly based on the physical characteristics of the robot's dynamics model and the control design requirements. Positive definite, symmetric, and bounded, with its inverse matrix existing and bounded, the system model is often decomposed into a known nominal part and an unknown perturbation part for the convenience of controller design and implementation: where A is an invertible diagonal matrix representing the nominal inertia of each joint after decoupling; Δm covers model uncertainties and unmodeled dynamics, providing a basis for subsequent design of robust or adaptive control laws, enabling the controller to effectively compensate for system disturbances and parameter changes while utilizing prior model information.

[0102] In one or more possible embodiments, the derivative of formula (4) is calculated to obtain formula (7):

[0103] (7)

[0104] Substituting formula (5) into formula (7), we get formula (8):

[0105] (8)

[0106] Furthermore, substituting formula (6) into formula (8), we obtain formula (9):

[0107] (9)

[0108] in: , , Based on physical facts, it is generally reasonable to assume that external disturbances are bounded, therefore This represents the maximum possible value of an external disturbance, indicating that the disturbance is bounded. In the design of robot control systems, external disturbances are a key factor affecting tracking accuracy and system stability. The impact of external disturbances is centrally represented and separated from the system model to facilitate controller design. Represents external disturbances in the geodetic coordinate system Inverse of the system inertia matrix After mapping, the equivalent perturbation term generated at the joint acceleration level (which can be obtained according to formula (5));

[0109] In one or more possible embodiments, transforming formula (9) yields the following formula (10):

[0110] (10)

[0111] Where δ represents the input of the control input torque, meaning that as long as this control input torque is calculated and applied to the system, the stability and tracking accuracy of the closed-loop system can be ensured; the calculable term in the formula is used as the first input torque at the current moment: , This represents the first input torque at the current moment. and A constant greater than 0, For filtering error, Represents discontinuous symbolic functions; Represents the sliding mode surface vector of a non-singular terminal. and A constant greater than 0 The range is Finally, use This represents the uncertainty in the prediction approximation; the specific calculation method is explained later.

[0112] Step 303: Use the actual input torque and the actual running trajectory of the previous moment as inputs to the dynamic neural network to predict the unknown torque in the robot dynamics model at the current moment, and use the predicted unknown torque as the second input torque at the current moment.

[0113] In one or more possible embodiments, the input vector Z is used as the input to a dynamic neural network; wherein the input vector Z includes the system state, the tracking error, and the actual input torque at the previous moment; the system state is used to characterize the actual running trajectory at the current moment; the input vector Z is nonlinearly transformed by the weights and hidden layer activation functions of the dynamic neural network to obtain an approximate output for the unknown torque, and the approximate output is used as the second input torque at the current moment; wherein the approximate output includes an approximate error, and the approximate error is not greater than a preset value;

[0114] For unknown functions A dynamic neural network can be designed to approximate it; an ideal adaptive dynamic neural network can be designed as shown in formula (11), as follows:

[0115] (11)

[0116] in: Neural network weights, where T represents the transpose of the matrix; For the hidden layer activation function, this application uses a Gaussian function. Where is the number of hidden layer nodes, P represents the number of joints / links (i.e., the system order), and Z is the input to the neural network. ,in These represent joint angular displacement, angular velocity, and angular acceleration, respectively, all of which are system state vectors. It is worth noting that vector Z contains... This represents the actual input torque at the previous moment, not the actual input torque at the current moment; To approximate the error, we have: ;

[0117] In one or more possible embodiments, the actual adaptive dynamic neural network can be designed as follows (12):

[0118] (12)

[0119] in: This represents the unknown parts of the predicted model, such as parameter perturbations, unmodeled dynamics, nonlinear coupling terms (Coriolis force, centrifugal force, gravity, friction), and external disturbances. It is the approximate output of the unknown torque, and the approximate output is used as the second input torque at the current moment. Let Z represent the Gaussian function, and let Z be the input to the neural network. To approximate the error; This indicates the preset update rate. The obtained neural network weights, This indicates the preset update rate. The gain is the diagonal matrix gain, and j represents the number of hidden layer nodes. Let represent the hidden layer activation function, and s be the sliding mode surface vector constructed based on the tracking error. Represents the weights of a dynamic neural network. This represents the positive constant damping coefficient.

[0120] In one or more possible embodiments, the weights of the dynamic neural network are updated according to a preset update rate, which is related to the tracking error and the actual input torque at the previous moment; specifically, the preset update rate is calculated according to the following formula:

[0121]

[0122] in, This indicates the preset update rate. Let j be the gain matrix, and j represent the number of hidden layer nodes. This represents the hidden layer activation function (Gaussian function), and the input to the neural network is Z. ,in These represent joint angular displacement, angular velocity, and angular acceleration, respectively, all of which are system state vectors. It is worth noting that vector Z contains... This represents the actual input torque at the previous moment, not the actual input torque at the current moment. s is the sliding surface vector constructed based on the tracking error. Represents the weights of a dynamic neural network. This represents the positive constant damping coefficient.

[0123] In one or more possible embodiments, in the design of adaptive control for robots based on dynamic neural networks, both "ideal" and "practical" neural network models are presented. This is a typical approach that balances theoretical completeness and engineering feasibility, aiming to transition from theoretical assumptions to implementable algorithms, thereby constructing a robust controller with strict stability guarantees and the ability to learn online. First, the ideal neural network model is expressed as follows: The model theoretically assumes the existence of a set of optimal weights W and a sufficient number of hidden layer nodes, enabling the neural network to operate with bounded error. (satisfy The ideal network approximates the lumped uncertainty N in the system. Here, "ideal" does not mean directly achievable, but rather to provide a reference upper bound for performance in subsequent stability analysis, indicating that the system's uncertainty can essentially be approximated by the neural network structure with controllable approximation error, thus laying the foundation for proving the stability of the entire closed-loop system. Secondly, the actual neural network model, based on the ideal structure, introduces an online adaptive update law for the weights: The design of the above update rate has clear engineering significance: the first item The weights are adjusted in real time based on the current sliding mode variable s, enabling the neural network to dynamically track changes in system uncertainty and achieve online learning and real-time compensation for unknown dynamics; the second term The damping term (correction term) prevents the weights from drifting or growing unbounded when the continuous excitation is insufficient or the tracking error is small, thereby enhancing the robustness of the neural network in long-term operation and avoiding over-parameterization or divergence. In summary, the feasibility and error boundary of neural network approximation are first theoretically established, and then a practical adaptive law with online learning and self-stabilizing mechanisms is designed. It not only ensures that the control system meets the stability requirements in the Lyapunov sense in theory, but also provides an algorithm structure that can be calculated and executed in real time in the actual system, thus effectively solving the problems of tracking accuracy and robustness caused by model uncertainty, parameter perturbation and external interference in robot control.

[0124] Step 304: Determine the actual input torque at the current moment based on the first input torque and the second input torque, and control the linkage robot to move according to the actual input torque at the current moment.

[0125] In one or more possible embodiments, the formula for calculating based on the first input torque and the second input torque is formula (10), specifically:

[0126] (10)

[0127] The first input torque in formula (10) is It has two levels of influence: based on the power term of the auxiliary variable r (i.e., the filtering error) This ensures that the tracking error converges quickly within a finite time; while the linear term based on the sliding mode variable s And power terms ( Together, they constitute a continuous sliding mode control law. Its purpose is to significantly reduce high-frequency chattering caused by the traditional sign function sign(s) while ensuring strong robustness, thereby reducing energy loss and extending the life of the actuator; the second input torque is... , representing the real-time approximation of the lumped uncertainty N of the system by the dynamic neural network, predicts and compensates for unknown torques caused by model uncertainty, parameter perturbations, nonlinear friction, and external disturbances in real time through online learning and adaptive weight adjustment, thereby effectively reducing model dependence and improving the controller's adaptability to complex dynamic environments; ultimately, the nominal model Handling known nominal dynamics; Online compensation for unknown dynamics; while O provides robustness and suppresses chattering. By combining model-based compensation, data-driven learning, and robust control, this method achieves high-precision, smooth, and robust tracking of the desired trajectory while ensuring global stability and finite-time convergence.

[0128] In one or more possible embodiments, such as Figure 4 As shown, this invention proposes a robust robot control architecture based on data-driven and structurally adaptive approaches. First, the controller (corresponding to Equation 10) integrates the desired trajectory and system feedback to calculate the actual input torque, forming control commands. This actual input torque incorporates nominal model compensation, robust sliding mode control, and neural network approximation terms, and acts on the rigid body model (i.e., the robot's dynamics model) to drive the actual system motion. The lumped uncertainty N (containing all unmodeled dynamics and disturbances) is separated and approximated online from the rigid body dynamics in real time, and learned and predicted using a structurally adaptive dynamic neural network, outputting... As an estimate of the unknown part N, the output will be... The data is fed back to the controller in real time to recalculate the actual input torque and generate control commands, forming a complete closed loop of "control-execution-learning-compensation". This architecture replaces the reliance on accurate models with data-driven online learning and combines a time axis synchronization strategy to ensure the real-time performance of predictions, ultimately achieving high-precision and robust tracking control under model uncertainty and external disturbances.

[0129] In one or more possible embodiments, substituting equations (10), (11), and (12) into equation (9) yields a closed-loop system:

[0130] (13)

[0131] in: Neural network weights, It is an online approximation of the weights of a neural network. It is the neural network weight approximation error. .

[0132] Therefore, for the known model (1) of the linkage robot, the controller is designed as (10), and the final closed-loop system is (13).

[0133] In one or more possible embodiments, such as Figure 5As shown, based on the control method provided in this application, a complete "physical system-digital model-learning prediction" system architecture diagram is presented, clearly demonstrating the implementation path from a partially known physical model to fully data-driven intelligent compensation. The complete dynamic model of the robot is explicitly decomposed into two parts: a "known nonlinear model" and an "unknown nonlinear model." The unknown part is then learned and synchronously predicted online using a data-driven method. The nonlinear model of the robot body refers to the part that can be accurately described by mechanistic modeling such as the Lagrange method (local mechanistic model). The nonlinear model of the robot body (internal state / unmodeled dynamics) refers to all uncertain dynamics that cannot be accurately described by a fixed mechanistic model due to parameter perturbations, complex friction, assembly errors, and environmental coupling (such as contact force in unstructured terrain). The time-axis synchronized data-driven prediction of the unknown model in this application is precisely for predicting the unmodeled dynamics. The state is determined based on real-time I / O data such as the actual rotation angle of the robot joints and control commands (given rotation angle, calculated actual input torque at the previous moment). Utilizing real-time I / O data, an adaptive dynamic neural network learns online and approximates the unmodeled dynamics. This network adaptively compensates for the inherent delays caused by sensing, communication, and computation, ensuring that the predicted output of the digital model is strictly synchronized with the current state of the physical robot, thus providing accurate and timely compensation signals for real-time control. The controller combines the known parts from the mechanistic model with the estimated unknown parts from the data-driven predictor to generate the final control torque, driving each joint to achieve precise rotation angle tracking. Ultimately, a robust intelligent control system capable of adapting to uncertainties online is constructed, effectively solving the accuracy and stability challenges faced by traditional model-dependent control in complex and variable environments.

[0134] To ensure that the drive control method of this application can achieve the stability of the closed-loop system, the following two aspects are used for proof:

[0135] Proof 1: All signals in the system are bounded.

[0136] Choose the Lyapunov function:

[0137] (14)

[0138] in, The selected Lyapunov candidate function is a scalar function used to analyze the stability of the closed-loop system. By proving that the function is positive definite and its derivative is negative definite, the conclusion that the system is stable can be drawn. s represents the sliding mode surface vector, which is a key indicator for measuring the tracking performance of the system. s=0 means that the system has reached the ideal tracking state. Indicates the transpose of s; The specific formula for calculating the approximation error of neural network weights is as follows: , Neural network weights, It is an online approximation of the weights of a neural network; : is the gain matrix The inverse matrix; tr( ) represents the trace operation of a matrix, which calculates the sum of the elements on the main diagonal of the matrix;

[0139] right Find the time derivative, substitute formula (13) into formula (14) to obtain formula (15):

[0140] (15)

[0141] If A Then there is Therefore, it exists: And there are: Therefore, according to formula (15), we obtain formula (16):

[0142] (16)

[0143] Therefore, the weight update rate for designing an adaptive dynamic neural network is:

[0144] (17)

[0145] Substituting formula (17) into formula (16), we get formula (18):

[0146] (18)

[0147] Because there are: And there are: ,in It is the Frobenius norm of the matrix, used to quantify the size or energy of the matrix; This represents a known upper bound on the weights of an ideal neural network; therefore, according to formula (18), formula (19) is further obtained:

[0148] (19)

[0149] In formula (19): and If the constants are greater than 0 and are all positive definite diagonal matrices, then The smallest eigenvalue , The smallest eigenvalue ,get: ;

[0150] Let the vector be i-th component. Let i be a positive integer, and the number of joints is the number of units i; therefore... ,p represents the number of joints; because ,so For the sliding mode surface vector s, since ,so ,get ;

[0151] and According to the Cauchy-Schwarz inequality and and ,get and ,in, This represents the maximum value of the external disturbance;

[0152] In formula (19), Y is expressed using formula (19-1):

[0153] (19-1)

[0154] If it exists:

[0155] (20)

[0156] Further solving equation (20) yields:

[0157] (twenty one)

[0158] As long as one of the conditions in formula (20) is met, such that Thus making Therefore, we can conclude that the system is eventually uniformly bounded, and the bound is:

[0159] (twenty two)

[0160] (twenty three)

[0161] From proof 1, we know that all signals in system (13) are bounded, therefore: Established; among them, A known upper bound constant representing the output vector of the activation function of a neural network.

[0162] Proof 2: Based on the premise that all signals in the system are bounded, the system achieves finite-time convergence, i.e., global stability.

[0163] The Lyapunov function is chosen as follows:

[0164] (twenty four)

[0165] Differentiating formula (24) yields:

[0166] (25)

[0167] in , This is the maximum value of the sum of the disturbance and the approximation error.

[0168] because:

[0169] Therefore, (24) can be written as:

[0170] (26)

[0171] According to Young's inequality Thus, we obtain formula (27):

[0172] (27)

[0173] Assumption Then formula (26) can be written as:

[0174] (28)

[0175] Further, it can be written as:

[0176] (29)

[0177] Based on formula (29), we can further derive formula (30):

[0178] (30)

[0179] For equation (30) Representing Lyapunov functions At the initial time t=0, the value is: Let Q be an arbitrarily given, small positive number; there exists a finite time T such that when Occasionally, If the condition is always met, a larger value can be selected. This allows the systematic error to approach the zero domain within a finite amount of time.

[0180] To verify the beneficial effects of the controller designed in this invention, a simulation was performed using a two-link planar robot model built with Matlab / Simulink.

[0181] The specific model parameters are as follows:

[0182]

[0183] in:

[0184]

[0185]

[0186] The design given value is: The amplitude is measured in radians (rad).

[0187] The simulation control parameters are: in formula (3), the set constant is... In formula (4), a constant is set. , in formula (10), , To design a dynamic neural network approximation, a controller is designed for the (9) open-loop system:

[0188] (10)

[0189] Uncertainty of system model use To perform time-axis synchronous prediction, in formula (12), For 11th-order neural network nodes, , This is the gain matrix.

[0190] The design parameters for link 1 are given trajectory, actual trajectory, and tracking trajectory error, as detailed below. Figure 6 As shown, Figure 6 As can be seen, the given trajectory of link 1 basically coincides with the actual trajectory, and the tracking error of joint 1 of the linkage robot can reach 10. -3 The system can achieve stability within 1 second, and its operation is on the order of magnitude (rad).

[0191] The design parameters for link 2 are given trajectory, actual trajectory, and tracking trajectory error, as detailed below. Figure 7 As shown, Figure 7 As can be seen, the given trajectory of link 2 basically coincides with the actual trajectory, and the tracking error of joint 2 of the linkage robot can reach 10. -3 The system can achieve stability within 1 second, and its operation is on the order of magnitude (rad).

[0192] Specifically, such as Figure 8 As shown, it can be seen that the controller designed in this invention has a bounded control input. Both theoretically and experimentally, it is reflected that the input energy is essentially bounded, that is, the input energy can be predicted.

[0193] Specifically, such as Figure 9As shown, the simulation curves between the estimated N and the actual N of links 1 and 2 are presented, and different colors are used to distinguish them. The uncertainty of the system model is predicted using the following formula: use By performing time-axis synchronous prediction, a mathematical model of the unknown parts of the system is obtained, from... Figure 9 It can be seen from this that (Estimation N) can synchronously follow N without time delay, and Synchronous prediction uses the first derivative to automatically optimize its feedback mechanism, thereby achieving structural adaptation to unknown models;

[0194] The robot drive control method provided in this application has the following advantages:

[0195] (1) It eliminates the heavy dependence on the system model when designing the controller and designs a data-driven control method based on time axis synchronization. By designing a dynamic neural network method that adopts the structure of system data for adaptive control (formulas (12) and (17)), the uncertainty of the system model is mitigated. By performing time-axis synchronous prediction, a mathematical model of the unknown parts of the system was obtained;

[0196] (2) By dynamically designing the weight update rate of the neural network, the disadvantages of traditional neural networks, which usually require manual adjustment of hyperparameters and maintaining a fixed network structure during training, are avoided. The dynamic neural network of this application can automatically optimize these parameters through real-time learning and feedback mechanisms, thereby achieving structural adaptation.

[0197] (3) By monitoring the system's error and control input energy in real time, the weight update rate is dynamically adjusted to change the network dynamics and achieve the time axis synchronization goal. It can be seen from formula (17) that the Gaussian function Input The control input of the closed-loop system is related to the system error e. The objective of this invention is to make e approach 0, and to control the input. Bounded, meaning the input energy is controllable, therefore this invention is based on e, The indicators are used to dynamically adjust the weight update rate to change the dynamic characteristics of the neural network, thereby achieving the goal of time axis synchronization.

[0198] (4) Improve the stability of the system by using non-singular terminal sliding mode. The sliding surface is designed as formula (4). By improving the sliding surface design, the singularity problem that may occur in traditional terminal sliding mode is eliminated. At the same time, the finite-time convergence characteristics are retained. This avoids the impact on the stability analysis of the closed-loop system caused by directly using the symbol function and the disadvantages of traditional sliding mode controllers that require knowledge of internal and external disturbances and uncertainty bounds.

[0199] (5) Theoretically, it is proven that the controller designed in this invention (Equation (10)) can achieve closed-loop stable control of the closed-loop system (Equation (13)) obtained from a partially known model of the linkage robot (Equation (1)). A Lyapunov function (Equation (14)) is designed to prove that all signals in the closed-loop system are bounded. A Lyapunov function (Equation (24)) is designed to prove that the system converges in finite time, i.e., it is globally stable. The advantage of finite-time convergence to 0 is fast response, high-precision control, and enhanced system stability.

[0200] (6) Predictable input energy: Most current controller designs start from the stable execution of the output end, without considering the energy at the input end. The controller designed in this invention integrates the control input of the closed-loop system with the system's input and output data. Theoretically, it has been proven that all signals in the system are bounded, meaning that the input energy is inherently bounded and predictable.

[0201] (7) The effectiveness of the control algorithm designed in this invention is verified by using a nonlinear model of a linkage robot built on Matlab / Simulink.

[0202] The application also provides a robot drive control device, such as Figure 10 As shown, it includes:

[0203] The error determination module 1001 is used to calculate the tracking error based on the expected trajectory and actual running trajectory of each joint of the linkage robot at the current moment.

[0204] The first input torque determination module 1002 is used to calculate the tracking error using a sliding mode control algorithm to obtain the first input torque at the current moment;

[0205] The second input torque determination module 1003 is used to use the actual input torque and the actual running trajectory of the previous moment as inputs to the dynamic neural network, predict the unknown torque in the robot dynamics model at the current moment, and use the predicted unknown torque as the second input torque at the current moment.

[0206] The drive module 1004 is used to determine the actual input torque at the current moment based on the first input torque and the second input torque, and to control the linkage robot to move based on the actual input torque at the current moment.

[0207] In one or more possible embodiments, the second input torque determination module is specifically used for:

[0208] The input vector Z is used as the input to the dynamic neural network; wherein, the input vector Z includes the system state, the tracking error, and the actual input torque at the previous moment; the system state is used to characterize the actual running trajectory at the current moment;

[0209] The input vector Z is nonlinearly transformed by the weights and hidden layer activation functions of a dynamic neural network to obtain an approximate output of the unknown torque, and the approximate output is used as the second input torque at the current moment; wherein the approximate output includes an approximation error, and the approximation error is not greater than a preset value.

[0210] In one or more possible embodiments, a weight update module is further included, which is used to update the weights of the dynamic neural network according to a preset update rate, the update rate being related to the tracking error and the actual input torque at the previous moment.

[0211] In one or more possible embodiments, the weight update module is specifically used for:

[0212] The preset update rate is calculated using the following formula:

[0213]

[0214] in, This indicates the preset update rate. The gain is the diagonal matrix gain, and j represents the number of hidden layer nodes. Let represent the hidden layer activation function, and s be the sliding mode surface vector constructed based on the tracking error. Represents the weights of a dynamic neural network. This represents the positive constant damping coefficient.

[0215] In one or more possible embodiments, the first input torque determining module is specifically used for:

[0216] The filtering error is determined based on the tracking error and its derivative.

[0217] A non-singular terminal sliding surface is constructed based on the filtered error signal; wherein, the non-singular terminal sliding surface is used to characterize the degree of deviation between the expected trajectory and the actual running trajectory of the linkage robot;

[0218] Based on the filtered error signal and the non-singular terminal sliding surface, the first input torque at the current moment is calculated using the following formula:

[0219]

[0220] in, This represents the first input torque at the current moment. and A constant greater than 0, For filtering error, Represents discontinuous symbolic functions; Represents the sliding mode surface vector of a non-singular terminal. and A constant greater than 0 The range is .

[0221] This application also provides an electronic device, including at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the robot drive control method described above.

[0222] like Figure 11 As shown, the device includes a processor 1101, a memory 1102, a communication interface 1103, and a bus 1104. The processor 1101, the memory 1102, and the communication interface 1103 are interconnected via the bus 1104.

[0223] Processor 1101 is configured to read instructions from memory 1102 and execute them, so that at least one processor can execute the robot drive control method provided in the above embodiments.

[0224] The memory 1102 is used to store various instructions and programs of the robot drive control method provided in the above embodiments.

[0225] Bus 1104 can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of representation, Figure 11 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0226] Processor 1101 can be a central processing unit (CPU), a network processor (NP), a graphics processing unit (GPU), or any combination of CPU, NP, and GPU. It can also be a hardware chip. The aforementioned hardware chip can be an application-specific integrated circuit (ASIC), a programmable logic device (PLD), or a combination thereof. The aforementioned PLD can be a complex programmable logic device (CPLD), a field-programmable gate array (FPGA), a generic array logic (GAL), or any combination thereof.

[0227] In addition, this application also provides a computer-readable storage medium, such as Figure 12 As shown, the computer storage medium stores a computer program that is used to cause the computer to perform any of the methods described in the above embodiments.

[0228] The memory may include readable media in the form of volatile memory, such as random access memory (RAM) 1201 and / or cache memory 1202, and may further include read-only memory (ROM) 1203.

[0229] The memory may also include a program / utility 1205 having a set (at least one) of program modules 1204, such program modules 1204 including but not limited to: an operating system, one or more application programs, other program modules, and program data, each or some combination of these examples may include an implementation of a network environment.

[0230] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0231] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to this application. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0232] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0233] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0234] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A robot drive control method, characterized in that, include: The tracking error is calculated based on the expected trajectory and actual running trajectory of each joint of the linkage robot at the current moment. The filtering error signal is determined based on the tracking error and its derivative. A non-singular terminal sliding surface is constructed based on the filtered error signal; wherein, the non-singular terminal sliding surface is used to characterize the degree of deviation between the expected trajectory and the actual running trajectory of the linkage robot; Based on the filtered error signal and the non-singular terminal sliding surface, the first input torque at the current moment is calculated using the following formula: ;in, This represents the first input torque at the current moment. and A constant greater than 0, This is the filtering error signal. Represents discontinuous symbolic functions; Represents the sliding mode surface vector of a non-singular terminal. and A constant greater than 0 The range is ; The input vector Z is used as the input to the dynamic neural network; wherein, the input vector Z includes the system state, the tracking error, and the actual input torque at the previous moment; the system state is used to characterize the actual running trajectory at the current moment; The input vector Z is nonlinearly transformed by the weights and hidden layer activation functions of a dynamic neural network to obtain an approximate output for the unknown torque, and the approximate output is used as the second input torque at the current moment; wherein the approximate output includes an approximation error, and the approximation error is not greater than a preset value; Based on the first input torque and the second input torque, the actual input torque at the current moment is determined, and the linkage robot is controlled to move according to the actual input torque at the current moment.

2. The method according to claim 1, characterized in that, Also includes: The weights of the dynamic neural network are updated according to a preset update rate, which is related to the tracking error and the actual input torque at the previous moment.

3. The method according to claim 2, characterized in that, The preset update rate is calculated using the following formula: in, This indicates the preset update rate. The gain is the diagonal matrix gain, and j represents the number of hidden layer nodes. Let represent the hidden layer activation function, and s be the sliding mode surface vector constructed based on the tracking error. Represents the weights of a dynamic neural network. This represents the positive constant damping coefficient.

4. A robot drive control device, characterized in that, include: The error determination module is used to calculate the tracking error based on the expected trajectory and actual running trajectory of each joint of the linkage robot at the current moment. The first input torque determination module is used to determine the filter error signal based on the tracking error and the derivative of the tracking error; A non-singular terminal sliding surface is constructed based on the filtered error signal; wherein, the non-singular terminal sliding surface is used to characterize the deviation between the desired trajectory and the actual running trajectory of the linkage robot; based on the filtered error signal and the non-singular terminal sliding surface, the first input torque at the current moment is calculated using the following formula: ;in, This represents the first input torque at the current moment. and A constant greater than 0, This is the filtering error signal. Represents discontinuous symbolic functions; Represents the sliding mode surface vector of a non-singular terminal. and A constant greater than 0 The range is ; The second input torque determination module is used to take the input vector Z as the input of a dynamic neural network; wherein the input vector Z includes the system state, the tracking error, and the actual input torque at the previous moment; the system state is used to characterize the actual running trajectory at the current moment; the input vector Z is nonlinearly transformed by the weights and hidden layer activation functions of the dynamic neural network to obtain an approximate output of the unknown torque, and the approximate output is used as the second input torque at the current moment; wherein the approximate output includes an approximate error, and the approximate error is not greater than a preset value; The drive module is used to determine the actual input torque at the current moment based on the first input torque and the second input torque, and to control the linkage robot to move based on the actual input torque at the current moment.

5. The apparatus according to claim 4, characterized in that, It also includes a weight update module, which is used to update the weights of the dynamic neural network according to a preset update rate, wherein the update rate is related to the tracking error and the actual input torque at the previous moment.

6. An electronic device, characterized in that, include: At least one processor, and a memory communicatively connected to said at least one processor, wherein: The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the method as described in any one of claims 1-3.

7. A computer-readable medium storing computer-executable instructions, characterized in that, The computer-executable instructions are used to perform the method as described in any one of claims 1-3.

Images