Adaptive backstepping fault-tolerant control method for rope-driven flexible robot based on neural network

Abstract

The application discloses a rope-driven flexible robot based on neural network adaptive backstepping fault-tolerant control method, comprising the following steps: S1, obtaining a dynamic model and giving a desired reference trajectory; S2, introducing a quaternion to eliminate error and obtaining tracking error of a robot working end; S3, designing a backstepping fault-tolerant control law, according to a robot model and a control target of trajectory tracking, designing a control law of a robot trajectory tracking controller and determining control parameters; S4, introducing an RBF neural network model to approximate unknown quantities which are difficult to directly obtain in the control law; S5, analyzing stability and convergence of the backstepping fault-tolerant system, adjusting control parameters of the controller and outputting trajectory tracking results. The application designs an RBF neural network adaptive backstepping fault-tolerant controller for a rope-driven flexible continuous robot, on the basis of guaranteeing stable tracking of the system by using the backstepping control scheme, a fault-tolerant control scheme is added, so that safety of the robot is ensured when a fault occurs in an actuator.

Description

Technical Field

[0001] This invention relates to the field of trajectory tracking technology for robot systems, and in particular to a fault-tolerant control method for a rope-driven flexible robot based on neural network adaptive inversion. Background Technology

[0002] In applications requiring highly precise and detailed control, rope-driven flexible continuous robots necessitate accurate and rapid control schemes to ensure their continued development in practical applications. Therefore, obtaining a reliable and stable control scheme is crucial. However, the inherent high nonlinearity of the robot after modeling, along with the elastic properties of the materials, undoubtedly poses challenges to its stability. Inverse control, as a recursive nonlinear controller design method, achieves global stability by progressively designing virtual control variables and constructing Lyapunov functions.

[0003] Tendon-driven continuous robots have attracted widespread attention due to their simple structure and ease of implementation, and significant progress has been made in their controllers. Alqumsan et al. first designed a robust controller for a rope-driven continuous robot. Subsequently, they proposed a multi-sliding surface control method based on an adaptive RBF neural network.

[0004] (Modeling and Adaptive Neural Network Control for a Soft Robotic Arm With Prescribed Motion Constraints) effectively solves the uncertainty problem under unmatched conditions by using an RBF neural network as an uncertainty approximator. However, its controller still needs to directly obtain the spatial derivatives of the internal forces of the links, which is difficult to achieve in practical applications. Yang et al. considered the unmodeled dynamics of the robot system and designed an adaptive neural network controller using backstepping and an RBF neural network to solve the motion constraint problem of continuous robots. However, like most controllers, it did not consider actuator failures. In fact, control systems often fail due to problems with actuators, sensors, or the system itself. Given that continuous robots are often used in surgery or industrial inspection, their failures can lead to serious losses or even endanger personal safety. Therefore, designing effective fault-tolerant control schemes to maintain system stability and ensure acceptable control performance is crucial. Summary of the Invention

[0005] To address the technical problems existing in the prior art, this invention proposes an RBF neural network adaptive inversion fault-tolerant controller for rope-driven flexible continuous robots. This scheme, while ensuring stable tracking of the system through inversion control, introduces a fault-tolerant mechanism to ensure the robot's safe operation even when actuators malfunction.

[0006] The present invention is achieved by at least one of the following technical solutions.

[0007] The rope-driven flexible robot adopts a neural network-based adaptive inversion fault-tolerant control method, which includes the following steps: S1. Establish the dynamic model of the robot based on the structure of the rope-driven flexible continuous robot, and obtain the position of the robot's working end effector; S2. Compare the actual position of the robot's end effector with the expected reference trajectory to obtain the tracking error of the robot's end effector position; S3. Based on the tracking error information of the position, design the inversion control law, introduce the fault-tolerant model to form the inversion fault-tolerant system, and design the control law of the robot trajectory tracking controller and determine the control parameters based on the robot model and the control objective of trajectory tracking. S4. Introduce the RBF neural network model to redesign the control law for unknown quantities that are difficult to obtain directly in the approximate control law. S5. Analyze the stability and convergence of the RBF neural network adaptive inversion fault-tolerant system, adjust the control parameters of the controller, and output the trajectory tracking results.

[0008] Furthermore, in step S1, the structure of the rope-driven flexible continuous robot includes an elastic main rod, multiple support plates connected in series through the main rod, and four ropes that are parallel and symmetrical to each other in pairs. The four ropes are connected to the main rod through a series of support plates.

[0009] Furthermore, in step S2, truncation error is eliminated by quaternions to obtain the actual position of the robot's end effector.

[0010] Furthermore, step S3 includes the following steps: S31. Considering the external disturbances experienced by the robot system, for x For a system on an axis, let the first state variable be... For the end of the rod at The position of the axis, the second state variable For the end of the rod at The first derivative of the position of the axis with respect to time will The result of the two ropes on both sides of the axis being equivalent to a single rope achieving negative tension is... ; S32. Based on the control objectives of the robot system state, and considering fault-tolerant control, set the actuator effectiveness coefficient. Then there is Equivalent result of the two ropes on both sides of the axis ,in It is a control law; S33. Design an inverse fault-tolerant control law and use adaptive parameter estimation to estimate the actuator effectiveness coefficients. Assuming the desired reference trajectory is The control objective is that after a partial actuator failure occurs, the controller can quickly correct the fault, and when... The closed-loop system is stable. ,in This indicates the actual speed of the robot's end effector. This indicates the expected reference speed of the robot's end effector.

[0011] Furthermore, in step S3, the design of the inversion fault-tolerant control law includes: defining a first Lyapunov function based on the error between the desired position and the actual position of the robot end effector; defining a second error variable based on the virtual control variable and the second state variable; and defining a second Lyapunov function based on the first Lyapunov function and the actuator effectiveness coefficient, so that the error variable tends to zero, thereby obtaining a control law that makes the entire system asymptotically stable.

[0012] Furthermore, in step S4, the approximation term of the RBF neural network model is defined as: (1); in Represents the approximation terms of a neural network. This represents an estimate of the actuator effectiveness coefficient. This represents the output of the Gaussian function. Gaussian function The independent variable, Let be the first derivative of the internal force of the rod with respect to space and time. For external load distribution force, Represents a vector in The values ​​on the axis, It is the ideal weight of the network. It is the approximation error of the neural network; The estimated value ,in, The estimated values ​​of the network weights are taken as follows: To estimate the error, then estimation error .

[0013] Furthermore, in step S4, the redesigned control law is: (2); in, It is the mass density of the robot's main shaft. It is the cross-sectional area of ​​the robot's main shaft. It is the mass density of the robot's main shaft. It is the cross-sectional area of ​​the robot's main shaft. It is a positive number. for The midpoint between the two ropes on either side of the axis. Indicates the actuator effectiveness coefficient The estimated value, This indicates the desired tracking speed of the robot's end effector. It is a positive number. This represents the first derivative of the error between the desired and actual positions of the robot's end effector with respect to time. express The estimated value, This indicates the strength of the robustness term. The robust term is represented by a symbolic function.

[0014] Further, in step S5, the stability and convergence of the RBF neural network adaptive inversion fault-tolerant system are analyzed, including: Based on the second Lyapunov function in step S3 and the third Lyapunov function defined to obtain the adaptive rate of neural network weights and the adaptive rate of actuator effectiveness coefficients, the time derivative of the third Lyapunov function is described by the error between the expected position and the actual position of the robot end effector and the first derivative of the error with respect to time. According to the LaSalle invariance principle, the control system is asymptotically stable if and only if the error between the expected position and the actual position of the robot end effector and the first derivative of the error with respect to time are both zero.

[0015] A computer device according to the present invention includes a memory and a processor, the memory being electrically connected to the processor, the memory storing a computer program, which, when executed by the processor, causes the processor to implement the method described herein.

[0016] The present invention provides a computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor implements the method described herein.

[0017] Compared with the prior art, the present invention has the following advantages and beneficial effects: 1. This invention demonstrates that the inversion controller has good dynamic performance and tracking accuracy. In the actual control of continuum robots, it is difficult to obtain an accurate model due to the limitations of sensors. The invention introduces the part that is difficult to obtain in the RBF neural network approximation model.

[0018] 2. This invention introduces a fault-tolerant model on the basis of the inversion controller, which ensures that the robot can still operate safely when the actuator fails. Attached Figure Description

[0019] Figure 1 This is a flowchart of a method for adaptive inversion fault-tolerant control of a rope-driven flexible robot based on a neural network, according to the present invention. Figure 2 This is a schematic diagram of the structure of the rope-driven flexible continuous robot in an embodiment of the present invention; Figure 3 This is a schematic diagram of the robot end effector trajectory under different control schemes under a constant partial failure fault in an embodiment of the present invention; Figure 4 This is a schematic diagram of robot end-effector tracking error and speed under different control schemes under constant partial failure faults in embodiments of the present invention; Figure 5 In this embodiment of the invention, under a constant-value partial failure fault, the actual tension of the rope and the controller control input are... Schematic diagram. Detailed Implementation

[0020] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0021] like Figure 1 As shown in the figure, this embodiment of a rope-driven flexible robot adopts an adaptive inversion fault-tolerant control method based on a neural network, which includes the following steps: S1. Obtain the dynamic model and desired reference trajectory of the robot based on the structure of the rope-driven flexible continuous robot.

[0022] Specifically, in this embodiment, the specific process of step S1 is as follows: S11, the structure of the rope-driven flexible continuous robot is as follows: Figure 2 As shown, the rope-driven continuous robot mainly consists of a central elastic main rod 1, support disks 2 threaded onto the elastic main rod 1, and four parallel and symmetrical drive ropes 3. These ropes 3 are connected to the elastic main rod 1 through a series of support disks 2. The mass of the support disks 2 and the ropes 3 is negligible, as is the friction between the support disks 2 and the ropes 3.

[0023] This invention uses Cosserat link theory to model the robot's main link and rope separately, and then couples the two models to obtain the robot's dynamic model.

[0024] S12. The robot's dynamic model is as follows: (1); in It is a spatial position variable, namely the arc length of the main rod. L The length of the main stem, It is a time variable. This is the centerline position of the robot's main shaft. The rotation matrix of the robot's main link. Let be the curvature vector of the rod in the local coordinate system. The rate of change of the rod's position relative to the arc length. It is the velocity of the rod in the local coordinate system. It is the angular velocity of the rod in the local coordinate system; Subscript and Let represent the first derivatives of the variables with respect to space and time, respectively. and Let be the first derivatives of the robot's main shaft's centerline position with respect to space and time, respectively. and Let be the first derivatives of the rotation matrix of the robot's main link with respect to space and time, respectively. and Let be the first derivatives of the curvature vector in the local coordinate system with respect to space and time, respectively. and Let be the first derivatives of the rate of change of the rod's position with respect to arc length, with respect to space and time, respectively. and It is the first derivative of the rod's velocity in the local coordinate system with respect to space and time, respectively. and It is the first derivative of the rod's angular velocity in the local coordinate system with respect to space and time, respectively; superscript This represents a mapping from a three-dimensional vector space to its antisymmetric matrix. for antisymmetric matrix, for Antisymmetric matrix; superscript This represents the initial value of the variable. for initial value, for initial value, for initial value, for initial value, subscript Indicates external load, subscript This indicates the effect derived from the rope, that is For external load distribution force, For external load distributed torque, The force distributed in the rope, The distributed torque of the rope is given per unit arc length. The applied force and torque are defined as follows: and , It is the mass density of the robot's main shaft. It is the cross-sectional area of ​​the robot's main shaft. Here is the rotational inertia matrix. Here are the shear and tensile stiffness matrices. Here are the bending and torsional stiffness matrices.

[0025] S13. The model of the robot's four ropes is as follows: In the global coordinate system, assume the first... The path of the root rope is represented as It satisfies the following relationship: (2); in Indicates the first The offset of the root rope from the center of the cross-section of the robot's main rod in the local coordinate system: (3); in and They are respectively x On the y-axis and the first The offset function between the root rope and the center of the cross section of the robot's main rod; Assuming internal forces and The forces distributed in the rope are tangent in direction, and neglecting friction and inertia. and distributed moment This is obtained through the following relationship: (4); in It is the first Tension on the rope n For the number of ropes, for antisymmetric matrix, for antisymmetric matrix, Let be a spatial rotation matrix, which is used to rotate the matrix in space. Taking the first and second partial derivatives, we get: (5); In the formula for The first derivative with respect to space, for The second derivative with respect to space; for The first derivative with respect to space, for The second derivative with respect to space; The rate of change of the rod's position relative to the arc length. It is the first derivative of the rate of change of the rod position with respect to the arc length with respect to space; for antisymmetric matrix, for antisymmetric matrix, It is a spatial rotation matrix.

[0026] As one embodiment, a given reference motion trajectory ,and .

[0027] S2. Introduce quaternions to eliminate truncation error, obtain the actual position of the robot's end effector, feed it back to the controller, and subtract it from the expected reference trajectory in step S1 to obtain the tracking error of the robot's end effector position.

[0028] Specifically, in this embodiment, the specific process of step S2 is as follows: S21. Introduction of Quaternions for: (6); in Quaternion The real part, The imaginary unit, The coefficient corresponding to the imaginary unit. Quaternion. First derivative with respect to space for: (7); in , They are exist The curvature component of the axis.

[0029] Then the rotation matrix It can be represented as: (8); The position of the robot's end effector in the local coordinate system is linked to the actual position of the robot's end effector in the global coordinate system obtained by the camera using a rotation matrix.

[0030] S22. Obtain the actual position of the robot's end effector using high-speed cameras installed around the working environment. Actual position of the end effector of a rope-driven flexible continuous robot Compared with the expected reference trajectory Tracking error for: (9); in Represents a vector in The values ​​on the axis, i.e. for exist The values ​​are taken on the axis. The control objective is the actual position of the end effector of the tethered flexible continuous robot. Able to track the desired reference trajectory tracking error It eventually converges to 0.

[0031] S3. Based on the position tracking error, design the inversion control law, introduce the fault-tolerant model to form an inversion fault-tolerant system, and design the control law of the robot trajectory tracking controller and determine the control parameters based on the robot model and the control objective of trajectory tracking. Specifically, in this embodiment, the specific process of step S3 is as follows: S31. Considering the external disturbances experienced by the robot system, for x For a system on an axis, let the first state variable be 1. The second state variable 2 is The following state equations for the robot system are obtained: (10); in for The first derivative with respect to time, for The first derivative with respect to time, where For the end of the rod at The position of the axis for The first derivative with respect to time, for Substituting equations (1) to (5) into equation (10) with respect to the second derivative with respect to time, we get: (11); in Let be the first derivative of the internal force of the rod with respect to space and time. For the perturbation experienced at the end effector of a tethered flexible continuous robot, the subscript is... Represents a vector in The values ​​on the axis, The rotation matrix of the robot's main link. , Let be the first derivative of the rotation matrix of the robot's main link with respect to time. It is the velocity of the rod in the local coordinate system. It is the first derivative of the rod's velocity with respect to time in the local coordinate system. for The antisymmetric matrix; It is the angular velocity of the rod in the local coordinate system. It is the mass density of the robot's main shaft. It is the cross-sectional area of ​​the robot's main shaft. Here are the shear and tensile stiffness matrices. Here are the bending and torsional stiffness matrices; for initial value, The rate of change of the rod's position relative to the arc length. for antisymmetric matrix, Let be the first derivative of the curvature vector in the local coordinate system with respect to space. For external load distribution force, The force distributed in the rope.

[0032] To achieve the control objectives described above, since it only considers control... The tracking problem on the axis only requires controlling one of the four ropes. Two strands on the axial side are sufficient, thus distributing the force of the rope. The relationship with the tension of the two ropes is expressed as: (12); in As an intermediate quantity, for The midpoint between the two ropes on either side of the axis. Viewed as relative The two ropes on either side of the axis are equivalent to a single rope capable of achieving negative tension. , It is the tension between the two ropes. Therefore, It can be further written as: (13); Subscript Represents a vector in The values ​​on the axis, for This indicates the distributed force of the external load.

[0033] S32. Based on the control objectives of the robot system state, and considering fault-tolerant control, set the actuator effectiveness coefficient. ( ), It is a control law. Therefore: (14); in It is a control law.

[0034] The fault-tolerant model employs adaptive parameter estimation, namely the actuator effectiveness coefficient. Assuming the desired reference trajectory is The control objective is that after a partial actuator failure occurs, the controller can quickly correct the fault, and The closed-loop system is stable. ,in This indicates the actual speed of the robot's end effector. This indicates the expected reference speed of the robot's end effector.

[0035] S33. Design the inverse fault-tolerant control law and define it. The error between the desired position and the actual position of the robot's end effector. The first derivative of the error with respect to time: (15); In order to achieve Define the first Lyapunov function and its derivative : (16); Define virtual control variables for: (17); Define the error variable as a positive number. Substituting into (16), we get: (18); right Differentiation yields: (19); Define the actuator effectiveness coefficient and ,in This represents the actuator effectiveness coefficient. express The estimated value, express The estimation error.

[0036] In order to achieve Define the second Lyapunov function. for: (20); right Differentiation yields: (twenty one); Control laws are typically designed as follows: (twenty two); in , .but: (twenty three); It is evident that if ,but .

[0037] S4. Introduce the RBF neural network model and use the Gaussian function for weighted summation to approximate the unknowns in the control law that are difficult to obtain directly, including the derivative of internal forces with respect to spatial position variables and external forces.

[0038] Specifically, in this embodiment, step S4 involves introducing an RBF neural network model to approximate unknown quantities that are difficult to obtain directly in the control law. Therefore, in this invention, an RBF neural network is used to approximate the derivatives of internal forces with respect to spatial position variables, external forces, and external disturbances that are difficult to obtain directly in the control law. An overall approximation is performed. The following Gaussian function is used: (twenty four); in It is the input from the network. Indicates the center of the Gaussian function. The variance of the Gaussian function is represented. It is the first Hidden layer nodes.

[0039] This is an approximation term for the RBF neural network. Definition: (25); in It is the output of the network's Gaussian function. It is the ideal weight of the network. Yes Exact value, It is the approximation error of the neural network. This represents the maximum approximation error of the neural network. ,in Represents the Gaussian function. This represents the independent variable of the function.

[0040] Define the approximation term of the RBF neural network The estimated value : (26); in, The estimated values ​​of the network weights are taken as follows: To estimate the error, where If these are the ideal weights of the network, then estimation error : (27); Redesign the control law: (28); in satisfy , This indicates the strength of the robustness term. To represent robust terms as symbolic functions, This represents the expected reference acceleration at the robot's end effector.

[0041] S5. Analyze the stability and convergence of the RBF neural network model adaptive inversion fault-tolerant system, adjust the control parameters of the controller, and output the trajectory tracking results.

[0042] Specifically, in this embodiment, step S5 involves analyzing the stability and convergence of the RBF neural network adaptive inversion fault-tolerant system and defining a third Lyapunov function. : (29); in ; The time derivative can be described as: (30); in Indicates the adaptive rate of the parameter. This represents the adaptive rate of the neural network. For intermediate process variables; Therefore, the adaptive rate of the parameter is chosen: (31); Determine the adaptive rate of the neural network: (32); at this time: (33); By using , : (34); in This represents the output of the Gaussian function. , This represents the magnitude of the adaptive rate strength, therefore, , ,thereby Both are bounded. Because if and only if... hour, That is, when , According to the LaSalle invariance principle, the closed-loop control system of the tendon-driven continuum robot is asymptotically stable, that is, when... , and ,thereby ,because ,but By selecting adjustable parameters, in one embodiment, the desired trajectory is designed as follows: m, the rope-driven flexible continuous robot outputs rope tension under the action of RBF neural network adaptive inversion fault-tolerant system, drives the robot's working end to move, and obtains the actual position of the working end of the rope-driven flexible continuous robot by measuring the sensor and calculating the position tracking error.

[0043] The performance of the controller was verified through numerical simulation in MATLAB, and compared with PD control, backflip fault-tolerant control (BFTC), and sliding mode fault-tolerant control (SMFTC). The specific process is as follows: In the simulation experiment, the controller's goal was to achieve... Axis trajectory tracking. The desired trajectory is determined by... m is given. Furthermore, the initial tension of the tendons in the continuum robot is... Simultaneously, PD control, sliding mode fault-tolerant control (SMFTC), back-fault-tolerant control (BFTC), and adaptive back-fault-tolerant control (ABFTC) are added for comparison to illustrate the advantages of the proposed control scheme. The controller parameters are as follows: , , , , ,and , The initial value is The parameters of the Gaussian function are as follows: ,in This represents the initial value of the parameter adaptation rate. , Given the fixed parameters of the Gausky function, the gravitational acceleration is 9.81 N / kg, and the direction is... Axial direction. The parameters of the continuum robot are shown in Table 1: Table 1 Parameters of Rope-Driven Continuous Robot

[0044] The simulated actuator experienced a constant-value failure. , occurred in time At point s, It is given by the following formula: (35); like Figure 3As shown, the adaptive inversion fault-tolerant control performs well in tracking the desired trajectory both before and after a partial failure of the actuator with constant value, and it can quickly recover to the desired trajectory after the failure, demonstrating excellent performance. The inversion fault-tolerant control also shows good tracking performance, but its recovery speed is slightly slower than that of the adaptive inversion fault-tolerant control. Although the proportional-derivative control strategy has a slight deviation, it can still effectively track the path overall. In contrast, the sliding mode fault-tolerant control exhibits a larger deviation after the failure and recovers more slowly.

[0045] Figure 4 The tracking errors of four control strategies are presented, along with the actual velocity curves under the adaptive inversion fault-tolerant control strategy. The tracking error data clearly demonstrates that the proposed control strategy significantly outperforms the others in terms of robustness and accuracy. Specifically, the mean normalized root mean square error (NRMSE) between the actual and desired trajectories under adaptive inversion fault-tolerant control, inversion fault-tolerant control, proportional-derivative control, and sliding mode fault-tolerant control are 3.52%, 6.19%, 6.47%, and 9.39%, respectively. These data indicate that the proposed controller has a significant advantage in tracking performance. Furthermore, the velocity curves under the adaptive inversion fault-tolerant strategy also meet expectations, further validating its effectiveness.

[0046] Figure 5 The experiment demonstrates the variation between the actual tension on the rope and the adaptive inversion fault-tolerant control input. At 6.5 seconds, the actuator partially failed, but the controller successfully corrected this failure using its fault-tolerant control strategy.

[0047] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A fault-tolerant control method for a rope-driven flexible robot based on neural network adaptive inversion, characterized in that: Includes the following steps: S1. Establish the dynamic model of the robot based on the structure of the rope-driven flexible continuous robot, and obtain the position of the robot's working end effector; S2. Compare the actual position of the robot's end effector with the expected reference trajectory to obtain the tracking error of the robot's end effector position; S3. Based on the tracking error information of the position, design the inversion control law, introduce the fault-tolerant model to form the inversion fault-tolerant system, and design the control law of the robot trajectory tracking controller and determine the control parameters based on the robot model and the control objective of trajectory tracking. S4. Introduce the RBF neural network model to redesign the control law for unknown quantities that are difficult to obtain directly in the approximate control law. S5. Analyze the stability and convergence of the RBF neural network adaptive inversion fault-tolerant system, adjust the control parameters of the controller, and output the trajectory tracking results.

2. The method for adaptive inversion fault-tolerant control of a rope-driven flexible robot based on neural networks according to claim 1, characterized in that, In step S1, the structure of the rope-driven flexible continuous robot includes an elastic main rod, multiple support plates connected in series through the main rod, and four ropes that are parallel and symmetrical to each other in pairs. The four ropes are connected to the main rod through a series of support plates.

3. The method for adaptive inversion fault-tolerant control of a rope-driven flexible robot based on neural networks according to claim 1, characterized in that, In step S2, truncation error is eliminated by quaternions to obtain the actual position of the robot's end effector.

4. The method for adaptive inversion fault-tolerant control of a rope-driven flexible robot based on neural networks according to claim 1, characterized in that, Step S3 includes the following steps: S31. Considering the external disturbances experienced by the robot system, for x For a system on an axis, let the first state variable be... For the end of the rod at The position of the axis, the second state variable For the end of the rod at The first derivative of the position of the axis with respect to time will The result of the two ropes on both sides of the axis being equivalent to a single rope achieving negative tension is... ; S32. Based on the control objectives of the robot system state, and considering fault-tolerant control, set the actuator effectiveness coefficient. Then there is Equivalent result of the two ropes on both sides of the axis ,in It is a control law; S33. Design an inverse fault-tolerant control law and use adaptive parameter estimation to estimate the actuator effectiveness coefficients. Assuming the desired reference trajectory is The control objective is that after a partial actuator failure occurs, the controller can quickly correct the fault, and when... The closed-loop system is stable. ,in This indicates the actual speed of the robot's end effector. This indicates the expected reference speed of the robot's end effector.

5. The method for adaptive inversion fault-tolerant control of a rope-driven flexible robot based on a neural network, as described in claim 4, is characterized in that... In step S3, the design of the inversion fault-tolerant control law includes: defining a first Lyapunov function based on the error between the expected position and the actual position of the robot end; defining a second error variable based on the virtual control variable and the second state variable; and defining a second Lyapunov function based on the first Lyapunov function and the actuator effectiveness coefficient, so that the error variable tends to zero, thereby obtaining a control law that makes the entire system asymptotically stable.

6. The method for adaptive inversion fault-tolerant control of a rope-driven flexible robot based on neural networks according to claim 1, characterized in that, In step S4, the approximation term of the RBF neural network model is defined as: (1)； in This represents an approximation term of a neural network. This represents an estimate of the actuator effectiveness coefficient. This represents the output of the Gaussian function. Gaussian function The independent variable, Let be the first derivative of the internal force of the rod with respect to space and time. For external load distribution force, Represents a vector in The values ​​on the axis, It is the ideal weight of the network. It is the approximation error of the neural network; The estimated value ,in, The estimated values ​​of the network weights are taken as follows: To estimate the error, then estimation error .

7. A method for adaptive inversion fault-tolerant control of a rope-driven flexible robot based on a neural network, as described in claim 6, is characterized in that... In step S4, the redesigned control law is: (2)； in, It is the mass density of the robot's main shaft. It is the cross-sectional area of ​​the robot's main shaft. It is the mass density of the robot's main shaft. It is the cross-sectional area of ​​the robot's main shaft. It is a positive number. for The midpoint between the two ropes on either side of the axis. Indicates the actuator effectiveness coefficient The estimated value, This indicates the desired tracking speed of the robot's end effector. It is a positive number. This represents the first derivative of the error between the desired and actual positions of the robot's end effector with respect to time. express The estimated value, This indicates the strength of the robustness term. The robust term is represented by a symbolic function.

8. A method for adaptive inversion fault-tolerant control of a rope-driven flexible robot based on a neural network, as described in claim 5, is characterized in that... In step S5, the stability and convergence of the RBF neural network adaptive inversion fault-tolerant system are analyzed, including: Based on the second Lyapunov function in step S3 and the third Lyapunov function defined to obtain the adaptive rate of neural network weights and the adaptive rate of actuator effectiveness coefficients, the time derivative of the third Lyapunov function is described by the error between the expected position and the actual position of the robot end effector and the first derivative of the error with respect to time. According to the LaSalle invariance principle, the control system is asymptotically stable if and only if the error between the expected position and the actual position of the robot end effector and the first derivative of the error with respect to time are both zero.

9. A computer device comprising a memory and a processor, the memory being electrically connected to the processor, the memory storing a computer program, characterized in that: When the computer program is executed by the processor, it causes the processor to implement the method as described in any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the processor implements the method as described in any one of claims 1 to 8.

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