Multi-flexible robot system preset index adaptive fault-tolerant control method and system

Abstract

This invention discloses an adaptive fault-tolerant control method and system for a multi-flexible robot system with preset indices, belonging to the field of fault-tolerant control technology for control systems. The method includes: establishing a dynamic model of the multi-flexible robot and a virtual leader model containing hub angle position, elastic vibration, and total displacement; constructing an intermittent actuator fault model including the number of faults, intervals, and unknown times; approximating system uncertainties using a radial basis function neural network; defining the tracking error and reconstructing the error dynamic equation, introducing a strictly decreasing function to construct a preset index set of boundary error state variables; converting constrained errors into unconstrained variables using a strictly increasing function; designing an adaptive fault-tolerant controller based on the unconstrained variables, and using a projection operator to update the estimated parameters online. This invention achieves consistent angular position tracking and suppression of elastic vibration, with the error converging to a predefined residual set, requiring no prior fault information, thus improving the system's robustness and engineering practicality.

Description

Technical Field

[0001] This invention belongs to the field of fault-tolerant control technology of control systems, specifically relating to an adaptive fault-tolerant control method and system for preset indicators of a multi-flexible robot system. Background Technology

[0002] As a key component of a multi-flexible robot system, the actuator's core function is to convert control signals into force or torque outputs, thereby driving the robot joints and end effectors to complete designated tasks. During the operation of a multi-flexible robot system, the actuator directly bears the impact of external disturbances and load fluctuations, making it the most vulnerable component to failure in the entire system. Therefore, ensuring the safe and reliable operation of the actuator is crucial to guaranteeing the safe operation of the entire multi-flexible robot system. Since the timing, mode, and magnitude of actuator failures are completely unpredictable, effectively eliminating their impact on the system is one of the most challenging problems in the design of multi-flexible robot control systems. If the impact on the system can be eliminated before a failure occurs (or without the need for failure information), the reliability and safety of the system can be directly improved. Therefore, inventing an adaptive fault-tolerant control method to solve the actuator failure control problem of multi-flexible robots has significant engineering application value.

[0003] Currently, adaptive consistency control has proven to be an effective strategy for solving the problems of angular position modulation and elastic vibration suppression in multi-flexible robots with actuator failures due to its advantages such as simple structure, strong adaptability, and good scalability. However, most existing research results only address the control problem of one-time failures, i.e., all actuator states remain unchanged after the failure occurs. During the long-term operation of multi-flexible robots, their actuators often experience various unknown intermittent failures, i.e., the actuators frequently switch between normal modes and various failure modes. Such failures not only cause intermittent jumps in fault parameters at the time of failure, thus triggering undesirable intermittent elastic vibrations, but also cause the estimated parameters in the controller to become unbounded.

[0004] Therefore, inventing an adaptive consistency fault-tolerant control method to solve the intermittent actuator failure control problem of multi-flexible robots has important practical engineering significance. Summary of the Invention

[0005] The technical problem this invention aims to solve is to address the shortcomings of the prior art by providing a pre-defined adaptive fault-tolerant control method and system for multi-flexible robot systems. This method achieves consistent angular position tracking between the leader and follower and effectively suppresses elastic vibrations caused by intermittent faults. Simultaneously, angular position tracking errors and end-effector elastic vibration errors converge to a predefined set of residuals. This addresses the problem that most existing adaptive fault-tolerant control techniques only address permanent or one-time faults and cannot effectively handle intermittent faults caused by frequent switching between normal operation and various fault modes of the actuator.

[0006] The present invention adopts the following technical solution: An adaptive fault-tolerant control method for pre-defined parameters of a multi-flexible robot system includes the following steps: S1. For a multi-flexible robot system containing one leader and N followers, establish the first... A dynamic model of a follower flexible robot, the dynamic model including hub angle position, elastic vibration of flexible link at spatial position, and total robot displacement calculated from hub angle position and elastic vibration; S2. Construct a virtual dynamic leader that generates the desired joint angle position and establish its dynamic model; S3. For the end load actuator and the hub actuator, establish an intermittent actuator fault model. The fault model includes characteristic parameters such as the number of fault occurrences, the fault occurrence interval, and the unknown fault time. S4. A radial basis function neural network is used to approximate the uncertainty function in the multi-flexible robot system, and an approximation model of the uncertainty function is obtained. S5. Based on the dynamic model obtained in steps S1 and S2, define the first... Based on the elastic vibration error, position error, and total displacement error between the follower flexible robot and the leader, an error dynamic equation is established. After reconstructing the error dynamic equation by combining the fault model in step S3 and the approximation model in step S4, the leader and the leader are defined respectively. The boundary error state variables of a follower flexible robot are then constructed by introducing a strictly decreasing function with respect to time to establish a preset index set for the boundary error state variables. S6. Based on the preset index set obtained in step S5, a strictly increasing function with respect to time is introduced to convert the boundary error state variables constrained by the preset index set into unconstrained boundary error state variables. S7. Based on the unconstrained boundary error state variables obtained in step S6, design the leader controller and the first... An adaptive preset index fault-tolerant controller for a follower flexible robot; S8. Using the projection operator, the update law of the estimated parameters in the controller described in step S7 is used to update the estimated parameters such as the neural network estimated weights and fault parameters in the controller in real time online.

[0007] Preferably, in step S1, the first i Dynamic model of a follower flexible robot: No. The dynamic model following the flexible robot is described as follows:

[0008] in, For the first i A follower flexible robot in spatial position ,time Lateral vibration acceleration of the flexible connecting rod at the location, For the first i Deformation of the flexible link in a follower flexible robot Spatial location The first-order partial derivative, For the first i Deformation of the flexible link in a follower flexible robot Spatial location The second-order partial derivative, For the first i Deformation of the flexible link in a follower flexible robot Spatial location The third partial derivative, For the first i Deformation of the flexible link in a follower flexible robot Spatial location The fourth-order partial derivative, For the first i The hub / joint angle position of the follower flexible robot Regarding time The first derivative, For the first i The hub / joint angle position of the follower flexible robot Regarding time The second derivative, The mass per unit length of the robot link. Let be the moment of inertia of the wheel hub. For the bending stiffness of the robot link, For the end-effector load mass; and These represent system uncertainties, Indicates boundary control input, , Indicates hub control input, .

[0009] Preferably, in step S2, the dynamic model of the virtual dynamic leader includes parameters related to the leader hub angle position, the elastic vibration of the flexible link at the spatial position, the total displacement of the leader, the leader end load input, and the leader hub input.

[0010] Preferably, in step S3, the intermittent actuator fault model is:

[0011]

[0012] in, , , , For unknown fault parameters, The number of times the fault occurred. Indicates the first The interval where the secondary fault occurred Indicates the time of an unknown failure.

[0013] Preferably, the intermittent actuator failure model satisfies the following: within the same failure time interval, partial failure and lock-up failure of the actuator do not occur simultaneously; the partial failure is... , and , The lock-up fault is , and , .

[0014] Preferably, in step S4, the approximation model of the radial basis function neural network is:

[0015] in, and These represent the inputs to the radial basis function neural network, respectively. and These represent the hidden layer output and the estimated output weight vector of the output layer of a radial basis function neural network, respectively.

[0016] Preferably, in step S5, the preset index set of the boundary error state variables satisfies the following conditions:

[0017]

[0018] in, For design constants, For the first i The first follower flexible robot j The effectiveness factor of each actuator For the first i The first follower flexible robot j Fault bias parameters for each actuator , , , as well as All are design constants.

[0019] Preferably, in step S6, for the first A state variable with unconstrained boundary error that follows the flexible robot. for:

[0020]

[0021] in, For design constants, For the first i The first follower flexible robot j Estimated fault parameters for each actuator For the first i The first follower flexible robot j Estimated fault bias parameters for each actuator.

[0022] Preferably, in step S8, the parameter update formula for the projection operator is:

[0023]

[0024]

[0025]

[0026]

[0027]

[0028] in, , , , , and These are the estimated parameters in the controller. , , , These are all design parameters. , To design the matrix.

[0029] Secondly, embodiments of the present invention provide an adaptive fault-tolerant control system for a multi-flexible robot system with preset indicators, comprising: Modules for building blocks containing a leader and N A multi-flexible robotic system with multiple followers was established. A dynamic model of a follower flexible robot is constructed, and a virtual dynamic leader with desired joint angle positions is generated and its dynamic model is established. It is a positive integer, 1≤ ≤ N The follower dynamic model includes the hub angle position, the elastic vibration of the flexible link at the spatial position, and the total robot displacement calculated from the hub angle position and the elastic vibration. The fault module is used to establish intermittent actuator fault models for end load actuators and hub actuators, including the number of fault occurrences, fault occurrence intervals, and characteristic parameters of unknown fault times. The approximation module is used to approximate the uncertainty function in a multi-flexible robot system using a radial basis function neural network, and obtain an approximation model of the uncertainty function. The error module is used to define elastic vibration error, position error and total displacement error according to the dynamic model of the follower and the leader and to establish the error dynamic equation. After reconstructing the error dynamic equation by combining the fault model and the approximation model, the boundary error state variables of the leader and the follower are defined respectively. At the same time, a strictly decreasing function with respect to time is introduced to construct a preset index set of the boundary error state variables. The variable module is used to introduce a strictly increasing function with respect to time based on a preset set of indicators, and to convert the boundary error state variables constrained by the preset set of indicators into unconstrained boundary error state variables. The design module is used to design the leader controller and the second controller based on the unconstrained boundary error state variables. An adaptive preset index fault-tolerant controller for a follower flexible robot; The update module is used to design the update law of the estimated parameters in the controller using the projection operator, and to update the estimated parameters such as the neural network estimated weights and fault parameters in the controller in real time online.

[0030] Thirdly, a computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described adaptive fault-tolerant control method for preset indicators of a multi-flexible robot system.

[0031] Fourthly, embodiments of the present invention provide a computer-readable storage medium including a computer program, which, when executed by a processor, implements the steps of the above-described adaptive fault-tolerant control method for preset indicators of a multi-flexible robot system.

[0032] Fifthly, a chip includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the aforementioned adaptive fault-tolerant control method for preset indicators of a multi-flexible robot system.

[0033] Sixthly, embodiments of the present invention provide an electronic device, including a computer program, wherein when the computer program is executed by the electronic device, it implements the steps of the above-described adaptive fault-tolerant control method for preset indicators of a multi-flexible robot system.

[0034] Compared with the prior art, the present invention has at least the following beneficial effects: An adaptive fault-tolerant control method for multi-flexible robot systems with preset indices is proposed. This method constructs a preset index set by introducing a strictly decreasing function. Instead of merely pursuing asymptotic stability, it mandates that tracking and vibration errors remain within a user-defined convergence envelope at any given time. Combining an intermittent fault model and neural network approximation, this method can simultaneously handle parameter uncertainties and frequent actuator switching failures without requiring a fault detection mechanism. This design fundamentally solves the problem of large overshoots or even system instability that occur in traditional fault-tolerant control at the moment of a fault, ensuring the transient performance and steady-state accuracy of multi-flexible robots under complex working conditions, and significantly improving the system's safety and reliability.

[0035] Furthermore, the high-precision modeling method can realistically reflect the elastic deformation mechanism of the flexible arm during high-speed motion, especially the coupling effect between the end load and the linkage vibration. By directly utilizing this refined model in the controller design, higher-order modal vibrations can be effectively suppressed, avoiding control overflow or residual vibrations caused by unmodeled dynamics due to model simplification. This lays a solid physical foundation for achieving high-precision angular position tracking and vibration suppression.

[0036] Furthermore, by generating a smooth desired trajectory, the model effectively filters out high-frequency abrupt changes in the command signal, reducing the impact on the actuator. In addition, the presence of a virtual leader makes the topology of the multi-robot system more flexible, supports a distributed control architecture, reduces communication burden, and ensures that the entire cluster maintains consistent motion behavior and vibration suppression even when the network topology changes or some nodes fail.

[0037] Furthermore, by explicitly including the estimation term of the fault parameter in the control law, the system can quickly adjust the control gain for compensation at the moment of fault occurrence, disappearance and mode switching, effectively preventing the violent oscillation of the system state caused by the jump of fault parameters, and ensuring the continuity and smoothness of the control process.

[0038] Furthermore, by utilizing the local approximation and fast convergence characteristics of radial basis function neural networks, the unknown uncertainty functions in multi-flexible robot systems are accurately approximated, effectively solving the control error problem caused by system modeling uncertainty.

[0039] Furthermore, by constructing a preset index set through a strictly decreasing function, a time-varying constraint range is set for the boundary error, realizing the dual preset of error transient and steady-state indexes, and making the convergence process of angular position tracking error and elastic vibration error adjustable.

[0040] Furthermore, by using a strictly increasing function to transform constrained boundary errors into unconstrained variables, the complexity of controller design under constraints is effectively solved, and the design process of adaptive fault-tolerant controllers is simplified.

[0041] Furthermore, by designing an online update law for the estimated parameters through the projection operator, the boundedness of the estimated parameters such as the neural network estimation weights and fault parameters in the controller is effectively guaranteed, breaking through the technical bottleneck of unbounded estimated parameters in traditional adaptive control under intermittent faults.

[0042] It is understood that the beneficial effects of the second to sixth aspects mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0043] In summary, the method of this invention designs a preset index adaptive fault-tolerant control scheme for intermittent actuator failures in multi-flexible robots, breaking through the limitations of traditional one-time failure control. Through precise modeling, neural network approximation, time-varying index constraints, and projection operator parameter updates, it achieves consistent angular position tracking and suppression of elastic vibration, with controllable error convergence, bounded parameter estimation, and no need for prior fault information, thus greatly improving the system's robustness and engineering practicality.

[0044] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0045] Figure 1 This is a topology diagram of undirected communication for multiple flexible robots. Figure 2 Diagram showing the joint angle positions; Figure 3 The error diagram of the elastic vibration at the follower's end; Figure 4 This is a diagram showing the joint angle position error. Figure 5 The diagram shows the elastic vibration error of the follower under preset index control, where (a) is... (b) is (c) is (d) is ; Figure 6 The diagram shows the elastic vibration error of the follower under conventional control, where (a) is... (b) is (c) is (d) is ; Figure 7 A schematic diagram of a computer device provided in an embodiment of the present invention; Figure 8 This is a block diagram of a chip according to an embodiment of the present invention; Figure 9 This is a schematic diagram of the method steps of the present invention.

[0046] Among them, 60. Computer equipment; 61. Processor; 62. Memory; 63. Computer program; 600. Electronic device; 610. Processing unit; 620. Storage unit; 6201. Random access memory unit; 6202. Cache memory unit; 6203. Read-only memory unit; 6204. Program / utility; 6205. Program module; 630. Bus; 640. Display unit; 650. Input / output interface; 660. Network adapter; 700. External device. Detailed Implementation

[0047] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0048] In the description of this invention, it should be understood that the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0049] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0050] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes such combinations. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Additionally, the character " / " in this invention generally indicates that the preceding and following objects have an "or" relationship.

[0051] It should be understood that although terms such as first, second, third, etc., may be used in the embodiments of the present invention to describe the preset range, these preset ranges should not be limited to these terms. These terms are only used to distinguish the preset ranges from one another. For example, without departing from the scope of the embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0052] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0053] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0054] Multi-flexible robot systems often exhibit characteristics such as high nonlinearity, time-varying parameters, and modeling uncertainty. Due to the universal approximation characteristics of neural network / fuzzy logic systems, adaptive neural consistency control has attracted widespread attention in the control of uncertain multi-flexible robot systems. This invention provides an adaptive fault-tolerant control method with preset indices for multi-flexible robot systems with intermittent actuator failures. First, an intermittent failure model of the end effector and hub actuator is established, and the uncertain functions in the system are approximated using a radial basis function neural network. Second, angular position tracking error and end effector elastic vibration error are established, and the boundary error state variables of the system are established using these errors. Third, a strictly decreasing function is introduced to construct a preset index set for the boundary state variables, and a strictly increasing function is introduced to transform the boundary error state variables under constraints into unconstrained boundary error state variables. Finally, based on the unconstrained boundary error state variables, an adaptive preset index fault-tolerant control method is designed, and the estimated parameters in the controller are updated online using a projection operator to ensure the boundedness of parameter estimation.

[0055] Please see Figure 9 The present invention discloses an adaptive fault-tolerant control method for a multi-flexible robot system with preset indicators, comprising the following steps: S1, Considering a multi-flexible robot network consisting of a leader and It consists of 1,000 followers. (This refers to the 1,000 followers.) A flexible robot follows Indicates the angular position of the wheel hub. , Indicates spatial location Elastic vibration of the flexible link and Indicates the length of the robot's links; This represents the robot's total displacement; No. The dynamic model following the flexible robot is described as follows:

[0056] in, , , , , as well as , ; This represents the mass per unit length of a robot link. This represents the moment of inertia of the wheel hub. This indicates the bending stiffness of the robot's linkage. Indicates the mass of the robot's end effector load; and This indicates system uncertainty, and and ; , , indicating boundary control input, , , indicating hub control input.

[0057] S2. There exists a virtual dynamic leader with the desired joint angle position. ; Joint angle position The dynamic model is described as follows:

[0058] in, , , , and With the Following the same pattern as the flexible robot, , Indicates the leader's position Elastic vibration of the flexible link, This represents the total displacement of the leader. Show the leader's end load input, This indicates the leader's hub input.

[0059] S3, set This indicates the input signal of the end-load actuator. This represents the input signal of the hub actuator, and the intermittent actuator fault model is selected. The fault model for intermittent actuators is selected as follows:

[0060]

[0061] in, , as well as Indicates unknown fault parameters; Indicates the number of times the fault occurred. ; Indicates the first The interval where the secondary fault occurred and Indicates the time of unknown failure, and .

[0062] Based on the above fault model, we have: 1) , and , This indicates that the actuator has experienced partial failure, meaning that the actuator lost its effectiveness during the failure period. , ; 2) , and , This indicates that the actuator has a lock-up fault, meaning that during the fault time interval, the actuator is not affected by the control input signal; 3) It should be noted that , That is, within the same fault time interval, only one of the two types of faults can occur on the same actuator.

[0063] S4. Radial basis function neural networks, with their local approximation characteristics and fast convergence capabilities, can effectively approximate uncertainties in the system that cannot be modeled, and achieve high-precision real-time control. The uncertainty function in a multi-flexible robot system is approximated using a radial basis function neural network. The approximation model can be described as follows:

[0064] in, This represents the output weight vector of the network. This represents the output of the hidden layer nodes in the network, and , As the center value, Let Variance be the variance.

[0065] Due to the system , Since it is an uncertain function, a radial basis function neural network is used for approximation. , The approximation model is:

[0066] in, and These represent the inputs to the radial basis function neural network. and These represent the hidden layer output and the estimated output weight vector of the output layer of a radial basis function neural network, respectively.

[0067] S5. Introduce a strictly decreasing function with respect to time. Construct a preset index set for the boundary error state variables, where , as well as All are design constants; Definition of the first The elastic vibration error and positional error that follow the relationship between the flexible robot and the leader are: and Therefore, the total displacement error is defined as follows: .

[0068] Therefore, the first The dynamic equation for the error between the flexible robot and the leader is:

[0069] in, and and . and .

[0070] In each fault time interval Inside, assuming there is One actuator has a lock-up fault. Therefore, in each fault time interval Inside, using approximation models and fault models, the first The dynamic equation for the error between the flexible robot and the leader is rewritten as:

[0071] in, , and , These represent the unknown parameters caused by partial failures and lock-up faults, respectively, which will be estimated in the controller.

[0072] For the leader, the boundary error state variable is defined as:

[0073]

[0074] in, These are design parameters.

[0075] definition , , For the first A flexible robot follows, and the boundary error state variable is defined as:

[0076]

[0077] in, For design parameters; The consistency error is defined as follows: ,in, Indicates the first The neighborhood of a flexible robot To follow the robot With the robot The adjacency weights between them express and There is information exchange between them; express and There was no information exchange between them.

[0078] definition , , Therefore, a strictly decreasing function is introduced. Construct a preset index set for boundary error state variables.

[0079] For the A state variable following the flexible robot, representing boundary error. , The following inequalities are satisfied:

[0080]

[0081] in, ; Design constant; and ; , , , as well as These are all design constants. For any , It is necessary to choose the appropriate one. , Make the inequality , If true, then the system's state variables regarding boundary error are... , Transient indices can be established. Because... and Both are decreasing functions, therefore the boundary error state variables , They eventually converge to the residual set. and Inside, and , Therefore, the system's state variables regarding boundary errors... , Preset steady-state indices can be established.

[0082] S6. Introduce a strictly increasing function with respect to time. The constrained boundary error state variables are converted into unconstrained boundary error state variables, where , , for design constants and Design functions; Introduce a strictly increasing function with respect to time. Convert the constrained boundary error state variable into an unconstrained boundary error state variable.

[0083] For the A state variable with unconstrained boundary error that follows the flexible robot. , Defined as:

[0084]

[0085] in, , , for design constants and and .

[0086] S7. Utilizing unconstrained error state variables Design an adaptive preset index fault-tolerant control method; For leaders, the controller is designed as follows:

[0087]

[0088]

[0089] in, , , , All are design constants. , and , .

[0090] Using unconstrained error state variables , Design an adaptive preset index fault-tolerant control method.

[0091] For the The adaptive fault-tolerant controller designed to accompany the flexible robot is as follows:

[0092]

[0093]

[0094] in, , Design constant; and ; , and , .

[0095] S8. Employ a projection operator to ensure the estimated parameters in the controller. Boundedness.

[0096] For the estimated parameters in the controller , , , , and Using projection operator Real-time online updates:

[0097]

[0098]

[0099]

[0100]

[0101]

[0102] in, , , , All are design parameters and , To design the matrix.

[0103] In another embodiment of the present invention, a preset index adaptive fault-tolerant control system for a multi-flexible robot system is provided. This system can be used to implement the above-mentioned preset index adaptive fault-tolerant control method for a multi-flexible robot system. Specifically, the preset index adaptive fault-tolerant control system for a multi-flexible robot system includes a construction module, a fault module, an approximation module, an error module, a variable module, a design module, and an update module.

[0104] The building module is used to construct a system containing a leader and... N A multi-flexible robotic system with multiple followers was established. A dynamic model of a follower flexible robot is constructed, and a virtual dynamic leader with desired joint angle positions is generated and its dynamic model is established. It is a positive integer, 1≤ ≤ N The follower dynamic model includes the hub angle position, the elastic vibration of the flexible link at the spatial position, and the total robot displacement calculated from the hub angle position and the elastic vibration. The fault module is used to establish intermittent actuator fault models for end load actuators and hub actuators, including the number of fault occurrences, fault occurrence intervals, and characteristic parameters of unknown fault times. The approximation module is used to approximate the uncertainty function in a multi-flexible robot system using a radial basis function neural network, and obtain an approximation model of the uncertainty function. The error module is used to define elastic vibration error, position error and total displacement error according to the dynamic model of the follower and the leader and to establish the error dynamic equation. After reconstructing the error dynamic equation by combining the fault model and the approximation model, the boundary error state variables of the leader and the follower are defined respectively. At the same time, a strictly decreasing function with respect to time is introduced to construct a preset index set of the boundary error state variables. The variable module is used to introduce a strictly increasing function with respect to time based on a preset set of indicators, and to convert the boundary error state variables constrained by the preset set of indicators into unconstrained boundary error state variables. The design module is used to design the leader controller and the second controller based on the unconstrained boundary error state variables. An adaptive preset index fault-tolerant controller for a follower flexible robot; The update module is used to design the update law of the estimated parameters in the controller using the projection operator, and to update the estimated parameters such as the neural network estimated weights and fault parameters in the controller in real time online.

[0105] This invention provides a terminal device comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, graphics processing units (GPUs), tensor processing units (TPUs), digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions to achieve a corresponding method flow or function. The processor described in this embodiment can be used in the operation of a preset index adaptive fault-tolerant control method for a multi-flexible robot system, including: For a multi-flexible robot system comprising one leader and N followers, establish the first A dynamic model of a follower flexible robot is constructed, comprising the hub angle position, the elastic vibration of the flexible link at the spatial position, and the total robot displacement calculated from the hub angle position and elastic vibration. A virtual dynamic leader with the desired joint angle position is generated, and its dynamic model is established. An intermittent actuator fault model is established for the end effector and hub actuator, comprising characteristic parameters including the number of fault occurrences, fault occurrence intervals, and unknown fault times. A radial basis function neural network is used to approximate the uncertainty function in the multi-flexible robot system, obtaining an approximation model of the uncertainty function. Based on the obtained dynamic model, the first... Based on the elastic vibration error, positional error, and total displacement error between the follower flexible robot and the leader, an error dynamic equation is established. After reconstructing the error dynamic equation by combining a fault model and an approximation model, the leader and the leader are defined respectively. The boundary error state variables of a follower flexible robot are determined; then, a strictly decreasing function with respect to time is introduced to construct a preset index set for the boundary error state variables; based on the obtained preset index set, a strictly increasing function with respect to time is introduced to convert the boundary error state variables constrained by the preset index set into unconstrained boundary error state variables; based on the obtained unconstrained boundary error state variables, a leader controller and a follower flexible robot are designed respectively. An adaptive preset index fault-tolerant controller for a follower flexible robot; an update law for the estimated parameters in the controller is designed using a projection operator, and the estimated parameters such as the neural network estimation weights and fault parameters in the controller are updated online in real time.

[0106] Please see Figure 7 The terminal device is a computer device. In this embodiment, the computer device 60 includes a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable on the processor 61. When executed by the processor 61, the computer program 63 implements the preset index adaptive fault-tolerant control method for the multi-flexible robot system in this embodiment. To avoid repetition, these details are not elaborated here. Alternatively, when executed by the processor 61, the computer program 63 implements the functions of each model / unit in the preset index adaptive fault-tolerant control system for the multi-flexible robot system in this embodiment. To avoid repetition, these details are not elaborated here.

[0107] Computer device 60 can be a desktop computer, laptop, handheld computer, cloud server, or other computing device. Computer device 60 may include, but is not limited to, a processor 61 and a memory 62. Those skilled in the art will understand that... Figure 7 This is merely an example of computer device 60 and does not constitute a limitation on computer device 60. It may include more or fewer components than shown, or combine certain components, or different components. For example, computer device may also include input / output devices, network access devices, buses, etc.

[0108] The processor 61 may be a Central Processing Unit (CPU), or other general-purpose processors, graphics processing units (GPUs), tensor processing units (TPUs), digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0109] The memory 62 can be an internal storage unit of the computer device 60, such as a hard disk or memory of the computer device 60. The memory 62 can also be an external storage device of the computer device 60, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc. equipped on the computer device 60.

[0110] Furthermore, the memory 62 may include both internal storage units of the computer device 60 and external storage devices. The memory 62 is used to store computer programs and other programs and data required by the computer device. The memory 62 can also be used to temporarily store data that has been output or will be output.

[0111] Please see Figure 8 The terminal device is an electronic device 600, which is manifested in the form of a general-purpose computing device. The components of the electronic device may include, but are not limited to: at least one processing unit 610, at least one storage unit 620, a bus 630 connecting different platform components (including storage unit 620 and processing unit 610), a display unit 640, etc.

[0112] The storage unit stores program code, which can be executed by the processing unit 610 to perform the steps described in the method section of this specification according to various exemplary embodiments of the present invention. For example, the processing unit 610 can perform actions such as... Figure 9 The steps are shown in the figure.

[0113] Storage unit 620 may include a readable medium in the form of a volatile storage unit, such as random access memory (RAM) 6201 and / or cache memory 6202, and may further include a read-only memory (ROM) 6203.

[0114] Storage unit 620 may also include a program / utility 6204 having a set (at least one) program module 6205, such program module 6205 including but not limited to: 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.

[0115] Bus 630 can represent one or more of several types of bus structures, including a memory cell bus or memory cell controller, a peripheral bus, a graphics acceleration port, a processing unit, or a local bus using any of the multiple bus structures.

[0116] Electronic device 600 can also communicate with one or more external devices 700 (e.g., keyboard, pointing device, Bluetooth device, etc.), and with one or more devices that enable a user to interact with electronic device 600, and / or with any device that enables electronic device 600 to communicate with one or more other computing devices (e.g., router, modem). This communication can be performed via input / output interface 650. Furthermore, electronic device 600 can also communicate with one or more networks (e.g., local area network, wide area network, and / or public network, such as the Internet) via network adapter 660. Network adapter 660 can communicate with other modules of electronic device 600 via bus 630. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with electronic device 600, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage platforms.

[0117] Example 4 This invention also provides a storage medium, specifically a computer-readable storage medium, which is a memory device in a terminal device for storing programs and data. It is understood that the computer-readable storage medium here can include both built-in storage media in the terminal device and extended storage media supported by the terminal device; it can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, the storage space also stores one or more instructions suitable for loading and execution by a processor, which can be one or more computer programs (including program code). More specific examples of the computer-readable storage medium include: an electrical connection with one or more wires, a portable disk, a hard disk, random access memory, read-only memory, erasable programmable read-only memory, optical fiber, portable compact disk read-only memory, optical storage device, magnetic storage device, or any suitable combination thereof.

[0118] Computer-readable storage media also include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable storage medium can also be any readable medium other than a readable storage medium that can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the readable storage medium can be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, radio frequency, etc., or any suitable combination thereof.

[0119] Program code for performing the operations of this invention can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java and C++, and conventional procedural programming languages ​​such as C or similar languages. The program code can execute entirely on the user's computing device, partially on the user's computing device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0120] One or more instructions stored in a computer-readable storage medium can be loaded and executed by a processor to implement the corresponding steps of the adaptive fault-tolerant control method for preset indicators of the multi-flexible robot system in the above embodiments; one or more instructions in the computer-readable storage medium are loaded and executed by the processor in the following steps: For a multi-flexible robot system comprising one leader and N followers, establish the first A dynamic model of a follower flexible robot is constructed, comprising the hub angle position, the elastic vibration of the flexible link at the spatial position, and the total robot displacement calculated from the hub angle position and elastic vibration. A virtual dynamic leader with the desired joint angle position is generated, and its dynamic model is established. An intermittent actuator fault model is established for the end effector and hub actuator, comprising characteristic parameters including the number of fault occurrences, fault occurrence intervals, and unknown fault times. A radial basis function neural network is used to approximate the uncertainty function in the multi-flexible robot system, obtaining an approximation model of the uncertainty function. Based on the obtained dynamic model, the first... Based on the elastic vibration error, positional error, and total displacement error between the follower flexible robot and the leader, an error dynamic equation is established. After reconstructing the error dynamic equation by combining a fault model and an approximation model, the leader and the leader are defined respectively. The boundary error state variables of a follower flexible robot are determined; then, a strictly decreasing function with respect to time is introduced to construct a preset index set for the boundary error state variables; based on the obtained preset index set, a strictly increasing function with respect to time is introduced to convert the boundary error state variables constrained by the preset index set into unconstrained boundary error state variables; based on the obtained unconstrained boundary error state variables, a leader controller and a follower flexible robot are designed respectively. An adaptive preset index fault-tolerant controller for a follower flexible robot; an update law for the estimated parameters in the controller is designed using a projection operator, and the estimated parameters such as the neural network estimation weights and fault parameters in the controller are updated online in real time.

[0121] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0122] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0123] Please see Figure 1 A simulation experiment was conducted using a multi-robot network consisting of one leader and four followers to verify the tracking consistency error and elastic vibration suppression indices of the proposed control scheme. The leader was labeled as... Followers are labeled 1-4.

[0124] The robot parameters are selected as follows: , , , , .

[0125] The robot's uncertainties are selected as follows: , .

[0126] The initial conditions for the leader are selected as follows: , , .

[0127] The design parameters selected in the controller are: , , , .

[0128] The initial conditions to follow are: , , .

[0129] The design constants selected in the controller are: , , , , , , , , .

[0130] The initial conditions for the adaptive parameters are chosen as follows: , , .

[0131] The default indicator function is selected as follows: and , , .

[0132] The intermittent failure model for the actuator at the end load is selected as follows:

[0133] in, , as well as In each time zone Within, the output of the first actuator loses its effectiveness. The second actuator is locked in During the remaining time intervals, both actuators operated without failure.

[0134] Furthermore, the intermittent failure model for the actuator in the wheel hub is selected as follows:

[0135] in, , as well as In each time zone Inside, the first actuator is locked in The output of the second actuator loses its effectiveness. During the remaining time intervals, both actuators operated without failure.

[0136] Fault parameters selected as , and , Time interval and Select as as well as , , , , , , ; , , , , , , .

[0137] Validation Result Analysis Please see Figure 2 Follower joint angle It can converge to the leader joint angle Within a very small neighborhood, i.e., in the presence of unknown intermittent actuator failures, the designed preset index control scheme can achieve leader-follower angular position tracking consistency.

[0138] Please see Figure 3 and Figure 4 Even with the influence of intermittent jumps in unknown fault parameters, the end-effector elastic vibration error and joint angle position tracking error It always resides within the compact set defined by the index function.

[0139] Please see Figure 5 Elastic vibration error No undesirable large overshoot occurred at the time of the fault. That is, the proposed preset index control method can effectively suppress elastic vibration caused by intermittent jumps in unknown fault parameters.

[0140] In addition, from Figure 4 , Figure 5 and Figure 6 It can also be seen that the end-effector elastic vibration error of the traditional control scheme Joint angle position tracking error and elastic vibration error Unexpected large overshoots occurred at all times during the unknown fault events. Therefore, in terms of effectively suppressing the impact of intermittent jumps in unknown fault parameters on the system, the pre-defined target control scheme is superior to the traditional control scheme.

[0141] In summary, this invention provides a pre-defined adaptive fault-tolerant control method and system for multi-flexible robot systems. Addressing the technical challenge of unknown intermittent failures in actuators of multi-flexible robot systems, it overcomes the limitation of traditional control methods that can only handle one-time failures. By constructing a dynamic and fault model that closely matches actual motion characteristics, and combining it with a radial basis function neural network to accurately approximate system uncertainties, effective fault tolerance can be achieved without prior fault information. Simultaneously, by introducing strictly decreasing / increasing functions to achieve the pre-defined constraint and unconstrained transformation of boundary errors, the angular position tracking error and end-effector elastic vibration error converge to a predefined residual set, enabling controllable adjustment of both transient and steady-state error accuracy. This approach achieves precise leader-follower angular position tracking consistency while effectively suppressing elastic vibrations caused by fault parameter jumps. Furthermore, by designing parameter update laws using projection operators, it ensures the boundedness of estimated parameters such as neural network estimation weights and fault parameters in the controller, completely solving the problem of unbounded parameter divergence in traditional adaptive control and preventing system instability. Moreover, the control method forms a complete closed-loop logic, and the corresponding control system adopts a modular design with matching functions and clear logic among modules, possessing both good engineering feasibility and scalability. It can adapt to the complex working conditions of long-term operation of multiple flexible robots, significantly improving the system's robustness, control accuracy, and practical application value.

[0142] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0143] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0144] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this invention can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0145] In the embodiments provided by this invention, it should be understood that the disclosed devices / terminals and methods can be implemented in other ways. For example, the device / terminal embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0146] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0147] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0148] If the integrated module / unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, a recording medium, a USB flash drive, a portable hard drive, a magnetic disk, an optical disk, a computer memory, a read-only memory (ROM), a random-access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, etc.

[0149] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus, and computer program products according to embodiments of this application. It will 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... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0150] 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.

[0151] 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.

[0152] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A pre-defined adaptive fault-tolerant control method for a multi-flexible robot system, characterized in that, Includes the following steps: S1, for cases containing a leader and N A multi-flexible robotic system with multiple followers was established. A dynamic model of a follower flexible robot, the dynamic model including hub angle position, elastic vibration of flexible link at spatial position, and total robot displacement calculated from hub angle position and elastic vibration; S2. Construct a virtual dynamic leader that generates the desired joint angle position and establish its dynamic model; S3. For the end load actuator and the hub actuator, establish an intermittent actuator fault model. The fault model includes characteristic parameters such as the number of fault occurrences, the fault occurrence interval, and the unknown fault time. S4. A radial basis function neural network is used to approximate the uncertainty function in the multi-flexible robot system, and an approximation model of the uncertainty function is obtained. S5. Based on the dynamic model obtained in steps S1 and S2, define the first... Based on the elastic vibration error, position error, and total displacement error between the follower flexible robot and the leader, an error dynamic equation is established. After reconstructing the error dynamic equation by combining the fault model in step S3 and the approximation model in step S4, the leader and the leader are defined respectively. The boundary error state variables of a follower flexible robot are then constructed by introducing a strictly decreasing function with respect to time to establish a preset index set for the boundary error state variables. S6. Based on the preset index set obtained in step S5, a strictly increasing function with respect to time is introduced to convert the boundary error state variables constrained by the preset index set into unconstrained boundary error state variables. S7. Based on the unconstrained boundary error state variables obtained in step S6, design the leader controller and the first... An adaptive preset index fault-tolerant controller for a follower flexible robot; S8. Using the projection operator, the update law of the estimated parameters in the controller described in step S7 is used to update the estimated parameters such as the neural network estimated weights and fault parameters in the controller in real time online.

2. The adaptive fault-tolerant control method for preset indicators of a multi-flexible robot system according to claim 1, characterized in that, In step S1, the first i Dynamic model of a follower flexible robot: No. The dynamic model following the flexible robot is described as follows: in, For the first i A follower flexible robot in spatial position ,time Lateral vibration acceleration of the flexible connecting rod at the location, For the first i Deformation of the flexible link in a follower flexible robot Spatial location The first-order partial derivative, For the first i Deformation of the flexible link in a follower flexible robot Spatial location The second-order partial derivative, For the first i Deformation of the flexible link in a follower flexible robot Spatial location The third partial derivative, For the first i Deformation of the flexible link in a follower flexible robot Spatial location The fourth-order partial derivative, For the first i The hub / joint angle position of the follower flexible robot Regarding time The first derivative, For the first i The hub / joint angle position of the follower flexible robot Regarding time The second derivative, The mass per unit length of the robot link. Let be the moment of inertia of the wheel hub. For the bending stiffness of the robot link, For the end-effector load mass; and These represent system uncertainties, Indicates boundary control input, , Indicates hub control input, .

3. The adaptive fault-tolerant control method for preset indicators of a multi-flexible robot system according to claim 1, characterized in that, In step S2, the dynamic model of the virtual dynamic leader includes parameters related to the leader hub angle position, the elastic vibration of the flexible link at the spatial position, the total displacement of the leader, the leader end load input, and the leader hub input.

4. The adaptive fault-tolerant control method for preset indicators of a multi-flexible robot system according to claim 1, characterized in that, In step S3, the intermittent actuator fault model is as follows: in, , , , For unknown fault parameters, The number of times the fault occurred. Indicates the first The interval where the secondary fault occurred Indicates the time of an unknown failure.

5. The adaptive fault-tolerant control method for preset indicators of a multi-flexible robot system according to claim 4, characterized in that, The intermittent actuator failure model satisfies the following: within the same failure time interval, partial failure and lock-up failure of the actuator do not occur simultaneously; the partial failure is... , and , The lock-up fault is , and , .

6. The adaptive fault-tolerant control method for preset indicators of a multi-flexible robot system according to claim 1, characterized in that, In step S4, the approximation model of the radial basis function neural network is: in, and These represent the inputs to the radial basis function neural network, respectively. and These represent the hidden layer output and the estimated output weight vector of the output layer of a radial basis function neural network, respectively.

7. The adaptive fault-tolerant control method for preset indicators of a multi-flexible robot system according to claim 1, characterized in that, In step S5, the preset index set of the boundary error state variables satisfies the following conditions: in, For design constants, For the first i The first follower flexible robot j The effectiveness factor of each actuator For the first i The first follower flexible robot j Fault bias parameters for each actuator , , , as well as All are design constants.

8. The adaptive fault-tolerant control method for preset indicators of a multi-flexible robot system according to claim 1, characterized in that, In step S6, for the first A state variable with unconstrained boundary error that follows the flexible robot. for: in, For design constants, For the first i The first follower flexible robot j Estimated fault parameters for each actuator For the first i The first follower flexible robot j Estimated fault bias parameters for each actuator.

9. The adaptive fault-tolerant control method for preset indicators of a multi-flexible robot system according to claim 1, characterized in that, In step S8, the parameter update formula for the projection operator is: in, , , , , and These are the estimated parameters in the controller. , , , These are all design parameters. , To design the matrix.

10. A pre-defined adaptive fault-tolerant control system for a multi-flexible robot system, characterized in that, include: Modules for building blocks containing a leader and N A multi-flexible robotic system with multiple followers was established. A dynamic model of a follower flexible robot is constructed, and a virtual dynamic leader with desired joint angle positions is generated and its dynamic model is established. It is a positive integer, 1≤ ≤ N The follower dynamic model includes the hub angle position, the elastic vibration of the flexible link at the spatial position, and the total robot displacement calculated from the hub angle position and the elastic vibration. The fault module is used to establish intermittent actuator fault models for end load actuators and hub actuators, including the number of fault occurrences, fault occurrence intervals, and characteristic parameters of unknown fault times. The approximation module is used to approximate the uncertainty function in a multi-flexible robot system using a radial basis function neural network, and obtain an approximation model of the uncertainty function. The error module is used to define elastic vibration error, position error and total displacement error according to the dynamic model of the follower and the leader and to establish the error dynamic equation. After reconstructing the error dynamic equation by combining the fault model and the approximation model, the boundary error state variables of the leader and the follower are defined respectively. At the same time, a strictly decreasing function with respect to time is introduced to construct a preset index set of the boundary error state variables. The variable module is used to introduce a strictly increasing function with respect to time based on a preset set of indicators, and to convert the boundary error state variables constrained by the preset set of indicators into unconstrained boundary error state variables. The design module is used to design the leader controller and the second controller based on the unconstrained boundary error state variables. An adaptive preset index fault-tolerant controller for a follower flexible robot; The update module is used to design the update law of the estimated parameters in the controller using the projection operator, and to update the estimated parameters such as the neural network estimated weights and fault parameters in the controller in real time online.

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