Flexible robot arm intelligent fault-tolerant tracking control method with uncertain parameters

Abstract

The present application belongs to the field of control science and engineering and robot control technology, and relates to an intelligent fault-tolerant tracking control method for a flexible manipulator with uncertain parameters, comprising: constructing a state perception and rigid-flexible coupling control model for forming a control state vector and a chained uncertain expression; constructing a specified time performance boundary and an error transformation, so that the problem is converted into an equivalent error bounded problem; designing a dynamic gain and a hierarchical backstepping controller for generating a virtual control quantity and a final control input; constructing a dynamic surface filter; constructing a joint estimation and fault-tolerant compensation for estimating parameter uncertainty, external disturbance, unknown nonlinear terms and fault terms; and processing state constraints and input saturation. The present application can effectively improve the tracking accuracy, vibration suppression capability, fault recovery capability and operation safety of the flexible manipulator under non-ideal working conditions, and is suitable for space operations, industrial assembly, medical operations and unmanned operations in dangerous environments.

Description

Technical Field

[0001] This invention belongs to the fields of control science and engineering and robot control technology, and relates to an intelligent fault-tolerant tracking control method for a flexible manipulator with uncertain parameters. It is an intelligent fault-tolerant tracking control method for flexible manipulators under conditions of parameter uncertainty, external disturbance, concurrent faults and constraints. Background Technology

[0002] Flexible robotic arms are an important branch of robotic systems, characterized by lightweight design, high compliance, low energy consumption, and good environmental adaptability. They have broad application prospects in fields such as industrial automation, aerospace on-orbit operations, power line inspection, and minimally invasive medical procedures. Unlike rigid robotic arms, flexible robotic arms exhibit significant elastic deformation during operation, leading to strong nonlinearity, strong coupling, and high-dimensional dynamic characteristics, significantly increasing the difficulty of control.

[0003] In engineering applications, flexible robotic arms commonly suffer from parameter uncertainties. For example, mass, inertia, joint stiffness, and friction parameters are difficult to identify accurately and may drift with changes in load, temperature, or long-term wear. Furthermore, the system is susceptible to external disturbances (impact, environmental vibration, base disturbance, etc.), further reducing trajectory tracking accuracy.

[0004] Furthermore, actuator and sensor failures are key factors affecting system reliability. Common failures include actuator efficiency degradation, input dead zone, bias failure, jamming failure, and sensor misalignment failure. Most existing methods typically only handle single types of failures or single types of uncertainties, making it difficult to effectively cope with concurrent operating conditions involving "parameter uncertainty + external disturbance + failure + vibration + constraints".

[0005] Existing research on flexible robotic arm modeling methods mainly includes modally truncated ODE (Ordinary Differential Equation) models, PDE (Partial Differential Equation) boundary control models, and ODE-PDE coupled models. ODE models are easy to implement with a controller but may introduce modeling errors; PDE models provide more accurate descriptions but are complex to implement; coupled models balance accuracy and structural description capabilities but have a higher computational burden. For control strategies, common methods include robust control, adaptive control, sliding mode control, neural network control, and fuzzy control, but multi-objective cooperative control still faces challenges such as real-time performance, complex stability proofs, and difficulties in engineering implementation.

[0006] Therefore, there is a need for an intelligent fault-tolerant tracking control method that is structurally clear, engineering-featured, rigorously proven in terms of stability, and capable of simultaneously addressing multi-source uncertainties and faults, in order to significantly improve the reliability, safety, and control performance of flexible robotic arms under complex working conditions.

[0007] Further analysis of existing technologies reveals that traditional linear control methods such as PID and LQR are highly dependent on model accuracy. When the system exhibits significant nonlinear coupling or input saturation time-varying faults, they often only guarantee local or asymptotic stability, failing to provide adjustable time-varying performance. For high-frequency repetitive tasks in industrial production lines and on-orbit docking of space robotic arms, control systems not only require stability but also error compression within a finite task window, placing higher demands on the transient quality of the control law.

[0008] While some existing fault-tolerant control studies can handle actuator gain reduction or bias faults, most of these works assume a single fault type that can be distinguished a priori, lacking a unified framework for handling faults with unknown types, occurrence times, and amplitudes. In practical engineering, actuator faults are often accompanied by cascading effects such as amplified measurement noise, changes in friction characteristics, and drive saturation. Compensating only for a single fault item can easily lead to overcompensation, estimation coupling, and control chattering.

[0009] Furthermore, in the control of flexible robotic arms, there is an inherent coupling contradiction between trajectory tracking and vibration suppression: increasing tracking stiffness often excites high-frequency flexible vibrations, while enhancing vibration damping may sacrifice response speed. Existing methods that design these two aspects separately struggle to guarantee optimal overall performance and are more prone to abrupt changes in control gain during the boundary approach phase when state constraints exist. To address these issues, a comprehensive control method is urgently needed that can unify modeling, estimation, and constraint handling, and possess rigorous stability proofs. Summary of the Invention

[0010] To address the issues of decreased control accuracy, insufficient stability, and engineering implementation difficulties in flexible robotic arms under conditions of parameter uncertainty, external disturbances, flexible vibration, actuator / sensor failures, and coexisting state constraints, this invention proposes an intelligent fault-tolerant tracking control method for flexible robotic arms with uncertain parameters. This method combines "multi-source uncertainty estimation" and "constraint-satisfying control" through a series of techniques including state perception, joint estimation, time-bound constraint transformation, hierarchical backstepping control, barrier constraint handling, and fault-tolerant compensation. This enables online estimation and compensation of unknown uncertainties and fault terms, improving trajectory tracking accuracy, vibration suppression capability, and system safety. It is suitable for complex operating environments with parameter uncertainty, external disturbances, actuator / sensor failures, and input saturation constraints.

[0011] The technical solution of the present invention is as follows:

[0012] A method for intelligent fault-tolerant tracking control of a flexible robotic arm with uncertain parameters includes the following steps:

[0013] Step 1: Construct a state-aware and rigid-flexible coupling control model to form the control state vector and chain-like uncertainty expression.

[0014] Step 2: Construct the specified time performance boundary and error transformation, and the problem is transformed into an equivalent error bounded problem.

[0015] Step 3: Design a dynamic gain and hierarchical backstepping controller to generate virtual control variables and final control inputs.

[0016] Step 4: Construct a dynamic surface filter.

[0017] Step 5: Construct a joint estimation and fault-tolerant compensation to estimate parameter uncertainties, external disturbances, unknown nonlinearities, and faults.

[0018] Step 6: Process state constraints.

[0019] The beneficial effects of this invention are:

[0020] First, a joint estimation architecture is used to separately estimate and collaboratively compensate for multi-source uncertainties and various types of faults, reducing estimation coupling and improving compensation accuracy. Second, by jointly designing a time performance function, a dynamic gain mechanism, and a barrier Lyapunov function, trajectory tracking and vibration suppression within a specified time are achieved while maintaining compliance with state constraints. Third, an auxiliary dynamic system and fault compensation mechanism are used to handle actuator saturation and fault impacts, ensuring that the closed-loop system remains stable and performs well under concurrent input saturation and fault conditions. Attached Figure Description

[0021] Figure 1 This is a diagram of the overall control architecture of the present invention.

[0022] Figure 2 The trajectory tracking curve is shown under early actuator failure conditions.

[0023] Figure 3 The tracking error curve is shown under the condition of early actuator failure (failure occurs at 2 seconds).

[0024] Figure 4 The trajectory tracking curve is for the actuator failure condition in the later stage.

[0025] Figure 5 The tracking error curve is shown under the condition of actuator failure in the later stage (failure occurs at 6 seconds). Detailed Implementation

[0026] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.

[0027] The present invention provides an intelligent fault-tolerant tracking control method for a flexible robotic arm with uncertain parameters, comprising: constructing a state-aware and rigid-flexible coupled control model; constructing a specified time performance boundary and error transformation; designing a dynamic gain and hierarchical backstepping controller; constructing a dynamic surface filter; constructing a joint estimation and fault-tolerant compensation; and handling state constraints and input saturation. The above steps form a closed loop within the same control cycle: the state-aware result enters the model expression and error transformation; the error transformation result drives the hierarchical controller; estimation compensation and constraint compensation jointly correct the control input; and the robotic arm state after execution is fed back to the next control cycle. The specific steps are as follows:

[0028] Step 1: Construct a state-aware and rigid-flexible coupled control model to form the control state vector and chain-like uncertainty expression;

[0029] This step corresponds to Figure 1 State perception and model building are performed. Through joint encoders, rotor encoders, speed measurement, end-effector pose measurement, and actuator drive feedback interfaces, the joint angles, joint angular velocities, rotor angles, rotor angular velocities, end-effector pose, actuator input commands, and actual actuator output commands of the flexible robotic arm are collected. Within the same control cycle, a control state vector for the flexible robotic arm is formed, thus completing state perception. Model building establishes the dynamic relationship between the joint side and the actuator side based on the control state vector of the flexible robotic arm.

[0030] After obtaining the control state vector of the flexible robotic arm, a rigid-flexible coupled dynamic model is established based on the joint-side dynamics of the robotic arm and the rotor-side dynamics of the actuator. This model describes the state evolution of the flexible robotic arm under normal driving, parameter drift, external disturbance, and fault conditions, and is further refined for subsequent uncertainty estimation and fault-tolerant control law design. Serial chain-like indeterminate expression.

[0031] Specifically, the following rigid-flexible coupled dynamic model is established using the Euler-Lagrange method:

[0032]

[0033]

[0034] in, , and These represent the joint position, velocity, and acceleration of the robotic arm, respectively. , and These represent the angular position, velocity, and acceleration of the actuator rotor, respectively. For inertia, For the Coriolis force and centripetal force terms, For the gravitational term, For friction; , , These represent the joint flexibility stiffness, actuator rotational inertia, and damping term, respectively. This is the torque input for the actuator.

[0035] Considering the uncertainties of the transmission system, the zero-point drift caused by the elastic deformation of the connecting rod, and external vibration disturbances, the rigid-flexible coupling dynamic model is equivalently reorganized as follows: tiered chain-like uncertain control channel:

[0036] hour,

[0037] hour,

[0038]

[0039] in, The first control channel for the flexible robotic arm Order state vector, for The derivative of for The first step of the chain-like uncertain control channel Order state vector; For the first order basis functions, For the first unknown parameter vector of order, For the first Step control channel gain, For the first External disturbances or unmodeled dynamic terms; For the first order basis functions, The first control channel for the flexible robotic arm Order state vector, For the first unknown parameter vector of order, For the first Step control channel gain, For the first External disturbances or unmodeled dynamic terms, This is the actual output.

[0040] No. The tracking error of a flexible robotic arm is defined as follows: , This represents the desired trajectory of the flexible robotic arm. For a preset steady-state accuracy... and the specified time If positive numbers exist and Greater than time The absolute value of makes The first moment Tracking error of flexible robotic arm If the following formula is satisfied, then the tracking error is said to be stable for the specified actual tracking time:

[0041]

[0042] in, To control time, This is the upper bound of the transient error allowed before the specified time is reached.

[0043] In the specific implementation process, the state perception updates the state vector cyclically according to the preset sampling period. When the sensor signal has a short-term abnormality, bias or drift, the abnormality is not directly discarded as invalid data, but is sent as a fault item to be estimated into the subsequent joint estimation, thereby improving the availability of the state under fault conditions.

[0044] Step 2: Construct the specified time performance boundary and error transformation, and the problem is transformed into an equivalent error bounded problem;

[0045] To facilitate control law design, this step transforms the time-varying constraint problem of the original tracking error into an equivalent bounded error problem. Therefore, subsequent steps only need to ensure that the transformed error variable is bounded to indirectly guarantee that the original tracking error meets the specified time convergence requirement.

[0046] This step corresponds to Figure 1 The performance constraints in this process are the pre-containment performance constraints of the hierarchical backstepping controller. The time-tolerant controller constructs a time-varying performance boundary function based on the desired trajectory, initial error range, preset steady-state accuracy, and specified time. This function ensures that the tracking error gradually shrinks according to the preset boundary in the initial stage of control and remains within the preset steady-state accuracy range after the specified time. The original tracking error is then converted into an equivalent error variable for use in step 3. The specific process is as follows:

[0047] To ensure A chain-like uncertain control channel can be used for backstepping control design, under the following design conditions:

[0048] No. First-order control gain The direction is known to be positive and does not change during the control process; there are two unknown positive constants. and This makes the following equation true:

[0049]

[0050] Expected trajectory Its first and second derivatives are both bounded.

[0051] In the time domain, the first Upper bound of allowable transient error before the specified time is reached There exists an upper bound. , making .

[0052] Given the known direction of the control gain, the boundedness of the desired trajectory, and the boundedness of the disturbance, to transform the specified time convergence requirement into a constrained problem where the error always remains within the time-varying boundary, the following specified time performance boundary function is constructed. :

[0053]

[0054] in, To define the time performance boundary function, The initial error boundary and satisfying time The absolute value is less than , To preset steady-state accuracy, For a specified time. Specified time performance boundary function. It has the following characteristics: (1) exist Continuous and The order is differentiable; (2) exist The upper bound is monotonically decreasing; (3) hour, ,and exist The smooth connection requirement is met. This is achieved by setting initial error boundaries. This can prevent singularities from occurring in the error transformation at the initial moment.

[0055] because Given the allowable boundary of tracking error, the following error transformation is further constructed:

[0056]

[0057] in, The first time error after transformation The equivalent error variable.

[0058] when hour, At that time, if the first equivalent error variable exist If the upper bound remains, then Therefore, the tracking control objective is transformed into constructing a time-tolerant fault control strategy, enabling... Bounded; then combined exist Then equals the preset steady-state accuracy This ensures that the original tracking error meets the specified time performance requirements.

[0059] In practice, the preset steady-state accuracy, specified time, and initial error boundary can be determined based on the robot arm's task requirements, the actuator's maximum output capacity, and the allowable end effector deviation. For high-precision positioning tasks, a smaller steady-state accuracy can be selected; for large-range, rapid motion tasks, the initial error boundary can be appropriately relaxed to avoid excessive control input.

[0060] Step 3: Design a dynamic gain and hierarchical backstepping controller to generate virtual control variables and final control inputs;

[0061] This step corresponds to Figure 1 The hierarchical control is described above. The hierarchical backstepping controller is the core controller of the aforementioned time-tolerant fault-tolerant controller. First, the hierarchical backstepping controller generates the basic control input using the equivalent error obtained in step 2 as input. After completing the joint estimation in step 5, the estimated compensation quantity is incorporated into the basic control input to form the control quantity to be constrained and corrected for fault-tolerant execution. The hierarchical backstepping controller generates a dynamic control gain based on the magnitude of the equivalent error and... The hierarchical structure of the cascaded uncertain control channel constructs virtual control variables and final control inputs layer by layer.

[0062] In the specific control process, when the error is large, the dynamic gain is kept within a relatively flat range to avoid excessive actuator input; as the error gradually decreases, the dynamic gain automatically increases to enhance the error convergence speed and steady-state control accuracy. This dynamic gain is then introduced into the backstepping control law of each layer, so that each error subsystem stabilizes step by step.

[0063] Specifically, before designing the hierarchical backstepping control law, the following dynamic control gain function is first designed based on the feedback mechanism. :

[0064]

[0065] in, For error variables, and These are all design parameters. It is a natural exponential function. For natural numbers. Dynamic control gain function. It has the following properties: (1) Follow (1) Decrease and increase, gradually decrease as |κ| increases; (2) When hour, You can select the smaller one Enhance the convergence capability during the small error phase; (3) when hour, This ensures that the control gain remains bounded during the large error phase, preventing excessive control input.

[0066] Compared to using a constant gain, the dynamic control gain function of this invention... It is an error feedback regulator: when the error is large, the gain gradually converges to a constant to avoid excessive control input; when the error is small, the gain is automatically amplified to improve steady-state accuracy and convergence speed.

[0067] After obtaining the dynamic control gain, the backstepping method is used to construct the virtual control quantity and the final basic control input. For the first equivalent error of order, For the first Virtual control quantity, For the first The output of the first-order dynamic surface filter, For the first Order Adaptive Parameter Combination The estimated value, ,in, For the first unknown parameter vector of order, For the first The estimated value of the upper bound of the derivative of the first-order virtual control variable. and All of these are selectable non-negative or positive design parameters.

[0068] for Choose a first-order positive definite function ,in, For the first-order parameter estimation error, For the first-order adaptive parameter combination The estimated value, This is the first-order equivalent error. For By differentiating and combining Young's inequality to handle the cross terms, a first-order virtual control quantity is constructed. for:

[0069]

[0070] in, , For non-negative design parameters, , For the process of differentiating the error transformation, from , and the bounded coupling terms generated by its derivative, . for The derivative of These are first-order basis functions; Adaptive update law Designed as follows:

[0071]

[0072] in, For positive design parameters. The first-order virtual control quantity... and the first-order adaptive update law Substitution The derivative expression, and using We can obtain:

[0073]

[0074] in, For the constant term related to the bounded perturbation, This is to disturb the upper bound.

[0075] For the intermediate control layer , define the first equivalent error variable , No. Filtering error ,in, For the first The output of the first-order dynamic surface filter.

[0076] The aforementioned intermediate control layer corresponds to ;when When the system enters the final control channel, the final control input replaces the virtual control quantity to complete the closed-loop control.

[0077] Select the first positive definite function ,in, For the first The upper bound of the derivative of the intermediate virtual control quantity. For the first An estimate of the upper bound of the derivative of the intermediate virtual control variable. . .right Differentiate and apply Young's inequality to construct the 1st... intermediate virtual control quantity for:

[0078]

[0079] in, , For the first Order-order nonnegative design parameters. The corresponding adaptive update law is:

[0080]

[0081] in, For the first The derivative of the estimated upper bound of the derivative of the intermediate virtual control quantity. For the first Order Adaptive Parameter Combination The derivative of the estimated value, and These are positive design parameters. Utilizing... achievable The derivative satisfies:

[0082]

[0083] in, This is a constant term related to the bounded perturbation.

[0084] for , define the first equivalent error , No. Filtering error Select the first positive definite function .right After differentiation, design the final control input. for:

[0085]

[0086] in, , For non-negative design parameters, For the first Order Adaptive Parameter Combination The estimated value, For the first First-order basis functions For the first The derivative of the output of the first-order dynamic surface filter. positive definite function The adaptive update law is:

[0087]

[0088] in, and For positive design parameters, For the first The derivative of the estimated upper bound of the derivative of the intermediate virtual control quantity. For the first Order Adaptive Parameter Combination The derivative of the estimated value.

[0089] In practice, the final control input output by the hierarchical backstepping controller is not directly applied to the actuator. Instead, it is first fused with the subsequent joint estimated compensation, constraint compensation, and saturation compensation, and then converted into actuator drive instructions by fault-tolerant execution.

[0090] Therefore, step 3 provides the basic control input; step 5 provides parameter, disturbance and fault estimation compensation; and step 6 provides constraint and saturation compensation. Together, these three form the final drive command applied to the actuator.

[0091] Step 4: Construct a dynamic surface filter;

[0092] This step is used in conjunction with the hierarchical backstepping controller in step 3. Since the backstepping method requires differentiating the virtual control quantity of the previous layer when designing the virtual control quantity layer by layer, directly performing analytical differentiation would increase the online calculation load and may amplify measurement noise. Therefore, a dynamic surface filter is set between adjacent control layers of the hierarchical backstepping controller.

[0093] The dynamic surface filter receives the virtual control quantity from the previous layer and outputs a smoothed filtered signal. The control law of the next layer is calculated based on this filtered signal, thereby reducing the real-time calculation burden of the controller and reducing high-frequency control chattering.

[0094] To overcome the "complexity explosion" problem caused by repeated analytical differentiation of the virtual control law in the traditional backstepping method, a nonlinear filter is introduced to replace the calculation of high-order derivatives of the virtual control quantity. For the intermediate control layer... , define the first equivalent error , No. Filtering error ,in, For the first The output of the first-order nonlinear filter satisfies time, The dynamic surface filter is constructed as follows:

[0095]

[0096] in, These are positive design parameters. Replacing explicit higher-order derivatives with dynamic surfaces can significantly reduce the online computational load of the controller and improve real-time performance. In the filter... This term is used to suppress error propagation in intermediate layers and improve the stability of multilayer control structures.

[0097] In practice, the parameters of the dynamic surface filter are selected based on the controller sampling period and the actuator bandwidth, so that the filtered output can follow the changes of the virtual control quantity without introducing excessive phase lag.

[0098] Step 5: Construct a joint estimation and fault-tolerant compensation system to estimate parameter uncertainties, external disturbances, unknown nonlinearities, and fault terms;

[0099] This step corresponds to Figure 1 The joint estimation process receives the flexible robotic arm's control state vector, tracking error, equivalent error, and actuator torque input in each control cycle, and estimates parameter uncertainties, external disturbances, unknown nonlinearities, and actuator or sensor faults, respectively.

[0100] Each estimation result is input as a compensation quantity into the hierarchical backstepping controller to reduce the impact of model uncertainty, external disturbances, and concurrent faults on trajectory tracking accuracy. By estimating and coordinating the compensation of multiple uncertainties separately, overcompensation or chattering caused by a single compensation channel bearing all uncertainties can be avoided.

[0101] Specifically, the joint estimation method comprehensively utilizes multiple estimation mechanisms to perform online estimation and compensation for uncertainties and faults in the control channel of the flexible robotic arm. Each estimation mechanism generates estimation results for uncertainties from different sources, and forms an estimated value of the comprehensive compensation term in the fault-tolerant compensation channel, which is then uniformly input into the hierarchical backstepping controller to participate in control quantity correction. This invention constructs the corresponding estimator or observer according to the following input, output, and update relationships:

[0102] Adaptive parameter estimator: used for online updating of unknown parameter estimates. This compensates for uncertainties in parameters such as inertia, damping, stiffness, and friction. Adaptive law. Setting up leakage items This suppresses parameter drift while maintaining estimation capability. (Learning rate parameter) The selection of the method needs to take into account both the convergence speed and the smoothness of the estimation.

[0103] Disturbance observer: used for online estimation of external disturbances And unmodeled dynamics. In controller design, the upper bound of the disturbance. It is absorbed into the constant term through scaling by Young's inequality. In addition, a robust term is introduced into the control law to suppress the effects of disturbances.

[0104] Fault estimator: Used to estimate equivalent fault terms formed by actuator efficiency degradation, input dead zone, bias fault, jamming fault, and sensor deviation fault. The fault estimation results, along with parameter estimates, disturbance estimates, and neural network compensation values, are used to construct the final control input.

[0105] Step 6: Process state constraints;

[0106] This step corresponds to Figure 1 The constraint processing and fault-tolerant execution stages are connected to the hierarchical backstepping controller output obtained in step 3. For constrained states such as joint displacement, joint velocity, and end effector deflection, the barrier constraint processing quantity is connected to the hierarchical backstepping controller, introducing a barrier constraint processing mechanism to ensure that the constrained state is always kept within a preset safety range during the control process.

[0107] To address state constraints such as joint displacement, joint velocity, and end effector deflection, a barrier Lyapunov function (BLF) is introduced to directly encode state boundary information within the Lyapunov function. This is achieved by selecting a symmetric barrier Lyapunov function. ,in, To constrain the boundary, For constrained state variables, ensure that the constrained variables remain within the safe range throughout the entire control process. Inside. The key property of BLF is: when hour, This naturally generates a repulsive force in the control law to prevent overstepping the limit.

[0108] In the specific implementation process, when the actuator driving instruction exceeds its physical limit, the actual driving instruction after the output limit is executed with fault tolerance. At the same time, the difference before and after the limit is fed back to the auxiliary dynamic system as saturation error to reduce the impact of input saturation on closed-loop stability.

[0109] Simulation verification:

[0110] To verify the fault-tolerant tracking performance of the control method of this invention under actuator failure conditions, numerical simulation was performed based on a fourth-order flexible joint manipulator simulation model. Simulation model parameters include link mass. Link length l = 7.5, gravitational acceleration Joint flexibility parameters Actuator inertial parameters The damping parameter B = 0.95.

[0111] In the simulation, a continuously differentiable periodic desired trajectory is selected as the tracking target. The state perception, joint estimation, time-bound performance constraints, dynamic gain adjustment, hierarchical control, and fault-tolerant compensation mechanisms described in this invention are applied to the flexible robotic arm object. To examine the impact of the fault occurrence time on the control performance, early actuator fault conditions and late actuator fault conditions are set up respectively, and the changes in system output, desired trajectory, and tracking error are recorded.

[0112] In early actuator failure conditions, the actuator failure occurs in the early stages of the control process. Figure 2 It is evident that after the fault occurred, the system output still followed the expected trajectory and did not exhibit continuous divergence; Figure 3 It is evident that the tracking error, after a brief adjustment following the fault, converges back to near zero and remains within the preset error boundary, indicating that the joint estimation and fault compensation mechanism can restore tracking performance after the initial fault impact.

[0113] In the later stage of actuator failure, the system had essentially entered a stable tracking state before the failure occurred. Figure 4 It is evident that the system output remained largely consistent with the expected trajectory after the fault occurred; Figure 5 It is evident that the amplitude of the error disturbance caused by the fault is small, and the tracking error approaches zero again after the fault recovery phase, indicating that the method of the present invention still has good anti-interference and recovery capabilities when an actuator fault occurs after the system has been running stably.

[0114] The simulation results show that, in both early and late fault scenarios, the control method of this invention can effectively track the desired trajectory, and the tracking error converges back to the preset range after the fault disturbance. Therefore, the simulation results verify the fault-tolerant tracking capability of this invention under conditions of parameter uncertainty, external disturbance, and actuator fault, and also verify the effectiveness of the specified time performance constraints, joint estimation compensation, and hierarchical control structure.

Claims

1. A method for intelligent fault-tolerant tracking control of a flexible robotic arm with uncertain parameters, characterized in that, Includes the following steps: Step 1: Construct a state-aware and rigid-flexible coupling control model to form the control state vector and chain-like uncertainty expression; The system collects the joint angles, joint angular velocities, rotor angles, rotor angular velocities, end-effector pose, actuator input commands, and actual actuator output commands of the flexible robotic arm, and forms a control state vector of the flexible robotic arm within the same control cycle, thereby completing state perception. A rigid-flexible coupled dynamic model was established based on the joint-side dynamics of the robotic arm and the rotor-side dynamics of the actuator, and further refined into... Serial chain-like indeterminate expression; Step 2: Construct the specified time performance boundary and error transformation, and the problem is transformed into an equivalent error bounded problem; The time-tolerant controller constructs a time-varying performance boundary function based on the desired trajectory, initial error range, preset steady-state accuracy, and specified time. This function causes the tracking error to gradually shrink according to the preset boundary in the initial stage of control and remain within the preset steady-state accuracy range after the specified time. The original tracking error is then converted into an equivalent error variable for use in step 3. This transforms the time-varying constraint problem of the original tracking error into an equivalent bounded error problem. Step 3: Design a dynamic gain and hierarchical backstepping controller to generate virtual control variables and final control inputs; The hierarchical backstepping controller first uses the equivalent error obtained in step 2 as input to generate the basic control input; After completing the joint estimation in step 5, the estimated compensation amount is incorporated into the basic control input to form the control amount to be constrained and corrected for fault-tolerant execution. The hierarchical backstepping controller generates dynamic control gain based on the equivalent error magnitude, and based on... The hierarchical structure of the cascaded uncertain control channel constructs virtual control variables and final control inputs layer by layer; Step 4: Construct a dynamic surface filter; To cooperate with the hierarchical backstepping controller in step 3, a dynamic surface filter is set between adjacent control layers of the hierarchical backstepping controller; the dynamic surface filter receives the virtual control quantity of the upper layer and outputs a smoothed filtered signal, and the control law of the lower layer is calculated based on the filtered signal; Step 5: Construct a joint estimation and fault-tolerant compensation system to estimate parameter uncertainties, external disturbances, unknown nonlinearities, and fault terms; The joint estimation receives the control state vector, tracking error, equivalent error and actuator torque input of the flexible robotic arm in each control cycle, and estimates the parameter uncertainty, external disturbance, unknown nonlinearity and actuator or sensor fault terms respectively. The estimation results are used as compensation inputs to the hierarchical backstepping controller. Step 6: Process state constraints; For constrained states that include joint angles, joint velocities, and end-effector deflections, the barrier constraint processing parameters are connected to the hierarchical backstepping controller, introducing a barrier constraint processing mechanism to ensure that the constrained state remains within a preset safety range during the control process.

2. The intelligent fault-tolerant tracking control method for a flexible robotic arm with uncertain parameters according to claim 1, characterized in that, Step 1 is as follows: The following rigid-flexible coupled dynamic model is established using the Euler-Lagrange method: in, , and These represent the joint position, velocity, and acceleration of the robotic arm, respectively. , and These represent the angular position, velocity, and acceleration of the actuator rotor, respectively. For inertia, For the Coriolis force and centripetal force terms, For the gravitational term, For friction; , , These represent the joint flexibility stiffness, actuator rotational inertia, and damping term, respectively. For actuator torque input; The rigid-flexible coupling dynamics model can be equivalently rearranged as follows: tiered chain-like uncertain control channel: hour, hour, in, The first control channel for the flexible robotic arm Order state vector, for The derivative of for The first step of the chain-like uncertain control channel Order state vector; For the first order basis functions, For the first unknown parameter vector of order, For the first Step control channel gain, For the first External disturbances or unmodeled dynamic terms; For the first order basis functions, The first control channel for the flexible robotic arm Order state vector, For the first unknown parameter vector of order, For the first Step control channel gain, For the first External disturbances or unmodeled dynamic terms, This is the actual output; No. The tracking error of a flexible robotic arm is defined as follows: , This represents the desired trajectory of the flexible robotic arm; for a preset steady-state accuracy... and the specified time If positive numbers exist and Greater than time The absolute value of makes The first moment Tracking error of flexible robotic arm If the following formula is satisfied, then the tracking error is said to be stable for the specified actual tracking time: in, To control time, This is the upper bound of the transient error allowed before the specified time is reached.

3. The intelligent fault-tolerant tracking control method for a flexible robotic arm with uncertain parameters according to claim 1, characterized in that, Step 2 is as follows: To ensure A chain-like uncertain control channel can be used for backstepping control design, under the following design conditions: No. First-order control gain The direction is known to be positive and does not change during the control process; there are two unknown positive constants. and This makes the following equation true: Expected trajectory Its first and second derivatives are both bounded; In the time domain, the first Upper bound of allowable transient error before the specified time is reached There exists an upper bound. , making ; Given that the control gain direction is known, the desired trajectory is bounded, and the perturbation is bounded, to transform the specified time convergence requirement into a constrained problem where the error always remains within the time-varying boundary, the following specified time performance boundary function is constructed. : in, To define the time performance boundary function, The initial error boundary and satisfying time The absolute value is less than , To preset steady-state accuracy, For a specified time; Further construct the following error transformation: in, The first time error after transformation Equivalent error variable; when hour, At that time, if the first equivalent error variable exist If the upper bound remains, then .

4. The intelligent fault-tolerant tracking control method for a flexible robotic arm with uncertain parameters according to claim 1, characterized in that, Step 3 is as follows: Before designing the hierarchical backstepping control law, the following dynamic control gain function is first designed based on the feedback mechanism. : in, For error variables, and These are all design parameters. It is a natural exponential function. It is a natural number; After obtaining the dynamic control gain, the backstepping method is used to construct the virtual control quantity and the final basic control input; For the first equivalent error of order, For the first Virtual control quantity, For the first The output of the first-order dynamic surface filter, For the first Order Adaptive Parameter Combination The estimated value, ,in, For the first unknown parameter vector of order, For the first The estimated value of the upper bound of the derivative of the first-order virtual control variable. and All are selectable non-negative or positive design parameters; for Choose a first-order positive definite function ,in, For the first-order parameter estimation error, For the first-order adaptive parameter combination The estimated value, This is the first-order equivalent error; for By differentiating and combining Young's inequality to handle the cross terms, a first-order virtual control quantity is constructed. for: in, , For non-negative design parameters, , For the process of differentiating the error transformation, from , and the bounded coupling terms generated by its derivative, for The derivative of These are first-order basis functions; Adaptive update law Designed as follows: in, For positive design parameters; the first-order virtual control quantity is... and the first-order adaptive update law Substitution The derivative expression, and using We can obtain: in, For the constant term related to the bounded perturbation, To perturb the upper bound; For the intermediate control layer , define the first equivalent error variable , No. Filtering error ,in, For the first The output of the first-order dynamic surface filter; when When the system enters the final control channel, the final control input replaces the virtual control quantity to complete the closed-loop control. Select the first positive definite function ,in, For the first The upper bound of the derivative of the intermediate virtual control quantity. For the first An estimate of the upper bound of the derivative of the intermediate virtual control variable. ;right Differentiate and apply Young's inequality to construct the 1st... intermediate virtual control quantity for: in, , For the first The order nonnegative design parameters; the corresponding adaptive update law is: in, For the first The derivative of the estimated upper bound of the derivative of the intermediate virtual control quantity. For the first Order Adaptive Parameter Combination The derivative of the estimated value, and Positive design parameters; utilizing achievable The derivative satisfies: in, For constant terms related to bounded perturbations; for , define the first equivalent error , No. Filtering error Select the first positive definite function ;right After differentiation, design the final control input. for: in, , For non-negative design parameters, For the first Order Adaptive Parameter Combination The estimated value, For the first First-order basis functions For the first The derivative of the output of the first-order dynamic surface filter; positive definite function The adaptive update law is: in, and For positive design parameters, For the first The derivative of the estimated upper bound of the derivative of the intermediate virtual control quantity. For the first Order Adaptive Parameter Combination The derivative of the estimated value.

5. The intelligent fault-tolerant tracking control method for a flexible robotic arm with uncertain parameters according to claim 1, characterized in that, Step 4 is as follows: Introducing nonlinear filters to replace the calculation of higher-order derivatives of virtual control quantities; for intermediate control layers , define the first equivalent error , No. Filtering error ,in, For the first The output of the first-order nonlinear filter satisfies time, The dynamic surface filter is constructed as follows: in, These are positive design parameters.

6. The intelligent fault-tolerant tracking control method for a flexible robotic arm with uncertain parameters according to claim 1, characterized in that, Step 5 is as follows: Joint estimation comprehensively utilizes multiple estimation mechanisms to perform online estimation and compensation for uncertainties and faults in the control channel of the flexible robotic arm. Each estimation mechanism generates estimation results for uncertainties from different sources, and forms an estimated value of the comprehensive compensation term in the fault-tolerant compensation channel. These estimates are then uniformly input into the hierarchical backstepping controller to participate in control quantity correction. Corresponding estimators or observers are constructed according to the input, output, and update relationships. Adaptive parameter estimator: used for online updating of unknown parameter estimates. To compensate for uncertainties in inertia, damping, stiffness, and friction; Adaptive law ; Disturbance observer: used for online estimation of external disturbances Unmodeled dynamics; in controller design, upper bound of disturbances It is absorbed into the constant term through scaling by Young's inequality. In addition, robust terms are introduced into the control law to suppress the effects of disturbances; Fault estimator: used to estimate the equivalent fault terms formed by actuator efficiency decay, input dead zone, bias fault, jamming fault and sensor deviation fault; the fault estimation results, together with parameter estimates, disturbance estimates and neural network compensation quantities, participate in the construction of the final control input.

7. The intelligent fault-tolerant tracking control method for a flexible robotic arm with uncertain parameters according to claim 1, characterized in that, Step 6 is as follows: For state constraints including joint displacement, joint velocity, and end effector deflection, a barrier Lyapunov function (BLF) is introduced to directly encode state boundary information within the Lyapunov function; by selecting a symmetric barrier Lyapunov function... ,in, To constrain the boundary, For constrained state variables, ensure that the constrained variables remain within the safe range throughout the entire control process. Inside.

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