Two-wheel differential robot dynamic surface error tolerance control method based on fuzzy self-adaption

Abstract

The invention discloses a two-wheel differential robot dynamic surface error tolerance control method based on fuzzy self-adaption, belongs to the technical field of robot control, and aims to solve the problem that system nonlinearity, uncertainty, external disturbance and actuator faults cannot be processed at the same time without depending on an accurate system model and fault prior information, so that the system reliability is improved. The method comprises the steps of system modeling, control target and error definition, design of a control law structure based on a dynamic surface control idea, introduction of a fuzzy logic system, self-adaptive law design and fuzzy approximation and parameter updating. According to the method, the fault does not need to be specially diagnosed and isolated, the unknown fault can be effectively processed through fuzzy adaptive compensation, and the fault-tolerant capability and practicability of the system are greatly improved.

Description

Technical Field

[0001] This invention relates to the field of robot control technology, specifically to a dynamic surface fault-tolerant control method for a two-wheeled differential robot based on fuzzy adaptive control. Background Technology

[0002] Differential wheel mobile robots are widely used in warehousing and logistics, intelligent inspection and material handling on production lines due to their simple structure, low cost and flexible movement. These robots usually achieve straight-line movement and turning by adjusting the speed difference between the left and right drive wheels. At the same time, the robot is also affected by factors such as changes in wheel-ground friction coefficient, load changes, uneven ground and sideslip during actual operation, which leads to strong uncertainty and external disturbances in the system.

[0003] Currently, during long-term operation, the actuators such as drive motors and power amplifiers of this robot may experience efficiency degradation, partial failure, output bias, and jamming. If the control system does not have a corresponding fault-tolerant mechanism, once the performance of the actuators deteriorates, problems such as trajectory deviation, insufficient safety distance, or even collisions may easily occur, posing a threat to the safe operation of the robot. Therefore, while considering nonlinearity, uncertainty, and external disturbances, how to ensure that the two-wheeled differential robot can still stably and accurately track the reference trajectory when the actuators experience unknown failures is a key problem that urgently needs to be solved in current engineering applications.

[0004] Traditional PID control relies on linearized or simplified models, and its parameter tuning is highly sensitive to changes in operating conditions. When the load, friction, or gradient changes significantly, it is prone to large overshoot, slow response, and difficulty in eliminating steady-state errors. Although sliding mode control has a certain degree of robustness, the unavoidable chattering problem will exacerbate actuator wear, making it unsuitable for mobile robots that require smooth motion and low noise. Classical backstepping control methods can handle some strictly feedback nonlinear systems, but in multi-order systems, it requires continuous differentiation of the virtual control quantity, which can easily lead to the so-called "differential explosion." The control law expression is cumbersome, the computation is large, and it is not conducive to real-time embedded implementation.

[0005] In fault-tolerant control methods for actuator failures, one type relies on independent fault diagnosis and isolation modules, requiring accurate identification of the fault type and magnitude before switching or reconstructing the control law based on the diagnostic results. These methods are algorithmically complex, have high real-time requirements, and struggle to guarantee reliable diagnostic results in environments with limited sensor accuracy and high noise levels. Another type introduces fault compensation terms into the control law, but often assumes a known upper bound on the fault or a precisely obtainable model structure, which is inconsistent with the time-varying parameters and complex operating conditions of real-world robot systems.

[0006] In summary, existing technologies lack a fault-tolerant control method for two-wheeled differential robots that can simultaneously handle system nonlinearity, uncertainty, external disturbances, and actuator faults without relying on accurate system models and prior fault information, and whose control structure is suitable for embedded real-time implementation.

[0007] To address the above issues, a dynamic surface fault-tolerant control method for a two-wheeled differential robot based on fuzzy adaptive control is proposed. Summary of the Invention

[0008] The purpose of this invention is to provide a dynamic surface fault-tolerant control method for a two-wheeled differential robot based on fuzzy adaptive control. By using this invention, the problems mentioned above, such as the inability to simultaneously handle system nonlinearity, uncertainty, external disturbances, and actuator failures without relying on an accurate system model and prior fault information, are solved. In addition, it also solves the problem of fault tolerance in two-wheeled differential robots where the control structure is not suitable for embedded real-time implementation.

[0009] To achieve the above objectives, the present invention provides the following technical solution: a dynamic surface fault-tolerant control method for a two-wheeled differential robot based on fuzzy adaptive control, comprising the following steps: S1: System modeling, using the linear velocity and angular velocity or equivalent attitude variables of the two-wheeled differential robot as output, unifies the complex nonlinearity caused by the robot's operation into an unknown function, constructs state equations with strict feedback structures in the upper and lower layers, introduces an actuator fault model at the input of the drive motor, can uniformly describe the state data of the drive motor as an unknown gain term multiplied by the control signal and an unknown bias term independent of the control signal, and allows for unmodeled disturbances; S2: Control objective and error definition. Construct the desired output signal based on the reference trajectory given by the upper planning module, define the tracking error between the actual output and the reference output, and introduce intermediate error variables layer by layer according to the strict feedback structure. Set the control objective to ensure that all state variables and adaptive parameters are bounded under the influence of actuator failure, system parameter uncertainty and external disturbances, so that the output error can be converged. S3: Design the control law structure based on the dynamic surface control concept. Design the virtual control quantity according to the first-level error state without performing high-order derivatives. Use the virtual control quantity as the input of the first-order filter. Construct the dynamic surface through the output of the first-order filter. In the design of the second-level control law structure, use the variable that constructs the dynamic surface to replace the derivative of the virtual control. S4: Introduce a fuzzy logic system, taking the robot's state variables and error variables as inputs, and outputting them through pre-designed fuzzy rules and membership functions to approximate equivalent unknowns online; S5: Adaptive law design, constructing Lyapunov functions, analyzing the derivatives of Lyapunov functions, and then deriving the adaptive update law for fuzzy system parameters and fault compensation parameters. S6: Fuzzy Approximation and Parameter Update. The fuzzy logic system is invoked to calculate the estimated values ​​of unknown nonlinearities and fault terms based on the current state and error information. The fuzzy parameters and fault compensation parameters are updated by combining the adaptive law, and finally the control input for the left and right drive wheels is formed. The driver adjusts the motor parameters according to the control input, so that the robot's motion state gradually approaches the reference trajectory.

[0010] Furthermore, the control law is composed of error feedback terms, dynamic surface stabilization terms, fuzzy compensation terms, and fault adaptive compensation terms. By implementing the control law in discrete form on an industrial computer, embedded processor, or motion controller, and in conjunction with sensors, closed-loop control of the linear and angular velocities of a two-wheeled differential robot can be achieved.

[0011] Furthermore, in the reference trajectory processing, the control program reads the reference trajectory issued by the upper-level planning module and discretizes it on the time axis into a sequence of desired linear velocity and angular velocity.

[0012] Furthermore, real-time state acquisition and calculation are performed. Within each control cycle, the current state of the robot is estimated based on sensor data, and output error and intermediate error variables are calculated. Virtual control quantities are generated according to the dynamic surface structure, and the variables of the dynamic surface are obtained through a first-order filter.

[0013] Furthermore, in S3, the introduction of a first-order filter can transform the high-order derivative process in traditional backstepping control into the updating of the state of the first-order filter, simplifying the structure of the control law.

[0014] Furthermore, in S5, the adaptive update law can continuously adjust the fuzzy system parameters and fault compensation parameters based on the real-time measured error signals during the operation of the control system.

[0015] Furthermore, the sensor includes an encoder for speed measurement and mileage estimation, as well as an IMU for attitude measurement.

[0016] Furthermore, the reference trajectory must satisfy the condition of continuous differentiability in order to serve as the desired output and desired input of the controller.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention introduces an actuator fault model during the system modeling stage and incorporates the impact of faults into equivalent unknowns, which are then processed through fuzzy adaptive compensation, eliminating the need for additional complex fault diagnosis and isolation modules. This setting enables the control system to automatically adjust the compensation amount when the actuator experiences efficiency decay or bias of unknown type or magnitude, maintaining the robot's trajectory tracking performance without sudden changes, thereby improving the overall system's safety and reliability.

[0018] 2. The method of the present invention does not require special diagnosis and isolation of faults. It can effectively handle unknown faults through fuzzy adaptive compensation, which greatly improves the fault tolerance and practicality of the system.

[0019] 3. The fuzzy parameters in this invention are automatically adjusted by the adaptive law, eliminating the need for repeated manual tuning or pre-defined precise upper bound information, thereby enhancing the adaptability of the control method to different road surfaces, loads, and operating conditions. The method of this invention, through online approximation of the fuzzy logic system and adaptive parameter adjustment, can adapt to these changes in real time, ensuring the stability and reliability of control performance.

[0020] 4. This invention employs dynamic surface control technology. By inserting a first-order filtering stage between virtual control and actual control, the high-order differentiation process in traditional backstepping control is transformed into the updating of filter states, avoiding "differential explosion." This results in a relatively simple expression of the control law, lower real-time computation, and greater suitability for operation on resource-constrained embedded platforms. The method of this invention simplifies the control law structure, reduces computation, and enables efficient operation on embedded platforms, meeting the requirements of real-time control.

[0021] 5. The method proposed in this invention is relatively independent of the generation of the reference trajectory, and can be easily used in conjunction with various path planning and safety corridor planning methods. As long as a continuous and differentiable reference trajectory can be provided, it can be used as the desired output input of the controller, thereby maintaining the two-wheeled differential robot to run stably and accurately along the trajectory in scenarios with narrow channels, dense obstacles, or large load changes. Attached Figure Description

[0022] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0023] 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 embodiments of the present invention, and not all embodiments. 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.

[0024] To address the technical challenges of fault tolerance in two-wheeled differential robots that cannot simultaneously handle system nonlinearity, uncertainty, external disturbances, and actuator failures without relying on accurate system models and prior fault information, and whose control structures are unsuitable for embedded real-time implementation, such as... Figure 1 As shown, the following preferred technical solutions are provided: A dynamic surface fault-tolerant control method for a two-wheeled differential robot based on fuzzy adaptive control includes the following steps: System modeling, as detailed below: Using the linear velocity and angular velocity or equivalent attitude variables of the two-wheeled differential robot as outputs, the complex nonlinearities caused by wheel-ground interaction, load changes, and structural nonlinearities are uniformly represented as unknown functions, and then the state equations with strict feedback structures in the upper and lower layers are constructed.

[0025] An actuator fault model is introduced at the input of the drive motor, and factors such as motor efficiency decay, gain change and output bias are uniformly described as unknown gain terms multiplied by the control signal and unknown bias terms unrelated to the control signal, and a certain amount of unmodeled disturbances are allowed.

[0026] In practical applications, the motion of two-wheeled differential robots is affected by a variety of complex factors. The interaction between the wheels and the ground changes with the ground material and flatness. The increase or decrease of the load also directly affects the robot's motion characteristics. At the same time, the nonlinearity of the robot's own structure cannot be ignored. Representing these complex nonlinearities as unknown functions can simplify the construction of the system model and better reflect the actual operating conditions.

[0027] As the power output component of a robot, the actuator inevitably experiences various faults during long-term operation. Motor efficiency decay leads to a decrease in output power, gain changes affect the transmission of control signals, and output bias causes the actuator output to deviate from the ideal value. These faults all affect the robot's trajectory tracking performance. By introducing an actuator fault model containing unknown gain terms, unknown bias terms, and unmodeled disturbances at the input of the drive motor, the fault state of the actuator can be comprehensively and realistically reflected, providing an accurate model basis for subsequent fault-tolerant control.

[0028] The control objective and error are defined as follows: The desired output signal is constructed based on the reference trajectory given by the upper-level planning module. The tracking error between the actual output and the reference output is defined. Intermediate error variables are introduced layer by layer according to a strict feedback structure. The control objective is set to ensure that all state variables and adaptive parameters are bounded and that the output error converges to zero or a sufficiently small neighborhood under the conditions of actuator failure, system parameter uncertainty and external disturbance.

[0029] The upper-level planning module generates a reference trajectory that the robot needs to track based on the specific application scenario and task requirements. This reference trajectory is the target path for the robot's movement. After constructing the desired output signal, the tracking error can be obtained by comparing the actual output with the desired output. This error directly reflects the robot's trajectory tracking accuracy. Then, intermediate error variables are introduced layer by layer according to a strict feedback structure, which can decompose the complex control problem into multiple simple sub-problems, facilitating the design of subsequent control laws. By setting the control objective, the performance indicators that the system needs to achieve under various complex working conditions are clarified, namely, ensuring the boundedness of state variables and adaptive parameters, avoiding system instability, and minimizing the output error to ensure that the robot can accurately track the reference trajectory.

[0030] The control law structure is designed based on the concept of dynamic surface control, as follows: a virtual control quantity is designed according to the error state of the first layer, and no higher-order derivatives are performed. The virtual control quantity is used as the input of a first-order filter, and a dynamic surface is constructed through the output of the first-order filter. In the design of the second-layer control law, the dynamic surface variable is used to replace the derivative of the virtual control.

[0031] Traditional backstepping control methods require multiple high-order derivatives of the virtual control quantity when dealing with multi-order systems. This not only leads to cumbersome control law expressions and high computational load, but also easily causes the "differential explosion" phenomenon, affecting the real-time performance and stability of the system. This invention adopts the concept of dynamic surface control. By designing a virtual control quantity and inputting it into a first-order filter, a dynamic surface variable is obtained. This dynamic surface variable is used to replace the derivative of the virtual control in the design of the second-level control law, effectively avoiding the high-order derivative process and thus eliminating the "differential explosion" problem. Moreover, the introduction of the first-order filter makes the control law structure simpler, the numerical calculation more stable, and reduces the complexity of the control algorithm, providing favorable conditions for the real-time implementation of the control law on an embedded platform.

[0032] Introducing a fuzzy logic system, as follows: Using the robot's state variables and error variables as inputs, and generating outputs through pre-designed fuzzy rules and membership functions, the system performs online approximation of "equivalent unknowns," including unknown nonlinearities of the system, changes in actuator efficiency, and biases.

[0033] Fuzzy logic systems possess powerful nonlinear approximation capabilities, enabling them to handle complex systems that are difficult to describe using precise mathematical models. In this invention, unknown nonlinearities, actuator efficiency variations, and biases collectively constitute "equivalent unknowns," which can adversely affect the robot's control performance. This invention uses the robot's state variables and error variables as inputs to the fuzzy logic system, comprehensively reflecting the system's operating state and tracking error. By pre-designing reasonable fuzzy rules and membership functions, the "equivalent unknowns" are approximated online. Furthermore, the fuzzy logic system can adjust its output in real time based on the input information, thereby compensating for the impact of these unknowns on the system.

[0034] Compared with traditional control methods that rely on fixed parameter models, this invention uses fuzzy approximation to automatically adapt to parameter changes and disturbances under different operating conditions, reducing the dependence on precise mathematical models and thus improving the adaptability and robustness of the control method.

[0035] The adaptive law design is as follows: Based on Lyapunov stability theory, a Lyapunov function is constructed that includes error variables, dynamic surface errors, and fuzzy system parameter estimation errors. The derivative of this function is analyzed, and then the adaptive update law of fuzzy system parameters and fault compensation parameters is derived.

[0036] Lyapunov stability theory is an important tool for judging system stability. By constructing a suitable Lyapunov function and analyzing the sign of its derivative, the stability of the system can be determined. In this invention, the constructed Lyapunov function contains key information such as error variables, dynamic surface errors, and fuzzy system parameter estimation errors, which can comprehensively reflect the stability of the system. By analyzing the derivative of the Lyapunov function, the adaptive update law of fuzzy system parameters and fault compensation parameters is derived, enabling the control system to continuously adjust these parameters according to the real-time measured error signals during operation.

[0037] As the parameters are continuously updated, the accuracy of fuzzy approximation gradually improves, and the fault compensation effect is continuously optimized. Thus, without prior estimation of the fault upper bound and accurate model parameters, adaptive compensation for unknown nonlinearities and actuator faults can be achieved to ensure the stability and tracking accuracy of the system.

[0038] Generate the actual control inputs as follows: By integrating the error feedback term, dynamic surface stability term, fuzzy compensation term, and fault adaptive compensation term, the actual control input expression for the left and right drive wheels is obtained.

[0039] The error feedback term can adjust the control input in a timely manner according to the magnitude and trend of the tracking error, so that the system can move in the direction of reducing the error; the dynamic surface stabilization term is used to ensure the stability of the dynamic surface, so as to ensure that the dynamic surface variables can accurately track the virtual control quantity; the fuzzy compensation term is used to compensate for the adverse effects of unknown nonlinearity of the system and actuator failure; the fault adaptive compensation term is specifically designed to compensate for actuator failure, so as to improve the fault tolerance of the system; combining these four terms, the actual control input expression of the left and right drive wheels can be formed, so that the control input can not only ensure the closed-loop stability of the system, but also take into account the robustness to faults and uncertainties, thereby ensuring that the robot can stably and accurately track the reference trajectory under various complex working conditions.

[0040] The control law is implemented as follows: By implementing the control law in discrete form on an industrial computer, embedded processor, or motion controller, and then combining it with sensors such as encoders and IMUs, closed-loop control of the linear and angular velocities of a two-wheeled differential robot can be achieved.

[0041] Industrial computers, embedded processors, and motion controllers are common control units, each with different performance characteristics and applicable scenarios. Users can choose the appropriate control unit based on their actual needs. Implementing control laws in discrete form allows for adaptation to the digital signal processing methods of control units, facilitating the writing and debugging of control programs. Encoders are used to measure the rotational speed of the drive wheels, providing feedback signals for speed closed-loop control. IMUs are used to measure the robot's posture information, such as angular velocity and acceleration, which helps to accurately estimate the robot's motion state. By analyzing the data collected by these sensors, the control unit can understand the robot's operating status in real time and output corresponding control commands according to the control law to adjust the rotational speed of the left and right drive wheels, achieving closed-loop control of the robot's linear and angular velocities, thereby ensuring the robot's trajectory tracking accuracy.

[0042] Reference trajectory processing is as follows: The control program reads the reference trajectory issued by the upper-level planning module and discretizes it on the time axis into a sequence of desired linear velocity and angular velocity.

[0043] The reference trajectory issued by the upper-level planning module is usually continuous, while the control cycle of the control unit is discrete. Therefore, it is necessary to discretize the continuous reference trajectory on the time axis to obtain the desired linear velocity and angular velocity sequence corresponding to the control cycle. This allows the control unit to calculate the corresponding control input based on the current desired velocity value in each control cycle, thereby achieving real-time control of the robot.

[0044] The accuracy of discretization affects the trajectory tracking accuracy of the robot. Therefore, it is necessary to reasonably select the discretization step size according to the size of the control cycle and the complexity of the reference trajectory to ensure that the desired velocity sequence after discretization can accurately reflect the characteristics of the original reference trajectory.

[0045] Real-time status acquisition and calculation, as detailed below: Within each control cycle, the current robot state is estimated based on sensor data, the output error and intermediate error variables are calculated, virtual control quantities are generated according to the dynamic surface structure, and dynamic surface variables are obtained through a first-order filter.

[0046] Within each control cycle, sensors such as encoders and IMUs collect real-time data on the robot's wheel speed and posture. The control program uses this data and appropriate estimation algorithms to accurately estimate the robot's current state, such as linear velocity, angular velocity, and position. Then, based on the estimated robot state and the discretized desired velocity sequence, the output error between the actual and desired output is calculated, and intermediate error variables are calculated layer by layer according to a strict feedback structure. Finally, a virtual control quantity is designed based on the first-level error state and input into a first-order filter to obtain dynamic surface variables. This series of real-time acquisition and calculation processes provides accurate input information for subsequent fuzzy approximation and parameter updates, ensuring that the control law can be adjusted according to the robot's real-time state.

[0047] Fuzzy approximation and parameter update are detailed below: The fuzzy logic system is invoked to calculate the estimated values ​​of unknown nonlinear and fault terms based on the current state and error information. The fuzzy parameters and fault compensation parameters are then updated using an adaptive law to form the control input for the left and right drive wheels. The driver then adjusts the motor current or voltage according to the control input, so that the robot's motion state gradually approaches the reference trajectory.

[0048] The fuzzy logic system calculates the estimated value of the "equivalent unknown term" based on the current state information of the robot and the calculated error information, using pre-designed fuzzy rules and membership functions. This estimated value forms the basis of the fuzzy compensation term. Then, according to the adaptive law, combined with the current error signal and dynamic surface error information, the fuzzy system parameters and fault compensation parameters are updated to continuously optimize the accuracy of fuzzy approximation and the effect of fault compensation. Finally, based on the updated parameters and various compensation terms, the final control input for the left and right drive wheels is formed and sent to the driver. The driver adjusts the motor current or voltage according to the control input, changes the motor output speed, and thus adjusts the speed of the left and right drive wheels, so that the robot's motion state gradually approaches the reference trajectory, achieving accurate trajectory tracking.

[0049] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0050] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A dynamic surface fault-tolerant control method for a two-wheeled differential robot based on fuzzy adaptive control, characterized in that, Includes the following steps: S1: System modeling, using the linear velocity and angular velocity or equivalent attitude variables of the two-wheeled differential robot as output, unifies the complex nonlinearity caused by the robot's operation into an unknown function, constructs state equations with strict feedback structures in the upper and lower layers, introduces an actuator fault model at the input of the drive motor, can uniformly describe the state data of the drive motor as an unknown gain term multiplied by the control signal and an unknown bias term independent of the control signal, and allows for unmodeled disturbances; S2: Control objective and error definition. Construct the desired output signal based on the reference trajectory given by the upper planning module, define the tracking error between the actual output and the reference output, and introduce intermediate error variables layer by layer according to the strict feedback structure. Set the control objective to ensure that all state variables and adaptive parameters are bounded under the influence of actuator failure, system parameter uncertainty and external disturbances, so that the output error can be converged. S3: Design the control law structure based on the dynamic surface control concept. Design the virtual control quantity according to the first-level error state without performing high-order derivatives. Use the virtual control quantity as the input of the first-order filter. Construct the dynamic surface through the output of the first-order filter. In the design of the second-level control law structure, use the variable that constructs the dynamic surface to replace the derivative of the virtual control. S4: Introduce a fuzzy logic system, taking the robot's state variables and error variables as inputs, and outputting them through pre-designed fuzzy rules and membership functions to approximate equivalent unknowns online; S5: Adaptive law design, constructing Lyapunov functions, analyzing the derivatives of Lyapunov functions, and then deriving the adaptive update law for fuzzy system parameters and fault compensation parameters. S6: Fuzzy Approximation and Parameter Update. The fuzzy logic system is invoked to calculate the estimated values ​​of unknown nonlinearities and fault terms based on the current state and error information. The fuzzy parameters and fault compensation parameters are updated by combining the adaptive law, and finally the control input for the left and right drive wheels is formed. The driver adjusts the motor parameters according to the control input, so that the robot's motion state gradually approaches the reference trajectory.

2. The dynamic surface fault-tolerant control method for a two-wheeled differential robot based on fuzzy adaptive control according to claim 1, characterized in that: The control law consists of an error feedback term, a dynamic surface stabilization term, a fuzzy compensation term, and a fault adaptive compensation term. The control law is implemented in discrete form on an industrial computer, embedded processor, or motion controller. Combined with sensors, it can achieve closed-loop control of the linear and angular velocities of a two-wheeled differential robot.

3. The dynamic surface fault-tolerant control method for a two-wheeled differential robot based on fuzzy adaptive control according to claim 2, characterized in that: Reference trajectory processing involves the control program reading the reference trajectory issued by the upper-level planning module and discretizing it on the time axis into a sequence of desired linear and angular velocities.

4. The dynamic surface fault-tolerant control method for a two-wheeled differential robot based on fuzzy adaptive control according to claim 3, characterized in that: Real-time state acquisition and calculation: In each control cycle, the current state of the robot is estimated based on sensor data, and the output error and intermediate error variables are calculated. Virtual control quantities are generated according to the dynamic surface structure, and the variables of the dynamic surface are obtained through a first-order filter.

5. The dynamic surface fault-tolerant control method for a two-wheeled differential robot based on fuzzy adaptive control according to claim 4, characterized in that: In S3, the introduction of a first-order filter can transform the high-order derivative process in traditional backstepping control into the updating of the state of the first-order filter, simplifying the structure of the control law.

6. The dynamic surface fault-tolerant control method for a two-wheeled differential robot based on fuzzy adaptive control according to claim 5, characterized in that: In S5, the adaptive update law can continuously adjust the fuzzy system parameters and fault compensation parameters based on the real-time measured error signals during the operation of the control system.

7. The dynamic surface fault-tolerant control method for a two-wheeled differential robot based on fuzzy adaptive control according to claim 6, characterized in that: The sensors include encoders for speed measurement and mileage estimation, as well as IMUs for attitude measurement.

8. The dynamic surface fault-tolerant control method for a two-wheeled differential robot based on fuzzy adaptive control according to claim 7, characterized in that: The reference trajectory must satisfy the condition of being continuously differentiable in order to serve as the desired output and desired input of the controller.

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