A robot low-communication load fault-tolerant control method for complex working conditions

Abstract

The application relates to the technical field of robot control, in particular to a robot low-communication load fault-tolerant control method for complex working conditions, which comprises the following steps: constructing a robot system dynamics model containing unknown dynamics of a system, external disturbance and multiplicative and additive faults of actuators; combining actual positions and expected positions of joints in the robot system, defining a constrained joint position tracking error according to a preset performance function, and then converting the constrained error variable into an unconstrained error variable through a bijective error transformation; constructing a virtual control law, and designing a speed tracking error and an error compensation signal through a finite time command filter; introducing a fuzzy logic system to approximate the unknown dynamics of the system; designing a fixed-time disturbance observer for estimating a composite disturbance; combining a relative threshold event trigger mechanism to construct a final fault-tolerant control law; and the application can ensure the robot trajectory tracking precision and the global consistent boundedness of closed-loop system signals under the conditions of unknown model, actuator fault and external disturbance.

Description

Technical Field

[0001] This invention relates to the field of robot control technology, and specifically to a low-communication-load fault-tolerant control method for robots under complex working conditions. Background Technology

[0002] Traditional robot control strategies are typically designed based on the ideal assumptions of a fully known system model and fault-free actuators. However, in real-world complex applications such as aerospace, deep-sea exploration, and precision medicine, systems often face complex disturbances including parameter uncertainties, time-varying external disturbances, and multiplicative and additive faults in actuators. These disturbances can significantly increase the system's trajectory tracking error, and even trigger strong oscillations, severely compromising the stability and dynamic tracking performance of the closed-loop system.

[0003] Existing control methods, such as traditional PID control or conventional adaptive fault-tolerant control, struggle to comprehensively address multi-source uncertainties and strict kinematic / dynamic constraints. They generally suffer from slow convergence speed and insufficient robustness, and cannot impose strict quantitative constraints on the system's transient performance (e.g., maximum overshoot, convergence speed) and steady-state performance (e.g., steady-state error range). In particular, the following two limitations remain prominent: First, the lack of a pre-defined performance theory guarantee for the entire evolution of the tracking error makes it difficult to ensure that the error remains within the pre-defined performance range. Second, the lack of a fixed-time rapid observation and active compensation mechanism for complex disturbances and sudden faults, while insufficient consideration of the limited communication resources in networked control makes it difficult to effectively reduce unnecessary control signal transmission while maintaining high performance. Summary of the Invention

[0004] To effectively address the trajectory tracking control problem of robots under conditions of unknown dynamics, simultaneous multiplicative and additive actuator failures, and coexisting external disturbances, and to reduce communication resource consumption in networked systems, this invention proposes a low-communication-load fault-tolerant control method for robots in complex working conditions, comprising:

[0005] S1. Construct a dynamic model of the robot system that includes unknown system dynamics, external disturbances, and multiplicative and additive faults of the actuators;

[0006] S2. Combining the actual and desired positions of the joints in the robot system, define the constrained joint position tracking error according to the preset performance function;

[0007] S3. By using bijective error transformation, the constrained joint position tracking error is converted into an unconstrained error variable, ensuring that the joint position tracking error is always within the preset limits;

[0008] S4. Construct a virtual control law based on unconstrained error variables, and design speed tracking error and error compensation signals through a finite-time command filter;

[0009] S5. Introduce fuzzy logic systems to approximate the unknown dynamics of the system;

[0010] S6. Based on the unknown dynamics of the system approximated by the fuzzy logic system, a fixed-time disturbance observer is designed to estimate the complex disturbances, including external disturbances and multiplicative and additive faults of actuators.

[0011] S7. Based on the speed tracking error, error compensation signal and fixed-time disturbance observer, combined with the relative threshold event triggering mechanism, the final fault-tolerant control law is constructed.

[0012] The beneficial effects of this invention are:

[0013] First, by introducing a preset performance function and a bijective error transform, the transient overshoot and convergence rate of the system can be strictly constrained while ensuring minimal steady-state error, significantly improving its transient and steady-state performance. Second, to address model perturbations, external disturbances, and multiple actuator faults, a fuzzy logic system and a fixed-time disturbance observer are combined to achieve rapid and accurate compensation for unknown disturbances and faults, greatly enhancing the system's robustness and fault tolerance. Furthermore, by introducing a finite-time command filter and Nussbaum gain, the "explosion" problem of differential calculations in traditional backstepping methods is effectively avoided, and the design difficulties caused by unknown control directions are resolved; simultaneously, a static event triggering mechanism based on relative thresholds significantly reduces communication resource consumption. In summary, this method achieves high-precision trajectory tracking while effectively mitigating the adverse effects of mechanical wear, possessing good engineering feasibility and practical application value. Attached Figure Description

[0014] Figure 1 This is an overall flowchart of the control method of the present invention;

[0015] Figure 2 This is a schematic diagram of the rotation trajectory tracking of joint 1 and joint 2 in the robot system of the present invention;

[0016] Figure 3 This is a schematic diagram of the velocity tracking of joint 1 and joint 2 in the robot system of the present invention;

[0017] Figure 4 This is a schematic diagram of the rotation tracking error of joint 1 and joint 2 of the robot system under the preset performance function constraint of the present invention;

[0018] Figure 5 This is a schematic diagram of the actual output torque and continuous control signal of joint 1 in the robot system of the present invention;

[0019] Figure 6 This is a schematic diagram of the actual output torque and continuous control signal of joint 2 in the robot system of the present invention;

[0020] Figure 7 This is a schematic diagram of the weight estimation in the fuzzy logic system (FLS) of this invention;

[0021] Figure 8 This is a schematic diagram illustrating the evolution process of the Nussbaum variable, the adaptive control parameter, in this invention.

[0022] Figure 9 This is a schematic diagram illustrating the evolution of the Nussbaum function in this invention.

[0023] Figure 10 This is a schematic diagram of the control signal triggering interval of joint 1 in the robot system under the event triggering mechanism of the present invention;

[0024] Figure 11 This is a schematic diagram of the control signal triggering interval of joint 2 in the robot system under the event triggering mechanism of the present invention. Detailed Implementation

[0025] 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.

[0026] There is an urgent need to develop a new robust fault-tolerant control method that can meet multiple requirements such as preset performance constraints, accurate estimation of fixed-time disturbances, handling of unknown control directions, and reduction of communication load in real-world environments where the system dynamics model is unknown, multiple actuator faults coexist, and multiple sources of disturbances coexist. Theoretically, it should ensure that the trajectory tracking error converges rapidly to the preset performance range within a finite time, thereby meeting the needs of high-precision, high-safety, and high-reliability robot engineering applications.

[0027] Therefore, this invention provides a low-communication-load fault-tolerant control method for robots under complex working conditions. For details, please refer to [link / reference needed]. Figure 1 ,include:

[0028] S1. Construct a dynamic model of the robot system that includes unknown system dynamics, external disturbances, and multiplicative and additive faults of the actuators.

[0029] In some embodiments, step S1 specifically includes:

[0030] S11. Construct a dynamic model of the robot system with Eulerian-Lagrange multi-input multi-output characteristics, expressed as:

[0031] (1)

[0032] In the formula, Represents the joint position vector. Represents the joint velocity vector. Represents the joint acceleration vector. Represents the inertia matrix. Represents the centripetal-Coriolis force matrix. Represents the gravity vector. Indicates the control input torque. Represents an unknown external disturbance vector; Represents the set of real numbers. The dimension of a vector or matrix.

[0033] S12. The uncertainty of the robot system dynamics model is expressed as:

[0034] (2)

[0035] In the formula, This represents the nominal inertia matrix of the robot system. This represents the unknown inertia matrix of the robot system. This represents the nominal centripetal force and Coriolis force of a robot system. This represents the unknown centripetal force and Coriolis force of the robot system. This represents the nominal gravity term of the robot system. This represents the unknown gravity term of the robot system.

[0036] S13. Introduce an actuator fault model to effectively control input torque. This can be further expressed as:

[0037] (3)

[0038] in, Represents the multiplicative fault matrix. This indicates an additive fault in the actuator (constant or slow time-varying). This represents the actual discrete control signal.

[0039] S14. Define two state variables, namely the joint's actual position vector. With the actual velocity vector of the joint ,in , The dynamic model of the robot system is transformed into a state equation form (also known as a second-order system), which includes unknown system dynamics, external disturbances, and multiplicative and additive faults of the actuators, and is expressed as:

[0040] (4)

[0041] In the formula, This represents the dynamic update item of the nominal model of the robot system. This represents the unmodeled dynamic uncertainty of the robot system. This represents a combined disturbance of external disturbances and additive faults in the robot system. satisfy ,Right now It is continuously differentiable and its derivative is bounded. This indicates the upper bound of the derivative of the composite perturbation. Represents the actual position vector of the joint The time derivative is equivalent to the joint velocity vector of the robot system. Represents the actual velocity vector of the joint The time derivative is equivalent to the joint acceleration vector of the robot system. Represents the composite disturbance term The time derivative, ||·||, represents the operation of taking the Euclidean norm of a vector.

[0042] S2. Combining the actual and desired positions of the joints in the robot system, define the constrained joint position tracking error according to the preset performance function (PPF).

[0043] In some embodiments, the joint position tracking error is defined as follows, combining the actual and desired positions of the joints in the robot system:

[0044] (5)

[0045] , , ,

[0046] in, This represents the joint position tracking error of the robot system. This represents the actual joint position vector of the robot system at time t. This represents the desired joint position vector of the robot system; Indicates the robot system's first Joint position tracking error of each joint, Indicates the robot system's first The actual joint position vector of each joint. Indicates the robot system's first The expected joint position vectors of each joint; from this, we can obtain:

[0047]

[0048] To ensure that the joint position tracking error of the robot system remains within a preset range, the following must be met:

[0049] (6)

[0050] In the formula, , This indicates the set scaling factor. Indicates the robot system's first Each subsystem defines an exponentially preset performance function. To constrain the maximum overshoot, convergence rate, and steady-state error, the first... The exponential preset performance function defined for each subsystem is expressed as follows:

[0051] (7)

[0052] In the formula, Indicates the initial value. Indicates the final value. t represents the decay rate, and t represents the time parameter.

[0053] S3. By using bijective error transformation, the constrained joint position tracking error is converted into an unconstrained error variable, ensuring that the joint position tracking error is always within the preset limits.

[0054] In some embodiments, the constrained joint position tracking error is converted into an unconstrained error variable through bijective error transformation, as follows:

[0055] (8)

[0056] In the formula, Indicates the robot system's first The unconstrained error variable after mapping of the joint position tracking error of each joint.

[0057] Furthermore, the transformed unconstrained error variable... Taking the time derivative, we get:

[0058] (9)

[0059] (10)

[0060] (11)

[0061] In the formula, Represents unconstrained error variables The result of taking the derivative with respect to time t, Indicates the robot system's first The time derivative of the joint position tracking error of each subsystem (i.e., joint). Indicates the robot system's first The expected velocity of each joint. Indicates the robot system's first Preset performance functions for each subsystem Time derivative, Indicates the robot system's first The actual joint velocity vector of each joint. This represents the time-varying proportional coefficient. This represents the boundary contraction compensation term.

[0062] To facilitate subsequent control law design, Rewritten in compact vector form:

[0063] (12)

[0064] This represents the actual velocity vector of the joints in the robot system. This represents the desired velocity of the joints in the robot system. Represents the time-varying scaling factor matrix. This represents the boundary shrinkage compensation term matrix.

[0065] S4. Construct a virtual control law based on unconstrained error variables, and design speed tracking error and error compensation signals through a finite-time command filter (FTCF).

[0066] In some embodiments, the unconstrained error variable after the stable transformation is... Constructing local Lyapunov functions , is represented as:

[0067] (13)

[0068] For local Lyapunov functions Take the derivative and substitute it into the unconstrained error variable. vector form derivative ,get:

[0069] (14)

[0070] To ensure that the time derivative of the local Lyapunov function satisfies negative definiteness, the following virtual control law needs to be designed:

[0071] (15)

[0072] In the formula, This represents the constructed virtual control signal. This represents the desired velocity of the joints in the robot system. Represents the time-varying scaling factor matrix. , These represent the positive definite gain matrices for linear error feedback and nonlinear error feedback, respectively. Represents the boundary contraction compensation term matrix; Represents the unconstrained error variable. This represents a fractional power parameter.

[0073] To address the differential "explosion" problem that occurs during differentiation in the traditional backstepping method and to ensure the robot system has a fast response capability, the following finite-time command filter is introduced:

[0074] (16)

[0075] In the formula, This represents the smoothed tracking signal after filtering by the virtual control law. This represents the derivative estimate of the virtual control law. This represents the filter gain parameter. Represents the absolute value function. The sign function is defined as follows: it returns 1 when the independent variable is greater than 0; it returns 0 when the independent variable is equal to 0; and it returns -1 when the independent variable is less than 0. This represents the smoothed tracking signal after filtering by the virtual control law. Time derivative, Derivative estimation of virtual control law Time derivative, , Represents the fractional power parameter of the finite-time command filter;

[0076] virtual control signal Input a finite-time command filter to generate a filtered signal Define the speed tracking error of the robot system for:

[0077] (17)

[0078] To eliminate transient filtering errors caused by finite-time command filters Impact on system stability, construction of error compensation signal The adaptive update law is as follows:

[0079] (18)

[0080] In the formula, This represents the time derivative of the error compensation signal.

[0081] Therefore, the true position tracking error after compensation Represented as:

[0082] (19)

[0083] right Find the time derivative, and and Substitute and use the relational expression We can obtain:

[0084] (20)

[0085] In the formula, Indicates the true position tracking error The time derivative.

[0086] Substituting the virtual control law formula (15) into the above formula (20) The simplified dynamic compensation error is obtained by considering the following terms:

[0087] (twenty one)

[0088] Constructing Lyapunov functions For Lyapunov functions Find the time derivative:

[0089] (twenty two)

[0090] In the formula, Represents Lyapunov functions The time derivative.

[0091] Furthermore, speed tracking error The time derivative can be expressed as:

[0092] (twenty three)

[0093] Therefore, we can conclude that:

[0094] (twenty four)

[0095] This represents the smoothed tracking signal after filtering by the virtual control law, which can be used as the feedforward reference speed. This represents the nominal inertia matrix of the robot system.

[0096] Substitute the original dynamic model (4) into the equation and use the relational expression Equation (25) can be obtained, which lays the foundation for subsequent reasoning:

[0097] (25)

[0098] S5. Introduce a fuzzy logic system (FLS) to approximate the unknown dynamics of the system.

[0099] In some embodiments, a fuzzy logic system is introduced to approximate the unknown dynamics of the system, expressed as:

[0100] (26)

[0101] in, This represents the unmodeled dynamic uncertainty of the robot system. Represents the ideal weight matrix. This represents the fuzzy basis function vector in a fuzzy logic system. This represents the bounded approximation error generated by a fuzzy logic system when approximating unknown dynamics, satisfying... , The positive constant bound represents the range of the maximum approximation error; .

[0102] Furthermore, the weight estimation error is defined as... ,in To estimate the optimal weights; to design the estimate of the optimal weights. The update law is:

[0103] (27)

[0104] in, This represents the gain parameter of the fuzzy logic system. This indicates the leakage factor.

[0105] S6. Design a fixed-time disturbance observer (FxTDOB) to estimate complex disturbances including external disturbances and multiplicative and additive actuator faults;

[0106] In some embodiments, the fixed-time perturbation observer is represented as:

[0107] (28)

[0108] In the formula, This represents the estimated actual velocity of the joint. This represents the actual velocity vector of the joints in the robot system. This represents the dynamic update item of the nominal model of the robot system. This represents the estimation of unmodeled dynamic uncertainties by the fuzzy logic system. Represents the Nussbaum gain matrix. This represents the equivalent nominal control signal. , , , This represents the gain parameter. , , , Denotes the fractional exponent parameters, respectively satisfying , , , , Represents the absolute value function. The sign function is defined as follows: it returns 1 when the independent variable is greater than 0; it returns 0 when the independent variable is equal to 0; and it returns -1 when the independent variable is less than 0. This represents the estimated value of the composite disturbance, i.e., the observer output value. Represents the estimated actual velocity of the joint. Time derivative, This represents the time derivative of the composite disturbance estimate;

[0109] S7. Based on the velocity tracking error, error compensation signal and fixed-time disturbance observer, the Nussbaum gain is introduced to process the unknown control direction. Combined with the relative threshold event triggering mechanism, a final fault-tolerant control law that can effectively reduce communication resources is constructed.

[0110] In some embodiments, continuous virtual control signals are defined as The discrete control signal actually transmitted to the actuator is Measurement error triggered by the event for:

[0111] (29)

[0112] Therefore, the discrete control signal actually acting on the system is:

[0113] (30)

[0114] Substituting into the system dynamics, the multiplicative fault term becomes , and Both are bounded.

[0115] Construct a global Lyapunov function that includes the states of all subsystems. :

[0116] (31)

[0117] in, , , , This represents the actual position tracking error after compensation. This indicates the speed tracking error of the robot system. This represents the trace operation on a matrix. This represents the weight estimation error of a fuzzy logic system. This represents the gain parameter of the fuzzy logic system.

[0118] right Find the time derivative :

[0119] (32)

[0120] To ensure that formula (32) satisfies negative definiteness, Nussbaum gain is introduced, and a continuous virtual control signal is designed. for:

[0121] (33)

[0122] (34)

[0123] in, Represents the Nussbaum gain matrix. This represents the Nussbaum auxiliary parameter vector. Represents the nominal control law matrix. This represents the speed error feedback gain matrix. This indicates the speed tracking error of the robot system. This represents the smoothed tracking signal after filtering by the virtual control law, i.e., the feedforward reference velocity. This represents the positive definite diagonal control gain matrix. Represents the fractional power parameter. This represents the output value of the fixed-time perturbation observer. , , This represents the robust damping term.

[0124] The final fault-tolerant control law is composed of equations (33)-(34).

[0125] Furthermore, an event triggering condition based on a relative threshold is designed, expressed as:

[0126] (35)

[0127] In the formula, , For trigger parameters, and ; This indicates the measurement error triggered by the event. Represents the actual discrete control signal; in During this period, the control input remains constant. , Indicates the first The timing of this event trigger.

[0128] Furthermore, the Nussbaum gain matrix The expression is:

[0129] (36)

[0130] (37)

[0131] In the formula, Represents the Nussbaum auxiliary parameter vector. Indicates the robot system's first The internal independent variables of the Nussbaum function for each joint No. Nussbaum function.

[0132] Specifically, to ensure the stability of the closed-loop system, the update law for the internal independent variables of the Nussbaum function is designed as follows:

[0133] (38)

[0134] in, Indicates the robot's first Nussbaum parameters for each joint Time derivative, Indicates the robot system's first Speed ​​tracking error of each joint Indicates the robot system's first The nominal control law of each joint.

[0135] In some embodiments, to verify the effectiveness of the method of the present invention, a simulation experiment is conducted in the MATLAB 2018b environment, with the specific settings as follows:

[0136] The simulation object is a two-degree-of-freedom robot, and its complete dynamic model expression is as follows:

[0137]

[0138] in:

[0139]

[0140]

[0141]

[0142] In the formula, , , . , These represent the masses of link 1 and link 2, respectively. , These represent the physical lengths of link 1 and link 2, respectively. These represent the moments of inertia of joint 1 and joint 2, respectively. These represent the positions of the centers of mass of joint 1 and joint 2, respectively. , Let these represent the joint position vectors of joint 1 and joint 2, respectively. , Let represent the joint velocity vectors of joint 1 and joint 2, respectively. It represents the acceleration due to gravity.

[0143] The nominal model is defined as: , , The multiplicative fault matrix is ​​set as follows: Actuator additive fault settings: The external unknown disturbance vector is set as follows: The dynamic model parameter values ​​are set as shown in Table 1 below, and the control parameter values ​​are set as shown in Table 2 below.

[0144] Table 1 Dynamic model parameters

[0145]

[0146] Table 2 Control Parameters

[0147]

[0148] Furthermore, the desired trajectory is set as follows: The total simulation time is set to 20s. An adaptive step size is selected for sampling. Other design parameters are referenced in Table 2.

[0149] Simulation results are as follows Figures 2 to 11 As shown. Figure 2 and Figure 3 The figures show the angular position and angular velocity tracking curves for robot joints 1 and 2, respectively. As can be seen, under complex conditions involving external compound disturbances and multiplicative and additive actuator faults, the proposed controller can drive the two joints to converge to the desired trajectory quickly, smoothly, and with high precision, demonstrating excellent dynamic disturbance rejection and tracking performance. Figure 4Joint position tracking error curves under the predefined performance function (PPF) constraint are presented. Combined with bijective error transformation, the joint position tracking error of the two joints is strictly limited within the performance envelope throughout the entire simulation cycle, indicating that this mechanism not only guarantees a very small steady-state error, but also effectively constrains the maximum transient overshoot and convergence rate. Figure 5 and Figure 6 The results show that by using the Finite-Time Command Filter (FTCF), the system effectively overcomes the problems of "explosion" and transient impact in the differential calculation of the traditional backstepping method. The overall control torque is smooth and does not exceed the physical limit, and high-frequency chattering is significantly suppressed. Figure 7 The evolution of adaptive weights in a fuzzy logic system (FLS) is demonstrated, and its effectiveness in online compensation of unmodeled nonlinear dynamics is verified. Figure 8 and Figure 9 The rapid convergence of the Nussbaum parameters indicates that the Nussbaum gain mechanism successfully overcomes the control direction uncertainty problem caused by actuator multiplicative faults. Finally, Figure 10 and Figure 11 The event triggering behavior of the static event triggering mechanism is demonstrated, with triggering rates of only 0.48% and 0.87% for joint 1 and joint 2, respectively. This indicates that the designed discretization triggering strategy effectively filters redundant continuous signal transmissions, reduces update frequency, and saves network communication resources while ensuring global tracking accuracy.

[0150] Furthermore, this series of smooth and robust control characteristics not only achieves efficient utilization of communication bandwidth, but also helps reduce wear and tear on mechanical hardware and extend equipment lifespan, thus fully verifying the feasibility and reliability of the proposed preset performance fault-tolerant control strategy in practical engineering applications.

[0151] This invention can ensure trajectory tracking accuracy even when the robot's dynamics model is unknown, actuator malfunctions exist, and external disturbances occur. It ensures that the tracking error meets strict preset performance constraints, significantly reduces communication resource consumption, and guarantees that all signals in the closed-loop system are globally consistent and bounded.

[0152] 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 low-communication-load fault-tolerant control method for robots under complex working conditions, characterized in that, Includes the following steps: S1. Construct a dynamic model of the robot system that includes unknown system dynamics, external disturbances, and multiplicative and additive faults of the actuators; S2. Combining the actual and desired positions of the joints in the robot system, define the constrained joint position tracking error according to the preset performance function; S3. By using bijective error transformation, the constrained joint position tracking error is converted into an unconstrained error variable, ensuring that the joint position tracking error is always within the preset limits; S4. Construct a virtual control law based on unconstrained error variables, and design speed tracking error and error compensation signals through a finite-time command filter; S5. Introduce fuzzy logic systems to approximate the unknown dynamics of the system; S6. Based on the unknown dynamics of the system approximated by the fuzzy logic system, a fixed-time disturbance observer is designed to estimate the complex disturbances, including external disturbances and multiplicative and additive faults of actuators. S7. Based on the speed tracking error, error compensation signal and fixed-time disturbance observer, combined with the relative threshold event triggering mechanism, the final fault-tolerant control law is constructed.

2. The low-communication-load fault-tolerant control method for robots under complex working conditions according to claim 1, characterized in that, Step S1 includes: S11. Construct a dynamic model of the robot system with Eulerian-Lagrange multi-input multi-output characteristics, expressed as: ， In the formula, Represents the joint position vector. Represents the joint velocity vector. Represents the joint acceleration vector. Represents the inertia matrix. Represents the centripetal-Coriolis force matrix. Represents the gravity vector. Indicates the control input torque. Represents the vector of unknown external disturbance; Represents the set of real numbers. Represents the dimension of a vector or matrix; S12. The uncertainty of the robot system dynamics model is expressed as: ， In the formula, This represents the nominal inertia matrix of the robot system. This represents the unknown inertia matrix of the robot system. This represents the nominal centripetal force and Coriolis force of a robot system. This represents the unknown centripetal force and Coriolis force of the robot system. This represents the nominal gravity term of the robot system. This represents the unknown gravity term of the robot system; S13. Introduce an actuator fault model, represented as: ， in, Indicates the control input torque. Represents the multiplicative fault matrix. This indicates an additive fault in the actuator. This represents the actual discrete control signal; S14. Define the joint actual position vector With the actual velocity vector of the joint ,in , The dynamic model of the robot system is transformed into a state equation form, which includes unknown system dynamics, external disturbances, and multiplicative and additive faults of the actuators, as follows: ， In the formula, This represents the dynamic update item of the nominal model of the robot system. This represents the unmodeled dynamic uncertainty of the robot system. This represents a combined disturbance of external disturbances and additive faults in the robot system. satisfy ,Right now It is continuously differentiable and its derivative is bounded. This indicates the upper bound of the derivative of the composite perturbation. Represents the actual position vector of the joint Time derivative, Represents the actual velocity vector of the joint Time derivative, Represents the composite disturbance term The time derivative, ||·||, represents the operation of taking the Euclidean norm of a vector.

3. The low-communication-load fault-tolerant control method for robots under complex working conditions according to claim 1, characterized in that, The joint position tracking error in step S2 is expressed as follows: ， ， In the formula, Indicates the robot system's first Joint position tracking error of each joint, Represents the dimension of a vector or matrix; Indicates the robot system's first The actual joint position vector of each joint. Indicates the robot system's first The expected joint position vector of each joint; , This indicates the set scaling factor. Indicates the robot system's first The exponential predefined performance function defined for each subsystem is expressed as follows: ， In the formula, Indicates the initial value. Indicates the final value. t represents the decay rate, and t represents the time parameter.

4. The low-communication-load fault-tolerant control method for robots under complex working conditions according to claim 1, characterized in that, The unconstrained error variable obtained from step S3 is expressed as follows: ， In the formula, Indicates the robot system's first Joint position tracking error of each joint, Indicates the robot system's first The unconstrained error variable after mapping of the joint position tracking error of each joint. Indicates the robot system's first Each subsystem defines an exponential preset performance function. , This indicates the scaling factor set.

5. The low-communication-load fault-tolerant control method for robots under complex working conditions according to claim 1, characterized in that, Step S4 includes: Define virtual control law Represented as: ， In the formula, This represents the desired velocity of the joints in the robot system. Represents the time-varying scaling factor matrix. , These represent the positive definite gain matrices for linear error feedback and nonlinear error feedback, respectively. Represents the boundary contraction compensation term matrix; Represents the unconstrained error variable. Indicates the fractional power parameter; Introducing a finite-time command filter, expressed as: ， In the formula, This represents the smoothed tracking signal after filtering by the virtual control law. This represents the derivative estimate of the virtual control law. This represents the filter gain parameter. Represents the absolute value function. Represents a symbolic function. This represents the smoothed tracking signal after filtering by the virtual control law. Time derivative, Derivative estimation of virtual control law Time derivative, , Represents the fractional power parameter of the finite-time command filter; Define the speed tracking error of a robot system for: ， In the formula, This represents the actual velocity vector of the joint; To eliminate transient filtering errors caused by finite-time command filters Impact on system stability, construction of error compensation signal The adaptive update law is as follows: ， In the formula, This represents the time derivative of the error compensation signal.

6. The low-communication-load fault-tolerant control method for robots under complex working conditions according to claim 1, characterized in that, Introducing a fuzzy logic system to approximate the unknown dynamics of the system, expressed as: ， in, This represents the unmodeled dynamic uncertainty of the fuzzy logic system. The estimate, Represents the ideal weight matrix. This represents the fuzzy basis function vector in a fuzzy logic system. This represents the bounded approximation error generated by a fuzzy logic system when approximating unknown dynamics, satisfying... , The positive constant bound represents the range of the maximum approximation error; ; Define the weight estimation error as ,in To estimate the optimal weights; to design the estimate of the optimal weights. The update law is: ， in, This represents the gain parameter of the fuzzy logic system. This indicates the leakage factor.

7. A low-communication-load fault-tolerant control method for robots under complex working conditions according to claim 1, characterized in that, The fixed-time perturbation observer is represented as: ， ， In the formula, This represents the estimated actual velocity of the joint. This represents the actual velocity vector of the joints in the robot system. This represents the dynamic update item of the nominal model of the robot system. This represents the estimation of unmodeled dynamic uncertainties by the fuzzy logic system. This represents the equivalent nominal control signal. , , , This represents the gain parameter. , , , Denotes the fractional exponent parameters, respectively satisfying , , , , Represents the absolute value function. Represents a symbolic function. This represents the estimated value of the composite disturbance. Represents the estimated actual velocity of the joint. Time derivative, This represents the time derivative of the composite disturbance estimate; This represents the Nussbaum gain matrix.

8. A low-communication-load fault-tolerant control method for robots under complex working conditions according to claim 1, characterized in that, The final fault-tolerant control law is expressed as: ， ， in, Represents continuous virtual control signals. Represents the Nussbaum gain matrix. Represents the Nussbaum auxiliary parameter vector. Represents the nominal control law matrix. This represents the speed error feedback gain matrix. This indicates the speed tracking error of the robot system. This represents the smoothed tracking signal after filtering by the virtual control law. This represents the positive definite diagonal control gain matrix. Represents the fractional power parameter. This represents the output value of the fixed-time perturbation observer. , , Indicates the robust damping term; Furthermore, an event triggering condition based on a relative threshold is designed, expressed as: ， In the formula, , For trigger parameters, and ; This indicates the measurement error triggered by the event. Represents the actual discrete control signal; in During this period, the control input remains constant. , Indicates the first The timing of this event trigger.

9. A low-communication-load fault-tolerant control method for robots under complex working conditions according to claim 7 or 8, characterized in that, Nussbaum gain matrix The expression is: ， （37） In the formula, Represents the Nussbaum auxiliary parameter vector. Indicates the robot system's first The internal independent variables of the Nussbaum function for each joint No. Nussbaum functions; The internal update law of the Nussbaum function is designed as follows: ， in, Indicates the robot's first Nussbaum parameters for each joint Time derivative, Indicates the robot system's first Speed ​​tracking error of each joint Indicates the robot system's first The nominal control law of each joint.

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