Multi-joint rigid robot finite time adaptive fault-tolerant control method and system

Abstract

The present application belongs to the technical field of rigid manipulator position tracking control, and specifically discloses a multi-joint rigid manipulator finite-time adaptive fault-tolerant control method and system. The present application estimates the failure degree of sensor and actuator faults, parameter uncertainty and external disturbance and the like of the manipulator through adaptive technology. The present application uses a log-type barrier Lyapunov function to constrain the state error of the system. The present application uses a fuzzy logic system to approximate the unknown nonlinear term and unknown disturbance of the manipulator joint. In addition, the present application also designs an adaptive control law and a finite-time controller to realize fault-tolerant control. The present application can effectively reduce the influence of sensor and actuator faults on control accuracy, has good position tracking effect, and can guarantee that the system output position is constrained to a specified range within a limited time.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of rigid manipulator position tracking control, and particularly relates to a multi-joint rigid manipulator finite-time adaptive fault-tolerant control method and system. BACKGROUND

[0002] The manipulator itself is a complex nonlinear system with high nonlinearity, parameter uncertainty and external disturbance. However, due to the significant advantages of the manipulator in improving the production environment, improving the production efficiency and reducing the manufacturing cost, the manipulator is widely used in production and life. For example, the manipulator is indispensable in space exploration, deep sea exploration, military manufacturing and precision part processing, which is closely related to the advantages of the manipulator itself.

[0003] With the improvement of the requirement for product quality, the control requirement for the manipulator system is also higher and higher. In particular, in actual industrial production, the control requirement for the manipulator is higher. For example, the manipulator often needs to complete the specified action in a limited space range or complete the fixed task amount in a limited time in order to improve the yield. At the same time, the manipulator system is often disturbed by some external disturbances or the elements of the manipulator system fail, and it is difficult to ensure that the manipulator system can still work normally in this case. Therefore, it is necessary to effectively control the manipulator system.

[0004] The traditional PID control is widely used in the industrial field because it does not need the model information of the controlled object. However, the actuator is inevitably subject to failure in a long-term repeated motion condition, which affects the grasping and placing operations of the manipulator. The use of the manipulator sensor can realize the perception and measurement of the surrounding environment, and when the sensor circuit is short-circuited or fails, the control accuracy of the manipulator is affected. Once the failure occurs, the manipulator under the traditional PID control cannot work normally.

[0005] Fault-tolerant control refers to taking effective measures to compensate for the fault when the actuator element, sensor element or other components in the control system fail, so as to realize the stability of the system and keep the performance index within a reasonable range. Therefore, in order to improve the stability and reliability of the manipulator system and improve the overall control performance of the system, an effective fault-tolerant control method is needed to solve the sensor and actuator failure to maintain the robustness of the system and improve the trajectory tracking performance of the manipulator system. SUMMARY

[0006] The present application aims at providing a multi-joint rigid manipulator finite time adaptive fault-tolerant control method, effectively reducing the influence of sensor and actuator faults on control accuracy, having good position tracking effect, and being capable of guaranteeing that the system output position is constrained to a specified range within a limited time.

[0007] In order to achieve the above-mentioned purpose, the present application adopts the following technical solutions:

[0008] The multi-joint rigid manipulator finite time adaptive fault-tolerant control method comprises the following steps:

[0009] Step 1. A mathematical model of a multi-joint rigid manipulator dynamics system considering unknown disturbances is established, and a mathematical model of manipulator sensor faults and manipulator actuator faults is established;

[0010] Step 2. A manipulator finite time adaptive fault-tolerant controller considering sensor and actuator faults is designed, the system output is constrained to a small neighborhood range of the expected position within a limited time, and all closed-loop signals are guaranteed to be bounded;

[0011] Step 3. A Lyapunov function of the system is selected for derivation, and it is proved that the manipulator system controlled by the manipulator finite time adaptive fault-tolerant controller considering sensor and actuator faults designed in step 2 is Lyapunov stable;

[0012] Step 4. The manipulator finite time adaptive fault-tolerant controller considering sensor and actuator faults designed in step 2 is used to realize the finite time adaptive fault-tolerant control of the multi-joint rigid manipulator.

[0013] In addition, on the basis of the multi-joint rigid manipulator finite time adaptive fault-tolerant control method, the present application further proposes a multi-joint rigid manipulator finite time adaptive fault-tolerant control system adapted thereto, which adopts the following technical solutions:

[0014] The model construction module is used for establishing a mathematical model of a multi-joint rigid manipulator dynamics system considering unknown disturbances, and establishing a mathematical model of manipulator sensor faults and manipulator actuator faults;

[0015] The controller design module is used for designing a manipulator finite time adaptive fault-tolerant controller considering sensor and actuator faults, constraining the system output to a small neighborhood range of the expected position within a limited time, and guaranteeing that all closed-loop signals are bounded;

[0016] The stability evaluation module is used to select the Lyapunov function of the system for derivation, and to prove that the robot arm system controlled by the finite-time adaptive fault-tolerant controller of the robot arm, which takes into account sensor and actuator failures, is Lyapunov stable.

[0017] And a fault-tolerant control module, based on a finite-time adaptive fault-tolerant controller for robotic arms that takes into account sensor and actuator failures, to achieve finite-time adaptive fault-tolerant control of multi-joint rigid robotic arms.

[0018] Furthermore, based on the aforementioned finite-time adaptive fault-tolerant control method for multi-joint rigid robotic arms, this invention also proposes a computer device comprising a memory and one or more processors.

[0019] The memory stores executable code, and when the processor executes the executable code, it implements the steps of the finite-time adaptive fault-tolerant control method for the multi-joint rigid manipulator described above.

[0020] Furthermore, based on the aforementioned finite-time adaptive fault-tolerant control method for multi-joint rigid manipulators, this invention also proposes a computer-readable storage medium storing a program. When executed by a processor, this program implements the steps of the aforementioned finite-time adaptive fault-tolerant control method for multi-joint rigid manipulators.

[0021] The present invention has the following advantages:

[0022] As described above, this invention relates to a finite-time adaptive fault-tolerant control method and system for a multi-joint rigid robotic arm. Specifically, this invention proposes a fault-tolerant control method to address sensor and actuator failures in the robotic arm, improving system control performance and ensuring system stability. The method uses a fuzzy logic system to approximate the unknown nonlinear terms of the robotic arm joints, exhibiting strong robustness to changes in system parameters and making it more suitable for practical applications. Furthermore, this invention combines finite-time techniques with adaptive control to constrain the robotic arm's output position to a small neighborhood of the desired position, further enhancing system control performance. This invention effectively reduces the impact of sensor and actuator failures on control accuracy, provides good position tracking, and ensures that the robotic arm system's output position is constrained to a specified range within a finite time. Attached Figure Description

[0023] Figure 1 This is a flowchart of a finite-time adaptive fault-tolerant control method for a multi-joint rigid robotic arm in an embodiment of the present invention.

[0024] Figure 2 This is a tracking response curve of the joint's angular position and desired angular position after adopting the control method of this invention.

[0025] Figure 3 is the tracking response curve diagram of the joint two-angle position and the expected angle position after the control method of the application is adopted.

[0026] Figure 4 is the system control law u waveform diagram after the control method of the application is adopted.

[0027] Figure 5 is the system adaptive law waveform diagram after the control method of the application is adopted.

[0028] Figure 6 is the system adaptive law waveform diagram after the control method of the application is adopted. DETAILED DESCRIPTION

[0029] The application will be further described in detail below in combination with the drawings and specific embodiments:

[0030] Embodiment 1

[0031] This embodiment 1 describes a multi-joint rigid manipulator finite-time adaptive fault-tolerant control method. The general idea of the method is as follows: when the manipulator system is running normally, if a sensor or an actuator suddenly fails, in the case of unknown fault parameters, the control law is designed by using adaptive technology, the failure degree of the fault is estimated and updated online, and effective compensation is performed, so as to achieve the purpose of fault-tolerant control of the manipulator system. Specifically, the application mainly carries out the following work: first, the application estimates the failure degree of the sensor and actuator fault, parameter uncertainty and external disturbance of the manipulator through adaptive technology; the state error of the system is constrained by using the log-type barrier Lyapunov function; the unknown nonlinear term and unknown disturbance of the manipulator joint are approximated by using the fuzzy logic system; the adaptive control law and the finite-time controller are designed to realize fault-tolerant control, and the finite-time technology has the advantages of fast tracking speed and high control precision. The convergence speed of the manipulator system is accelerated by introducing the finite-time technology.

[0032] As shown in Figure 1 , the multi-joint rigid manipulator finite-time adaptive fault-tolerant control method comprises the following steps:

[0033] Step 1. A mathematical model of a multi-joint rigid manipulator dynamics system considering unknown disturbances is established, and mathematical models of manipulator sensor faults and manipulator actuator faults are established.

[0034] The mathematical model of the multi-joint rigid manipulator dynamics system is shown in formula (1);

[0035] ​​

[0036] where q ∈ R n denotes the joint position vector, denotes the joint velocity vector, denotes the joint acceleration vector; M(q) ∈ R n*n is a positive definite inertia matrix, is the Coriolis and centrifugal force matrix, G(q) ∈ R n denotes the gravity vector, τ d ∈ R n is the disturbance term, u F (t) ∈ R n is the joint motor torque control input vector.

[0037] R n , R n*n denote the n-dimensional real number set, n-dimensional vector space, respectively;

[0038] The mathematical model of the manipulator actuator fault is expressed as follows:

[0039]

[0040] where u i denotes the designed control input, F denotes the fault, denotes the control signal affected by the actuator fault; φ ai (t) denotes the bias fault, which is a bounded unknown function; ρ ai denotes the actuator gain fault degree.

[0041] The mathematical model of the manipulator sensor fault is expressed as follows:

[0042]

[0043] where x1 = q, the measured system state variables are x 1m (t), x 2m (t); ρ s1 , ρ s2 denote the unknown diagonal matrix of the sensor gain fault, ρ s1 = diag[ρ 1,s1 , ρ 2,s1 ], ρ s2 = diag[ρ 1,s2 , ρ 2,s2 ].

[0044] For a multi-joint manipulator system, denote the minimum value of the gain fault in the multi-joint fault, respectively, d1 = 1, 2, d2 = 1, 2; φ s1 (t), φ s2(t)∈R n×n This indicates a sensor bias fault.

[0045] φ s1 (t)=[φ 1,s1 (t),φ 2,s1 (t)] T , φ s2 (t)=[φ 1,s2 (t),φ 2,s2 (t)] T .

[0046] φ s1 (t),φ s2 (t) and its derivative exist and are bounded; φ 1,s1 (t),φ 2,s1 (t) indicates a fault in the offset of the joint position sensors 1 and 2, φ 1,s2 (t),φ 2,s2 (t) indicates a fault in the bias of the speed sensors of joint one and two.

[0047] When there is no sensor failure, ρ s1 =I,ρ s2 =I,φ s1 (t)=0,φ s2 (t) = 0, where I is the identity matrix.

[0048] Define x1 = q, Equation (1) is then transformed into a second-order system, as shown in Equation (4).

[0049]

[0050] Where y represents the system output.

[0051] Step 2. Design a finite-time adaptive fault-tolerant controller for the robotic arm that takes into account sensor and actuator failures, constraining the system output to a small neighborhood of the desired position within a finite time while ensuring that all closed-loop signals are bounded.

[0052] In the case of unknown fault parameters, an adaptive technology is used to design a control law that estimates and updates the degree of failure of the fault online and performs effective compensation. A finite-time adaptive fault-tolerant controller for the robotic arm that takes into account sensor and actuator faults is designed. Finally, the system output is constrained to a small neighborhood of the desired position within a finite time, while ensuring that all closed-loop signals are bounded.

[0053] Define speed error: Z i,2 =x i,2m -α i,1 Among them, Z i,2 Indicates speed error, x i,2mSystem velocity state variable of the ith joint measurement, a i,1 is the virtual control law, i = 1, 2,..., n.

[0054] Define V x1m as:

[0055]

[0056] where V x1m is the designed Lyapunov function, k bi is the designed parameter, x i,1m is the measured system state variable of the ith joint; define x i,1m (0) as the initial value of x i,1m , k bi (0) as the initial value of k bi , then |x i,1m (0)| < k bi (0).

[0057] Differentiate formula (5) to obtain:

[0058]

[0059] where,

[0060] Since ψ is bounded, set as the upper bound of ψ, define μ1 is obtained by definition;

[0061] According to , we can obtain:

[0062]

[0063] The virtual control law a i,1 is designed as:

[0064]

[0065] where k1 > 0, 0 < γ < 1, S1 > 0, and k1, γ, S1 are all design constants.

[0066]

[0067] Set where is the estimate of μ1, is the estimate of .

[0068] Set the adaptive control law as:

[0069]

[0070] where, n ψ ,σ ψ are normal numbers; the Lyapunov function V1 of the system is selected as:

[0071]

[0072] The derivative of V1 is taken, and formula (8) is substituted into it to obtain:

[0073]

[0074] The Lyapunov function V2 of the system is selected as:

[0075]

[0076] where, M ij represents the i-row j-column element in the positive inertia matrix, and the derivative of formula (11) is taken to obtain:

[0077]

[0078] where, f i is a bounded nonlinear function.

[0079]

[0080] C ij represents the i-row j-column element in the Coriolis force and centrifugal force matrix, and G i represents the i-th element in the gravity matrix.

[0081] contains external disturbances, where, φ ai represents the actuator bias fault, and τ i,d represents the disturbance term.

[0082] Let be the estimated value of p i , and the fuzzy logic system is the real control law of the system is taken as:

[0083]

[0084] where, k2>1, S2>0, k2 and S2 are design constants, represents the fuzzy logic system; formula (13) is substituted into formula (12) to obtain:

[0085]

[0086] An adaptive fuzzy control law is designed, and n fuzzy rules are constructed to constitute a fuzzy system. The i-th fuzzy rule is in the form of R i : if x1 is x2 is …, x n is then y is B i ;

[0087] x k 's membership function in the rule is B i ; where i = 1, 2, …, n, k = 1, 2, …, n;

[0088] The output of the fuzzy system is given by

[0089]

[0090] where denotes x j 's membership function, and θ denotes θ = [θ1, θ2, …, θ n ] T , θ i denotes the i-th number in θ;

[0091] ξ(x) = [ξ1(x), ξ2(x), …, ξ n (x)] T ;

[0092]

[0093] The fuzzy approximation of f i is performed respectively by using , and the corresponding fuzzy system is designed as

[0094]

[0095] where θ i is the weight vector of the fuzzy logic system , and θ u,i denotes the u-th element of θ i ; define as the optimal weight vector, and p i as the optimal approximation constant, then there exists the following inequality for

[0096]

[0097] where denotes the fuzzy logic system when the optimal weight vector is used;​

[0098] Let

[0099] the estimation error of θ, denote the u-th element of

[0100] Design adaptive control law respectively:

[0101]

[0102]

[0103] where β, k, υ i is a positive constant;

[0104] So far, the finite-time adaptive fault-tolerant controller of the manipulator considering sensor and actuator faults is designed.

[0105] Step 3. Select the Lyapunov function of the system to derive and prove that the manipulator system controlled by the finite-time adaptive fault-tolerant controller of the manipulator considering sensor and actuator faults designed in step 2 is Lyapunov stable.

[0106] From Young's inequality, we have:

[0107]

[0108]

[0109] Let the Lyapunov function V3 of the system be:

[0110]

[0111] Differentiate equation (22) and substitute equations (16) and (19) to obtain:

[0112]

[0113] Substitute equations (17) and (18) into equation (23) to obtain:

[0114]

[0115] Substitute equations (20) and (21) into equation (24) to obtain:

[0116]

[0117] Take k2>1, M ij <σ0, σ0 represents Mij Upper bound, therefore When denotes 0 < γ < 1, When ,

[0118] Therefore, we have:

[0119] Further, we have:

[0120] Because the external disturbance is bounded, there exists D such that:

[0121] Substitute the above equation and equations (26) and (27) into equation (25) and rearrange to obtain:

[0122]

[0123] Rewrite equation (28) as:

[0124]

[0125]

[0126]

[0127] Rewrite equation (29) as:

[0128]

[0129]

[0130] where 0 < Θ < 1.

[0131] According to equation (30), if V3 > η / (1-Θ)c0, then Z i ∈ {V3 ≤ η / (1-Θ)c0}; according to equation (31), if then Z Therefore, Z i will converge to the following region:

[0132]

[0133] Therefore, the system converges in finite time, and the convergence time T r is:

[0134]

[0135] wherein, from formula (5), it is obtained that

[0136] |x 1m |<k b1 ;

[0137] wherein, x 1m represents a measured position state vector; from |ρ s1 x1|=|x 1m -φ s1 |≤|x 1m |+|φ s1 |<k b1 +|φ s1 |it is known that:

[0138]

[0139] definition then |x1|<k c1 Therefore, the multi-joint rigid manipulator system controlled by the manipulator finite-time adaptive fault-tolerant controller considering sensor and actuator faults is Lyapunov stable.

[0140] Step 4. A multi-joint rigid manipulator finite-time adaptive fault-tolerant controller considering sensor and actuator faults is realized by using the manipulator finite-time adaptive fault-tolerant controller considering sensor and actuator faults designed in step 2.

[0141] As shown in Figure 2 , the process of realizing control of the multi-joint manipulator system is as follows:

[0142] First, the failure degree of the actuator and sensor faults is estimated based on adaptive technology, and a fuzzy logic system is used to approximate the unknown nonlinear terms and unknown disturbances of the joints of the manipulator.

[0143] Second, an adaptive control law and a finite-time controller are designed to realize fault-tolerant control.

[0144] To verify the effectiveness of the method of the application, the application also simulates and verifies a two-link rigid manipulator system using the method of the application in the MATLAB / Simulink environment.

[0145] The inertia matrix of the two-joint manipulator is set as M(q):

[0146] wherein:

[0147]

[0148] wherein, m1 represents the mass of the first link, and m2 represents the mass of the second link.

[0149] L1 represents the length of the first link, L2 represents the length of the second link, L c1 represents the distance from the first joint to the center of mass of the first link, L c2 represents the distance from the second link to the center of mass of the second link.

[0150] θ1 represents the rotation angle of the first link, θ2 represents the rotation angle of the second link.

[0151] I1 represents the moment of inertia of the first link, I2 represents the moment of inertia of the second link.

[0152]

[0153] The Coriolis and centrifugal force matrix of the two-joint robot arm is set as:

[0154] where:

[0155]

[0156] The gravity matrix of the two-joint robot arm is set as:

[0157] where:

[0158]

[0159] k c1 = e 1-t + 0.1, k c2 = e 1-t + 0.1, k b1 = k c1 - |x 1d |, k b2 = k c2 - |x 2d |, t represents time.

[0160] x 1d x 2d represents the desired position of the joints one and two.

[0161] Other parameters of the system are set as follows:

[0162] m1 = 0.765 kg, m2 = 0.765 kg, L1 = 0.25 m, L2 = 0.25 m, L c1 = 0.15 m, L c2 = 0.15 m;

[0163] p a = [0.8, 0.8], p adenotes a diagonal matrix, where the elements are ai .

[0164] φ a = [0.2(1-e -t ), 0.2(1-e -t )], φ s1 = [0.02sin(t); 0.01cos(t)], φ s2 = [0.02sin(t); 0.01cos(t)];

[0165] When t≤6s

[0166] When t>6s

[0167] The external disturbance τ d of the system is set as

[0168] The initial state of the system is set as [x 11 , x 21 , x 12 , x 22 ]=[1.5, 1.5, 0, 0].

[0169] The tracked desired position is x d =[0, 0] T .

[0170] The fuzzy membership function is taken as:

[0171] Wherein, r=1, 2, 3, 4, s=1, 2, 3, the mean c s is selected as-1.5, 0 and 1.5, and the variance σ s is all set as 0.6.

[0172] The control parameters are set as: k1=16, k2=1.2, S1=0.8, S2=0.2, k=4.5, β=[35, 15], n ψ =0.95, σ ψ =0.6, υ1=0.002, υ2=0.002, and γ=0.8.

[0173] The corresponding simulation results are shown in Figures 2 to 6 , wherein:

[0174] Figure 2 The tracking trajectory of joint one of the two-link mechanical arm under the method of the application is shown, Figure 3 The tracking trajectory of joint two of the two-link mechanical arm under the method of the application is shown.

[0175] By Figure 2 And Figure 3 It can be seen that the joint position can track the given target trajectory well, and has high control accuracy.

[0176] Figure 4 u is the control law of joint one and joint two of the two-link mechanical arm after the control method of the application is adopted.

[0177] By Figure 4 It can be seen that the control law is bounded and periodic.

[0178] Figure 5 u is the adaptive control law of joint one and joint two of the two-link mechanical arm after the control method of the application is adopted. Figure 6 u is the adaptive control law of joint one and joint two of the two-link mechanical arm after the control method of the application is adopted.

[0179] By Figure 5 And Figure 6 It can be seen that the adaptive law is bounded and periodic, and can effectively estimate the fault.

[0180] For the multi-joint mechanical arm system considering sensor and actuator faults, the method of the application ensures that the output error is all constrained within a specified range, so that the system can achieve smaller output fluctuation, more stable operation, and faster convergence speed.

[0181] In summary, the method of the application can effectively reduce the influence of sensor and actuator faults on control accuracy, has good position tracking effect, and can therefore ensure that the output position of the mechanical arm system is constrained within a specified range within a limited time.

[0182] Embodiment 2

[0183] This embodiment 2 describes a multi-joint rigid mechanical arm finite time adaptive fault-tolerant control system, which is based on the same inventive concept as the multi-joint rigid mechanical arm finite time adaptive fault-tolerant control method in the above-mentioned embodiment 1.

[0184] A model construction module is configured to establish a mathematical model of a multi-joint rigid mechanical arm dynamics system considering unknown disturbances, and to establish mathematical models of mechanical arm sensor faults and mechanical arm actuator faults;

[0185] A controller design module is configured to design a mechanical arm finite time adaptive fault-tolerant controller considering sensor and actuator faults, to constrain the system output within a small neighborhood range of the expected position within a limited time, and to ensure that all closed-loop signals are bounded;

[0186] The stability evaluation module is used to select a Lyapunov function of the system to prove that the manipulator system controlled by the designed manipulator finite-time adaptive fault-tolerant controller considering sensor and actuator faults is Lyapunov stable.

[0187] The fault-tolerant control module is based on the designed manipulator finite-time adaptive fault-tolerant controller considering sensor and actuator faults, and realizes the finite-time adaptive fault-tolerant control of the multi-joint rigid manipulator.

[0188] It should be noted that in the multi-joint rigid manipulator finite-time adaptive fault-tolerant control system, the implementation process of the functions and roles of each functional module is specifically described in the implementation process of the corresponding steps in the method of the above-mentioned embodiment 1, and will not be repeated here.

[0189] Embodiment 3

[0190] This embodiment 3 describes a computer device for implementing the multi-joint rigid manipulator finite-time adaptive fault-tolerant control method described in the above-mentioned embodiment 1.

[0191] The computer device includes a memory and one or more processors. The executable code is stored in the memory, and when the processor executes the executable code, the steps of the multi-joint rigid manipulator finite-time adaptive fault-tolerant control method are implemented.

[0192] The computer device in this embodiment is any device or apparatus with data processing capability, which will not be repeated here.

[0193] Embodiment 4

[0194] This embodiment 4 describes a computer readable storage medium for implementing the multi-joint rigid manipulator finite-time adaptive fault-tolerant control method described in the above-mentioned embodiment 1.

[0195] The computer readable storage medium in this embodiment 4 has a program stored thereon, and when the program is executed by a processor, the steps of the multi-joint rigid manipulator finite-time adaptive fault-tolerant control method are implemented.

[0196] The computer readable storage medium is the internal storage unit of any device or apparatus with data processing capability, such as a hard disk or memory, or the external storage device of any device with data processing capability, such as a plug-in hard disk, a smart media card (SMC), an SD card, a flash card, etc.

[0197] Of course, the above description is only the preferred embodiment of the present application, and the present application is not limited to the above-described embodiments. It should be noted that any skilled person in the art can make all equivalent substitutions and obvious modifications under the teaching of the present application, and all such substitutions and modifications shall fall within the scope of the present application, and shall be protected by the present application.

Claims

1. A finite-time adaptive fault-tolerant control method for a multi-joint rigid robotic arm, characterized in that, Includes the following steps: Step 1. Establish a mathematical model of the dynamic system of a multi-joint rigid manipulator considering unknown disturbances, and at the same time establish mathematical models of sensor failures and actuator failures of the manipulator. Step 2. Design a finite-time adaptive fault-tolerant controller for the robotic arm that takes into account sensor and actuator failures, constraining the system output to a small neighborhood of the desired position within a finite time while ensuring that all closed-loop signals are bounded; Step 3. Select the Lyapunov function of the system for derivation, and prove that the robotic arm system controlled by the finite-time adaptive fault-tolerant controller for the robotic arm designed in Step 2, which considers sensor and actuator failures, is Lyapunov stable. Step 4. Using the finite-time adaptive fault-tolerant controller for the robotic arm designed in Step 2, which considers sensor and actuator failures, finite-time adaptive fault-tolerant control of the multi-joint rigid robotic arm is achieved. Step 1 specifically involves: The mathematical model of the dynamic system of the multi-joint rigid manipulator is shown in Equation (1); (1) in, Represents the joint position vector. Represents the joint velocity vector. Represents the joint acceleration vector; It is a positive definite inertial matrix. The matrix represents the Coriolis force and the centrifugal force. Represents the gravity vector. It is a distractor. It is the torque control input vector of the joint motor; The mathematical model for robotic arm actuator failure is expressed as follows: (2) in, This represents the control input of the design, and F represents a fault. This indicates a control signal affected by an actuator malfunction; The bias fault is represented by a bounded unknown function; Indicates the degree of actuator gain failure; The mathematical model for robot arm sensor failure is as follows: (3) in, , For the measured system state variables, ; , The unknown diagonal matrix representing sensor gain faults. , ; For multi-joint robotic arm systems , These represent the minimum gain fault value in a multi-joint fault; in, ; , This indicates a sensor bias fault; , , , Its derivative exists and is bounded; , This indicates a fault in the offset of the joint position sensors 1 and 2. , This indicates a fault in the offset of the speed sensors at joint one and two. When there is no sensor malfunction I is the identity matrix; definition Then equation (1) is transformed into a second-order system, as shown in equation (4); (4) Where y represents the system output; Step 2 specifically involves: Define speed error: ;in, Indicates speed error, Indicates the first The system velocity state variables measured at each joint For virtual control laws, ; definition for: (5) in, The Lyapunov function representing the design, Indicates design parameters, Indicates the first The measurement system state variables for each joint; definition express initial value, express The initial value is then ; Differentiating formula (5) yields: (6) in, , ; because There is a boundary, so it is assumed express The upper bound is defined. , Derived from the definition; according to get: ； Virtual control law Designed as follows: (7) in, ,and , , These are all design constants; = ； set up ,in, yes The estimated value, yes The estimated value; Assume an adaptive control law , They are respectively: (8) in, , , , All are positive numbers; select the Lyapunov function of the system. for: (9) right Differentiating and substituting equation (8) into the equation, we get: (10) Selecting the Lyapunov function of the system for: (11) in, Let i represent the element in row i and column j of the positive definite inertia matrix. Taking the derivative of equation (11) yields: (12) in, It is a bounded nonlinear function; ； This represents the element in row i and column j of the Coriolis force and centrifugal force matrix. This represents the i-th element in the gravity matrix; Includes external disturbances. ; in, This indicates an actuator bias fault. Indicates distractor items; make , yes The estimated value, For a fuzzy logic system, the true control law of the system is taken as: (13) ;in, , , All are design constants. Representing a fuzzy logic system; substituting equation (13) into equation (12) yields: (14) Design an adaptive fuzzy control law and construct... The fuzzy system is constructed using fuzzy rules, the first... The form of the fuzzy rule is as follows: :if yes , yes , ..., yes ,but yes ; The membership function is in the rule , It is a fuzzy set; where, , ; The output of the fuzzy system is given by the following formula: (15) in, express membership function, express , express The i-th number in; ； ， ； respectively right The fuzzy system design for fuzzy approximation is as follows: (16) in, For fuzzy logic systems The weight vector, express The One element; definition This is the optimal weight vector. To achieve the optimal approximation of the constant, then for The following inequalities exist: (17) in, A fuzzy logic system for representing the optimal weight vector; set up , express The estimation error, express The u-th element; Design an adaptive control law , They are respectively: (18) (19) in, , , , It is a positive number; At this point, the design of a finite-time adaptive fault-tolerant controller for a robotic arm that takes into account sensor and actuator failures is complete.

2. The finite-time adaptive fault-tolerant control method for a multi-joint rigid robotic arm according to claim 1, characterized in that, Step 3 specifically involves: We obtain the following from Young's inequality: (20) (21) Suppose the Lyapunov function of the system for: (22) Differentiating equation (22) and substituting equations (16) and (19) into the equation, we get: (23) Substituting equations (17) and (18) into equation (23), we get: (24) Substituting equations (20) and (21) into equation (24), we get: (25) Pick , express The upper realm, therefore ;when , In expression (25) , hour, ;when hour, ; In summary: (26) Therefore, we get: (27) Because of external disturbances Since it is bounded, there exists a D such that: ; Substituting the above equations and equations (26) and (27) into equation (25) and rearranging, we get: (28) Formula (28) can be rewritten as: (29) ； ； ； Formula (29) can be rewritten as follows: (30) (31) in, ; According to equation (30), if ,So ,but ; According to equation (31), if ,So ,but ; therefore It will converge to the following region: ； Therefore, the system converges in a finite time, and the convergence time... for: ； in, The initial time is represented by formula (5): ； in, Represents the measured position state vector; by It was learned that: ； definition ,but ; Therefore, the robotic arm system controlled by the finite-time adaptive fault-tolerant controller of the robotic arm, which takes into account sensor and actuator failures, is stable under Lyapunov conditions.

3. The finite-time adaptive fault-tolerant control method for a multi-joint rigid robotic arm according to claim 1, characterized in that, Step 4 specifically involves: First, the failure degree of actuator and sensor faults is estimated based on adaptive technology, and the unknown nonlinear terms and unknown disturbances of the robotic arm joints are approximated by a fuzzy logic system. Secondly, an adaptive control law and a finite-time controller are designed to achieve fault-tolerant control for faults.

4. The finite-time adaptive fault-tolerant control method for a multi-joint rigid robotic arm according to claim 1, characterized in that, In step 2, under the condition of unknown fault parameters, an adaptive technology is used to design a control law to estimate and update the failure degree of the fault online and to perform effective compensation. A finite-time adaptive fault-tolerant controller for the robotic arm that takes into account sensor and actuator faults is designed. Finally, the system output is constrained to a small neighborhood of the desired position within a finite time, while ensuring that all closed-loop signals are bounded.

5. The finite-time adaptive fault-tolerant control method for a multi-joint rigid robotic arm according to claim 1, characterized in that, In step 2, the degree of actuator gain failure The division is as follows: when This indicates that the i-th actuator can operate normally; when This indicates a partial failure in the i-th actuator; when This indicates that the i-th actuator has completely failed.

6. A finite-time adaptive fault-tolerant control system for a multi-joint rigid manipulator for implementing the finite-time adaptive fault-tolerant control method for a multi-joint rigid manipulator as described in claim 1, characterized in that, The finite-time adaptive fault-tolerant control system for the multi-joint rigid robotic arm includes: The model building module is used to establish a mathematical model of the dynamic system of a multi-joint rigid manipulator considering unknown disturbances, and to establish mathematical models of sensor failures and actuator failures of the manipulator. The controller design module is used to design a finite-time adaptive fault-tolerant controller for a robotic arm that takes into account sensor and actuator failures. It constrains the system output to a small neighborhood of the desired position within a finite time while ensuring that all closed-loop signals are bounded. The stability evaluation module is used to select the Lyapunov function of the system for derivation, and to prove that the robot arm system controlled by the finite-time adaptive fault-tolerant controller of the robot arm, which takes into account sensor and actuator failures, is Lyapunov stable. And a fault-tolerant control module, based on a finite-time adaptive fault-tolerant controller for robotic arms that takes into account sensor and actuator failures, to achieve finite-time adaptive fault-tolerant control of multi-joint rigid robotic arms.

7. A computer device comprising a memory and one or more processors; characterized in that, The memory stores executable code, and when the processor executes the executable code, it implements the steps of the finite-time adaptive fault-tolerant control method for a multi-joint rigid manipulator as described in any one of claims 1 to 5.

8. A computer-readable storage medium having a program stored thereon; characterized in that, When the program is executed by the processor, it is used to implement the steps of the finite-time adaptive fault-tolerant control method for a multi-joint rigid manipulator as described in any one of claims 1 to 5.

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