Preset performance fault-tolerant control method under motor failure of tendon-driven mechanical arm

Abstract

The invention provides a preset performance fault-tolerant control method under motor failure of a tendon-driven mechanical arm. The preset performance fault-tolerant control method comprises the following steps: constructing a tendon-driven mechanical arm system model with actuator fault, external interference and system parameter uncertainty; designing a tendon-driven mechanical arm trajectory tracking error model and a fixed time sliding mode observer; an improved preset performance function is constructed, so that the trajectory tracking position error of each joint of the mechanical arm meets a preset performance boundary; and a fixed-time preset performance fault-tolerant controller is designed, so that trajectory tracking errors of all joints of the mechanical arm are converged to a preset performance boundary within fixed time. According to the method, non-singular terminal sliding mode control is combined with the preset performance function, so that the performance boundary constraint of the tracking error is realized while the stability of the fixed time of the system is ensured; by dynamically adjusting the boundary of the performance function, the problem of control precision degradation under the actuator fault working condition is effectively solved, and the robustness and trajectory tracking precision of the system are remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical field of robotic arm control, and in particular to a preset performance fault-tolerant control method under failure of a tendon-driven robotic arm motor. Background Art

[0002] Tendon-driven robotic arms are widely used in space exploration and on-orbit maintenance missions due to their lightweight and highly flexible nature. However, the complex and ever-changing space environment makes long-term, high-intensity robotic arm operation prone to partial failure of joint actuators. Furthermore, they face challenges such as time-varying external disturbances and unknown inertial parameters, which can severely impact trajectory tracking accuracy and system stability.

[0003] Among existing control methods, finite-time control can achieve rapid error convergence, but the convergence time depends on the initial state. Preset performance control can constrain the error bounds, but traditional preset performance functions converge slowly and are difficult to handle actuator failures. Therefore, a control strategy that combines fixed-time convergence, preset performance constraints, and fault tolerance is urgently needed. Summary of the Invention

[0004] In response to the shortcomings of the existing technology, the present invention provides a preset performance fault-tolerant control method under the failure of the motor of a tendon-driven robotic arm, aiming to solve the trajectory tracking control problem of a tendon-driven spatial robotic arm under the combined working conditions of actuator failure, external disturbance and unknown parameters, ensuring that the system converges within a fixed time and the tracking error meets the preset performance boundary.

[0005] The technical solution of the present invention is: a preset performance fault-tolerant control method under the failure of a tendon-driven manipulator motor, comprising the following steps:

[0006] S1), building a tendon-driven robotic arm system model with actuator failure, external interference and system parameter uncertainty;

[0007] S2), designing a trajectory tracking error model for a tendon-driven robotic arm;

[0008] S3), design a fixed-time sliding mode observer to estimate the system lumped uncertainty;

[0009] S4) Construct an improved preset performance function and introduce a conversion function to make the trajectory tracking position error e of each joint of the robot arm i Meet preset performance boundaries;

[0010] S5) Design a fixed-time preset performance fault-tolerant controller, and use the fixed-time preset performance fault-tolerant controller to make the tracking error of each joint of the robotic arm converge to the preset performance boundary within a fixed time.

[0011] Preferably, in step S1), the expression of the tendon-driven manipulator system model with actuator failure, external interference and system parameter uncertainty is:

[0012]

[0013] Among them, M0(θ), τ s0 Represent the inertia matrix M(θ), Coriolis force and centrifugal force matrix respectively Moment τ of rope deformation loss s The known nominal term of ; θ is the joint angle; is the joint angular velocity; is the joint angular acceleration; I m =J m i m Motor output control torque; i m J is the motor current output torque; m The Jacobian matrix representing the current-torque relationship; is the uncertainty term; d(t) is the external bounded disturbance term; ΔM(θ), and Δτ s Represent M(θ), τ s The uncertain part of γ(tT f ) represents the time configuration function of the fault; T f Indicates the time when the fault occurs; t is the time; represents the fault vector of the system.

[0014] Preferably, in step S2), the trajectory tracking error model of the tendon-driven manipulator is:

[0015]

[0016] in, is the velocity tracking error vector; is the first-order derivative of x1; is the first-order derivative of the lumped uncertainty x2 under system failure.

[0017] Preferably, in step S3), the expression of the fixed-time sliding mode observer is:

[0018]

[0019] Where, represent the first-order derivatives of the observer state variables; A0 is the full-drive system parameter; μ1 and μ2 are positive definite diagonal matrices, and λ min (μ1)>0 and λmin (μ2)>1,λ min (·) represents the minimum eigenvalue of the matrix; ζ(e1) is the nonlinear sliding mode convergence function; Sat(ζ(e1),ε,-ε) is the saturation function; ε represents the preset error fixed value.

[0020] As an example, in step S3), the nonlinear sliding mode convergence function ζ(e1) is designed as follows: w :

[0021]

[0022] Where, is the conversion function; is the first-order derivative of the estimated error e1; s w With conversion function sliding mode variables; Λ1 and Λ2 represent positive definite diagonal matrices; α1>1 and 0<α2 are known parameters; sig represents the sign function.

[0023] Preferably, in step S4), the improved preset performance function is:

[0024]

[0025] Where, ρ 0i , ρ ∞i Represent the initial value and the preset steady-state value respectively; i Represents the system control parameters; T i represents the upper bound of the convergence time.

[0026] As a preference, in step S4), the position error e of each joint trajectory tracking of the robotic arm is i Meet the preset performance boundaries, namely:

[0027]

[0028] Among them, χ i ρ i (t), are preset upper and lower bounds of performance respectively;

[0029] And define the conversion error vector ε1: Among them, e i is the trajectory tracking position error of the i-th joint; ρ i is the improved preset performance function; ψ is the conversion function; Indicates custom parameters.

[0030] Preferably, in step S5), the sliding surface s of the fixed-time preset performance fault-tolerant controller is fixed; that is:

[0031] s = ε2 + K1sig q (ε1) + K2G p (ε1); (30)

[0032] In the formula, ε2 is the conversion error auxiliary variable, e is the robotic arm trajectory tracking position error vector; is the velocity tracking error vector; A is a diagonal positive definite matrix, A = diag(a1,…,a n ); is the first derivative of ρ i ; K1 and K2 are constant diagonal positive definite matrices; ε1 is the conversion error vector, e i is the trajectory tracking position error of the i-th joint; ρ i is the improved preset performance function; G p (ε1) = [g p ,…,g(ε 11 ),…,g p (ε 1n )] T ; g p (ε 1i ) is a piecewise function, δ and p are positive constants satisfying 0 < δ ≤ 1 and 0 < p < 1 respectively; ε 1i represents the conversion error vector of the i-th joint; q is a known positive constant; sig q (ε1) = [sig q (ε 11 ),…,sig q (ε 1n )] T ; sig​​​​​​​​​​​​​​​​​​​​rf are the control torques of each part respectively.

[0036] The beneficial effects of the present invention are:

[0037] 1. By combining non-singular terminal sliding mode control with a preset performance function, the present invention achieves performance boundary constraints on tracking errors while ensuring the system's fixed-time stability. By dynamically adjusting the performance function boundary, the problem of control accuracy degradation under actuator fault conditions is effectively resolved, significantly improving the system's robustness and trajectory tracking accuracy.

[0038] 2. By constructing a fixed-time sliding mode observer and a non-singular fixed-time sliding mode preset performance fault-tolerant controller, the present invention systematically solves the problems of actuator fault fault-tolerant control, composite uncertainty suppression, and tracking error preset performance constraints;

[0039] 3. The fixed-time sliding mode observer of the present invention achieves fast and accurate estimation of lumped uncertainty. Its upper bound on convergence time is independent of the initial state of the system. Compared with the finite-time extended state observer, it has better transient response characteristics and steady-state accuracy, providing a reliable feedforward compensation basis for the implementation of subsequent control strategies.

[0040] 4. Under the same composite working conditions, the proposed FTSMPPC can converge to a neighborhood near the zero point more quickly within a fixed time. Moreover, the convergence time is not constrained by the initial state of the system and always remains within the preset performance boundary, showing higher steady-state accuracy and fault tolerance performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 This is a flowchart of the method of Example 1 of the present invention;

[0042] Figure 2 A comparison diagram of the trajectory tracking position error curve of joint 1 in Example 2 of the present invention;

[0043] Figure 3 A comparison diagram of the position error curve of the trajectory tracking of joint 2 in Example 2 of the present invention;

[0044] Figure 4 This is a comparison diagram of the trajectory tracking position curve of joint 1 in Example 2 of the present invention;

[0045] Figure 5 This is a comparison diagram of the trajectory tracking position curve of joint 2 in Example 2 of the present invention;

[0046] Figure 6 This is a comparison diagram of the output motor current curve of joint 1 in Example 2 of the present invention;

[0047] Figure 7This is a comparison diagram of the output motor current curve of joint 2 in Example 2 of the present invention;

[0048] Figure 8 This is a comparison diagram of the tracking trajectory curve of the end of the robotic arm in Example 2 of the present invention;

[0049] Figure 9 Graphs showing joint angle tracking trajectory, joint trajectory tracking position error, cable tension, and control input motor current under the fault mode of motors 1 and 3 completely failing and motors 2 and 4 failing 50% in Example 3 of the present invention;

[0050] Figure 10 Graphs showing joint angle tracking trajectory, joint trajectory tracking position error, cable tension, and control input motor current under the fault mode of motors 1 and 3 completely failing and motors 2 and 4 failing 60% in Example 3 of the present invention;

[0051] Figure 11 Graphs of joint angle tracking trajectory, joint trajectory tracking position error, cable tension, and control input motor current under the fault mode of motors 1 and 3 completely failing and motors 2 and 4 failing 70% in Example 3 of the present invention. DETAILED DESCRIPTION

[0052] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings:

[0053] like Figure 1 As shown, this embodiment provides a preset performance fault-tolerant control method for a tendon-driven manipulator motor failure, comprising the following steps:

[0054] S1) Construct a tendon-driven robotic arm system model with actuator failure, external interference and system parameter uncertainty; specifically, the following steps are included:

[0055] S11) Establish the system equation of the tendon-driven spatial manipulator with external interference and system parameter uncertainty, namely:

[0056]

[0057] Where, M0(θ), τ s0 Represent the inertia matrix M(θ), Coriolis force and centrifugal force matrix respectively Moment τ of rope deformation loss s The known nominal term of ; θ is the joint angle; is the joint angular velocity; is the joint angular acceleration; I m =J m i m Motor output control torque; i m J is the motor current output torque;m The Jacobian matrix representing the current-torque relationship; is the uncertainty term; d(t) is the external bounded disturbance term; ΔM(θ), and Δτ s Represent M(θ), τ s The uncertain part;

[0058] S12) According to formula (1), we can get:

[0059]

[0060] S13) When the actuator is in a fault state, the tendon-driven robotic arm system model is:

[0061]

[0062] Where, γ(tT f ) represents the time configuration function of the fault; T f Indicates the time when the fault occurs; t is the time; represents the fault vector of the system.

[0063] Wherein, the time configuration function of the fault γ(tT f )for:

[0064] γ(tT f )=diag{γ1(tT f ),γ2(tT f ),...,γ n (tT f )}; (4)

[0065] Where, γ i represents the i-th state equation;

[0066] The time curve of each state equation is expressed as:

[0067]

[0068] Where, l i >0 indicates the development of fault, when l i When it is less than the preset fault threshold, it indicates an initial fault; when l i When it is greater than the preset fault threshold, the actuator has a sudden fault.

[0069] The actuator faults include bias faults and gain faults. Based on the actuator faults, the control input is described as:

[0070] I mc =ΓI m +ΔIm ; (6)

[0071] Where Γ and ΔI m Represent gain fault and bias fault respectively; I mc is the actual control input; I m Output control torque to the motor;

[0072] The working states of the actuator are divided into:

[0073] 1) When Γ=1, ΔI m =0, it means the joint actuator works normally;

[0074] 2) When Γ≠1, ΔI m =0, it means that the joint actuator has a partial failure state;

[0075] 3) When Γ=1, ΔI m ≠0, it means that the joint actuator has a bias fault state;

[0076] 4) When Γ≠1, ΔI m ≠0, it means that the joint actuator has a combined fault of bias fault and partial failure fault.

[0077] The fault vector of the system Described as:

[0078]

[0079] Where I is the identity matrix;

[0080] Substituting equation (7) into equation (3), the model of the tendon-driven manipulator system is obtained as follows:

[0081]

[0082] S2) Design the trajectory tracking error model of the tendon-driven manipulator, as follows:

[0083] S21), define the robot arm trajectory tracking position error vector e, speed tracking error vector and acceleration tracking error They are:

[0084] e=θ-θ d ; (9)

[0085]

[0086] Where θ d 、 are the expected joint angle, expected joint angular velocity, and expected joint angular acceleration, respectively;

[0087] Substituting equations (10) and (11) into equation (1), we obtain:

[0088]

[0089] S22) According to the full drive system theory, a controller is obtained, namely:

[0090]

[0091] Where A0 is the all-wheel drive system parameter;

[0092] S23) Substitute equation (13) into equation (12) to obtain the trajectory tracking error model:

[0093]

[0094] in, represents the lumped uncertainty under system faults;

[0095] make: Then the trajectory tracking error model of equation (14) is rewritten as:

[0096]

[0097] Where, y is the system output.

[0098] S3) Design a fixed-time sliding mode observer to estimate the system's lumped uncertainty, which includes model parameter uncertainty, external disturbances, and uncertainty caused by actuator failures. Specifically, the following steps are included:

[0099] S31) Define the estimated error of the fixed-time sliding mode observer as:

[0100] e1=x1-z1, e2=x2-z2; (16)

[0101] Where, e1 and e2 are the estimated errors of the observer respectively; z1 and z2 represent the state variables of the observer respectively;

[0102] Then the expression of the fixed-time sliding mode observer is:

[0103]

[0104] Where, represent the first-order derivatives of the observer state variables; A0 is the full-drive system parameter; μ1 and μ2 are positive definite diagonal matrices, and λ min (μ1)>0 and λ min (μ2)>1,λmin (·) represents the minimum eigenvalue of the matrix; ζ(e1) is the nonlinear sliding mode convergence function; Sat(ζ(e1),ε,-ε) is the saturation function; ε represents the preset error fixed value.

[0105] in,

[0106]

[0107] In the formula, in order to achieve fixed-time convergence of the observer estimation error, ζ(e1) is designed as:

[0108]

[0109]

[0110] Where α1, β1>1 and 0<α2, β2<1 are known parameters; Λ1, Λ2, Λ3, Λ4 represent positive definite diagonal matrices; e 1n represents the nth joint angle tracking error; φ w is the state variable matrix; Sgn and sig represent the sign function; Represents the estimated upper limit of the estimated error e2; is the conversion function; is the conversion function The first derivative of ; is the first-order derivative of the estimated error e1; s w With conversion function The sliding mode variable.

[0111] in:

[0112]

[0113] Sgn(s w )=diag{sgn(s w1 ),...,sgn(s wn )}; (twenty one)

[0114]

[0115] Where s wn represents the nth variable of the sliding mode variable; T represents the transposition operation;

[0116] For the nonlinear sliding mode convergence function ζ(e1), the sliding mode surface s of the fixed-time sliding mode observer is designed. w :

[0117]

[0118] Among them, the conversion function as follows:

[0119]

[0120] Where η>0 is a known positive constant, is a known constant; e 1i is the tracking error of the i-th joint angle.

[0121] In this embodiment, the estimated error e1 of the fixed-time sliding mode observer is t Converges to the neighborhood near the origin, convergence time T t The following inequality is satisfied:

[0122]

[0123] Where Λ1, Λ2, Λ3, and Λ4 represent positive definite diagonal matrices; λ min (Λ1),λ min (Λ2),λ min (Λ3), λ min (Λ4) are the minimum eigenvalues ​​of Λ1, Λ2, Λ3, and Λ4 respectively; n represents the system order.

[0124] S4) Construct an improved preset performance function and introduce a conversion function to make the trajectory tracking position error e of each joint of the robot arm i Meet preset performance boundaries;

[0125] The improved preset performance function ρ constructed i (t), that is:

[0126]

[0127] Where, ρ 0i , ρ ∞i Represent the initial value and the preset steady-state value respectively; i is the system control parameter; T i represents the upper bound of the convergence time;

[0128] The preset performance function ρ i (t) is a bounded positive function with a definite upper bound on the convergence time and capable of achieving rapid convergence, and satisfies ρ ∞i ≤ρ i (t)≤ρ 0i and

[0129] The expression of the introduced conversion function ψ(x) is:

[0130]

[0131] Where, represents a custom parameter; x represents the input variable of the conversion function.

[0132] The tracking position error of each joint trajectory of the robotic arm is e i Meet the preset performance boundaries, namely:

[0133]

[0134] Among them, χ i ρ i (t), are preset upper and lower bounds of performance respectively;

[0135] And define the conversion error vector ε1: Among them, e i is the trajectory tracking position error of the i-th joint; ρ i Improved preset performance function.

[0136] S5) Design a fixed-time preset performance fault-tolerant controller, which enables the tracking error of each joint trajectory of the robotic arm to converge to the preset performance boundary within a fixed time through the fixed-time preset performance fault-tolerant controller; specifically, the following steps are included:

[0137] S51) Construct a sliding mode surface s of a fixed-time preset performance fault-tolerant controller; namely:

[0138] s=ε2+K1sig q (ε1)+K2G p (ε1); (30)

[0139] Where ε2 is the auxiliary variable of conversion error, e is the robot arm trajectory tracking position error vector; is the velocity tracking error vector; A is a diagonal positive definite matrix, A=diag(a1,…,a n ); is ρ i The first-order derivative of ; K1, K2 are constant diagonal positive definite matrices; ε1 is the conversion error vector, e i is the trajectory tracking position error of the i-th joint; ρ i For improved preset performance function; G p (ε1)=[g p (ε 11 ),…,g p (ε 1n )] T ;g p (ε 1i ) is a piecewise function, δ and p are positive constants satisfying 0 < δ ≤ 1 and 0 < p < 1 respectively; ε 1i represents the transformation error vector of the i-th joint; q is a known positive constant; sig q (ε1) = [sig q (ε 11 ), …, sig q (ε 1n )] T ; sig q (ε 1i ) = |ε 1i | q sgn(ε 1i ), i = 1, … n;

[0140] S52), construct a fixed-time preset performance fault-tolerant controller based on the sliding surface s, that is:

[0141] τ = τ0 + τ1 + τ2 + τ rf ; (31)

[0142] In the formula, τ represents the total control torque; τ0 is the nominal term of the manipulator system; τ1, τ2, τ rf are the control torques of each part.

[0143] Among them, the nominal term τ0 of the manipulator system is expressed as:

[0144]

[0145] In the formula, M0(θ), τ s0 respectively represent the inertia matrix M(θ), the Coriolis force and centrifugal force matrix the torque τ s lost due to rope deformation <0,

[0146]

[0147] [[ID=6,2]]In the formula, is the first derivative of the diagonal positive definite matrix A,

[0148] M q (ε1) = diag(q|ε 11 | q-1 [[ID=,4]]…, q|ε 1n | q-1 ;

[0149] H P (ε1) = diag(h p (ε 11 ), …, hp (ε 1n )),

[0150] B is a diagonal positive definite matrix, B=diag(b1,...,b n ), is an auxiliary variable;

[0151] Among them, τ1, τ2, τ rf Respectively expressed as:

[0152] τ1=-K0Sig σ (s); (35)

[0153]

[0154] Where K0 represents a positive symmetric matrix; σ>1,γ0<1 are known normal numbers; s0 represents a small positive number; u2 is an auxiliary variable;

[0155] in:

[0156]

[0157] Where, d M is an external disturbance; k is a known positive constant; M m 、C m 、T m is a known positive constant.

[0158] Example 2

[0159] This example verifies the effectiveness of a fixed-time preset performance fault-tolerant controller and compares it with a finite-time fault-tolerant controller;

[0160] The finite-time fault-tolerant controller is designed as follows:

[0161] τ=τ0+τ1

[0162]

[0163] Among them, k1, k2, is a positive constant, To satisfy A positive odd number, To satisfy A positive constant is a diagonal matrix.

[0164] The failure mode is set as follows: T f = 20s, the motors (number 6) and (number 8) of joint 2 completely fail. The external disturbance d(t) acting on each joint and the uncertainty of the system parameters are as follows:

[0165]

[0166] ΔM(θ)=diag(sin(0.1t),2sin(0.2t))(kg·m 2 )

[0167]

[0168] The control parameters of the fixed time preset performance controller FTSMPPC are shown in Table 1, and the control parameters of the finite time fault tolerant control FFTC are shown in Table 2:

[0169] Table 1 Control parameters of fixed time preset performance controller FTSMPPC

[0170]

[0171] Table 2 FFTC control parameters

[0172]

[0173] Figure 2 、 3 The comparison of the tracking position errors of each joint trajectory is given. Figure 3 、 4 The tracking position comparison of each joint trajectory is given; Figure 8 The tracking trajectory of the end-of-arm tracking is given. For a spatial manipulator system with partial failure of joint actuators, bounded external disturbances, and unknown inertial parameters, the proposed method has a significantly faster convergence speed of the joint trajectory tracking error than FFTC, and always remains within the preset performance boundary, showing good transient response speed and steady-state accuracy; while the convergence speed of the joint trajectory tracking error under the action of FFTC is slower, and at the same time, Figure 3 It can also be clearly seen that the trajectory tracking error of joint 2 is in the fault mode (T f =20s, the motors (No. 6) and (No. 8) of joint 2 completely failed) and showed large fluctuations, which obviously exceeded the preset performance boundary, and the anti-disturbance robustness and fault tolerance were poor.

[0174] Figure 6 、 7 A comparison of the control output currents for each joint is presented. It can be seen that in the early stages, compared to FFTC, the FTSMPPC proposed in Example 1 requires a smaller control input at joint 1, while the FTSMPPC proposed in joint 2 requires a larger control torque to achieve faster convergence and trajectory tracking control. In the middle and late stages, the control outputs required for trajectory tracking control are similar between the two.

[0175] Example 3

[0176] This example verifies the effectiveness of FTSMPPC under fault mode.

[0177] The sampling period is set to 0.1s, and the time is 160s. The initial state of the robot arm joint position is θ0 = 10°, and the expected trajectory is θ d =20sin(πt / 80), the FTSMPPC control parameters are shown in Table 3.

[0178] The failure modes are as follows:

[0179] 1) In 60s-100s, motors 1 and 3 completely fail, and motors 2 and 4 fail by 50%;

[0180] 2) In 60s-100s, motors 1 and 3 completely fail, and motors 2 and 4 fail by 60%;

[0181] 3) In 60s-100s, motors 1 and 3 completely fail, and motors 2 and 4 fail by 70%;

[0182] Table 3 Control parameters of fixed time preset performance controller FTSMPPC

[0183]

[0184] Figure 9-11 The curves of joint angle tracking trajectory, joint trajectory tracking position error, cable tension, and control input motor current are given under three different fault modes. The experimental results show that even in the extreme fault mode (failure rate of 70%), the manipulator system can converge to zero within a fixed time and always remain within the preset performance boundary, while ensuring the transient performance of the system and achieving strong robust trajectory tracking fault-tolerant control under actuator fault conditions. It is not difficult to see that in the switching interval of motor failure, the motor current and cable tension will fluctuate greatly, and more obvious chattering will occur, but the system will quickly stabilize and show good steady-state characteristics. The experimental results show that as the degree of motor failure increases, the FTSMPPC controller exhibits strong fault-tolerant performance. However, due to the limitations of the experimental platform equipment, when the motor fails at 70%, the motor output current is insufficient to offset the torque required for the manipulator joint movement, resulting in poor trajectory tracking performance in the fault interval.

[0185] The above embodiments and descriptions are only for explaining the principles and best embodiments of the present invention. Without departing from the spirit and scope of the present invention, the present invention may be subject to various changes and improvements, which shall fall within the scope of the invention to be protected.

Claims

1. A method for fault-tolerant control of a tendon-driven manipulator under motor failure, characterized in that: The steps include: S1), building a tendon-driven robotic arm system model with actuator failure, external interference and system parameter uncertainty; S2), designing a trajectory tracking error model for a tendon-driven robotic arm; S3), design a fixed-time sliding mode observer to estimate the system lumped uncertainty; S4) Construct an improved preset performance function and introduce a conversion function to make the trajectory tracking position error e of each joint of the robot arm i Meet preset performance boundaries; S5) Design a fixed-time preset performance fault-tolerant controller, and use the fixed-time preset performance fault-tolerant controller to make the tracking error of each joint of the robotic arm converge to the preset performance boundary within a fixed time.

2. The method for preset performance fault-tolerant control of a tendon-driven manipulator motor under failure according to claim 1, characterized in that: In step S1), the expression of the tendon-driven manipulator system model with actuator failure, external interference and system parameter uncertainty is: Among them, M0(θ), τ s0 Represent the inertia matrix M(θ), Coriolis force and centrifugal force matrix respectively Moment τ of rope deformation loss s The known nominal term of ; θ is the joint angle; is the joint angular velocity; is the joint angular acceleration; I m =J m i m Motor output control torque; i m J is the motor current output torque; m The Jacobian matrix representing the current-torque relationship; is the uncertainty term; d(t) is the external bounded disturbance term; ΔM(θ), and Δτ s Represent M(θ), τ s The uncertain part of γ(tT f ) represents the time configuration function of the fault; T f Indicates the time when the fault occurs; t is the time; represents the fault vector of the system.

3. The method for preset performance fault-tolerant control of a tendon-driven manipulator motor under failure according to claim 2, characterized in that: In step S1), the fault vector of the system Described as: Substituting equation (7) into equation (3), the model of the tendon-driven manipulator system with actuator failure, external interference and system parameter uncertainty is obtained as follows: Where I is the identity matrix; Γ and ΔI m Indicates gain fault and bias fault respectively.

4. The method for preset performance fault-tolerant control of a tendon-driven manipulator motor under failure according to claim 3, characterized in that: In step S1), the actuator fault includes a bias fault and a gain fault. According to the actuator fault, the control input is described as: I mc =ΓI m +ΔI m ; (6) Where Γ and ΔI m Represent gain fault and bias fault respectively; I mc is the actual control input; I m Output control torque to the motor; The working states of the actuator are divided into: 1) When Γ=1, ΔI m =0, it means the joint actuator works normally; 2) When Γ≠1, ΔI m =0, it means that the joint actuator has a partial failure state; 3) When Γ=1, ΔI m ≠0, it means that the joint actuator has a bias fault state; 4) When Γ≠1, ΔI m ≠0, it means that the joint actuator has a combined fault of bias fault and partial failure fault.

5. The method for preset performance fault-tolerant control of a tendon-driven manipulator motor under failure according to claim 4, characterized in that: In step S2), the trajectory tracking error model of the tendon-driven manipulator is designed, which specifically includes the following steps: S21), define the robot arm trajectory tracking position error vector e, speed tracking error vector and acceleration tracking error They are: e=θ-θ d (9) Where θ d 、 are the expected joint angle, expected joint angular velocity, and expected joint angular acceleration, respectively; Substituting equations (10) and (11) into equation (1), we obtain: S22) According to the full drive system theory, a controller is obtained, namely: Where A0 is the all-wheel drive system parameter; S23) Substitute equation (13) into equation (12) to obtain the trajectory tracking error model: in, represents the lumped uncertainty under system faults; make: Then the trajectory tracking error model of equation (14) is rewritten as: Where, y is the system output.

6. The method for preset performance fault-tolerant control of a tendon-driven manipulator motor under failure according to claim 5, characterized in that: In step S3), the expression of the fixed-time sliding mode observer is: Where, represent the first-order derivatives of the observer state variables; A0 is the full-drive system parameter; μ1 and μ2 are positive definite diagonal matrices, and λ min (μ1)>0 and λ min (μ2)>1,λ min (·) represents the minimum eigenvalue of the matrix; ζ(e1) is the nonlinear sliding mode convergence function; Sat(ζ(e1),ε,-ε) is the saturation function; ε represents the preset error fixed value.

7. The method for preset performance fault-tolerant control of a tendon-driven manipulator motor under failure according to claim 6, characterized in that: In step S3), the nonlinear sliding mode convergence function ζ(e1) is designed as follows: w : Where θ is the conversion function; is the first-order derivative of the estimated error e1; s w is a sliding mode variable with a transfer function θ; Λ1 and Λ2 represent positive definite diagonal matrices; α1>1 and 0<α2 are known parameters; sig represents the sign function.

8. The method for preset performance fault-tolerant control of a tendon-driven manipulator motor under failure according to claim 7, characterized in that: In step S4), the improved preset performance function is: Where, ρ 0i , ρ ∞i Represent the initial value and the preset steady-state value respectively; i Represents the system control parameters; T i represents the upper bound of the convergence time; The tracking position error of each joint trajectory of the robotic arm is e i Meet the preset performance boundaries, namely: in, χ i ρ i (t), are preset upper and lower bounds of performance respectively; And define the conversion error vector ε1: Among them, e i is the trajectory tracking position error of the i-th joint; ρ i is the improved preset performance function; ψ is the conversion function; θ i Indicates custom parameters.

9. The method for preset performance fault-tolerant control of a tendon-driven manipulator motor under failure according to claim 8, characterized in that: In step S5), the sliding surface s of the fixed-time preset performance fault-tolerant controller is designed as: s=ε2+K1sig q (ε1)+K2G p (ε1); (30) where ε2 is the conversion error auxiliary variable, e is the robotic arm trajectory tracking position error vector; is the velocity tracking error vector; A is a diagonal positive definite matrix, A = diag(a1, …, a n ); is the first derivative of ρ i ; K1 and K2 are constant diagonal positive definite matrices; ε1 is the conversion error vector, e i is the trajectory tracking position error of the i-th joint; ρ i is the improved preset performance function; G p (ε1) = [g p (ε 11 ), …, g p (ε 1n )] T ; g p (ε 1i ) is a piecewise function, δ and p are positive constants satisfying 0 < δ ≤ 1 and 0 < p < 1, respectively; ε 1i represents the transformation error vector of the i-th joint; q is a known positive constant; sig q (ε1)=[sig q (ε 11 ),…,sig q (ε 1n )] T ;sig q (ε 1i )=|ε 1i | q sgn(ε 1i ),i=1,…n.

10. The method for preset performance fault-tolerant control of a tendon-driven manipulator motor under failure according to claim 9, characterized in that: In step S5), the fixed time preset performance fault-tolerant controller is: τ=τ0+τ1+τ2+τ rf (31) Where τ represents the total control torque; τ0 is the nominal term of the manipulator system; τ1, τ2, τ rf are the control torques of each part respectively.

Images