A fault-tolerant controller design method for robotic systems

Abstract

The application discloses a fault-tolerant controller design method for a robot system, and relates to the field of accurate control and fault processing of the robot system. Firstly, an actuator partial failure fault, model uncertainty and external disturbance are considered, a robot dynamics open-loop system is established, an actuator input saturation nonlinearity is introduced, a control input vector is made to be more consistent with the constraint of an actual physical system, an improved preset performance function with better convergence performance is provided, a terminal sliding mode surface is designed based on a terminal sliding mode framework, and finally, a fixed-time preset performance fault-tolerant controller is designed based on the sliding mode surface. The application can efficiently process the actuator partial failure fault of the robot system, ensure the robustness of the modeling uncertainty and external disturbance of the robot system, effectively improve the dynamic response capability and steady-state control precision of the robot system, improve the safety and reliability of the robot system, and prolong the actual service life of the robot system.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of precise control and fault handling of robot systems, and in particular to a fault-tolerant controller design method for robot systems. BACKGROUND

[0002] The problem of high-precision control of robot systems has been a widely studied problem in the field of robot control, especially when the actuator part of the robot system fails. The rapid and accurate handling of such failures not only improves the safety and reliability of the robot system, but also ensures that the established control precision is maintained when the robot system fails, thereby not affecting the normal implementation of the work task. As is known, robots need to perform repetitive and tedious work tasks for a long time, and the key components, especially the actuator, are in a continuous working state for a long time, which causes a decline in performance and even failure. If these failures are not handled in a timely manner, the robot needs to be shut down for inspection and repair, which will greatly affect production efficiency and thus cause economic losses. Therefore, it is necessary to deeply study the fault-tolerant control problem of robot systems, and to quickly handle failures when common failures occur in the robot system, so as to improve the safety and reliability of the robot system, while ensuring the control precision of the robot system, which is a problem to be solved in future robot precise control technology.

[0003] At present, most of the fault-tolerant control methods proposed for uncertain robot systems only consider the steady-state performance of the robot system trajectory tracking error, i.e. the control precision when the robot system is stable, without considering the dynamic response performance of the robot system. If the robot system cannot quickly respond to solve the fault of the robot system when a fault occurs, the control precision of the robot system will also be affected. SUMMARY

[0004] In view of the shortcomings of the existing method, the present application provides a fault-tolerant controller design method for robot systems, which combines fixed-time control with preset performance control, and proposes a fixed-time preset performance fault-tolerant controller based on the design framework of terminal sliding mode, effectively solving the problem of high-performance trajectory tracking when the robot system fails. The present application limits the state of the robot system within the preset performance boundary based on the preset performance control, thereby ensuring the dynamic and steady-state performance of the robot system, and designs a fault-tolerant controller based on the preset performance function, so as to ensure the fixed-time convergence of the tracking error when the robot system fails.

[0005] The technical solution adopted by the present application to achieve the above-mentioned purpose is as follows:

[0006] A fault-tolerant controller design method for robot systems, comprising the following steps:

[0007] Step 1: Establish the robot dynamics open-loop system;

[0008] The robot dynamics open-loop system is:

[0009]

[0010] in, Respectively represent the position information, velocity information, and acceleration information of the robot system's rotational joints; M0(q) represents the nominal value of the robot system's inertia matrix, and ΔM(q) represents the uncertainty value of the robot system's inertia modeling; represents the nominal value of the centrifugal-Coriolis force matrix, represents the uncertainty value of the centrifugal force-Coriolis force modeling of the robot system; g0(q) represents the nominal value of the gravity vector of the robot system, Δg(q) represents the uncertainty value of the gravity modeling of the robot system; τ represents the control input vector; d∈R n represents the unknown input disturbance vector, n represents the degree of freedom of the robot system; Γ∈R n×n represents the failure rate matrix of the joint actuators of the robot system. It is a diagonal positive definite matrix used to characterize the health status of the actuator. A value of 1 indicates complete failure, otherwise it indicates partial failure.

[0011] Step 2: Introduce the actuator input saturation nonlinearity into the control input vector of the robot dynamics open-loop system to obtain the control input vector that introduces the actuator input saturation nonlinearity;

[0012] The control input vector that introduces the actuator input saturation nonlinearity is:

[0013]

[0014] Where τ(u) represents the control input vector that introduces the actuator input saturation nonlinearity, u represents the actuator input information; τ M Indicates the maximum amplitude of the control input; sig(u) is defined as sig(u)=[sign(u1)|u1|,…,sign(u i )|u i |…,sign(u n )|u n |] T , where u i Represents the i-th item of the actuator's input information u; sign() represents the sign function, and |||| represents the vector modulus function;

[0015] Step 3: Build an improved preset performance function;

[0016] The improved preset performance function is:

[0017]

[0018] Where ρ(t) represents the improved preset performance function; ρ0, ρ ∞ , T and l are the performance parameters of the function to be designed, where ρ0 represents the initial value, ρ ∞ represents the final convergence value, T is the fixed convergence time, l is the adjustment ratio parameter; t is the time variable, exp() represents the natural exponential function;

[0019] Step 4: Design the terminal sliding surface based on the improved preset performance function and the terminal sliding framework;

[0020] s=ε2+K1Sig r (ε1)+K2W p (ε1)

[0021] Sig r (ε1)=[sign(ε 11 )|ε 11 | r ,…,sign(ε 1i )|ε 1i | r …,sign(ε 1n )|ε 1n | r ] T

[0022] W p (ε1)=[w p (ε 11 ),…,w p (ε 1i ),…,w p (ε 1n )] T

[0023]

[0024] Where s is the designed terminal sliding surface; K1 and K2 are the diagonal positive definite matrices to be designed; e is the position error vector, that is, e=[e1,…,e i …,e n ] T , e i is the position error of the robot's i-th joint, and e i =q i -q id ,q i is the actual position value of the i-th joint, q id is the expected position value of the i-th joint, is the derivative of the position error vector e; ε1 is the position error vector after the position error vector e is converted, ε 1i is the i-th item in the converted position error vector ε1; ε2 is a vector consisting of the position error vector and its derivative, ρ(t) is the improved preset performance function of the design, is the derivative of ρ(t); A is a matrix composed of preset performance functions; is the upper boundary value of the preset performance to be designed, b is the lower boundary value of the preset performance to be designed; r and p are positive constants and satisfy 0<p<1, r>1; the symbol || represents the absolute value, ln() represents the natural logarithm symbol with the constant e as the base, diag() represents the diagonal matrix construction function; δ is the positive constant to be designed;

[0025] Step 5: Based on the designed robot dynamics open-loop system, the control input vector and terminal sliding surface with actuator input saturation nonlinearity are introduced to establish a fixed-time preset performance fault-tolerant controller;

[0026] u=u a +u b

[0027] u a =τ0+τ1+τ2

[0028]

[0029] The actuator input information u consists of two parts: the first item u of the control input a and the second term u of the control input b ; τ0 represents the nominal term of the control torque, τ1 represents the uncertainty information offset term, τ2 represents the mixed term composed of τ0 and τ1; K0 is the control gain proportional matrix; σ is the power exponential term; represents the lumped upper bound of the robot system interference and uncertainty; a is any constant greater than 0; λ min (Γ) represents the minimum eigenvalue of the matrix; k is the normal number to be designed; Sig σ (s) = [sign(s1) |s1| σ ,…,sign(s i )|s i | σ …,sign(s n )|s n | σ ] T , s i represents the i-th term of the terminal sliding surface;

[0030] u0 and u1 are defined as:

[0031]

[0032] u1=Ae-q d +K1Sig r (ε1)+K2W p (ε1)

[0033] M r (ε1)=diag(r|ε 11 | r-1 ,…,r|ε 1i | r-1 ,…,r|ε 1n | r-1 )

[0034] F p (ε1)=diag(f p (ε 11 ),…,f p (ε 1i ),…,f p (ε 1n ))

[0035]

[0036] in, is the derivative of matrix A; q d is the expected position value of each joint, Represents the second-order derivative of the desired position of each joint.

[0037] The present invention has the following beneficial effects and advantages:

[0038] 1. It simultaneously considers the problems of partial actuator failure, modeling uncertainty, external interference, and input saturation nonlinearity, improving the method's ability to be applied to actual physical systems and greatly broadening its scope of application and value.

[0039] 2. Based on the existing preset performance function, a preset performance function with better performance is proposed. This preset performance function is a novel fixed-time convergence preset performance function. Based on this function, a fixed-time preset performance active fault-tolerant controller is designed, so that after a partial failure of the actuator occurs in the uncertain robot system, the robot system can still ensure the rapid convergence of the dynamic stage and the high-precision stability of the stable stage, while taking into account the solution to the input saturation problem.

[0040] 3. Combining preset performance control with fixed-time control, a fixed-time preset performance fault-tolerant controller is proposed based on the terminal sliding mode architecture to ensure high-performance control when the robot system encounters partial actuator failure, ensure the rapid convergence of the robot system's trajectory tracking error, high-precision stability, and strong robustness to robot system failures, modeling uncertainties, and external interference, thereby improving the safety and reliability of the robot system. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 This is a flow chart of a method for designing a fault-tolerant controller that can be used in a robot system according to an embodiment of the present invention;

[0042] Figure 2 This is a tracking position error curve diagram when an actuator failure occurs in the dual-joint robot system in an embodiment of the present invention. DETAILED DESCRIPTION

[0043] To make the above-mentioned objects, features, and advantages of the present invention more readily apparent, the specific implementation methods of the present invention are described in detail below with reference to the accompanying drawings. The following description sets forth many specific details to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways than those described herein, and those skilled in the art may make similar modifications without departing from the scope of the invention. Therefore, the present invention is not limited to the specific implementation methods disclosed below.

[0044] A fault-tolerant controller design method that can be used in robotic systems, such as Figure 1 As shown, the following steps are included:

[0045] Step 1: Considering the partial failure of the actuator, model uncertainty and external disturbance, establish the robot dynamic open-loop system;

[0046] The robot dynamics open-loop system is:

[0047]

[0048] in, Respectively represent the position information, velocity information, and acceleration information of the robot system's rotational joints; M0(q) represents the nominal value of the robot system's inertia matrix, and ΔM(q) represents the uncertainty value of the robot system's inertia modeling; represents the nominal value of the centrifugal-Coriolis force matrix, represents the uncertainty value of the centrifugal force-Coriolis force modeling of the robot system; g0(q) represents the nominal value of the gravity vector of the robot system, Δg(q) represents the uncertainty value of the gravity modeling of the robot system; τ represents the control input vector; d∈R n represents the unknown input disturbance vector, n represents the degree of freedom of the robot system; Γ∈Rn×n represents the failure rate matrix of the joint actuator of the robot system. It is a diagonal positive definite matrix used to characterize the health status of the actuator. If its value is 1, it represents complete failure, otherwise it represents partial failure.

[0049] In this embodiment, external interference refers to interference information brought by the external environment in which the robot is located, such as interference torque introduced by external disturbances.

[0050] Step 2: Introduce actuator input saturation nonlinearity into the control input vector of the robot dynamics open-loop system to obtain the control input vector with actuator input saturation nonlinearity introduced, so that the control input vector is more consistent with the constraints of the actual physical system;

[0051] The control input vector that introduces the actuator input saturation nonlinearity is:

[0052]

[0053] Where τ(u) represents the control input vector that introduces the actuator input saturation nonlinearity, u represents the actuator input information; τ M Indicates the maximum amplitude of the control input; sig(u) is defined as sig(u)=[sign(u1)|u1|,…,sign(u i )|u i |…,sign(u n )|u n |] T , where u i Represents the i-th item of the actuator's input information u; sign() represents the sign function, and || || represents the vector modulus function;

[0054] Step 3: Construct an improved preset performance function with better convergence performance;

[0055] The preset performance function with improved convergence performance is:

[0056]

[0057] Where ρ(t) represents the improved preset performance function; ρ0, ρ ∞ , T and l are the performance parameters of the function to be designed, where ρ0 represents the initial value, ρ ∞ represents the final convergence value, T is the fixed convergence time, l is the adjustment ratio parameter; t is the time variable, exp() represents the natural exponential function;

[0058] Step 4: Designing a terminal sliding surface based on the terminal sliding mode framework according to the preset performance function with improved convergence performance;

[0059] s=ε2+K1Sigr (ε1)+K2W p (ε1)

[0060] Sig r (ε1)=[sign(ε 11 )|ε 11 | r ,…,sign(ε 1i )|ε 1i | r …,sign(ε 1n )|ε 1n | r ] T

[0061] W p (ε1)=[w p (ε 11 ),…,w p (ε 1i ),…,w p (ε 1n )] T

[0062]

[0063] Where s is the designed terminal sliding surface; K1 and K2 are the diagonal positive definite matrices to be designed; e is the position error vector, that is, e=[e1,…,e i …,e n ] T , e i is the position error of the robot's i-th joint, and e i =q i -q id ,q i is the actual position value of the i-th joint, q id is the expected position value of the i-th joint, is the derivative of the position error vector e; ε1 is the position error vector after the position error vector e is converted, ε 1i is the i-th item in the converted position error vector ε1; ε2 is a vector consisting of the position error vector and its derivative, ρ(t) is the improved preset performance function of the design, is the derivative of ρ(t); A is a matrix composed of preset performance functions; is the upper boundary value of the preset performance to be designed, b is the lower boundary value of the preset performance to be designed; r and p are positive constants and satisfy 0<p<1, r>1; the symbol || represents the absolute value, ln() represents the natural logarithm with the constant e (irrational number, approximately equal to 2.71828...) as the base, diag() represents the diagonal matrix construction function; δ is the positive constant to be designed;

[0064] Step 5: Based on the designed robot dynamics open-loop system, the control input vector and terminal sliding surface with actuator input saturation nonlinearity are introduced to establish a fixed-time preset performance fault-tolerant controller;

[0065] u=u a +u b

[0066] u a =τ0+τ1+τ2

[0067]

[0068] The actuator input information u consists of two parts: the first item u of the control input a and the second term u of the control input b ; τ0 represents the nominal term of the control torque, τ1 represents the uncertainty information offset term, τ2 represents the mixed term composed of τ0 and τ1; K0 is the control gain proportional matrix; σ is the power exponential term; represents the lumped upper bound of the robot system interference and uncertainty; a is any constant greater than 0; λ min (Γ) represents the minimum eigenvalue of the matrix; k is a small positive constant to be designed; symbol Sig σ The definition of (s) is the same as above, Sig σ (s) = [sign(s1) |s1| σ ,…,sign(s i )|s i | σ …,sign(s n )|s n | σ ] T , s i represents the i-th term of the terminal sliding surface;

[0069] u0 and u1 are defined as:

[0070]

[0071] u1=Ae-q d +K1Sig r (ε1)+K2W p (ε1)

[0072] M r (ε1)=diag(r|ε 11 | r-1 ,…,r|ε 1i | r-1 ,…,r|ε 1n | r-1)

[0073] F p (ε1)=diag(f p (ε 11 ),…,f p (ε 1i ),…,f p (ε 1n ))

[0074]

[0075] in, is the derivative of matrix A; q d is the expected position value of each joint, Represents the second-order derivative of the desired position of each joint;

[0076] This embodiment uses a dual-joint robot system as an example for illustration. The simulation period of the dual-joint robot system is set to 0.01s. The relevant parameters of the dual-joint robot system are set as follows:

[0077]

[0078]

[0079] In the formula, the definitions and values ​​of specific parameters are:

[0080]

[0081] p5=(m1+m2)L1g1,p6=m2L2g1,

[0082] m1=0.5kg, m2=1.5kg, L1=1.0m, L2=0.8m,

[0083] J1=5.0kg·m 2 ,J2=5.0kg·m 2 ,g1=9.8m / s 2 .

[0084] Wherein, m1 is the mass parameter of the first joint in the dual-joint robot system, m2 is the mass parameter of the second joint in the dual-joint robot system, L1 is the rod length parameter of the first joint in the dual-joint robot system, L2 is the rod length parameter of the second joint in the dual-joint robot system, J1 is the inertia parameter of the first joint in the dual-joint robot system, J2 is the inertia parameter of the second joint in the dual-joint robot system, and g1 is the gravitational acceleration parameter;

[0085] Taking into account the uncertainty of the robot system, the nominal parameters of the mass parameters m1 and m2 are taken as m 10= 0.4kg and m 20 =1.2kg, in addition, the external interference is:

[0086]

[0087] The maximum torque τ of two joints in a dual-joint robot system M , that is, the maximum amplitude of the control input is set to 120Nm, and the initial state and expected trajectory of the joint are set as:

[0088]

[0089] Finally, the failure rate matrix Γ of the joint actuators of the robot system is set as:

[0090] Γ=diag(0.32,0.45+0.05sin(t))

[0091] The preset performance parameters and control parameters are selected as shown in Table 1 and Table 2 respectively:

[0092] Table 1 Preset performance parameter settings

[0093]

[0094] Table 2 Control parameter setting table

[0095]

[0096] From the verification results, it can be seen that the fixed-time preset performance fault-tolerant controller proposed in the present invention realizes the robustness of the robot system when a partial actuator failure occurs, that is, it handles the failure problem of the robot system very well, and at the same time can greatly improve the dynamic response capability and steady-state control accuracy of the robot system. Because the input saturation problem is taken into account, the results can be directly applied to the actual robot system in the future. Since it can improve the safety of the system, it has certain application value and prospects.

[0097] also, Figure 2 This is a curve diagram of the tracking position error when an actuator failure occurs in the dual-joint robot system. It can be seen from the figure that when a failure occurs in the robot system, the position error of the robot system still has excellent dynamic convergence performance and steady-state accuracy, and the position error is limited to the preset performance boundary throughout the entire period, that is, the predetermined control goal is achieved.

[0098] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any way. Any simple modification, change and equivalent structural change made to the above embodiment based on the technical essence of the present invention shall still fall within the scope of protection of the technical solution of the present invention.

Claims

1. A fault-tolerant controller design method that can be used in a robot system, characterized in that: The following steps are involved: Step 1: Establish the robot dynamics open-loop system; Step 2: Introduce the actuator input saturation nonlinearity into the control input vector of the robot dynamics open-loop system to obtain the control input vector that introduces the actuator input saturation nonlinearity; Step 3: Build an improved preset performance function; Step 4: Design the terminal sliding surface based on the improved preset performance function and the terminal sliding framework; Step 5: Based on the designed robot dynamics open-loop system, the control input vector and terminal sliding surface with actuator input saturation nonlinearity are introduced to establish a fixed-time preset performance fault-tolerant controller; The control input vector for introducing actuator input saturation nonlinearity in step 2 is: ； in, represents the control input vector that introduces actuator input saturation nonlinearity, Represents the input information of the actuator; Indicates the maximum amplitude of the control input; Defined as ,in, Indicates the input information of the actuator No. item; Represents a symbolic function, symbol To take the absolute value, represents the vector modulo function; The improved preset performance function described in step 3 is: ； in, represents an improved preset performance function; , , and are the performance parameters of the function to be designed, where Indicates the initial value, represents the final convergence value, is a fixed convergence time, To adjust the proportional parameters; is the time variable, exp() represents the natural exponential function; The terminal sliding surface in step 4 is: ； ； ； ； ； ； in, is the designed terminal sliding surface; and is the diagonal positive definite matrix to be designed; is the position error vector, that is , For the robot The position error of each joint is , For the The actual position value of each joint, For the The expected position value of each joint, is the derivative of the position error vector e; is the position error vector after the position error vector e is converted, is the position error vector after transformation The item; is a vector consisting of the position error vector and its derivative, Improved preset performance functions for design, for The derivative of is a matrix composed of preset performance functions; is the upper boundary value of the preset performance to be designed, is the preset lower boundary value of the performance to be designed; and is a positive constant and satisfies ; ln() represents the natural logarithm symbol with constant e as the base, diag() represents the diagonal matrix construction function; is the positive constant to be designed.

2. According to the method for designing a fault-tolerant controller for a robot system as claimed in claim 1, the robot dynamics open-loop system in step 1 is: ； in, Respectively represent the position information, velocity information and acceleration information of the rotary joints of the robot system; represents the nominal value of the inertia matrix of the robot system, represents the uncertainty value of inertial modeling of the robot system; represents the nominal value of the centrifugal-Coriolis force matrix, represents the uncertainty value of centrifugal-Coriolis force modeling of the robot system; represents the nominal value of the gravity vector of the robot system, represents the uncertainty value of gravity modeling of the robot system; represents the control input vector; represents the unknown input interference vector, represents the degrees of freedom of the robot system; It represents the failure rate matrix of the joint actuator of the robot system. It is a diagonal positive definite matrix used to characterize the health status of the actuator. Its value is 1, which means complete failure, otherwise it means partial failure.

3. The fault-tolerant controller design method applicable to a robot system according to claim 1, characterized in that: The fixed time preset performance fault-tolerant controller in step 5 is: ； Among them, the input information of the actuator It consists of two parts: the first term of the control input and the second term of the control input ; represents the nominal term of the control torque, represents the uncertainty information offset term, Indicated by and a mixture of components; is the control gain proportional matrix; is the power exponent term; Represents the lumped upper bound of the robot system interference and uncertainty; a is any constant greater than 0; Indicates taking the minimum eigenvalue of the matrix; k is the normal number to be designed; , represents the i-th term of the terminal sliding surface; and Defined as: ； in, is a matrix The derivative of is the expected position value of each joint, Represents the second-order derivative of the desired position of each joint.

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