Fault-tolerant controller design method for robot system

Abstract

The invention discloses a fault-tolerant controller design method for a robot system, and relates to the field of precise control and fault processing of robot systems. The method comprises the following steps: firstly, considering a partial failure fault of an actuator, model uncertainty and external interference, establishing a robot dynamics open-loop system, then introducing actuator input saturation nonlinearity to enable a control input vector to better conform to the constraint of an actual physical system, and then proposing an improved preset performance function with better convergence performance. Then, designing a terminal sliding mode surface based on the terminal sliding mode framework; and finally, designing a fixed-time preset performance fault-tolerant controller based on the sliding mode surface. According to the method, the actuator part failure fault of the robot system can be efficiently processed, meanwhile, the modeling uncertainty of the robot system and the robustness of external interference are guaranteed, the dynamic response capability and the steady-state control precision of the robot system are effectively improved, the safety and the reliability of the robot system are improved, and the actual service life of the robot system is prolonged.

Description

Technical Field

[0001] The present invention relates to the field of precise control and fault handling of robot systems, and in particular to a method for designing a fault-tolerant controller that can be used for robot systems. Background Art

[0002] The high-precision control problem of robot systems has always been a widely studied problem by experts in the field of robot control, especially when the robot system has a partial failure of the actuator. The rapid and accurate handling of the fault can not only improve the safety and reliability of the robot system, but also maintain the robot system in the event of a failure. The established control accuracy can be guaranteed, so as not to affect the normal implementation of the task. As we all know, robots need to perform repetitive and tedious tasks for a long time, and their key components, especially the actuators, are in a continuous working state for a long time, resulting in performance degradation and even failure. If these faults cannot be handled in time, the robot needs to be shut down for inspection and repair, which will greatly affect production efficiency and bring certain economic losses. Therefore, it is necessary to conduct in-depth research on the fault-tolerant control problem of the robot system, so that the fault can be quickly handled after the common faults occur in the robot system, so as to improve the safety and reliability of the robot system and ensure the control accuracy of the robot system. This is an urgent problem to be solved in the future robot precision control technology.

[0003] At present, most of the fault-tolerant control methods proposed for uncertain robot systems generally only consider the steady-state performance of the robot system's trajectory tracking error, that is, the control accuracy when the robot system is stable, but do not consider the dynamic response performance of the robot system. If the robot system fails, if the failure cannot be quickly responded to and resolved, the control accuracy of the robot system will also be affected. Summary of the invention

[0004] In view of the shortcomings of the existing methods, the present invention provides a fault-tolerant controller design method that can be used for a robot system. The method combines fixed-time control with preset performance control, and proposes a fixed-time preset performance fault-tolerant controller based on a terminal sliding mode design framework, which effectively solves the problem of high-performance trajectory tracking when a robot system fails. The present invention limits the state of the robot system within a preset performance boundary based on the preset performance control, thereby ensuring the dynamic and steady-state performance of the robot system. At the same time, a fault-tolerant controller is designed based on the preset performance function, so that the fixed-time convergence of the tracking error can be guaranteed when a robot system fails.

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

[0006] A method for designing a fault-tolerant controller that can be used for a robot system comprises the following steps:

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

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

[0009]

[0010] in, They represent the position information, velocity information and acceleration information of the rotary joint of the robot system respectively; M0(q) represents the nominal value of the inertia matrix of the robot system, and ΔM(q) represents the uncertainty value of the inertia modeling of the robot system; represents the nominal value of the centrifugal-Coriolis force matrix, represents the uncertainty value of 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 actuator of the robot system, which is a diagonal positive definite matrix used to characterize the health status of the actuator. Its value is 1, which means full failure, otherwise it means partial failure;

[0011] 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 introducing actuator input saturation nonlinearity;

[0012] The control input vector that introduces 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 represents 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 function performance parameters 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: designing the terminal sliding surface according to the improved preset performance function and based on 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 ith 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 transformed, ε 1i is the i-th item in the converted position error vector ε1; ε2 is the position vector consisting of the error vector and its derivative, ρ is the preset performance function designed, is the derivative of ρ; 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 || means taking the absolute value, ln() represents the natural logarithm symbol with 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 of control input u 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 also takes into account the partial failure of the actuator, modeling uncertainty, external interference, and input saturation nonlinearity, improving the ability of the method to be applied to actual physical systems, 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. The 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 the uncertain robot system has a partial failure of the actuator, it can still ensure the rapid convergence of the robot system in the dynamic stage and the high-precision stability in the stable stage, while taking into account the solution to the input saturation problem.

[0040] 3. Combine preset performance control with fixed time control, and propose a fixed time preset performance fault-tolerant controller based on the terminal sliding mode architecture to ensure high performance control when the robot system has partial actuator failure, ensure the rapid convergence of the robot system 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 is a flow chart of a method for designing a fault-tolerant controller that can be used for a robot system in 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] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific implementation method of the present invention is described in detail below in conjunction with the accompanying drawings. In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without violating the connotation of the invention, so the present invention is not limited by the specific implementation 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 interference, establish the robot dynamics open-loop system;

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

[0047]

[0048] in, They represent the position information, velocity information and acceleration information of the rotating joints of the robot system respectively; M0(q) represents the nominal value of the inertia matrix of the robot system, and ΔM(q) represents the uncertainty value of the inertia modeling of the robot system; represents the nominal value of the centrifugal-Coriolis force matrix, represents the uncertainty value of 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 actuator of the robot system, which is a diagonal positive definite matrix used to characterize the health status of the actuator. If its value is 1, it means full failure, otherwise it means 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 disturbance.

[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 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 represents 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: Constructing a preset performance function with improved convergence performance;

[0055] Improved convergence performance The preset performance function with better performance is:

[0056]

[0057] Where ρ(t) represents the improved preset performance function; ρ0, ρ ∞ , T and l are the function performance parameters 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 a terminal sliding framework according to a preset performance function with improved convergence performance;

[0059] s=ε2+K1Sig r (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 ith 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 transformed, ε 1i is the i-th item in the converted position error vector ε1; ε2 is the position vector consisting of the error vector and its derivative, ρ is the preset performance function designed, is the derivative of ρ; 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 || means taking the absolute value, ln() represents the natural logarithm symbol 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] ua =τ0+τ1+τ2

[0067]

[0068] The actuator input information u consists of two parts: the first item of control input u 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] In this embodiment, a dual-joint robot system is used as an example for explanation. 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] p2=m2L1L2,

[0081] p4=p3+J2,

[0082] p5=(m1+m2)L1g1,p6=m2L2g1,

[0083] m1=0.5kg, m2=1.5kg, L1=1.0m, L2=0.8m,

[0084] J1=5.0kg·m 2 ,J2=5.0kg·m 2 ,g1=9.8m / s 2 .

[0085] Among them, 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;

[0086] 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 disturbance is:

[0087]

[0088] 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:

[0089]

[0090] Finally, the failure rate matrix Γ of the robot system joint actuator is set as:

[0091] Γ=diag(0.32,0.45+0.05sin(t))

[0092] The preset performance parameters and control parameters are selected as shown in Table 1 and Table 2 respectively:

[0093] Table 1 Preset performance parameter setting table

[0094]

[0095] Table 2 Control parameter setting table

[0096]

[0097] 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 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 consideration, the result 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.

[0098] also, Figure 2 This is a tracking position error curve 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 period, that is, the predetermined control goal is achieved.

[0099] 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 still falls within the protection scope of the technical solution of the present invention.

Claims

1. A fault-tolerant controller design method that can be used for a robot system, characterized in that: The following steps are involved: Step 1: Establish the robot dynamics open-loop system; 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 introducing actuator input saturation nonlinearity; Step 3: Build an improved preset performance function; Step 4: designing the terminal sliding surface according to the improved preset performance function and based on 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.

2. A fault-tolerant controller design method for a robot system according to claim 1, characterized in that: The robot dynamics open-loop system described in step 1 is: Among them, q, They represent the position information, velocity information and acceleration information of the rotary joint of the robot system respectively; M0(q) represents the nominal value of the inertia matrix of the robot system, and ΔM(q) represents the uncertainty value of the inertia modeling of the robot system; represents the nominal value of the centrifugal-Coriolis force matrix, represents the uncertainty value of 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 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. A fault-tolerant controller design method applicable to a robot system according to claim 2, characterized in that: The control input vector for introducing actuator input saturation nonlinearity in step 2 is: Where τ(u) represents the control input vector that introduces the actuator input saturation nonlinearity, u represents the actuator input information; τ M represents 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.

4. A fault-tolerant controller design method applicable to a robot system according to claim 3, characterized in that: The improved preset performance function described in step 3 is: Where ρ(t) represents the improved preset performance function; ρ0, ρ ∞ , T and l are the function performance parameters 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, and exp() represents the natural exponential function.

5. A fault-tolerant controller design method applicable to a robot system according to claim 4, characterized in that: The terminal sliding surface in step 4 is: s=ε2+K1Sig r (ε1)+K2W p (ε1) Sig r (ε1)=[sign(ε 11 )e 11 r ,…,sign(e 1i )e 1i r …,sign(e 1n )e 1n r ] T W p (ε1)=[w p (e 11 ),…,w p (e 1i ),…,w p (e 1n )] T 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 transformed, ε 1i is the i-th item in the converted position error vector ε1; ε2 is the position vector consisting of the error vector and its derivative, ρ is the preset performance function designed, is the derivative of ρ; 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 | | is the absolute value, ln() represents the natural logarithm symbol with constant e as the base, diag() represents the diagonal matrix construction function; δ is the positive constant to be designed.

6. A fault-tolerant controller design method applicable to a robot system according to claim 5, characterized in that: The fixed time preset performance fault-tolerant controller in step 4 is: in=in a +in b you a =τ0+τ1+τ2 The actuator input information u consists of two parts: the first item of control input u 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; u0 and u1 are defined as: u1=Ae-q d +K1Sig r (ε1)+K2W p (ε1) M r (ε1)=diag(r|ε 11 | r-1 ,…,r|e 1i | r-1 ,…,r|e 1n | r-1 ) F p (ε1)=diag(f p (e 11 ),…,f p (e 1i ),…,f p (e 1n )) 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.

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