Active Fault-Tolerant Control Method for Coupling Error Sliding Mode of Robot System

Abstract

The present invention discloses a coupled error sliding mode active fault-tolerant control method for a robot system, comprising the following steps: obtaining an estimated value of an actuator fault through a non-linear observer; setting different weight values for the position error of each joint of the robot system and adding them to form a weighted position error; obtaining the coupled position error of each joint by adding the integral of the weighted position error and the position error; designing a non-singular fast terminal sliding mode surface through the coupled position error to obtain an equivalent control law and a super-twisting switching control law; compensating for the actuator fault according to the fault-tolerant control law composed of the estimated value of the actuator fault, the equivalent control law and the super-twisting switching control law, and enabling the joint position to accurately track the desired trajectory within a finite time. The present invention effectively solves the adverse effect of the actuator fault on the position tracking effect during the control process, ensures the stability, safety and reliability of the system, and thus has extremely strong practicability.

Description

Technical Field

[0001] The present invention relates to the technical field of fault-tolerant control of robot systems, and more particularly, to a coupled error sliding mode active fault-tolerant control method for robot systems. Background Art

[0002] Robot systems have been widely used in fields such as aerospace exploration, automated industrial production, medical treatment, and daily life, greatly improving work efficiency and reducing the labor intensity of personnel. However, in actual applications, due to factors such as long service life, complex working environments, and improper human operations, robots are very prone to actuator failures, posing great challenges to system stability and tracking performance.

[0003] To compensate for actuator failures in robot systems, fault-tolerant control has been widely studied to improve the control performance of faulty robot systems and maintain system stability. Compared with passive fault tolerance, active fault tolerance has a higher tolerance for different faults and better controller operating performance when there is no fault.

[0004] Xie Shuai et al. [Xie Shuai, Chen Li, Yu Xiaoyan. Sliding Mode Fault-Tolerant Control of Space Robots Based on State Observers [J]. Modular Machine Tools & Automatic Manufacturing Techniques, 2022(06): 110-113+118] proposed a neural network integral sliding mode active fault-tolerant control scheme, which approximates actuator failures through neural network technology and then designs an integral sliding mode controller to compensate for actuator failures. However, in actual applications, the degree of faults suffered by each joint of the robot may be different, and this factor was not considered in this literature, so it is difficult to be practically applied to robot systems. Summary of the Invention

[0005] The main object of the present invention is to provide a coupled error sliding mode active fault-tolerant control method, computer device, and computer-readable storage medium for robot systems to solve the technical problem that the existing active fault-tolerant control method is difficult to be practically applied to robot systems.

[0006] To achieve the above object, according to the first aspect of the present invention, there is provided a coupled error sliding mode active fault-tolerant control method for robot systems, and the technical solution is as follows:

[0007] The coupled error sliding mode active fault-tolerant control method for robot systems includes the following steps:

[0008] Obtain an estimated value of the actuator failure through a non-linear observer;

[0009] Set different weight values for the position error of each joint of the robot system and add them to form a weighted position error; add the integral of the weighted position error to the position error to obtain the coupled position error of each joint;

[0010] Design a non-singular fast terminal sliding mode surface through the coupling position error to obtain the equivalent control law and the super-twisting switching control law;

[0011] According to the fault-tolerant control law composed of the estimated value of the actuator fault, the equivalent control law and the super-twisting switching control law, compensate for the actuator fault and enable the joint position to accurately track the desired trajectory within a finite time.

[0012] To achieve the above object, according to the second aspect of the present invention, there is provided a computer device, and the technical solution is as follows:

[0013] A computer device, characterized in that: the computer device includes a memory and a processor; the memory is used to store a computer program; the processor is used to execute the computer program and implement the coupling error sliding mode active fault-tolerant control method of the robot system described in the first aspect above when executing the computer program.

[0014] To achieve the above object, according to the third aspect of the present invention, there is provided a computer-readable storage medium, and the technical solution is as follows:

[0015] A computer-readable storage medium, characterized in that: a computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, the coupling error sliding mode active fault-tolerant control method of the robot system described in the first aspect above is implemented.

[0016] The present invention fully considers that the degree of faults suffered by each joint of the robot may be different, assigns weight values to the position errors of each joint, and uses the coupling position error to design the fault-tolerant control law, which can further achieve precise compensation for the actuator faults suffered by each joint, so that the position tracking error of the system quickly converges within a finite time, improves the position trajectory tracking performance of the robot system, and effectively suppresses the chattering phenomenon in the fault-tolerant control law. Thus, the present invention effectively solves the adverse effects of actuator faults on the position tracking effect during the control process, ensures the stability, safety and reliability of the system, and therefore has extremely strong practicability.

[0017] The following further describes the present invention in conjunction with the drawings and specific embodiments. The additional aspects and advantages of the present invention will be partially given in the following description, partially become apparent from the following description, or be understood through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The drawings constituting a part of the present invention are used to assist in understanding the present invention. The content provided in the drawings and the related descriptions in the present invention can be used to explain the present invention, but do not constitute an improper limitation to the present invention. In the drawings:

[0019] Figure 1 It is a schematic flow chart of the coupled error sliding mode active fault-tolerant control method for the robot system of the present invention.

[0020] Figure 2 It is a schematic block diagram of an embodiment of the computer device of the present invention. Detailed implementation manners

[0021] The present invention will be clearly and completely described below with reference to the accompanying drawings. Those of ordinary skill in the art will be able to implement the present invention based on these descriptions. Before describing the present invention with reference to the accompanying drawings, it should be particularly noted that:

[0022] The technical solutions and technical features provided in each part including the following description of the present invention can be combined with each other without conflict.

[0023] In addition, the embodiments of the present invention involved in the following description are usually only part of the embodiments of the present invention, rather than all of the embodiments. Therefore, all other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0024] Regarding the terms and units in the present invention. The terms "including", "having" and any variations thereof in the specification, claims and relevant parts of the present invention are intended to cover non-exclusive inclusion.

[0025] Figure 1 It is a schematic flow chart of an embodiment of the coupled error sliding mode active fault-tolerant control method for the robot system of the present invention. Figure 1 Among them, the "+" represents the addition operation symbol, the "-" represents the subtraction operation symbol, the "∫" represents the integral operation symbol, represents the matrix operation symbol.

[0026] Such as Figure 1 shown, the coupled error sliding mode active fault-tolerant control method for the robot system includes the following steps:

[0027] (1) Establish a dynamic model of an n-degree-of-freedom robot system affected by deviation and actuator faults with partial loss of effectiveness;

[0028] (2) Obtain an estimated value of the actuator fault through a non-linear observer;

[0029] (3) Set different weight values for the position error of each joint of the robot system and sum them to form a weighted position error; use the integral of the weighted position error plus the position error to obtain the coupled position error of each joint;

[0030] (4) Design a non-singular fast terminal sliding mode surface through the coupling position error, and obtain the equivalent control law and the super-twisting switching control law;

[0031] (5) Compensate for the actuator fault according to the fault-tolerant control law composed of the estimated value of the actuator fault, the equivalent control law and the super-twisting switching control law, and enable the joint position to accurately track the desired trajectory within a finite time.

[0032] The model is:

[0033]

[0034] The non-linear observer is:

[0035]

[0036] The joint position error e is:

[0037] e = q - q d Equation (3)

[0038] The weighted position error is:

[0039]

[0040] The coupling position error S is:

[0041]

[0042] The non-singular fast terminal sliding mode surface σ is:

[0043]

[0044] The equivalent control law τ eq is:

[0045]

[0046] The super-twisting switching control law τ st is:

[0047]

[0048] The fault-tolerant control law τ ∈ R n×1 is:

[0049]

[0050] In the above equations (1)-(9):

[0051] q is the joint position of the robot, q ∈ R n×1 ;

[0052] is the angular velocity of the robot, is the first derivative of q;

[0053] is the angular acceleration of the robot, is the second derivative of q;

[0054] R is the real number field; n is the number of joints of the robot system;

[0055] M(q) is the positive definite inertia matrix of the robot, M(q) ∈ R n×n ;

[0056] is the Coriolis force and centrifugal force terms of the robot,

[0057] G(q) is the gravity term of the robot, G(q) ∈ R n×1 ;

[0058] f is the actuator fault of the robot system, f = (I - δ)τ - Δτ f ;

[0059] I is the identity matrix, I = diag{1, 1, …, 1}, diag{...} is the diagonal matrix;

[0060] δ is the gain matrix of the actuator effectiveness loss situation, δ = diag[δ 1 , δ 2 , …, δ n , δ i ∈(0, 1) (i = 1, 2, …, n) is the effectiveness of the i-th actuator;

[0061] Δτ f is the bias fault of the robot system;

[0062] is the estimated value of the actuator fault, derived from Equation (2);

[0063] Z is the auxiliary variable of the nonlinear observer; is the first derivative of Z;

[0064] W(q) is the positive definite matrix, W(q) = H -1 M -1 (q), H is the invertible diagonal matrix, H -1 and M -1 (q) represent the inverse matrices corresponding to H and M(q) respectively;

[0065]

[0066] qd represents the desired joint position; is the desired joint angular acceleration, which is the second derivative of q d ;

[0067] Γ is the weight coefficient matrix, ω i is the weight coefficient of the i-th joint position error;

[0068] and α are coupling coefficients, both being constants greater than 0;

[0069] Λ is the exponent in the coupling position error, Λ = diag{λ 1 , λ 2 , …, λ n}, λ i is a sub-element in Λ, 0 < λ i < 1;

[0070] and Λ satisfy denotes the absolute value of, is the sign function with respect to ;

[0071] is the first derivative of S; is the first derivative of;

[0072] β 1 and β 2 are positive constants;

[0073] ψ and ξ are the exponents in the non-singular fast terminal sliding mode surface, ψ = diag{ψ 1 , ψ 2 , …, ψ n}, ξ = diag{ξ 1 , ξ 2 , …, ξ n}, ψ i and ξ i are the sub-elements in ψ and ξ respectively, 1 < ξ i < 2, ψ i > ξ i ;

[0074] k 1 、k 2 are the switching control gains, satisfying is a positive constant;

[0075] is the product of k 2 and sign(σ), v is obtained by taking the The value obtained by integration.

[0076] The system stability and position tracking performance of the present invention are proved by the Lyapunov function as follows:

[0077] First, select the Lyapunov candidate function of the system as:

[0078]

[0079] Derive Equation A to get:

[0080]

[0081] Among them, is the second derivative of S; is the first derivative of σ;

[0082] Derive the second derivative of Equation (3) to obtain Combined with the above Equations (1)-(9), we can further obtain:

[0083]

[0084] Among them, represents the estimation error of the actuator fault, is usually bounded, that is, there exists represents the 2-norm of, and |σ| represents the absolute value of σ.

[0085] By comparing Equation B and Equation C, we can get:

[0086]

[0087] For the convenience of proof, write Equation D as a separate subsystem:

[0088]

[0089] Among them, k 1i and k 2i are respectively the sub-elements in the switching control gains k 1 and k 2

[0090] Next, define the Lyapunov function again:

[0091]

[0092] Among them, θ is a partial term in the first equation of Equation E, and its specific expression is ​Q is a positive definite symmetric matrix related to the switching control gain, and its specific expression is

[0093] Taking the derivative of equation F gives:

[0094]

[0095] where P is a positive definite symmetric matrix related to the switching control gain, and its specific expression is

[0096] Since the estimation error of the actuator fault is usually bounded, that is Then it can be further obtained that:

[0097]

[0098] where Since k 1 and k 2 satisfy Therefore, it can be known that is a positive definite symmetric matrix, so it can be obtained that indicating that the active fault-tolerant control method of the present invention can ensure the stability of the faulty robot system.

[0099] It can be further obtained that the time for the position tracking error of the robot system to reach convergence is:

[0100]

[0101] where λ max / min () represents the maximum / minimum eigenvalue, t ri represents the time when the coupled position error S i reaches the sliding mode surface σ i , t ei represents the time when the joint position error e i tends to 0, and V 2 (0) is the value of V 2 at t = 0.

[0102] Figure 2 This is a schematic block diagram of an embodiment of the computer device of the present invention.

[0103] As Figure 2 shown, the computer device includes a processor 120 and a memory 110, and the memory 110 stores a computer program 111. When the computer program 111 is executed by the processor 120, the computer device can execute the steps of the coupled error sliding mode active fault-tolerant control method of the robot system in the above method embodiment, and the specific implementation manner can be referred to the method embodiment, which will not be elaborated here.

[0104] The computer devices provided by the embodiments of the present invention may include, but are not limited to, smart phones, tablet computers, laptop computers, desktop computers, etc.

[0105] Among them, the processor 120 may include one or more processing cores, such as a 4-core processor, an 8-core processor, etc. The processor 120 may be implemented in at least one hardware form of DSP (Digital Signal Processing), FPGA (Field-Programmable Gate Array), and PLA (Programmable Logic Array). The processor 120 may also include a main processor and a coprocessor. The main processor is a processor for processing data in the wake state, also known as the CPU (Central Processing Unit); the coprocessor is a low-power processor for processing data in the standby state. In some embodiments, the processor 120 may be further integrated with a GPU (Graphics Processing Unit), and the GPU is responsible for rendering and drawing the content to be displayed on the display screen. In some embodiments, the processor 120 may further include an AI (Artificial Intelligence) processor, and the AI processor is used to process computational operations related to machine learning.

[0106] The memory 110 may include one or more computer-readable storage media, and the computer-readable storage media may be non-transitory. The memory 110 may further include high-speed random access memory and non-volatile memory, such as one or more disk storage devices and flash storage devices. In this embodiment, the memory 110 is at least used to store the following computer program 111. After the computer program is loaded and executed by the processor 120, it can implement the relevant steps of the coupled error sliding mode active fault-tolerant control method of the robot system disclosed in any of the foregoing embodiments. In addition, the resources stored in the memory 110 may further include an operating system 112 and data 113, etc., and the storage method may be temporary storage or permanent storage. Among them, the operating system 112 may include Windows, Unix, Linux, etc. The data 113 may include, but is not limited to, call data, hotspot data, etc.

[0107] In some embodiments, the computer device may further include a display screen 130, an input / output interface 140, a communication interface 150, a power supply 160, and a communication bus 170.

[0108] Those skilled in the art of the present technology can understand, Figure 2The structure shown does not constitute a limitation on the computer device, and may include more or fewer components than shown in the figure.

[0109] It can be understood that if the coupling error sliding mode active fault-tolerant control method of the robot system in the above embodiments is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and executes all or part of the steps of the methods in various embodiments of this application. The foregoing storage medium includes: USB flash drive, mobile hard disk, read-only memory (ROM), random access memory (RAM), electrically erasable programmable ROM, register, hard disk, removable disk, CD-ROM, magnetic disk, or optical disk, etc., all kinds of media that can store program codes.

[0110] Based on this, the embodiments of the present invention also provide a computer-readable storage medium. A computer program is stored on the computer-readable storage medium. When the computer program is executed by a processor, it implements the steps of the coupling error sliding mode active fault-tolerant control method of the robot system as described above. The specific implementation manner can refer to the method embodiments and will not be elaborated here.

[0111] The functions of the functional modules of the computer-readable storage medium described in the embodiments of the present invention can be specifically implemented according to the methods in the above method embodiments. The specific implementation process can refer to the relevant descriptions of the above method embodiments and will not be elaborated here.

[0112] The coupling error sliding mode active fault-tolerant control method, computer device, and storage medium provided by the embodiments of the present invention have been introduced in detail above. Each embodiment in the specification is described in a progressive manner. The key point of each embodiment is to illustrate the differences from other embodiments. The same or similar parts among the embodiments can be referred to each other.

[0113] Those skilled in the art of this technology can further realize that, combining the units and algorithm steps of each example described in the embodiments disclosed in this specification, they can be implemented by electronic hardware, computer software, or a combination of the two. To clearly illustrate the interchangeability of hardware and software, the components and steps of each example have been generally described according to functions in the above description. Whether these functions are executed in a hardware or software manner depends on the specific application and design constraints of the technical solution. Those skilled in the art of this technology can use different methods to implement the described functions for each specific application, but such implementation should not be considered to exceed the scope of this application.

[0114] It should be understood that the terms used in the specification of this application are only for the purpose of describing specific embodiments and are not intended to limit this application. As used in the specification of this application and the appended claims, unless the context clearly indicates otherwise, the singular forms "a", "an" and "the" are intended to include the plural forms.

[0115] It should also be understood that the term "and / or" used in the specification of this application and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes these combinations. It should be noted that in the specification of the present invention, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or system comprising a series of elements not only includes those elements, but also includes other elements not expressly listed, or also includes elements inherent to such process, method, article or system. Without further limitation, an element defined by the statement "comprising one..." does not exclude the presence of another identical element in the process, method, article or system comprising the element.

[0116] The serial numbers of the above embodiments of the present invention are only for description and do not represent the advantages or disadvantages of the embodiments. The above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art of this technology can easily think of various equivalent modifications or substitutions within the technical scope disclosed by the present invention, and these modifications or substitutions should all be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

[0117] The above has described the relevant content of the present invention. Specific examples are used in the specification of the present invention to elaborate on the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention. It should be pointed out that for those of ordinary skill in the art of this technology, without departing from the principle of the present invention, several improvements and modifications can be made to the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

Claims

1. Active fault-tolerant control method for coupling error of robot system by sliding mode, comprising the following steps: obtaining an estimated value of actuator fault through a non-linear observer; setting different weight values for the joint position error of the robot system and adding them to form a weighted position error; using the integral of the weighted position error plus the position error to obtain the coupling position error of each joint; designing a non-singular fast terminal sliding mode surface through the coupling position error to obtain an equivalent control law and a super-twisting switching control law; compensating for actuator faults according to the fault-tolerant control law composed of the estimated value of actuator fault, the equivalent control law and the super-twisting switching control law, and enabling the joint position to accurately track the desired trajectory within a finite time; wherein, the non-linear observer is: the joint position error is: e = q - q d the weighted position error is: the coupling position error is: the non-singular fast terminal sliding mode surface is: the equivalent control law is: the super-twisting switching control law is: Among them, Z is the auxiliary variable of the nonlinear observer; is the first derivative of Z; q ∈ R n×1 , and are the joint position, angular velocity, and angular acceleration of the robot respectively, R is the real number field, and n is the number of joints of the robot system; W(q) is a positive definite matrix, W(q) = H -1 M -1 (q), H is an invertible diagonal matrix, H -1 and M -1 (q) are the inverse matrices of H and M(q) respectively; is the Coriolis force and centrifugal force term of the robot, G(q) is the gravity term of the robot, G(q) ∈ R n×1 ; τ ∈ R n×1 is the fault-tolerant control law; f is the actuator fault of the robot system, f = (I - δ)τ - Δτ f ; is the estimated value of the actuator fault; q d represents the desired joint position; is the second derivative of q d ; is the weighted position error; is 's first derivative; e is the joint position error; Γ is the weight coefficient matrix, ω i is the weight coefficient of the i-th joint position error; S is the coupled position error; is the first derivative of S; and α are coupling coefficients, both are constants greater than 0; Λ is the exponent in the coupled position error, Λ = diag{λ 1 , λ 2 , …, λ n}, λ i is a sub-element in Λ, 0 < λ i < 1; represents 's absolute value, is the sign function of ; M(q) is the positive definite inertia matrix of the robot, M(q) ∈ R n×n ; σ is the non-singular fast terminal sliding mode surface; β 1 and β 2 are positive constants; ψ and ξ are the exponents in the non-singular fast terminal sliding mode surface, ψ = diag{ψ 1 , ψ 2 , …, ψ n}, ξ = diag{ξ 1 , ξ 2 ,…, ξ n}, ψ i and ξ i are sub - elements in ψ and ξ respectively, 1 < ξ i < 2, ψ i > ξ i ; τ eq is the equivalent control law; τ st is the super - twisting switching control law; k 1 , k 2 are the switching control gains, satisfying are positive constants; is the product of k 2 and sign(σ), and v is the value obtained by integrating .

2. The active fault-tolerant control method for coupling error of robot system by sliding mode according to claim 1, characterized in that: it further comprises the step of establishing a dynamic model of an n-degree-of-freedom robot system affected by actuator faults with deviation and partial loss of effectiveness, and the model is: where \(I\) is the identity matrix, \(I = diag\{1, 1, \cdots, 1\}\); \(\delta\) is the gain matrix of the actuator effectiveness loss, \(\delta = diag[\delta 1 , \delta 2 , \cdots, \delta n \), \(\delta i \in(0, 1)\) is the effectiveness of the \(i\)-th actuator, \(i\) is an integer between 1 and \(n\), \(diag\{\cdots\}\) is the diagonal matrix; \(\Delta\tau f \) is the deviation fault of the robot system.

3. The active fault-tolerant control method for coupling error of robot system by sliding mode according to claim 2, characterized in that: The fault-tolerant control law is as follows:

4. A computer device, characterized in that: the computer device comprises a memory and a processor; the memory is used for storing a computer program; the processor is used for executing the computer program and implementing the active fault-tolerant control method for coupling error of robot system by sliding mode according to any one of claims 1-3 when executing the computer program.

5. A computer-readable storage medium, characterized in that: a computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, the active fault-tolerant control method for coupling error of robot system by sliding mode according to any one of claims 1-3 is implemented.

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