A real-time fault monitoring and adaptive fixed-time fault-tolerant control method for a robot arm

Abstract

The application discloses a real-time fault monitoring and adaptive fixed-time fault-tolerant control method for a mechanical arm, which is applied to the field of mechanical arms and aims at the problem that current control methods of most mechanical arms are difficult to adapt to strict requirements of high precision, fast response and strong reliability in complex application scenarios and cannot quantize the severity of actuator faults in real time. First, a novel dynamic adjustment variable is designed to approximate an actuator LOE fault coefficient and compensate for the influence of faults on system operation. Second, an adaptive rate is designed to quickly and accurately estimate the upper bound of unknown nonlinearity of the system within a fixed time. On the basis of the designed dynamic adjustment variable and adaptive rate, an adaptive fixed-time fault-tolerant controller is designed in combination with a sliding mode control technology. The method can realize real-time fault monitoring and fast and high-precision fault-tolerant control of the mechanical arm.

Description

Technical Field

[0001] This invention belongs to the field of robotic arms, and specifically relates to a robotic arm control technology. Background Technology

[0002] As a core piece of equipment in automation and intelligent manufacturing, robotic arms have a rich application foundation and broad application prospects in various fields. In intelligent manufacturing, robotic arms can achieve high-precision and high-efficiency automated production, becoming a key tool for ensuring product quality and reducing labor costs. In the medical field, robotic arms-assisted surgery can improve surgical precision, reduce trauma, and promote the development of minimally invasive surgery. In the field of service robots, robotic arms can provide home services, rehabilitation training, and other services, effectively improving the quality of human life. In addition, robotic arms also play a crucial role in high-risk tasks such as space exploration and underwater operations. Regardless of the application scenario, stability, rapid response, and high-precision control are essential for robotic arms. However, robotic arms still face many technical challenges in practical applications, among which nonlinearity and actuator failure are two key issues. Because robotic arm systems are inherently nonlinear, their dynamic models contain complex coupling relationships and nonlinear characteristics, such as joint friction and parameter variations, which are often difficult or impossible to model accurately. These nonlinear factors affect the control accuracy and stability of the system. In addition, the actuator is the core component of the robotic arm. Its failure can lead to a decline in the performance of the robotic arm or even complete failure. However, when the robotic arm performs high-load or high-frequency motion tasks, it often faces the risk of actuator failure, such as loss of effectiveness (LOE) failure, offset failure or jamming failure. These failures can seriously threaten the stability and safety of the system. Therefore, fault tolerance is also indispensable for the robotic arm, especially in scenarios with high safety requirements.

[0003] Traditional robotic arm control techniques, including PID control, robust control, and model-based control strategies, exhibit certain limitations in practical applications. These methods are insufficient in terms of anti-interference capability, fault tolerance, flexibility, and dynamic response speed. They typically rely on accurate system models and preset control parameters, thus often performing poorly when faced with unknown nonlinearities or model uncertainties. When actuators fail, these methods also lack adaptive adjustment capabilities, potentially leading to significant performance degradation or even complete system failure. In highly dynamic task scenarios, traditional control methods struggle to simultaneously meet the requirements of fast response and high-precision control. Furthermore, to achieve faster convergence speeds or higher control accuracy, these methods often employ high-gain feedback, which can easily induce system oscillations, affecting the smoothness of robotic arm movements and increasing energy consumption. Furthermore, real-time monitoring of the health status and fault severity of robotic arm actuators allows operators to promptly understand the system's operating status and make appropriate arrangements. For example, if an operator discovers a serious fault in a robotic arm actuator, and the application scenario has high safety requirements, the equipment should be stopped immediately, and the actuator repaired or replaced. If the operator finds only a minor fault in the robotic arm actuator, and the controller's fault tolerance can largely compensate for its impact, and the application scenario has low safety requirements, the equipment can continue running for a certain period to save time. Many commonly used fault detection methods can only determine whether an actuator has malfunctioned, but cannot quantify the severity of the fault, and their real-time performance is also insufficient. Moreover, methods based on machine learning or deep learning require a large amount of fault data for training, which is difficult to obtain in practical applications.

[0004] In summary, most current robotic arm control methods struggle to meet the stringent requirements of high precision, rapid response, and strong reliability in complex application scenarios, and they also cannot quantify the severity of actuator failures in real time. Therefore, a novel robotic arm fault monitoring and fault-tolerant control method is urgently needed. This method should ensure rapid and high-precision motion control for systems with unknown nonlinearities, provide real-time feedback on the health status and fault severity of each actuator, and provide rapid fault tolerance after an actuator LOE (Logistic Expiration) failure occurs, thus ensuring the stability and reliability of the robotic arm. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes a real-time fault monitoring and adaptive fixed-time fault-tolerant control method for robotic arms, which can realize real-time fault monitoring and fast, high-precision fault-tolerant control of robotic arms.

[0006] The technical solution adopted in this invention is: a real-time fault monitoring and adaptive fixed-time fault-tolerant control method for robotic arms, comprising:

[0007] S1: Construct a Lagrangian dynamics model for an n-degree-of-freedom manipulator that considers partial actuator failures and unknown nonlinearities;

[0008] S2: Construct a non-singular fixed-time terminal sliding surface;

[0009] S3: Based on the sliding surface constructed in step S2, design an adaptive rate to estimate the upper bound of the unknown nonlinearity of the robotic arm within a fixed time.

[0010] S4: Design dynamic adjustment variables to approximate the failure coefficient of the actuator part;

[0011] S5: Based on the Lagrangian dynamics model of the robotic arm in step S1, the adaptive rate in step S3, and the dynamic adjustment variable in step S4, and combined with the sliding surface constructed in step S2, design an adaptive fixed-time fault-tolerant controller.

[0012] S6: Use the adaptive fixed-time fault-tolerant controller designed in step S5 to control the robotic arm with unknown nonlinearity and potential actuator failure.

[0013] The beneficial effects of this invention are as follows: First, this invention designs a novel dynamic adjustment variable to approximate the actuator LOE fault coefficient and compensate for the impact of faults on system operation. Simultaneously, this variable can be used to monitor the health status and fault severity of each actuator within the robotic arm in real time. Second, this invention designs an adaptive rate to quickly and accurately estimate the upper bound of the unknown nonlinearity of the system within a fixed time period, thereby ensuring controller robustness while avoiding the use of overestimated control gain and corresponding chattering phenomena. Based on the designed dynamic adjustment variable and adaptive rate, this invention combines sliding mode control technology to design an adaptive fixed-time fault-tolerant controller, ensuring that for robotic arms with actuator LOE faults and unknown nonlinearities, high-precision motion control can be achieved within a fixed time period independent of the system's initial state, without requiring any prior information related to the unknown nonlinearity and actuator faults. The method of this invention has the following advantages:

[0014] (1) This invention designs a dynamically adjustable variable to approximate the LOE failure coefficient of the robotic arm actuator and compensate for the impact of failure on the system. This variable can monitor the failure level of the actuator in real time, allowing operators to understand the health status of the equipment in a timely manner.

[0015] (2) The present invention designs an adaptive rate to estimate the upper bound of the unknown nonlinearity in the system, thereby ensuring the robustness of the controller while avoiding the use of overestimated control gain and corresponding chattering, and reducing energy consumption to a certain extent.

[0016] (3) The fault-tolerant controller designed in this invention can ensure that a robotic arm with unknown nonlinearity and actuator LOE fault can achieve high-precision following motion control within a fixed time that is independent of the initial state of the system, and does not require any prior information about unknown nonlinearity and actuator fault. Attached Figure Description

[0017] Figure 1 This is a flowchart of the method of the present invention;

[0018] Figure 2 This is a block diagram of the architecture of the method of the present invention;

[0019] Figure 3 This is a schematic diagram of the structure of the robotic arm in an embodiment of the present invention;

[0020] Figure 4 This refers to the results of the robotic arm's following motion under the influence of a fault in this embodiment of the invention, as well as the results of dynamically adjusting variables to approximate the actuator failure coefficient.

[0021] Among them, (a) is the actual trajectory and ideal trajectory of joints Q1-Q3, (b) is the position following error of joints Q1-Q3, and (c) is the approximation result of the actuator failure coefficient of joints Q1-Q3;

[0022] Figure 5 The following are the following results of the robotic arm following different initial system states in the embodiments of the present invention;

[0023] Where (a) represents the trajectory of joints Q1-Q3 under different initial states, and (b) represents the following error of joints Q1-Q3 under different initial states. Detailed Implementation

[0024] To facilitate understanding of the technical content of this invention by those skilled in the art, the following description, in conjunction with the accompanying drawings, further illustrates the invention.

[0025] This invention aims to design a fault monitoring and fault-tolerant control method to ensure fast and high-precision motion control even for robotic arms with unknown nonlinearities and actuator LOE (Loop Error of Effort) faults, with the following error converging to a zero neighborhood within a fixed time independent of the system's initial state. A key innovation of this invention is the design of a dynamically adjustable variable to approximate the actuator LOE fault coefficient. This variable is not only used in controller design to compensate for the adverse effects of faults on system operation, but also allows for real-time monitoring of the failure level of each actuator within the robotic arm. This enables operators to promptly understand the equipment's health status and make appropriate subsequent work arrangements, which is highly valuable in practical applications. Another prominent feature of this invention is the design of an adaptive rate to estimate the upper bound of the unknown nonlinearities in the system, thereby ensuring the robustness of the controller and avoiding the use of overestimated gain, thus preventing chattering phenomena easily caused by high gain. Based on the designed dynamically adjustable variable and adaptive rate, this invention combines fixed-time control and sliding mode control techniques to design an adaptive fixed-time fault-tolerant controller to achieve the above objectives.

[0026] like Figure 1 As shown, the real-time fault monitoring and adaptive fixed-time fault-tolerant control method for robotic arms proposed in this invention includes the following steps:

[0027] S1: Construct a Lagrangian dynamics model for an n-degree-of-freedom manipulator that considers actuator LOE failures and unknown nonlinearities.

[0028] Without considering the aforementioned adverse factors, the basic Lagrangian dynamics model of an n-DOF robotic arm is as follows:

[0029]

[0030] in These represent the angular position, velocity, and acceleration vectors of the joint, respectively. Represents the set of real numbers. It is an inertial matrix, and it is positive definite and symmetric. G(q) is the centripetal force and Coriolis force matrix, and G(q) is the gravity vector. It is the driving torque.

[0031] Robotic arms are generally affected by friction during movement, and it is often difficult or impossible to accurately model their nonlinear characteristics. Furthermore, due to the complex dynamic equations involved in robotic arms, model parameters are often difficult to obtain accurately, or physical parameters change in real time during system operation. These factors introduce model uncertainties. This invention collectively refers to these adverse factors as unknown nonlinearities and constructs the following robotic arm dynamic model considering the existence of actuator LOE faults and unknown nonlinearities:

[0032]

[0033] in Let Δ be the friction force vector, and Δ be the model uncertainty, which can be expressed as: Where △M, △C, and △G are the differences between the corresponding real and nominal matrices. Definition And assume d(t) and its derivative It is bounded, that is, it exists. and in and It is an unknown constant. Additionally, Ω = diag{ρ i} (i = 1, ..., n) is the actuator LOE failure coefficient matrix, and ρ i ≤ρ i ≤1, ρ i ∈(0,1). If ρ i =1 indicates that the actuator of the i-th joint of the robotic arm is not faulty, ρ i The smaller the size, the more serious the malfunction.

[0034] Those skilled in the art should note that the true matrix and the nominal matrix have the same form, only the parameters in the matrix are different. The parameters of the true matrix are the actual physical parameters of the system, which are unknown, while the parameters in the nominal matrix are the nominal parameters, which are known and are generally provided by the product manufacturer or measured by themselves.

[0035] S2: Construct the following non-singular fixed-time terminal sliding surface:

[0036]

[0037] Where s = [s1, ..., s n ] T , 0<α<1, β>1, e=[e1,…,e n ] T =q d -q is the following error vector for the joint angle position, q d It is an ideal joint angle position vector, and assumes q d and its derivative and All are bounded, that is, they exist. and Where ||·|| denotes the norm, and All are unknown constants. Function S α (e)=[s α (e1),…,s α (e n )] T , where sα (e i ) is defined as:

[0038]

[0039] Where δ is a very small constant, which is taken as 0.01 in this embodiment. In practical applications, it can be taken as needed. Function Sig β (e)=[sig β (e1),…,sig β (e n )] T , and sig β (e i ) = sgn(e i )|e i | β V1 and V2 are two positive definite parameter matrices, specifically defined as follows:

[0040]

[0041] Differentiating the sliding surface s and substituting model (2) into it, we get:

[0042]

[0043] Where Θ=M -1 (F+Δ)=M -1 d(t) is defined as the unknown nonlinearity of the system, and Θ=[θ1,…,θ n ] T , and H β (e) is the function Sig β The matrix form of the derivative of (e), F α (e) is a function S α The matrix form of the derivative of (e) is defined as follows:

[0044]

[0045] in

[0046]

[0047] S3: Design Adaptability Used to estimate unknown nonlinear θ i upper bound r i , where θ i It is the i-th element of vector Θ in equation (6), with an upper bound r. i It is an unknown constant, and |θ| i |≤r i Adaptive rate Designed as follows:

[0048]

[0049] in and The design parameters are positive, and q > 1. The estimation error is defined as...

[0050] S4: Design a dynamic adjustment variable to approximate the actuator LOE failure coefficient ρ i First, design the following nominal controller:

[0051]

[0052] where tanh(s)=[tanh(s1),…,tanh(s n )] T , And there are 0 <p<1。A s and B s The two positive definite parameter matrices are as follows:

[0053]

[0054] in, and All are positive design parameters. Define the inverse of matrix M as:

[0055]

[0056] Let M be a matrix -1 The elements in the array are i = 1, 2, ..., n, j = 1, 2, ..., m;

[0057] The dynamic adjustment variable is designed as follows:

[0058]

[0059] in and The design parameters are positive. The approximation error is defined as... Now regarding the error The convergence of the function is theoretically analyzed by defining the Lyapunov function as follows:

[0060]

[0061] According to equation (6), we can obtain:

[0062]

[0063] Differentiating V1 and substituting equation (15) into it, we get:

[0064]

[0065] According to -r i tanh(s i )s i ≤0.2785r i -r i |s i |and r i ≥|θ i Equation (16) can be written as:

[0066]

[0067] Through some calculations, the following inequality holds:

[0068]

[0069]

[0070] in Substituting (18) and (19) into (17) and combining them with Young's inequality, we get:

[0071]

[0072] in

[0073]

[0074] According to Lyapunov's stability theorem, the function V1 is ultimately uniformly bounded (UUB), i.e., V1(t) ≤ η1 / χ, t→∞. Therefore, the sliding surface s can be obtained. i Approximation error of dynamically adjusted variables Both are bounded, and Accordingly, it can be known E j and (i,j=1,…,n) are all bounded. Therefore, there exists an unknown constant that... For an unknown constant, it is used to indicate the existence of an unknown constant. satisfy Right now This variable is bounded.

[0075] S5: Based on the robotic arm dynamics model and adaptive rate obtained in the preceding steps and dynamic adjustment variables Combining sliding mode control technology, the following adaptive fixed-time fault-tolerant controller is designed:

[0076]

[0077] The definition of E is shown in equation (10). It is an estimate of matrix Ω, and the estimation error is defined as... The architecture block diagram of the method of this invention is as follows: Figure 2 As shown. The following motion error and adaptive rate r of the robotic arm using the designed controller (22) are now analyzed. i The convergence of the estimation error is theoretically analyzed by defining the Lyapunov function as follows:

[0078]

[0079] Taking the derivative with respect to V2, we get:

[0080]

[0081] Will Substituting into equation (24), we get:

[0082]

[0083] Through some calculations, the following inequality holds:

[0084]

[0085] Substituting equations (26) and (18) into equation (25), and combining them with Young's inequality, we obtain:

[0086]

[0087] in Simplifying equation (27) yields:

[0088]

[0089] in

[0090]

[0091] According to Lemma 1, V2 will converge to the following region:

[0092]

[0093] Where 0 < φ < 1, the convergence time T1 satisfies:

[0094]

[0095] Lemma 1 is defined as:

[0096] For the system If there exists a continuous radially unbounded function satisfy:

[0097]

[0098] in, This indicates that the independent variable x of the function V(x) is an n-dimensional constant, and the value of the function V(x) is a constant greater than or equal to 0. Let be the set of real numbers greater than 0, where a>0, b>0, 0<α<1, β>1, and 0<η<∞ are all constants. Then the system... The origin is stable over a fixed actual time, and

[0099]

[0100] Where 0 < φ < 1 ​​is a constant. The convergence time satisfies:

[0101]

[0102] According to the definition of function V2, the sliding surface s i and adaptive rate estimation error k i It will be at time It converges inward to the corresponding neighborhood of zero. Define the following constant:

[0103]

[0104] It can be seen that after t≥T1, |s i |≤ε i And e i s i ≤ε i |e i |, if in this stage|e i |≥δ, then s i satisfy:

[0105]

[0106] Multiply e by equation (36) i We can obtain:

[0107]

[0108] Define Lyapunov functions Differentiating it and substituting equation (37) into it, we get:

[0109]

[0110] According to Lemma 1, the following error e i It will converge to the following region:

[0111]

[0112] Where 0 < λ < 1. The convergence time satisfies:

[0113]

[0114] Based on the above analysis, for any initial system state, the robotic arm's following motion error e i converged to The time satisfies T≤T m =T max1 +T max2 The time limit T here m This is the most conservative estimate; the actual convergence time may be longer than T. m Much smaller.

[0115] S6: The designed adaptive fixed-time fault-tolerant controller is used to control a robotic arm with unknown nonlinearity and potential actuator LOE faults.

[0116] This invention utilizes the Quanser QArm robotic arm as the controlled object for experimental verification. The robotic arm consists of four joints (Q1-Q4), and its structural diagram is shown below. Figure 3 As shown. This invention only considers the motion of joints Q1, Q2, and Q3, and their ideal angular motion trajectories are all set to 0.5sin(2πt / 15) rad. Furthermore, at the 12th second, the efficiency coefficient of actuator Q1 is set to ρ1 = 0.4 to simulate an actuator LOE failure; at the 26th second, a failure of ρ2 = 0.6 is set for actuator Q2; and at the 35th second, a failure of ρ3 = 0.75 is set for actuator Q3.

[0117] like Figure 4 In the middle (a), the actual trajectory and ideal trajectory of joints Q1-Q3 are shown, as follows: Figure 4 In (b), the position following error of joints Q1-Q3 is shown. Figure 4 (c) shows the approximation results of the failure coefficients of joints Q1-Q3. It can be seen that during the overall operation of the robotic arm, joints Q1-Q3 consistently maintain a high level of tracking accuracy. After the sequential occurrence of actuator LOE failures at each joint, the corresponding dynamic adjustment variables promptly approximate the failure coefficients, thereby compensating for the impact of the failures on system operation and achieving rapid and effective fault tolerance. This ensures that the motion control effect of the robotic arm after actuator failure is almost identical to that before the failure. Furthermore, by monitoring the dynamic adjustment variables... It is possible to monitor the failure status of joints Q1-Q3 in real time, which is important. Figure 2 This is also illustrated in the diagram, such as Figure 2As shown, this embodiment uses three joints as an example for illustration. In actual applications, more joints may be designed. Figure 2 The ellipsis in the text can also display the actuator failure coefficients for more joints.

[0118] Furthermore, experiments were conducted with the robotic arm joints Q1-Q3 in three different initial positions to verify that the control effect of the designed method is independent of the system's initial state. Initial state 1 was Q1(0) = Q2(0) = Q3(0) = 0.1 rad; initial state 2 was Q1(0) = Q2(0) = Q3(0) = 0 rad; and initial state 3 was Q1(0) = Q2(0) = Q3(0) = -0.1 rad. Figure 5 In Figure (a), the trajectories of joints Q1-Q3 under different initial states are shown. Figure 5 Figure (b) shows the following error of joints Q1-Q3 under different initial states. It can be seen that even under different initial system states, joints Q1-Q3 converge to a consistent following effect within a fixed time. The time indicated in the figure is the upper bound T calculated when λ = φ = 0.9. m .

[0119] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

Claims

1. A real-time fault monitoring and adaptive fixed-time fault-tolerant control method for robotic arms, characterized in that, include: S1: The design takes into account the possibility of actuator partial failure and unknown nonlinearities. The Lagrangian dynamics model of the robotic arm with degrees of freedom; the Lagrangian dynamics model of the robotic arm described in step S1 is expressed as: ； in, It is the driving torque. It is the inertia matrix. G(q) is the centripetal force and Coriolis force matrix, and G(q) is the gravity vector. It is the actuator LOE fault coefficient matrix. Let the friction force vector be... These represent the angular position, velocity, and acceleration vectors of the joint, respectively. It is the model uncertainty, expressed as , The difference between the true inertia matrix and the nominal inertia matrix. The difference between the actual centripetal force and Coriolis force matrices and the nominal centripetal force and Coriolis force matrices. It is the difference between the actual gravity vector and the nominal gravity vector; S2: Construct a non-singular fixed-time terminal sliding surface; the sliding surface constructed in step S2 is represented as: ； in, , Indicates the first One sliding surface , , It is the following error vector of the joint angle position. , It is the ideal joint angle position vector. and They are two positive definite diagonal parameter matrices. , , It is a very small constant. ,and ; S3: Based on the sliding surface constructed in step S2, an adaptive rate is designed to estimate the upper bound of the unknown nonlinearity of the robotic arm within a fixed time period; the adaptive rate in step S3 is expressed as: ； in, , and The design parameters are positive, and have , Let be the upper bound of the unknown nonlinearity of the robotic arm. For adaptive rate, for The derivative; S4: Design a dynamic adjustment variable to approximate the failure coefficient of the actuator; the dynamic adjustment variable in step S4 is expressed as: ； in, For matrix The elements in and Positive design parameters The failure coefficient of the actuator section. As a dynamically adjustable variable, for The derivative of For the first The nominal controller corresponding to each joint; S5: Based on the Lagrangian dynamics model of the robotic arm in step S1, the adaptive rate in step S3, and the dynamic adjustment variable in step S4, combined with the sliding surface constructed in step S2, design an adaptive fixed-time fault-tolerant controller; the adaptive fixed-time fault-tolerant controller in step S5 is expressed as: ； in, For nominal controller, ; S6: Use the adaptive fixed-time fault-tolerant controller designed in step S5 to control the robotic arm with unknown nonlinearity and potential actuator failure.

2. The real-time fault monitoring and adaptive fixed-time fault-tolerant control method for robotic arms according to claim 1, characterized in that, The nominal controller is represented as: ； in, , It is a function The matrix form of the derivative, It is a function The matrix form of the derivative, , And there are , and It is a positive definite diagonal parameter matrix.

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