Mechanical arm system fixed time synchronous control method and system under actuator fault

Abstract

The invention discloses a fixed time synchronous control method and system for a mechanical arm system under actuator faults, and the method comprises the steps: constructing a fixed time sliding-mode observer according to the state information and control input information of the mechanical arm system; estimating total disturbance by adopting a fixed time sliding mode observer; the total disturbance comprises dynamic model parameter uncertainty and external disturbance; constructing a sliding mode variable based on a neural network sign function; on the basis of a sliding mode variable, total disturbance and a dynamic model of a mechanical arm system, actuator faults are considered, a fixed time synchronous controller is designed according to the Lyapunov stability principle, system errors and derivatives of the system errors can be converged at the same time, and the upper bound of stabilization time is irrelevant to an initial value; and the stability of the fixed time synchronous controller is verified, and if verification passes, the fixed time synchronous controller and the sliding mode variable based on the neural network sign function are applied to the mechanical arm system.

Description

Technical Field

[0001] The present invention relates to the technical field of robot arm control, and in particular to a method and system for fixed-time synchronization control of a robot arm system under actuator failure. Background Art

[0002] At present, the trajectory control problem of robotic arm systems has attracted widespread attention due to their wide application in modern industry. In practical engineering systems, robotic systems have high requirements for reliability, stability and safety. Therefore, it is very necessary to deal with disturbances, uncertainties, unknown frictions and even actuator failures. In addition, since actuator failures are sudden and uncertain, and the scale of failures is difficult to predict, actuator failures can be regarded as the most critical problem in the system. The lack of fault-tolerant control capabilities will lead to severe performance degradation and system instability, resulting in the failure of the control task. Fortunately, with the unremitting efforts of researchers, several fault-tolerant control schemes have been proposed to mitigate the impact of actuator failures and external disturbances on the performance of robotic arm systems.

[0003] Fault-tolerant control systems are divided into two approaches: active and passive. For passive fault-tolerant control approaches, robust control laws are designed to address actuator faults without the need to observe and estimate faults or reconstruct the controller. In contrast, active fault-tolerant control schemes aim to identify faults and then use the obtained diagnostic information to reconstruct the controller. Compared with passive fault-tolerant control, active fault-tolerant control shows better performance when the actuator faults are accurately estimated. Therefore, researchers have studied some active fault-tolerant control schemes for the reconstruction of actuator faults. It should be emphasized that most fault reconstruction methods cannot achieve reconstruction within a fixed time. In practical engineering, failure to implement fault reconstruction as soon as possible may lead to system performance degradation or even system instability. Therefore, further research is needed to consider fault-tolerant control with dynamic uncertainties and disturbances.

[0004] In addition, in the study of manipulator control systems, tracking rate is also an important performance indicator. The emergence of finite-time control meets the requirements for fast response performance of control systems. Although fixed-time control theory has made great progress, the convergence time of each state of the control system cannot be guaranteed to be the same. In certain specific operations, the present invention hopes that each state of the system can reach the specified position at the same time, such as the grasping task of the manipulator, the synchronous formation of the drone, etc. The fixed-time synchronous control method was proposed in , aiming to ensure the synchronous convergence of all state elements. However, few studies have focused on the fixed-time synchronous control of manipulator control systems with dynamic uncertainty and actuator failures. In addition, when the system state is far from equilibrium, the convergence rate of fixed-time synchronous control also needs to be further improved. Summary of the invention

[0005] In order to address the deficiencies of the prior art, the present invention provides a fixed-time synchronous control method and system for a robotic arm system under an actuator failure; the present invention is applicable to an uncertain robotic arm control system with actuator failures and external disturbances. When encountering an actuator failure, most fault reconstruction methods cannot achieve reconstruction as quickly as possible within a fixed time. In actual engineering, failure to implement fault reconstruction as quickly as possible may cause system performance degradation or even system instability. The present invention proposes a fast fixed-time synchronous control method based on observer technology, which can quickly reconstruct faults within a fixed time. In the face of the problem that the convergence time of each state of the control system cannot be guaranteed to be the same, the present invention proposes a control strategy that enables all system states to converge synchronously within a certain time.

[0006] On the one hand, a fixed time synchronization control method of a manipulator system under actuator failure is provided, comprising:

[0007] Establishing a dynamic model of the robotic arm system, wherein the dynamic model takes into account the existence of n joints in the robotic arm system, and also takes into account the uncertainty, external disturbances and actuator failures of the robotic arm system;

[0008] According to the state information and control input information of the robot system itself, a fixed-time sliding mode observer is constructed; the fixed-time sliding mode observer is used to estimate the total disturbance; the total disturbance includes: the uncertainty of the dynamic model parameters and the external disturbance;

[0009] Construct a sliding mode variable based on a neural network symbolic function; Based on the sliding mode variable, total disturbance and the dynamic model of the robotic arm system, considering the actuator failure, and according to the Lyapunov stability principle, design a fixed-time synchronous controller so that both the system error and the derivative of the system error can converge simultaneously, and the upper bound of the stable time is independent of the initial value;

[0010] The stability of the fixed-time synchronous controller is verified, and if the verification is passed, the fixed-time synchronous controller and the sliding mode variable based on the neural network symbolic function are applied to the robot arm system.

[0011] On the other hand, a fixed time synchronization control system for a manipulator system under actuator failure is provided, including:

[0012] An establishment module is configured to: establish a dynamic model of the robotic arm system, wherein the dynamic model takes into account the existence of n joints in the robotic arm system, and also takes into account the uncertainty, external disturbance and actuator failure of the robotic arm system;

[0013] The estimation module is configured to: construct a fixed-time sliding mode observer according to the state information and control input information of the robot system itself; use the fixed-time sliding mode observer to estimate the total disturbance; the total disturbance includes: the uncertainty of the dynamic model parameters and the external disturbance;

[0014] A design module is configured to: construct a sliding mode variable based on a neural network symbolic function; based on the sliding mode variable, the total disturbance and the dynamic model of the manipulator system, considering the actuator failure, and according to the Lyapunov stability principle, design a fixed time synchronization controller so that both the system error and the derivative of the system error can converge simultaneously, and the upper bound of the stable time is independent of the initial value;

[0015] A verification module is configured to verify the stability of the fixed-time synchronization controller, and if the verification is passed, apply the fixed-time synchronization controller and the sliding mode variable based on the neural network symbolic function to the robot arm system.

[0016] On the other hand, there is also provided an electronic device, comprising:

[0017] a memory for non-transitory storage of computer-readable instructions; and

[0018] a processor for executing the computer readable instructions,

[0019] When the computer-readable instructions are executed by the processor, the method described in the first aspect is executed.

[0020] On the other hand, a storage medium is provided, which non-temporarily stores computer-readable instructions, wherein when the non-temporary computer-readable instructions are executed by a computer, the method described in the first aspect is executed.

[0021] On the other hand, a computer program product is provided, comprising a computer program, wherein the computer program is used to implement the method described in the first aspect when running on one or more processors.

[0022] The above technical solution has the following advantages or beneficial effects:

[0023] (1) The present invention aims at the problem that most fault reconstruction methods cannot achieve reconstruction within a fixed time. In actual engineering, failure to implement fault reconstruction as soon as possible may lead to system performance degradation or even system instability. A fast fixed-time control method based on observer technology is designed to quickly reconstruct faults within a fixed time.

[0024] (2) In the current study, the convergence time of each state of the control system cannot be guaranteed to be the same. This paper proposes a new sliding mode variable based on the neural network symbol function. Different from the traditional fixed-time sliding mode variable, the proposed sliding mode variable can not only ensure a fast convergence rate, but also achieve synchronous convergence of the system state;

[0025] (3) The present invention proposes a fast fixed-time synchronous control method suitable for a robotic arm system with uncertain dynamics, actuator failures and external disturbances, in which all system states converge synchronously within a certain time. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0027] Figure 1 The figure is a flow chart of the method of the present invention.

[0028] FIG. 2( a ) is a diagram showing the trajectory tracking q of the fast fixed-time synchronous control of the present invention.

[0029] Fig. 2(b) Trajectory tracking with traditional fixed-time control.

[0030] FIG. 3( a ) shows the tracking error of the fast fixed-time synchronization control of the present invention.

[0031] Figure 3(b) shows the tracking error of traditional fixed-time control.

[0032] FIG. 4( a ) shows the average error of the fast fixed-time synchronization control of the present invention.

[0033] Figure 4(b) shows the average error of traditional fixed-time control.

[0034] FIG. 5( a ) is a control input of the fast fixed-time synchronization control of the present invention.

[0035] Figure 5(b) shows the control input of the traditional fixed-time control.

[0036] FIG6( a ) is a ratio of errors e1 and e2 of the fast fixed time synchronization control of the present invention.

[0037] Figure 6(b) shows the ratio of errors e1 and e2 in traditional fixed time control.

[0038] FIG. 7( a ) shows the system state of the first joint and its observed value based on the fast fixed-time synchronous control of the present invention.

[0039] FIG. 7( b ) shows the system state of the second joint and its observed value based on the fast fixed-time synchronous control of the present invention.

[0040] FIG8( a ) is a diagram showing the total system disturbance and its estimated value of the first joint based on the fast fixed-time synchronous control of the present invention;

[0041] FIG8( b ) shows the total system disturbance of the second joint and its estimated value based on the fast fixed-time synchronous control of the present invention.

[0042] Figure 9(a) shows the expected position trajectory q d Images of the control strategies in Article 1, Article 2, and the control strategy of the present invention are used respectively.

[0043] FIG9( b ) shows images of the joint position q using the control strategies in Article 1, Article 2, and the control strategy of the present invention.

[0044] FIG. 10( a ) shows the average error using the control strategy in Article 1 and the control strategy of the present invention.

[0045] FIG10( b ) shows the average error using the control strategy in Article 2 and the control strategy of the present invention.

[0046] Figure 11(a) shows the control input of the robotic arm system in Article 1.

[0047] Figure 11(b) shows the control input of the robotic arm system in Article 2.

[0048] FIG. 11( c ) is a control input of the robotic arm system of the present invention.

[0049] FIG. 12( a ) shows the state of the first joint system and its estimated value of the fast fixed-time synchronization control method of the present invention when a fault occurs.

[0050] FIG. 12( b ) shows the state of the second joint system and its estimated value of the fast fixed-time synchronization control method of the present invention when a fault occurs.

[0051] FIG. 13( a ) shows the total system disturbance and its estimated value of the first joint based on the fast fixed-time synchronous control of the present invention.

[0052] FIG. 13( b ) shows the total system disturbance of the second joint and its estimated value based on the fast fixed-time synchronous control of the present invention. DETAILED DESCRIPTION

[0053] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0054] Glossary: ​​Observer: A device or algorithm used in the field of automatic control to estimate the state of a system that cannot be directly measured. Specifically, the observer estimates the state signal of the system that cannot be directly measured based on the measurable output signal of the system (such as sensor data). In actual engineering applications, the state variables of many systems cannot be directly measured, so observers are needed to estimate these state variables.

[0055] Actuator failure: refers to the phenomenon in the control system that the actuator cannot execute the control command normally due to various reasons.

[0056] Fixed time synchronization: Fixed time synchronization control means that all errors of the system reach a stable state at the same time within a fixed time, and this synchronization time does not depend on the initial state of the system.

[0057] Embodiment 1: Figure 1 As shown, this embodiment provides a fixed time synchronization control method for a robotic arm system under actuator failure, including:

[0058] S101: Establishing a dynamic model of the robotic arm system, wherein the dynamic model takes into account the existence of n joints in the robotic arm system, and also takes into account the uncertainty, external disturbances and actuator failures of the robotic arm system;

[0059] S102: constructing a fixed-time sliding mode observer according to the state information and control input information of the robot system itself; using the fixed-time sliding mode observer, estimating the total disturbance; the total disturbance includes: the uncertainty of the dynamic model parameters and the external disturbance;

[0060] S103: Construct sliding mode variables based on neural network symbolic functions; Based on the sliding mode variables, total disturbance and dynamic model of the manipulator system, considering actuator failure, and according to the Lyapunov stability principle, design a fixed time synchronization controller so that both the system error and the derivative of the system error can converge simultaneously, and the upper bound of the stable time is independent of the initial value;

[0061] S104: Verify the stability of the fixed-time synchronization controller. If the stability is verified, apply the fixed-time synchronization controller and the sliding mode variable based on the neural network symbolic function to the robot arm system.

[0062] Furthermore, the S101: establishing a dynamic model of the robotic arm system, the dynamic model, taking into account the existence of n joints in the robotic arm system, and also taking into account the uncertainty, external disturbances and actuator failures of the robotic arm system, specifically includes:

[0063]

[0064] in, represents the generalized position, velocity, and acceleration. represents the inertia matrix, The matrix representing the Coriolis force and centrifugal torque, It's the force of gravity. is the friction effect, F=diag{f1,f2,...,f n} is the friction coefficient, f dis Unknown external disturbances, Represents the applied torque input.

[0065] When an actuator fault occurs, the control torque u is modeled as:

[0066] u=u nom +u f (2)

[0067] in, represents the command torque generated by the designed controller, A vector representing unknown actuator faults;

[0068] In addition, due to aging and wear, the parameters of the system cannot be accurately obtained in advance, and the friction and the disturbance f dis Therefore, the dynamic model formula (1) of the robot system is rewritten as:

[0069]

[0070] Among them, B n (q) = B(q) - ΔB(q), and G n (q) = G(q) - ΔG(q) and is the sum of the uncertainties.

[0071] Further, the S102: construct a fixed-time sliding mode observer according to the state information and control input information of the robot system itself; use the fixed-time sliding mode observer to estimate the total disturbance; the total disturbance includes: the uncertainty of the dynamic model parameters and the external disturbance, specifically including: the fixed time means that the system state will converge to the equilibrium point within a finite time starting from any initial condition, and this convergence time is consistent and bounded;

[0072] Introducing a state variable vector Then the dynamic model formula (3) is transformed into:

[0073]

[0074] in, τ=u nom as well as

[0075] Assume that the total disturbance d total (t) is a differentiable unknown signal, and the time derivative of the total disturbance is Existence constant satisfy

[0076] Next, a fixed-time sliding mode observer is constructed to estimate the total disturbance d total (t). First, define a new auxiliary variable for: Formula (5); where λ1 is a positive constant.

[0077] Considering the dynamic equation (4), we get the following results:

[0078]

[0079] in Then, the total disturbance d in formula (6) is total (t) is considered as an extended state And formula (6) can be expressed as:

[0080]

[0081] where h(t) is d total The time first derivative of (t).

[0082] Finally, the fixed-time sliding mode observer is designed as follows:

[0083]

[0084] in and and System status and disturbance The observer state, functions Φ1 and Φ2 are designed as follows:

[0085]

[0086] Among them, h1, g1, l1 and p1 are four positive odd integers, and h1>g1 and l1 <p1,k i >0 is the observer gain, i=1,2,...,6, and

[0087] Combining equations (7) and (8), we obtain the following dynamic equation of the observer error:

[0088]

[0089] Considering the robot arm system (3), the proposed observer (8) ensures that the observer error (10) converges to zero in a finite or fixed time, provided that Observer Error The origin can be reached after a steady-state time, which is:

[0090]

[0091] in, and (h1+g1) / 2g1>1 and 0<(l1+p1) / 2p1<1.

[0092] Infer will be reached in a fixed time, and the steady-state time can be estimated as:

[0093]

[0094] Through the above analysis, it can be concluded that the observer state and After a finite / fixed time, it converges to zero. The observer law formula (8) approximates the total disturbance d in a fixed time. total (t).

[0095] Further, the S103: constructing a sliding mode variable based on a neural network symbolic function; based on the sliding mode variable, the total disturbance and the dynamic model of the robotic arm system, considering the actuator failure, and according to the Lyapunov stability principle, designing a fixed time synchronization controller so that both the system error and the derivative of the system error can converge simultaneously, and the upper bound of the stable time is independent of the initial value, specifically including:

[0096] S103-1: Construct fixed-time synchronous stable system theory; S103-2: Construct fixed-time synchronous control strategy based on fixed-time synchronous stable system theory.

[0097] Furthermore, the S103-1: constructing a fixed time synchronous stable system theory includes:

[0098] For the following nonlinear system:

[0099]

[0100] Among them, α0>0 and β0>0 are two scalars, h0>0, g0>0, l0>0 and p0>0 are odd integers and satisfy h0>g0 and p0>l0. Then the equilibrium point of the system is fixed-time stable and the steady-state time is bounded to:

[0101]

[0102] Furthermore, the S103-2: constructing a fixed time synchronization control strategy based on the fixed time synchronization stable system theory includes:

[0103] Define the trajectory tracking error as e = qq d , where q d is the expected trajectory.

[0104] Introduced neural network symbolic function:

[0105] sig n (z) α =||z|| α sign n (z) (15)

[0106] sig c (z) α =[|z1| α sign c (z1),…,|z n | α sign c (z n )] T (16)

[0107] Where α is a positive constant. Neural network symbol function sign n and the classic symbolic function sign c They are defined as follows:

[0108]

[0109] in

[0110]

[0111] Where i=1,2,...,n.

[0112] Based on the introduced neural network symbolic function formula (15) and the fast fixed time stable system formula (13), a new sliding mode variable s is constructed. * , expressed as:

[0113]

[0114] Among them, α1 and β1 are positive constants, h2, g2, l2 and p2 are positive odd numbers, and h2>g2 and l2 <p2。

[0115] Then, the fixed time synchronization controller looks like this:

[0116] u nom = u nom_1 + u nom_2 (21)

[0117]

[0118] where α2, β2, and κ are positive constants, h3, g3, l3, and p3 are positive odd numbers, and h3 > g3 and l3 < p3 are satisfied, and the variables η1 and η2 satisfy:

[0119]

[0120] Due to the negative powers of η1 and η2 in the controller (23), when e = 0, a singularity problem will occur. To solve the singular value problem, the following modified sliding mode variables are designed:

[0121]

[0122] where the forms of the variables and their time derivatives are:

[0123]

[0124] and δ > 0 is a very small constant. The variable s * is:

[0125]

[0126] And the constants μ1 and μ2 are designed respectively as:

[0127]

[0128] And the fractional powers ρ1 ∈ (1, 4), l2 / p2 ∈ (0.5, 1), where h2, g2, l2, and p2 are positive odd numbers. It is worth emphasizing that by designing the modified sliding mode variables, the singularity problem can be eliminated, and the designed constants μ1 and μ2 ensure the continuity of the variables s c and . Based on the modified sliding mode variable (26), the controller can be designed as:

[0129] u nom = u nom_1 + u nom_2 (32)

[0130]

[0131] By applying the newly designed modified sliding mode variable formula (26) and the proposed controller formula (32), all states of the closed-loop system achieve fixed-time synchronous convergence, and the steady-state time is bounded and limited to:

[0132]

[0133] Furthermore, the S104: verifying the stability of the fixed time synchronization controller specifically includes:

[0134] Lyapunov candidate function V s for:

[0135] V s =s T s (36)

[0136] V s Taking the derivative with respect to time and using the controller (32), we obtain:

[0137]

[0138] If the variable s satisfies |s|>1, we can get When |s|≤1, we can get It can be concluded that all states will reach the surface of s = 0 within a certain time, and the convergence time of s is bounded as:

[0139]

[0140] When s=0 is reached, we can get:

[0141]

[0142] Then, choose another Lyapunov function as V e =e T e. V e The derivative is:

[0143]

[0144] If the variable s satisfies |s|>1, we can get When |s|≤1, we can get It can be concluded that the state e and will converge to zero in a certain amount of time:

[0145]

[0146] Assume that there are two error state variables e i and e j , their convergence times are T i and T j , and T j >T i In state e i and ej Before reaching the origin, The derivative of satisfies:

[0147]

[0148] Can get

[0149]

[0150] where c ij is a non-zero constant, since the variable e i At time T i A balance is reached, which results in:

[0151]

[0152] According to the above analysis, we can get e j (T i )=0. However, the variable e j The convergence time is T j Instead of T i , which contradicts the previous assumption. Therefore, all variables in state e(t) will reach equilibrium synchronously.

[0153] The present invention makes the following three contributions to the research on uncertain manipulator systems: (1) The present invention proposes a fixed-time sliding mode observer to achieve reconstruction of actuator failures and system uncertainties, where the observer error converges to the origin after a finite / fixed time. (2) A new sliding mode variable based on a neural network symbolic function is proposed. Different from the traditional fixed-time sliding mode variable, the proposed sliding mode variable can not only ensure a fast convergence rate, but also achieve synchronous convergence of system states. (3) A fast fixed-time synchronous control method is proposed, which is suitable for manipulator systems with uncertain dynamics, actuator failures and external disturbances, and all system states converge synchronously within a certain time.

[0154] This example verifies the invented control method through computer software MATLAB. In the following simulation, a dual-joint robotic arm system is considered, where the first joint refers to the first rotary joint of the robotic arm, which is the first movable part starting from the base of the robotic arm, and the second joint refers to the second rotary joint immediately after the first joint connected to the end effector of the robotic arm. The steps in the simulation are as follows:

[0155] (1) Selection of some specific physical values ​​of the robotic arm system: b1 represents the mass of the first joint, and the value of b1 is 0.5 kg; b2 represents the mass of the second joint, and the value of b2 is 1.5 kg; b 10 represents the standard value of b1, b 10 The value of is 0.4kg; b20 represents the standard value of b2, b 20 The value is 1.2kg; g represents the acceleration due to gravity, and the value of g is 9.81m / s 2 ; r1 represents the length of the first joint, and the value of r1 is 1m; r2 represents the length of the second joint, and the value of r2 is 0.8m; j1 represents the inertia of the first joint, and the value of j1 is 5kg·m 2 , j2 represents the inertia of the second joint; the value of j2 is 5kg·m 2 .

[0156] (2) Dynamic model of the dual-joint robotic arm system: with position vector q = [q1, q2] T The dynamic model of the dual-joint robot system is expressed by formula (1), and the system matrix is ​​as follows:

[0157]

[0158] in, a2=b2r1r2, a5 = (b1 + b2)r1 and a6 = b2r2. 10 and b 20 Represent the standard values ​​of parameters b1 and b2 respectively.

[0159] The initial value of the system state is: q(0) = [1.2, 1.5] T and

[0160] Friction force vector and external interference dis As shown below:

[0161]

[0162] (3) Compared with traditional fixed-time control: In order to demonstrate the stable characteristics of fixed-time synchronization, the proposed fixed-time synchronization controller (32) and the sliding mode variable using the neural network symbolic function (26) are applied to the manipulator system. Then, in order to provide a better comparison, a fixed-time control scheme using traditional symbolic functions is introduced and applied to the manipulator system, which is shown below. For system (3), the design of the fixed-time sliding mode variable is as follows:

[0163]

[0164] Where i = 1, 2, ..., n, and The control law is designed in the following way:

[0165]

[0166] The observer gains of the proposed fixed-time synchronous controller are: k1=4, k2=5, k3=3.5, k4=4, k5=5, k6=2, λ1=0.5, λ2=2, h1 / g1=13 / 9, l1 / p1=7 / 13, while the control gains are chosen as: α1=1, β1=1, α2=1, β2=1, h2 / g2=13 / 7, h3 / g3=13 / 7, l2 / p2=7 / 13, l3 / p3=7 / 13, δ=0.001.

[0167] The desired trajectory chosen is:

[0168]

[0169] Assume that the actuator works normally and there is no bias torque, that is, d i =1 and Where i=1,2.

[0170] In the following simulations, the comparison results of the proposed fast fixed-time synchronization control scheme and the traditional fixed-time control scheme are provided, as shown in Figure 2(a) and Figure 2(b).

[0171] Figures 2(a) and 2(b), and Figures 3(a) and 3(b) show the trajectory tracking and tracking errors of the two control schemes, indicating that both the proposed fast fixed-time synchronous control scheme and the traditional fixed-time control scheme provide good tracking performance. Figures 3(a) and 3(b) show the trajectory tracking errors and e1 and e2 under the proposed fast fixed-time synchronous control scheme and the traditional fixed-time control scheme. In Figure 3(a), it can be clearly seen that under the fast fixed-time synchronous control scheme of the present invention, the tracking errors e1 and e2 reach the origin synchronously at t=2.5s, while in Figure 3(b), it can be seen that the errors e1 and e2 converge to zero at different time instants. Specifically, e1 reaches equilibrium at t=2.5s, while e2 converges to zero at t=2.6s. In order to make the comparison more obvious, Figures 4(a) and 4(b) show the average error (e1(t)+e2(t)) / 2 when using two different control strategies. It can be clearly seen from Figure 4 (a) and Figure 4 (b) that when the fast fixed time synchronization control method of the present invention is used, the average error converges to zero faster. Therefore, the fast fixed time synchronization control method of the present invention has better performance.

[0172] Figures 5(a) and 5(b) show the control curves under the fast fixed-time synchronization control scheme of the present invention and the traditional fixed-time control scheme. Figures 6(a) and 6(b) show the error ratio e1(t) / e2(t) under the fast fixed-time control scheme of the present invention and the fixed-time control scheme. It can be observed from Figure 6(a) that the proposed fast fixed-time control method ensures that the ratio remains unchanged before the state reaches the origin. For the proposed fast fixed-time control method, this verifies the conclusion proposed by the present invention. In Figure 6(b), it can be clearly seen that the image has a lot of jitter, indicating that the proposed fast fixed-time synchronization control method has better performance. Figures 7(a) and 7(b) show the state under the fast fixed-time control scheme of the present invention. and its observed value Figure 8(a) and Figure 8(b) show the total system uncertainty (i.e.) and its observed values.

[0173] Comparison of the fast fixed-time control scheme of the present invention with the active fault-tolerant control in Article 1 and the non-singular fast terminal sliding mode control in Article 2:

[0174] Article 1 is "An Intelligent Actuator Fault Reconstruction Scheme for Robotic Manipulators" published by Bing Xiao et al. in IEEE Transactions on Cybernetics (vol.48.no.2pp.639-647); Article 2 is "Study of Nonsingular Fast Terminal Sliding-Mode Fault-Tolerant Control" published by Sendren Sheng-Dong Xu et al. in IEEE Transactions on Industrial Electronics (vol.62no.5pp.3906-3913). The control schemes of Article 1 and Article 2 are as follows:

[0175] Control scheme of article 1:

[0176]

[0177] Among them, K>0, κ1>0, κ2>0, k d >0,k p >0 is the parameter to be designed, ρ=δ1 / δ2, δ1 and δ2 are positive odd numbers satisfying δ1<δ2.

[0178] Control scheme of article 2:

[0179]

[0180] where α > 0, β > 0, p and q are positive odd numbers, and satisfy 1 < p / q < 2, and γ > p / q.

[0181] In the simulation test, the control gains of the proposed fast fixed-time synchronization control are the same as those in the above text. The control parameters of the scheme in Article 1 are K = 10, κ1 = 2, κ2 = 2, k p = 750, k d = 150 and ρ = 13 / 17. The control gains of the scheme in Article 2 are selected as α1 = 8, β1 = 6, γ = 9 / 5, p / q = 17 / 15, η = 10 and ν = 2. To simulate the influence of system faults, the actuator bias faults are considered. For the dual-joint manipulator system, the bias torque is expressed as u f = [u f1 , u f2 T . For the first actuator, the bias fault is:

[0182]

[0183] For the second actuator, it is assumed that the fault is u f2 = -0.8 N·m, which means there is a bias fault of -0.8 N·m. The selected desired trajectory is:

[0184]

[0185] The comparison results of the proposed fast fixed-time synchronization control, the control method in Article 1 and the control method in Article 2 are shown in Figures 9(a) and 9(b). Figures 9(a) and 9(b) show the trajectory tracking performance of the manipulator under uncertain dynamics, actuator faults and external disturbances, respectively, for the proposed fast fixed-time synchronization control, the control method in Article 1 and the control method in Article 2. It can be observed from these figures that the proposed fast fixed-time synchronization control, the control method in Article 1 and the control method in Article 2 can all successfully track the desired trajectory, which means that these three methods can compensate or estimate the total disturbance. However, by comparing the three algorithms, it can be found that the proposed fast fixed-time synchronization control method provides a faster tracking rate than the control method in Article 1 and the control method in Article 2.

[0186] ​For better comparison, Figures 10(a) and 10(b) show the average tracking errors of the proposed fast fixed-time synchronization control, the control method of Article 1, and the control method of Article 2. From the results of Figures 9(a) and 9(b), it can be seen that the fast fixed-time synchronization control scheme provides higher tracking accuracy and reaches a stable state faster than the control methods of Article 1 and Article 2. However, the control methods of Article 1 and Article 2 show lower tracking accuracy after a fault occurs. Therefore, the proposed scheme provides better control performance than the control methods of Article 1 and Article 2.

[0187] Figure 11(a) to Figure 11(c) The proposed fast fixed-time synchronization control, the control method of article 1 and the control input of the control method of article 2 are shown. Figure 11(a) to Figure 11(c) It can be seen that the fast fixed time synchronization control scheme provides continuous control input, while the control methods of Article 1 and Article 2 show chattering and large control torque. Figure 12(a) and Figure 12(b) show the state of the proposed fast fixed time synchronization control scheme when a fault occurs. and its observed value Figures 13(a) and 13(b) show the total disturbance of the system under the proposed fast fixed-time synchronization control scheme when a fault occurs. (including uncertain dynamics, actuator failures and external disturbances) and their observed values When a fault occurs suddenly, the estimation process will be completed in a short time. Figures 12(a) and 12(b), 13(a) and 13(b) show that the proposed fixed-time sliding mode observer guarantees good estimation performance. Therefore, under the control method proposed in the present invention, high-precision estimation can be obtained.

[0188] Embodiment 2: This embodiment provides a fixed-time synchronous control system for a manipulator system under an actuator failure, including: an establishment module, which is configured to: establish a dynamic model of the manipulator system, the dynamic model takes into account the existence of n joints in the manipulator system, and also takes into account the uncertainty, external disturbance and actuator failure of the manipulator system; an estimation module, which is configured to: construct a fixed-time sliding mode observer according to the state information and control input information of the manipulator system itself; use the fixed-time sliding mode observer to estimate the total disturbance; the total disturbance includes: the uncertainty of the dynamic model parameters and the external disturbance; A design module is configured to: construct a sliding mode variable based on a neural network symbolic function; based on the sliding mode variable, the total disturbance and the dynamic model of the robot system, considering the actuator failure, and according to the Lyapunov stability principle, design a fixed-time synchronous controller so that both the system error and the derivative of the system error can converge simultaneously, and the upper limit of the stable time is independent of the initial value; a verification module is configured to: verify the stability of the fixed-time synchronous controller, and if the verification is passed, apply the fixed-time synchronous controller and the sliding mode variable based on the neural network symbolic function to the robot system.

[0189] It should be noted that the above-mentioned establishment module, estimation module, design module and verification module correspond to steps S101 to S104 in Embodiment 1, and the examples and application scenarios implemented by the above-mentioned modules and the corresponding steps are the same, but are not limited to the contents disclosed in the above-mentioned Embodiment 1. It should be noted that the above-mentioned modules, as part of the system, can be executed in a computer system such as a set of computer executable instructions.

[0190] The description of each embodiment in the above embodiments has different emphases. For parts not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0191] The proposed system can be implemented in other ways. For example, the system embodiment described above is only illustrative, and the division of the modules is only a logical function division. In actual implementation, there may be other division methods, such as multiple modules can be combined or integrated into another system, or some features can be ignored or not executed.

[0192] Embodiment 3

[0193] This embodiment also provides an electronic device, including: one or more processors, one or more memories, and one or more computer programs; wherein the processor is connected to the memory, and the one or more computer programs are stored in the memory. When the electronic device is running, the processor executes the one or more computer programs stored in the memory so that the electronic device executes the method described in the above embodiment one.

[0194] It should be understood that in this embodiment, the processor may be a central processing unit CPU, and the processor may also be other general-purpose processors, digital signal processors DSP, application-specific integrated circuits ASIC, off-the-shelf programmable gate arrays FPGA or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0195] The memory may include a read-only memory and a random access memory, and provide instructions and data to the processor. A portion of the memory may also include a non-volatile random access memory. For example, the memory may also store information about the device type.

[0196] In the implementation process, each step of the above method can be completed by an integrated logic circuit of hardware in a processor or an instruction in the form of software.

[0197] The method in the first embodiment can be directly embodied as a hardware processor, or a combination of hardware and software modules in the processor. The software module can be located in a mature storage medium in the field such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory, or an electrically erasable programmable memory, a register, etc. The storage medium is located in the memory, and the processor reads the information in the memory and completes the steps of the above method in combination with its hardware. To avoid repetition, it will not be described in detail here.

[0198] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with this embodiment can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0199] Embodiment 4

[0200] This embodiment further provides a computer-readable storage medium for storing computer instructions. When the computer instructions are executed by a processor, the method described in the first embodiment is completed.

[0201] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for controlling a fixed-time synchronization of a robotic arm system under actuator failure, characterized in that it includes: Establishing a dynamic model of the robotic arm system, wherein the dynamic model takes into account the existence of n joints in the robotic arm system, and also takes into account the uncertainty, external disturbances and actuator failures of the robotic arm system; According to the state information and control input information of the robot system itself, a fixed-time sliding mode observer is constructed; The total disturbance is estimated by using a fixed-time sliding mode observer; The total disturbance includes: the uncertainty of the dynamic model parameters and external disturbance; Construct a sliding mode variable based on a neural network symbolic function; Based on the sliding mode variable, total disturbance and the dynamic model of the robotic arm system, considering the actuator failure, and according to the Lyapunov stability principle, design a fixed-time synchronous controller so that both the system error and the derivative of the system error can converge simultaneously, and the upper bound of the stable time is independent of the initial value; The stability of the fixed-time synchronous controller is verified, and if the verification is passed, the fixed-time synchronous controller and the sliding mode variable based on the neural network symbolic function are applied to the robot arm system.

2. The method for controlling a fixed-time synchronization of a manipulator system under actuator failure as claimed in claim 1, characterized in that: A dynamic model of the robotic arm system is established. The dynamic model takes into account the existence of n joints in the robotic arm system, as well as the uncertainty, external disturbances and actuator failures of the robotic arm system. Specifically, it includes: in, represents the generalized position, velocity, and acceleration; where represents the inertia matrix, The matrix representing the Coriolis force and centrifugal torque, It's the force of gravity. is the friction effect, F=diag{f1,f2,...,f n } is the friction coefficient, f dis Unknown external disturbances, represents the applied torque input; When an actuator fault occurs, the control torque u is modeled as: in=in nom +in f (2) in, represents the command torque generated by the designed controller, A vector representing unknown actuator faults; The dynamic model formula (1) of the robotic arm system is rewritten as: Among them, B n (q) = B(q) - ΔB(q), and G n (q) = G(q) - ΔG(q) and is the sum of the uncertainties.

3. The method for controlling a fixed-time synchronization of a manipulator system under actuator failure as claimed in claim 2, characterized in that: According to the state information and control input information of the robot system itself, a fixed-time sliding mode observer is constructed; The total disturbance is estimated by using a fixed-time sliding mode observer; The total disturbance includes: the uncertainty of the dynamic model parameters and external disturbances, specifically including: fixed time means that the system state will converge to the equilibrium point in a finite time starting from any initial conditions, and this convergence time is consistent and bounded; Introducing a state variable vector Then the dynamic model formula (3) is transformed into: in, τ=u nom as well as Assume that the total disturbance d total (t) is a differentiable unknown signal, and the time derivative of the total disturbance is Existence constant satisfy Next, a fixed-time sliding mode observer is constructed to estimate the total disturbance d total (t); First, define a new auxiliary variable for: Formula (5); where λ1 is a positive constant; Considering the dynamic equation (4), we get the following results: in Then, the total disturbance d in formula (6) is total (t) is considered as an extended state And formula (6) is expressed as: where h(t) is d total The time first derivative of (t); Finally, the fixed-time sliding mode observer is designed as follows: in and and System status and disturbance The observer state, functions Φ1 and Φ2 are designed as follows: Among them, h1, g1, l1 and p1 are four positive odd integers, and h1>g1 and l1 <p1,k i >0 is the observer gain, i=1,2,...,6, and Combining equations (7) and (8), we obtain the following dynamic equation of the observer error: Considering the robot arm system, the proposed observer (8) in formula (3) ensures that the observer error (10) converges to zero in a finite or fixed time, provided that Observer Error After reaching the origin, the steady-state time is: in, and (h1+g1) / 2g1>1 and 0<(l1+p1) / 2p1<1; Infer will be reached in a fixed time, and the steady-state time is estimated to be: Through the above analysis, it can be concluded that the observer state and After a finite / fixed time, it converges to zero. The observer law formula (8) approximates the total disturbance d in a fixed time. total (t).

4. The method for controlling a fixed-time synchronization of a manipulator system under actuator failure as claimed in claim 3, characterized in that: Construct a sliding mode variable based on a neural network symbolic function; Based on the sliding mode variable, total disturbance and the dynamic model of the robotic arm system, considering the actuator failure, according to the Lyapunov stability principle, design a fixed time synchronization controller so that both the system error and the derivative of the system error can converge at the same time, and the upper bound of the stable time is independent of the initial value, including: Construct the theory of fixed-time synchronous stable systems; Based on the fixed-time synchronous stable system theory, a fixed-time synchronous control strategy is constructed.

5. The method for controlling a fixed-time synchronization of a manipulator system under actuator failure as claimed in claim 4, characterized in that: Construct the theory of fixed-time synchronous stable systems, including: For the following nonlinear system: Among them, α0>0 and β0>0 are two scalars, If h0>0, g0>0, l0>0 and p0>0 are odd integers and satisfy h0>g0 and p0>l0, then the equilibrium point of the system is fixed-time stable and the steady-state time is bounded to:

6. The method for controlling a fixed-time synchronization of a manipulator system under actuator failure as claimed in claim 5, characterized in that: Based on the fixed-time synchronous stable system theory, a fixed-time synchronous control strategy is constructed, including: Define the trajectory tracking error as e = qq d , where q d is the desired trajectory; Introduced neural network symbolic function: sig n (from) α =||z|| α sign n (of) (15) sig c (from) α =[|z1| α sign c (z1),…,|z n | α sign c (from n )] T (16) Where α is a positive constant; the neural network symbol function sign n and the classic symbolic function sign c They are defined as follows: in Where i = 1, 2, ..., n; Based on the introduced neural network symbolic function formula (15) and the fast fixed time stable system formula (13), a new sliding mode variable s is constructed. * , expressed as: Among them, α1 and β1 are positive constants, h2, g2, l2 and p2 are positive odd numbers, and h2>g2 and l2 <p2; Then, the fixed time synchronization controller looks like this: in nom =in nom_1 +in nom_2 (21) where α2, β2, and κ are positive constants, h3, g3, l3, and p3 are positive odd numbers, and satisfy h3 > g3 and l3 < p3, and the variables η1 and η2 satisfy: Since there are negative powers of η1 and η2 in the controller formula (23), a singularity problem occurs when e = 0. In order to solve the singular value problem, the following modified sliding mode variables are designed: Here, the variables and their time derivatives are in the form: And δ>0 is a very small constant; the variable s * for: And the constants μ1 and μ2 are designed as: And fractional powers ρ1∈(1,4), l2 / p2∈(0.5,1), where h2, g2, l2 and p2 are positive odd numbers; Based on the modified sliding mode variable (26), the controller is designed as: in nom =in nom_1 +in nom_2 (32) By applying the newly designed modified sliding mode variable formula (26) and the proposed controller formula (32), it is obtained that all states of the closed-loop system achieve fixed-time synchronous convergence, and the steady-state time is bounded to:

7. The method for controlling a fixed-time synchronization of a manipulator system under actuator failure as claimed in claim 6, characterized in that: Verifying the stability of the fixed time synchronization controller specifically includes: Lyapunov candidate function V s for: V s =s T s (36) V s Taking the derivative with respect to time and using the controller (32), we obtain: If the variable s satisfies |s|>1, then we get When |s|≤1, we get It is concluded that all states will reach the surface of s = 0 within a certain time, and the convergence time of s is bounded as: When s=0 is reached, we get: Then, choose another Lyapunov function as V e =e T e; for V e The derivative is: If the variable s satisfies |s|>1, then we get When |s|≤1, we get The state e and will converge to zero in a certain amount of time: Assume that there are two error state variables e i and e j , their convergence times are T i and T j , and T j >T i ; In state e i and e j Before reaching the origin, The derivative of satisfies: get: where c ij is a non-zero constant, since the variable e i At time T i A balance is reached, which results in: According to the above analysis, we can get e j (T i )=0; however, the variable e j The convergence time is T j Instead of T i , which contradicts the previous assumption; therefore, all variables in state e(t) will reach equilibrium synchronously.

8. A fixed time synchronization control system for a manipulator system under actuator failure, characterized in that it includes: An establishment module is configured to: establish a dynamic model of the robotic arm system, wherein the dynamic model takes into account the existence of n joints in the robotic arm system, and also takes into account the uncertainty, external disturbance and actuator failure of the robotic arm system; An estimation module is configured to: construct a fixed-time sliding mode observer according to state information of the robot system itself and control input information; The total disturbance is estimated by using a fixed-time sliding mode observer; The total disturbance includes: the uncertainty of the dynamic model parameters and external disturbance; A design module is configured to: construct a sliding mode variable based on a neural network symbolic function; based on the sliding mode variable, the total disturbance and the dynamic model of the manipulator system, considering the actuator failure, and according to the Lyapunov stability principle, design a fixed time synchronization controller so that both the system error and the derivative of the system error can converge simultaneously, and the upper bound of the stable time is independent of the initial value; A verification module is configured to verify the stability of the fixed-time synchronization controller, and if the verification is passed, apply the fixed-time synchronization controller and the sliding mode variable based on the neural network symbolic function to the robot arm system.

9. An electronic device, comprising: a memory for non-transitory storage of computer readable instructions; as well as a processor for executing the computer readable instructions, When the computer-readable instructions are executed by the processor, the method described in any one of claims 1 to 7 is executed.

10. A storage medium, characterized in that: The computer-readable instructions are non-transitory stored, wherein when the non-transitory computer-readable instructions are executed by a computer, the method according to any one of claims 1 to 7 is performed.

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