Master-slave industrial robot system adaptive sliding mode trajectory tracking method

Abstract

The application discloses a master-slave industrial robot system adaptive sliding mode trajectory tracking method. Firstly, a disturbed robot system is modeled; a master-slave control method of a double robot system is designed with the help of a distributed control idea, and on this basis, a segmented preset sliding surface, a master-slave industrial robot trajectory tracking sliding mode controller and an adaptive law of controller parameters are designed by using switching control, adaptive control theory and sliding mode control principle, so that the master industrial robot can compensate for the lumped disturbance and overcome the influence of the actuator fault within a limited time, the tracking error of the target trajectory converges to the preset boundary within a limited time, and the slave industrial robot can overcome the influence of the lumped disturbance and the actuator fault and realize the asymptotic tracking of the trajectory of the master industrial robot. The application solves the problem of how the master-slave industrial robot system can quickly realize consistent trajectory tracking under the influence of internal parameter perturbation, external disturbance, transmission mechanism gap and actuator fault.

Description

Technical Field

[0001] This invention relates to industrial robot trajectory tracking control technology, and in particular to an adaptive sliding mode trajectory tracking method for a master-slave industrial robotic arm system. Background Technology

[0002] In recent years, robotics technology has developed rapidly, attracting increasing attention and finding widespread application in numerous fields. Since the last century, robots have gradually integrated into households, bringing much convenience to people's lives. In various dangerous environments such as geographical surveying, mine clearance, and rescue, robots, due to their integration of many high-tech technologies, can accomplish many tasks that are incapable of being performed by humans. Simultaneously, in the industrial production sector, robots have helped improve production efficiency, reduce production costs, and drive social progress.

[0003] Industrial robotic arm control is one of the most important and challenging problems in the practical application of robotics, and the collaborative control between robotic arm systems has gradually become a focus of attention. In recent years, many scholars have conducted extensive research in the field of robotic arm control and have achieved certain results. Currently, many industrial robotic arms, led by the Tianhe and Wentian robotic arms on the Chinese space station, have unparalleled advantages in material handling, hazardous area exploration, industrial transportation and assembly, and outer space exploration, and are therefore widely used.

[0004] Feedback control in industrial robotic arm systems mainly consists of three aspects: point stabilization, path following, and trajectory tracking. Point stabilization refers to the robot moving from a predetermined initial position to a final position. Path following involves following a specified trajectory from the initial position. Trajectory tracking refers to the ability to track a reference trajectory in real time. Because industrial robot systems generally exhibit strong coupling and nonlinear characteristics, achieving fast and accurate trajectory tracking and collaborative control has always been a research hotspot in the field of industrial robot control. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to provide an adaptive sliding mode trajectory tracking method for a master-slave industrial robotic arm system. This method solves the problem of how to achieve consistent tracking of the reference trajectory under conditions such as internal parameter perturbation, external interference, transmission mechanism backlash, and actuator failure in industrial robotic arm systems.

[0006] Technical solution: The present invention provides an adaptive sliding mode trajectory tracking method for a master-slave industrial robotic arm system, comprising the following steps:

[0007] S1. Based on the Euler-Lagrange equations, establish the kinematic and dynamic models of the industrial robotic arm affected by internal parameter perturbations, external disturbances, control hysteresis, and actuator failures, i.e., the master-slave industrial robotic arm model.

[0008] S2. Using the desired trajectory of the industrial robot and the kinematic and dynamic models established in step S1, design the master-slave industrial robot system structure and information interaction relationship based on the distributed control principle. That is, the master industrial robot system interacts with the host computer to obtain relevant information about the target trajectory and designs a controller to realize the master industrial robot's finite-time tracking control of the target trajectory; the state information of the master industrial robot is obtained from the industrial robot system to construct virtual signals and design a controller to realize the asymptotic tracking control of the slave industrial robot's trajectory of the master industrial robot.

[0009] S3. Using the switching control principle, sliding surfaces are designed for the master industrial robotic arm system and the slave industrial robotic arm system respectively.

[0010] S4. Based on the kinematic and dynamic models of the industrial robotic arm in step S1 and the sliding surface of the master-slave industrial robotic arm system established in step S3, design equivalent controllers for the master and slave industrial robotic arm systems to achieve system state convergence; use adaptive control methods combined with sliding mode control principles to design auxiliary controllers for the master and slave industrial robotic arm systems to compensate for lumped disturbances and actuator faults in the system, accelerate system state convergence speed, and achieve finite-time convergence of the master industrial robotic arm trajectory tracking error and asymptotic tracking of the slave industrial robotic arm trajectory to the master industrial robotic arm.

[0011] S5. Design adaptive laws for the controller parameters of the master and slave industrial robotic arm systems respectively to accelerate the compensation speed for unknown lumped disturbances, while avoiding overestimation of adaptive parameters.

[0012] Furthermore, the kinematic and dynamic models of the industrial robotic arm established in step S1 are as follows:

[0013] The main industrial robotic arm model is as follows:

[0014] The industrial robotic arm model is as follows:

[0015] in:

[0016] d τi =[d τi1 ,…,d τin ] T

[0017]

[0018] These represent the angle, angular velocity, and angular acceleration of each joint of the main industrial robotic arm. These represent the angle, angular velocity, and angular acceleration of each joint of the industrial robotic arm, respectively. n is the number of joints in the robotic arm, and i = 0, 1 are the corresponding markers for the master and slave industrial robotic arm systems, respectively. M i (q i ) is the positive definite symmetric inertia matrix of the master and slave industrial robotic arm systems. It is the matrix of centrifugal and Coriolis forces during the operation of the master and slave industrial robotic arms, G. i (q i ) is the gravity vector of the master and slave industrial robotic arms. It is the actual effective value of the master and slave industrial robotic arm system controllers, Ω i It is the gain fault coefficient, τ i It is an adaptive sliding mode controller for master and slave industrial robotic arm systems. The error is caused by system parameter perturbation, actuator bias fault, and actuator gain fault. di Lumped disturbance of master and slave industrial robotic arm systems, d τi The control hysteresis loop is generated by the gap between the master and slave industrial robotic arm transmission mechanisms, d i It is external interference with the torque of the master and slave industrial robotic arm systems, B l B r Z is the two intersection points of the hysteresis curve and the horizontal axis. l Z r It is the left and right critical points for the current control action to get rid of the hysteresis effect, U lt The vertical axis remains unchanged when the control action is affected by the hysteresis loop.

[0019] Furthermore, in step S2, the virtual signal The construction is as follows:

[0020]

[0021] in, It is the inverse matrix of M0(q0), where M0(q0) is the positive definite symmetric inertia matrix of the main industrial robotic arm system. G0(q0) is the centrifugal force and Coriolis force matrix of the main industrial robotic arm during operation, and G0(q0) is the gravity vector of the main industrial robotic arm. These represent the angles and angular velocities of the various joints of the main industrial robotic arm, τ. 0eq It is the equivalent controller of the main industrial robotic arm system, τ 0au It is the auxiliary controller of the main industrial robotic arm system, and the virtual signal The difference between the angular acceleration of the main industrial robotic arm system and the angular acceleration of the main industrial robotic arm system is:

[0022]

[0023] Where ||·|| refers to the 2-norm of the column vector. Ω0 represents the angular acceleration of each joint of the main industrial robotic arm, Ω0 is the gain fault coefficient of the main industrial robotic arm system, and d0 is the external interference on the torque of the main industrial robotic arm system. τ0 It is a control hysteresis loop caused by the gap in the transmission mechanism of the main industrial robotic arm system.

[0024] Furthermore, in step S3, the sliding surfaces of the master and slave industrial robotic arm systems are designed as follows:

[0025] The sliding surface design of the main industrial robotic arm is as follows:

[0026] The sliding surface design of industrial robotic arms is as follows:

[0027] Where s0 is the sliding surface of the primary industrial robotic arm, s1 is the sliding surface of the secondary industrial robotic arm, j = 1, ..., n, e0 = [e 01 ,…,e 0n ] T =q0-q d It is the trajectory tracking error of the main industrial robotic arm, e 0j It is the component of the corresponding joint, q d It is the target trajectory signal. Let e1 be the derivative of e0. 11 ,…e 1n ] T =q1-q0 is the trajectory tracking error of the industrial robotic arm, e 1j These are the components of the corresponding joints. Let be the derivative of e1, μ0 and μ1 be positive constants that adjust the convergence speed, θ1 be an intermediate variable, q0 represent the angles of each joint of the master robotic arm, q1 represent the angles of each joint of the slave robotic arm, and α0, a, b, m, c, η be positive constants that satisfy the conditions: a≥1 (designed as odd numbers), b>1 (designed as even numbers). Where c1 and c2 are designed to be odd numbers; n is the number of robotic arm joints, and r1 = (a1 + a2 - k3c)η c-a r2=(k3c-a1)η c-b , R(e0)=[R(e 01 ),…,R(e 0n )] T Where a1>0, a2>0, k3>0 are constants satisfying: a1+a2-k3c>0, a(a1+a2-k3c)+b(k3c-a1)=mc, η is the accuracy range for tracking error convergence within a finite time that can be preset; α0>|r2|, β 11 >0, β 12 >0, 0<γ 11 <1,γ 12>1, γ 13 >1, sign(·) represents the sign function. It is an intermediate variable with no actual physical meaning.

[0028] Furthermore, the adaptive sliding mode controller for the main industrial robotic arm in step S4 is designed as follows:

[0029] τ0=τ 0eq +τ 0au

[0030]

[0031]

[0032] Where μ0 is a constant that adjusts the convergence speed, τ0 is the adaptive sliding mode controller of the main industrial robotic arm system, and τ 0eq It is the equivalent controller of the main industrial robotic arm system, τ 0au It is the auxiliary controller for the main industrial robotic arm system. It is the inverse matrix of M0(q0), where M0(q0) is the positive definite symmetric inertia matrix of the main industrial robotic arm system. G0(q0) is the centrifugal force and Coriolis force matrix of the main industrial robotic arm during operation, and G0(q0) is the gravity vector of the main industrial robotic arm. It is the second derivative of the target trajectory, q0, These represent the angles and angular velocities of the various joints of the main industrial robotic arm. It is the derivative of R(e0), R(e0) = [R(e 01 ),…,R(e 0n )] T ,e0=[e 01 ,…,e 0n ] T =q0-q d , Let α0 be the derivative of e0, b be positive constants, ψ0 be the dynamic adaptive parameter, and κ be the derivative of e0. 01 κ m0 Λ0 is a positive constant. These are the adaptive parameters in the main industrial robotic arm controller, and their adaptive law is designed as follows:

[0033]

[0034] in, Ω0 describes the gain fault of the main industrial robot actuator, and s0 is the sliding surface of the main industrial robot.

[0035] Furthermore, in step S4, the adaptive sliding mode controller for the industrial robotic arm is designed as follows:

[0036] τ1=τ 1eq +τ 1au

[0037]

[0038]

[0039] Wherein, τ1 is the adaptive sliding mode controller from the industrial robotic arm system, τ 1eq From the equivalent controller of the industrial robotic arm system, τ 1au It is an auxiliary controller from an industrial robotic arm system. It is the inverse matrix of M1(q1), where M1(q1) is the positive definite symmetric inertia matrix of the industrial robotic arm system. G1(q1) is the centrifugal force and Coriolis force matrix generated during the operation of the industrial robotic arm, and G1(q1) is the gravity vector generated by the industrial robotic arm. These represent the angles and angular velocities of each joint in the industrial robotic arm. μ1 and α 11 It is a positive constant that adjusts the convergence speed. It is a virtual signal, e1 = [e 11 ,…e 1n ] T =q1-q0, Let q0 be the derivative of e1, and q0 represent the angles of each joint of the main industrial robotic arm. It is a dynamically adaptive parameter, γ 13 >1, β 11 >0, β 12 >0, ψ1 is the dynamic adaptive parameter, κ 11 >0,κ m1 >0, Ω is a positive constant. 1min This describes the maximum range of gain failures from industrial robotic arm actuators. It uses adaptive parameters from the industrial robotic arm controller to compensate for lumped disturbances from the industrial robotic arm. The error in information transmission between the master and slave industrial robotic arms is designed with the following adaptive law:

[0040]

[0041]

[0042] Among them, q0, These represent the angles and angular velocities of the various joints of the main industrial robotic arm. Ω1 describes a gain fault in an industrial robotic arm actuator.

[0043] Furthermore, in step S5, the parameters ψ of the master and slave industrial robotic arm controllers... i The specific design of the adaptive law is as follows:

[0044]

[0045] in, The parameters ψ of the master and slave industrial robotic arm controllers i The adaptive law, s i It is the sliding surface of the master-slave industrial robotic arm system, η i2 These are positive constants used to adjust the growth range of the adaptive parameters; Parameter κ i1 >0 is a positive integer. η3 is a positive constant, and ρ is an intermediate variable with no physical meaning, referring to h. s (||s i ||-η i2 ) and h s (ψ i -κ i2 The content in parentheses.

[0046] Based on the same inventive concept, the present invention provides an adaptive sliding mode trajectory tracking system for a master-slave industrial robotic arm system, comprising:

[0047] The model building unit is used to establish kinematic and dynamic models of industrial robotic arms, i.e. master-slave industrial robotic arm models, based on the Euler-Lagrange equations and affected by internal parameter perturbations, external disturbances, control hysteresis, and actuator failures.

[0048] The system architecture building unit is used to design the master-slave industrial robot system structure and information interaction relationship based on the distributed control principle, utilizing the expected trajectory of the industrial robot and the established kinematic and dynamic models. Specifically, the master industrial robot system interacts with the host computer to obtain relevant information about the target trajectory and designs a controller to achieve finite-time tracking control of the master industrial robot on the target trajectory; the system also obtains the state information of the master industrial robot from the industrial robot system to construct virtual signals and design a controller to achieve asymptotic tracking control of the slave industrial robot on the trajectory of the master industrial robot.

[0049] The sliding surface design unit is used to design sliding surfaces for the master industrial robotic arm system and the slave industrial robotic arm system respectively using the switching control principle.

[0050] The controller design unit is used to design equivalent controllers for the master and slave industrial robot arm systems based on the kinematic and dynamic models of the industrial robot arm and the sliding mode surface of the master and slave industrial robot arm systems to achieve system state convergence. Using adaptive control methods combined with the sliding mode control principle, auxiliary controllers are designed for the master and slave industrial robot arm systems to compensate for lumped disturbances and actuator faults in the system, accelerate the system state convergence speed, and achieve finite-time convergence of the master industrial robot arm trajectory tracking error and asymptotic tracking of the slave industrial robot arm trajectory to the master industrial robot arm.

[0051] The compensation unit is used to design adaptive laws for the controller parameters of the master and slave industrial robotic arm systems to accelerate the compensation speed for unknown lumped disturbances, while avoiding overestimation of the adaptive parameters.

[0052] Based on the same inventive concept, the present invention provides an electronic device, the device comprising:

[0053] Memory containing executable program code;

[0054] A processor coupled to the memory;

[0055] The processor calls the executable program code stored in the memory to execute the steps of the master-slave industrial robotic arm system adaptive sliding mode trajectory tracking method described above.

[0056] Based on the same inventive concept, the present invention provides a computer-readable storage medium storing computer instructions, which, when invoked, are used to execute the steps of the above-described adaptive sliding mode trajectory tracking method for a master-slave industrial robotic arm system.

[0057] Beneficial effects: Compared with the prior art, the advantages of this invention are as follows: Under complex working conditions including internal parameter perturbations, external disturbances, transmission mechanism backlash, and actuator failures, this invention enables the main industrial robotic arm to reach the sliding surface within a finite time, and the tracking error of the target trajectory can converge to a preset range within a finite time, eventually asymptotically converging to zero. Simultaneously, it achieves asymptotic tracking of the main industrial robotic arm trajectory from the industrial robotic arm system, with good tracking performance and strong robustness to unknown parameters and complex external disturbances. Attached Figure Description

[0058] Figure 1 This is a flowchart of the method of the present invention;

[0059] Figure 2 These are the design schematics of the master industrial robotic arm system and the slave industrial robotic arm system.

[0060] Figure 3 This is a schematic diagram of the industrial robotic arm used in the simulation of this invention;

[0061] Figure 4 This is a schematic diagram of the control hysteresis structure of the industrial robotic arm in this invention;

[0062] Figure 5 This is a schematic diagram illustrating the tracking of the actual trajectory and the desired trajectory of the master-slave industrial robotic arm system in this invention;

[0063] Figure 6 This is a schematic diagram illustrating the tracking of the actual and desired joint angular velocities of the master-slave industrial robotic arm system in this invention.

[0064] Figure 7 This is a schematic diagram of the control torque of the main industrial robotic arm system affected by actuator failure;

[0065] Figure 8 This is a schematic diagram of the control torque affected by actuator failure in an industrial robotic arm system.

[0066] Figure 9 It is a trend graph showing the changes in the sliding state of the master industrial robotic arm and the slave industrial robotic arm system;

[0067] Figure 10 This is a trend chart of the tracking error of the main industrial robotic arm system to the reference trajectory;

[0068] Figure 11 This is a trend chart of the tracking error of the main industrial robotic arm from the industrial robotic arm system. Detailed Implementation

[0069] The technical solution and beneficial effects of the present invention will be described in detail below with reference to the accompanying drawings. In this solution... Let ||x|| represent the derivative of a, and ||x|| represent the 2-norm of x. T This represents the transpose of x.

[0070] This invention primarily utilizes distributed principles to design equivalent and auxiliary controllers for master-slave industrial robotic arm systems to compensate for lumped disturbances and accelerate system state convergence. It also studies trajectory tracking control based on adaptive theory and sliding mode control technology. The core content of this invention is to address how to quickly stabilize the motion state and rapidly converge the tracking error under conditions including parameter perturbations, torque disturbances caused by external interference, control hysteresis caused by internal transmission mechanism backlash, and actuator failures.

[0071] like Figure 1 As shown, this invention provides an adaptive sliding mode trajectory tracking method for a master-slave industrial robotic arm system, comprising the following steps:

[0072] Step 1: Considering the internal parameter perturbation, external interference, control hysteresis and actuator failure of the industrial robotic arm system, establish the kinematic and dynamic models of the industrial robotic arm system based on the Euler-Lagrange equations, i.e., the master-slave industrial robotic arm model.

[0073] When actuator failure and control dead zone are not considered, the kinematic and dynamic models of the industrial robotic arm system are expressed as follows:

[0074] The main industrial robotic arm model is as follows:

[0075] The industrial robotic arm model is as follows:

[0076] Where: d0, d1 are the external disturbances to the torque of the master and slave industrial robotic arm systems, i = 0, 1 are the corresponding labels of the master and slave industrial robotic arm systems, j = 1, ..., n are the labels of each component, u i =[u i1 ,…,u in ] T It is the controller of the robotic arm system, u ij It is the corresponding component. These represent the angles, angular velocities, and angular accelerations of each joint in the master and slave industrial robotic arms, respectively; n is the number of joints in the robotic arm; M i (q i ) is the positive definite symmetric inertia matrix of the master and slave industrial robotic arm system. It is the matrix of centrifugal and Coriolis forces during the operation of the master and slave industrial robotic arms, G. i (q i ) is the gravity vector of the master and slave industrial robotic arms.

[0077] When an actuator malfunctions, the kinematic and dynamic models of the industrial robotic arm system are expressed as follows:

[0078] The main industrial robotic arm model is as follows:

[0079] The industrial robotic arm model is as follows:

[0080] in:

[0081] d τi =[d τi1 ,…,d τin ] T

[0082] in, These are the actual effective values ​​of the master and slave industrial robotic arm system controllers. It is the component corresponding to the actual effective value of the controller, Ω i It is the gain fault coefficient, τ i =τ ieq +τ iau It is an adaptive sliding mode controller for master and slave industrial robotic arm systems, where τ ieq It is an equivalent controller, τ iau It is an auxiliary controller, D di It is the lumped disturbance of the master and slave industrial robotic arm system, d τi The control hysteresis loop is generated by the gap between the master and slave industrial robotic arm transmission mechanisms, d i It is external interference with the torque of the master and slave industrial robotic arm systems. The torque error is caused by system parameter perturbation, actuator bias fault, and actuator gain fault. l B r Z is the two intersection points of the hysteresis curve and the horizontal axis. l Z r It is the left and right critical points for the current control action to get rid of the hysteresis effect, U lt The vertical axis remains unchanged when the control action is affected by hysteresis.

[0083] Step 2: Using the desired trajectory of the industrial robot and the kinematic and dynamic models established in Step S1, design the master-slave industrial robotic arm system structure and information interaction relationship based on the distributed control principle; such as... Figure 2 As shown: The main industrial robotic arm system interacts with the host computer to obtain relevant information about the target trajectory and designs a controller to achieve finite-time tracking control of the main industrial robotic arm on the target trajectory; the state information of the main industrial robotic arm can be obtained from the industrial robotic arm system to construct virtual signals and design a controller to achieve asymptotic tracking control of the main industrial robotic arm trajectory by the industrial robotic arm.

[0084] Based on the structural design of the master-slave industrial robotic arm system, a virtual signal for the slave industrial robotic arm is constructed.

[0085]

[0086] in, It is the inverse of the positive definite symmetric inertia matrix M0(q0) of the main industrial robotic arm system. G0(q0) is the centrifugal force and Coriolis force matrix of the main industrial robotic arm system during operation, and G0(q0) is the gravity vector of the main industrial robotic arm system. These represent the angles and angular velocities of each joint of the main industrial robotic arm; τ 0eq It is the equivalent controller of the main industrial robotic arm system, τ 0au It is the auxiliary controller for the main industrial robotic arm system. Meanwhile, structures based on virtual signals include:

[0087]

[0088] in, Represents the angular acceleration of each joint of the main industrial robotic arm; It is the inverse matrix of M0(q0). d τ0 It is the control hysteresis generated by the transmission mechanism gap of the main industrial robotic arm system, d0 is the external interference on the torque of the main industrial robotic arm system, and Ω0 is the gain fault coefficient of the main industrial robotic arm system.

[0089] Step 3: Using the switching control principle, design the sliding surfaces of the master and slave industrial robotic arm systems respectively:

[0090] The sliding surface design of the main industrial robotic arm is as follows:

[0091] The sliding surface design of industrial robotic arms is as follows:

[0092] Where s0 is the sliding surface of the main industrial robotic arm system, s1 is the sliding surface of the slave industrial robotic arm system, j = 1, ..., n, e0 = [e 01 ,…,e 0n ] T =q0-q d It is the trajectory tracking error of the main industrial robotic arm, e 0j It is the component of the corresponding joint, q d It is the target trajectory signal, e1 = [e 11 ,…e 1n ] T =q1-q0 is the trajectory tracking error of the industrial robotic arm, e 1j These are the components of the corresponding joints. and α and β are the derivatives of e0 and e1, respectively; μ0 and μ1 are positive constants that adjust the convergence rate; θ1 is an intermediate variable; α0, a, b, m, c, and η are positive constants that satisfy: a≥1 are designed to be odd numbers, and b>1 are designed to be even numbers. Where c1 and c2 are designed to be odd numbers, r1=(a1+a2-k3c)η c-a r2=(k3c-a1)η c-b , R(e0)=[R(e 01 ),…,R(e 0n )] T Where a1>0, a2>0, k3>0 are constants satisfying: a1+a2-k3c>0, a(a1+a2-k3c)+b(k3c-a1)=mc, and η is the accuracy range for tracking error convergence within a pre-defined finite time. α0>|r2|, β 11 >0, β12 >0, 0<γ 11 <1,γ 12 >1, γ 13 >1, Refers to sig b (e0) sign(·) represents the sign function. It is an intermediate variable with no actual physical meaning.

[0093] Step 4: Based on the design of the sliding surface, further design the adaptive sliding mode controller τ for the master and slave industrial robotic arm system based on the adaptive control principle and sliding mode control method. i It controls the master-slave industrial robotic arm system.

[0094] To achieve rapid tracking of the reference trajectory signal by the main industrial robotic arm, this invention designs an adaptive sliding mode controller τ0 for the main industrial robotic arm system based on the segmented sliding mode surface.

[0095] τ0=τ 0eq +τ 0au

[0096]

[0097]

[0098] in, It is the second derivative of the target trajectory. The derivative of R(e0), The middle element is And κ 01 >0,κ m0 >0. The adaptive parameters in the adaptive sliding mode controller of the main industrial robotic arm are used to compensate for lumped disturbances, and its adaptive law is designed as follows:

[0099]

[0100] in, ψ0 is a dynamic adaptive parameter, and its adaptive law is designed as follows:

[0101]

[0102] in, Parameter κ 01 and κ 02 For positive integers, η3 is a positive constant, and ρ is an intermediate variable with no physical meaning. For positive constants, Ω0, Ω 0minThe gain fault and the maximum range of the gain fault of the main industrial robotic arm actuator are described respectively.

[0103] Based on the adaptive sliding mode controller τ0, the derivative of s0 can be calculated as follows:

[0104]

[0105] Choose Lyapunov functions V0 and V1:

[0106]

[0107] in, in It is the coefficient of the upper bound of the lumped disturbance, and it is a positive constant.

[0108] Based on the kinematic and dynamic models of industrial robotic arm systems, the derivative of Lyapunov functions It will become:

[0109]

[0110] because Furthermore, according to the adaptive law: Therefore, based on the adaptive law, it is easy to determine the derivative of the Lyapunov function in structural design. And there are:

[0111]

[0112] Among them, due to Based on the structure of the adaptive law, it is known that there must exist a finite time such that... because Therefore, it can be concluded that the sliding surface s0 is reached in a finite amount of time. Once the system state of the main industrial robotic arm reaches the sliding surface: when|e 0j When |≥η, let Lyapunov function be used. Its derivative is:

[0113]

[0114] Based on the parameter settings and the Lyapunov stability principle, the tracking error will converge to the preset boundary |e| within a finite time. 0j |< within. when|e 0j |<η time:

[0115]

[0116] Since r1≥0 and α0>|r2|, according to Lyapunov stability theory, the tracking error will asymptotically converge to zero.

[0117] To overcome interference from lumped disturbances and transmission errors, and to achieve rapid tracking of the master industrial robotic arm's trajectory by the slave industrial robotic arm, this invention designs an adaptive sliding mode controller τ1 for the slave industrial robotic arm system based on the integral sliding mode surface.

[0118] τ1=τ 1eq +τ 1au

[0119]

[0120]

[0121] Wherein, τ1 is the adaptive sliding mode controller from the industrial robotic arm system, τ 1eq From the equivalent controller of the industrial robotic arm system, τ 1au It is an auxiliary controller for industrial robotic arm systems. G1(q1) is the centrifugal force and Coriolis force matrix generated during the operation of the industrial robotic arm system, and G1(q1) is the gravity vector generated by the industrial robotic arm system. These represent the angles and angular velocities of each joint in the industrial robotic arm. κ 11 >0,κ m1 >0, and The adaptive parameters in the industrial robotic arm controller are used to compensate for lumped disturbances and information transmission errors from the industrial robotic arm. The adaptive law is designed as follows:

[0122]

[0123]

[0124] in ψ1 is a dynamic adaptive parameter, and its adaptive law is designed as follows:

[0125]

[0126] in, Parameter κ 11 and κ 12 For positive integers, η3 is a positive constant, and ρ is an intermediate variable with no physical meaning. For positive constants, Ω1, Ω 1min It describes the range of failures and the maximum range of faults in industrial robotic arm actuators.

[0127] Since it has been proven that the main industrial robotic arm is stable within a finite time and that the tracking error converges, its control law is bounded, therefore: Therefore, we can obtain: in This is the coefficient representing the upper bound of the virtual signal error, and it is a positive constant. Based on the adaptive sliding mode controller τ1, the derivative of s1 can be calculated as:

[0128]

[0129] Select Lyapunov functions V4 and V5:

[0130]

[0131] Substituting π = 0, 1, 2 into the robotic arm dynamics model and controller, the derivative of the Lyapunov function... It will become:

[0132]

[0133] in thus The proof of the boundedness of the system state is complete.

[0134]

[0135]

[0136]

[0137] Among them, due to Based on the structure of the adaptive law, it is known that there must exist a finite time such that... because Therefore, it can be concluded that the sliding surface s1 is reached in a finite time, and s1≡0. Based on the sliding surface design of industrial robotic arms:

[0138]

[0139] Let Lyapunov function Its derivative is:

[0140]

[0141] Therefore, θ 1j It will converge to zero in a finite amount of time. Let Lyapunov function be... Its derivative is:

[0142]

[0143] According to Lyapunov's stability theory, the tracking error of the industrial robotic arm on the trajectory of the main industrial robotic arm will asymptotically converge to zero.

[0144] In summary, the present invention comprises a main industrial robotic arm sliding surface, a main industrial robotic arm adaptive sliding controller, a slave industrial robotic arm sliding surface, a slave industrial robotic arm adaptive sliding controller, and an adaptive law for control parameters.

[0145] In the embodiments of the present invention, a master-slave dual-joint industrial robotic arm of the same type is used, and its parameters are selected as follows:

[0146]

[0147] The initial pose of the industrial robotic arm is: q0(0) = [0.2, 2.1] T q1(0) = [0.4, 2] T , Lumped disturbance model is The reference trajectory is: The control hysteresis width is: B l =-0.5,B r =0.5. The sliding surface parameters of the main industrial robotic arm are designed as follows: α0=7, a=1, b=1, m=1, c=3 / 7, η=0.3, μ0=1, k3=1, ψ0(0)=10, ψ1(0)=10. The sliding surface parameters of the secondary industrial robotic arm are designed as follows: β 11 =1,β 12 =1,μ1=5,γ 11 =0.5,γ 12 =4γ 13 =6. The parameters in the sliding mode controller and adaptive law design are: κ i1 =8,κ i2 =8,η i2 =6,Ω imin =0.5, η3=0.02. To better fit the actual application scenario, when t≥2, a sudden actuator failure is considered, reducing the effective control torque to 50% of the previous value.

[0148] Figure 3 The image shows the structure of the dual-joint industrial robotic arm model used in the simulation. Figure 4 This demonstrates the control hysteresis loop in an industrial robotic arm. The target trajectory and the trajectory tracking results of the master and slave industrial robotic arms are shown below. Figure 5 and Figure 6 As shown; Figure 7 It is the control torque of the main industrial robotic arm system affected by actuator failure; Figure 8 It is the control torque affected by actuator failure in the industrial robotic arm system; Figure 9 These are the curves showing the change in sliding mode states of the master industrial robotic arm and the slave industrial robotic arm system. Figure 10 It is the convergence curve of the tracking error of the main industrial robotic arm system to the reference trajectory; Figure 11It is the convergence curve of the tracking error of the main industrial robotic arm from the industrial robotic arm system.

[0149] This invention discloses an adaptive sliding mode trajectory tracking method for a master-slave industrial robotic arm system. Considering the influence of various factors on the industrial robotic arm system, such as internal parameter perturbations, external disturbances, transmission mechanism backlash, and actuator failures, the disturbed robotic arm system is modeled. A master-slave control method for the dual-robotic arm system is designed using distributed control principles. Based on this, a segmented preset sliding surface, a master-slave industrial robotic arm trajectory tracking sliding mode controller, and an adaptive law for the controller parameters are designed using switching control, adaptive control theory, and sliding mode control principles. This enables the master industrial robotic arm to compensate for lumped disturbances and overcome the influence of actuator failures within a finite time, allowing the tracking error of the target trajectory to converge to a preset limit within a finite time. Simultaneously, the slave industrial robotic arm overcomes the influence of lumped disturbances and actuator failures while achieving asymptotic tracking of the master industrial robotic arm's trajectory. Finally, Lyapunov stability theory is used to prove that the master-slave industrial robotic arm system can achieve consistent asymptotic tracking of the target trajectory. This method solves the problem of how to quickly achieve consistent trajectory tracking in a master-slave industrial robotic arm system under the influence of internal parameter perturbations, external disturbances, transmission mechanism backlash, and actuator failures.

[0150] Based on the same inventive concept, the present invention provides an adaptive sliding mode trajectory tracking system for a master-slave industrial robotic arm system, comprising:

[0151] The model building unit is used to establish kinematic and dynamic models of industrial robotic arms, i.e. master-slave industrial robotic arm models, based on the Euler-Lagrange equations and affected by internal parameter perturbations, external disturbances, control hysteresis, and actuator failures.

[0152] The system architecture building unit is used to design the master-slave industrial robot system structure and information interaction relationship based on the distributed control principle, utilizing the expected trajectory of the industrial robot and the established kinematic and dynamic models. Specifically, the master industrial robot system interacts with the host computer to obtain relevant information about the target trajectory and designs a controller to achieve finite-time tracking control of the master industrial robot on the target trajectory; the system also obtains the state information of the master industrial robot from the industrial robot system to construct virtual signals and design a controller to achieve asymptotic tracking control of the slave industrial robot on the trajectory of the master industrial robot.

[0153] The sliding surface design unit is used to design sliding surfaces for the master industrial robotic arm system and the slave industrial robotic arm system respectively using the switching control principle.

[0154] The controller design unit is used to design equivalent controllers for the master and slave industrial robot arm systems based on the kinematic and dynamic models of the industrial robot arm and the sliding mode surface of the master and slave industrial robot arm systems to achieve system state convergence. Using adaptive control methods combined with the sliding mode control principle, auxiliary controllers are designed for the master and slave industrial robot arm systems to compensate for lumped disturbances and actuator faults in the system, accelerate the system state convergence speed, and achieve finite-time convergence of the master industrial robot arm trajectory tracking error and asymptotic tracking of the slave industrial robot arm trajectory to the master industrial robot arm.

[0155] The compensation unit is used to design adaptive laws for the controller parameters of the master and slave industrial robotic arm systems to accelerate the compensation speed for unknown lumped disturbances, while avoiding overestimation of the adaptive parameters.

[0156] Based on the same inventive concept, the present invention provides an electronic device, the device comprising:

[0157] Memory containing executable program code;

[0158] A processor coupled to the memory;

[0159] The processor calls the executable program code stored in the memory to execute the steps of the master-slave industrial robotic arm system adaptive sliding mode trajectory tracking method described above.

[0160] Based on the same inventive concept, the present invention provides a computer-readable storage medium storing computer instructions, which, when invoked, are used to execute the steps of the above-described adaptive sliding mode trajectory tracking method for a master-slave industrial robotic arm system.

[0161] The above embodiments are merely illustrative of the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solutions based on the technical concept proposed in this invention shall fall within the scope of protection of this invention.

Claims

1. An adaptive sliding mode trajectory tracking method for a master-slave industrial robotic arm system, characterized in that, Includes the following steps: S1. Based on the Euler-Lagrange equations, establish the kinematic and dynamic models of the industrial robotic arm, which are affected by internal parameter perturbations, external disturbances, control hysteresis, and actuator failures; the established kinematic and dynamic models of the industrial robotic arm are as follows: The main industrial robotic arm model is as follows: ; The industrial robotic arm model is as follows: ; in: ， ， ， , , These represent the angle, angular velocity, and angular acceleration of each joint of the main industrial robotic arm. , , These represent the angle, angular velocity, and angular acceleration of each joint of the industrial robotic arm. It refers to the number of joints in the robotic arm. These are the corresponding markings for the master industrial robotic arm system and the slave industrial robotic arm system. It is the positive definite symmetric inertia matrix of the master or slave industrial robotic arm system. It is the matrix of centrifugal and Coriolis forces during the operation of the main industrial robotic arm system or the slave industrial robotic arm. It is the gravity vector of the main industrial robotic arm system or the slave industrial robotic arm. It is the actual effective value of the controller of the main industrial robotic arm system or the slave industrial robotic arm system. It is the gain fault coefficient. It is an adaptive sliding mode controller for the master or slave industrial robotic arm system. It is the component corresponding to the actual effective value of the controller. The error is caused by system parameter perturbation, actuator bias fault, and actuator gain fault. It is a lumped disturbance in the main industrial robotic arm system or the slave industrial robotic arm system. It is a control hysteresis generated by the gaps in the main industrial robotic arm system or the transmission mechanism of the industrial robotic arm. It refers to external interference with the torque of the main or slave industrial robotic arm system. These are the two intersections of the hysteresis curve and the horizontal axis. It is the left and right critical points for the current control action to get rid of the hysteresis effect. The vertical axis remains unchanged when the control action is affected by hysteresis. S2. Using the desired trajectory of the industrial robot and the kinematic and dynamic models established in step S1, design the master-slave industrial robot system structure and information interaction relationship based on the distributed control principle. Specifically, the master industrial robot system interacts with the host computer to obtain relevant information about the target trajectory and designs a controller to achieve finite-time tracking control of the master industrial robot on the target trajectory; the state information of the master industrial robot is obtained from the industrial robot system to construct virtual signals and design a controller to achieve asymptotic tracking control of the slave industrial robot on the trajectory of the master industrial robot. S3. Using the switching control principle, sliding surfaces are designed for the master industrial robotic arm system and the slave industrial robotic arm system respectively. S4. Based on the kinematic and dynamic models of the industrial robotic arm in step S1 and the sliding surfaces of the master and slave industrial robotic arm systems established in step S3, design equivalent controllers for the master and slave industrial robotic arm systems respectively to achieve system state convergence; using adaptive control methods combined with sliding mode control principles, design auxiliary controllers for the master and slave industrial robotic arm systems respectively to compensate for lumped disturbances and actuator faults in the system, accelerate the system state convergence speed, and achieve finite-time convergence of the master industrial robotic arm trajectory tracking error and asymptotic tracking of the master industrial robotic arm trajectory by the slave industrial robotic arm; S5. Design adaptive laws for the controller parameters of the master industrial robotic arm system and the slave industrial robotic arm system respectively to accelerate the compensation speed for unknown lumped disturbances, while avoiding overestimation of adaptive parameters.

2. The adaptive sliding mode trajectory tracking method for a master-slave industrial robotic arm system according to claim 1, characterized in that, Virtual signal in step S2 The construction is as follows: ； in, , yes The inverse matrix, It is the positive definite symmetric inertia matrix of the main industrial robotic arm system. It is the matrix of centrifugal force and Coriolis force during the operation of the main industrial robotic arm. It is the gravity vector of the main industrial robotic arm. It is the equivalent controller of the main industrial robotic arm system. It is the auxiliary controller of the main industrial robotic arm system, and the virtual signal The difference between the angular acceleration of the main industrial robotic arm system and the angular acceleration of the main industrial robotic arm system is: ； in, It refers to the 2-norm of a column vector. It is the gain failure factor of the main industrial robotic arm system. It is external interference with the torque of the main industrial robotic arm system. It is a control hysteresis loop caused by the gap in the transmission mechanism of the main industrial robotic arm system.

3. The adaptive sliding mode trajectory tracking method for a master-slave industrial robotic arm system according to claim 1, characterized in that, In step S3, the sliding surfaces of the master industrial robotic arm system and the slave industrial robotic arm system are designed as follows: The sliding surface design of the main industrial robotic arm is as follows: ; The sliding surface design of industrial robotic arms is as follows: ; in, The sliding surface of the main industrial robotic arm. To extract from the sliding surface of an industrial robotic arm, , It is the trajectory tracking error of the main industrial robotic arm. These are the components of the corresponding joints. It is the target trajectory signal. for The derivative of It's from the trajectory tracking error of the industrial robotic arm. These are the components of the corresponding joints. for The derivative of and It is a positive constant that adjusts the convergence speed. It is an intermediate variable. It is a positive integer and satisfies the following conditions: Designed for odd numbers, Designed for even numbers, ,in Designed for odd numbers; , ,in , , It is a constant and satisfies: , It is the accuracy range within which the tracking error converges within a pre-set finite time. , , , , , , , , Represents the symbolic function. It is an intermediate variable with no actual physical meaning.

4. The adaptive sliding mode trajectory tracking method for a master-slave industrial robotic arm system according to claim 1, characterized in that, The adaptive sliding mode controller for the main industrial robotic arm in step S4 is designed as follows: ； in, It is a positive constant that adjusts the convergence speed. It is the adaptive sliding mode controller for the main industrial robotic arm system. It is the equivalent controller of the main industrial robotic arm system. It is the auxiliary controller for the main industrial robotic arm system. , yes The inverse matrix, It is the positive definite symmetric inertia matrix of the main industrial robotic arm system. It is the matrix of centrifugal force and Coriolis force during the operation of the main industrial robotic arm. It is the gravity vector of the main industrial robotic arm. It is the second derivative of the target trajectory. yes The derivative of , , for The derivative of It is a positive number. It is a dynamically adaptive parameter. , , For positive integers, These are the adaptive parameters in the main industrial robotic arm controller, and their adaptive law is designed as follows: ； in, , The gain fault of the main industrial robotic arm actuator is described. It is the sliding surface of the main industrial robotic arm.

5. The adaptive sliding mode trajectory tracking method for a master-slave industrial robotic arm system according to claim 1, characterized in that, In step S4, the adaptive sliding mode controller for the industrial robotic arm is designed as follows: ； in, It is an adaptive sliding mode controller from an industrial robotic arm system. It is an equivalent controller from an industrial robotic arm system. It is an auxiliary controller from an industrial robotic arm system. , yes The inverse matrix, It is derived from the positive definite symmetric inertia matrix of the industrial robotic arm system. It is the matrix of centrifugal force and Coriolis force during the operation of an industrial robotic arm. It is from the gravity vector of the industrial robotic arm. , and It is a positive constant that adjusts the convergence speed. It is a virtual signal. , for The derivative, It is a dynamically adaptive parameter. , , , It is a dynamically adaptive parameter. , For positive integers, This describes the maximum range of gain failures from industrial robotic arm actuators. It uses adaptive parameters from the industrial robotic arm controller to compensate for lumped disturbances from the industrial robotic arm. The error in information transmission between the master industrial robotic arm system and the slave industrial robotic arm is designed with the following adaptive law: ； in, , This describes a gain failure in an industrial robotic arm actuator.

6. The adaptive sliding mode trajectory tracking method for a master-slave industrial robotic arm system according to claim 1, characterized in that, Step S5: Parameters of the master industrial robotic arm system and the slave industrial robotic arm controller The specific design of the adaptive law is as follows: ； in, Are the parameters of the main industrial robotic arm system or the slave industrial robotic arm controller? The adaptive law, It is the sliding surface of the master-slave industrial robotic arm system. These are positive constants used to adjust the growth range of the adaptive parameters; ,parameter For positive integers, , For positive integers, Intermediate variables have no physical meaning and refer to... and The content within parentheses.

7. An adaptive sliding mode trajectory tracking system for a master-slave industrial robotic arm system, characterized in that, include: The model building unit is used to establish kinematic and dynamic models of an industrial robotic arm, i.e., a master-slave industrial robotic arm model, based on the Euler-Lagrange equations, which are affected by internal parameter perturbations, external disturbances, control hysteresis, and actuator failures. The established kinematic and dynamic models of the industrial robotic arm are as follows: The main industrial robotic arm model is as follows: ; The industrial robotic arm model is as follows: ; in: ， ， ， , , These represent the angle, angular velocity, and angular acceleration of each joint of the main industrial robotic arm. , , These represent the angle, angular velocity, and angular acceleration of each joint of the industrial robotic arm. It refers to the number of joints in the robotic arm. These are the corresponding markings for the master industrial robotic arm system and the slave industrial robotic arm system. It is the positive definite symmetric inertia matrix of the master or slave industrial robotic arm system. It is the matrix of centrifugal and Coriolis forces during the operation of the main industrial robotic arm system or the slave industrial robotic arm. It is the gravity vector of the main industrial robotic arm system or the slave industrial robotic arm. It is the actual effective value of the controller of the main industrial robotic arm system or the slave industrial robotic arm system. It is the gain fault coefficient. It is an adaptive sliding mode controller for the master or slave industrial robotic arm system. It is the component corresponding to the actual effective value of the controller. The error is caused by system parameter perturbation, actuator bias fault, and actuator gain fault. Lumped disturbances in the main industrial robotic arm system or the slave industrial robotic arm system. It is a control hysteresis generated by the gaps in the main industrial robotic arm system or the transmission mechanism of the industrial robotic arm. It refers to external interference with the torque of the main or slave industrial robotic arm system. These are the two intersections of the hysteresis curve and the horizontal axis. It is the left and right critical points for the current control action to get rid of the hysteresis effect. The vertical axis remains unchanged when the control action is affected by hysteresis. The system architecture building unit is used to design the master-slave industrial robot system structure and information interaction relationship based on the distributed control principle, utilizing the expected trajectory of the industrial robot and the established kinematic and dynamic models. Specifically, the master industrial robot system interacts with the host computer to obtain relevant information about the target trajectory and designs a controller to achieve finite-time tracking control of the master industrial robot on the target trajectory; the system also obtains the state information of the master industrial robot from the industrial robot system to construct virtual signals and design a controller to achieve asymptotic tracking control of the slave industrial robot on the trajectory of the master industrial robot. The sliding surface design unit is used to design sliding surfaces for the master industrial robotic arm system and the slave industrial robotic arm system respectively using the switching control principle. The controller design unit is used to design equivalent controllers for the master and slave industrial robot systems based on the kinematic and dynamic models of the industrial robot and the sliding mode surface of the master and slave industrial robot systems to achieve system state convergence. Using adaptive control methods combined with sliding mode control principles, auxiliary controllers are designed for the master and slave industrial robot systems to compensate for lumped disturbances and actuator faults in the system, accelerating system state convergence and achieving finite-time convergence of the master industrial robot's trajectory tracking error and asymptotic tracking of the master industrial robot's trajectory by the slave industrial robot. The compensation unit is used to design adaptive laws for the controller parameters of the main industrial robotic arm system and the slave industrial robotic arm system respectively, so as to accelerate the compensation speed for unknown lumped disturbances and avoid overestimation of adaptive parameters.

8. An electronic device, characterized in that, The device includes: Memory containing executable program code; A processor coupled to the memory; The processor calls the executable program code stored in the memory to execute the steps of the adaptive sliding mode trajectory tracking method for a master-slave industrial robotic arm system as described in any one of claims 1-6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions, which, when invoked, are used to perform the steps of the adaptive sliding mode trajectory tracking method for a master-slave industrial robotic arm system as described in any one of claims 1-6.

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