Flexible manipulator tracking control method and device under state restriction

Abstract

The present application relates to the technical field of mechanical arm control, and particularly relates to a flexible mechanical arm tracking control method and device under state restriction. The present application is aimed at a state-restricted mechanical arm system, a nonlinear conversion mechanism is combined with a state-restricted boundary function and an adjustable parameter to perform coordinate transformation on a flexible mechanical arm with joint state constraints, and by combining the state-restricted boundary function, both systems with state constraints and systems without state constraints can be taken into account. By introducing an artificially adjusted parameter, the rate of the converted parameter tending to infinity is changed, which is adjustable and can better cope with complex state-restricted situations. A global preset performance conversion mechanism is combined to control the tracking error, and a preset time disturbance observer is used to estimate the composite disturbance. The joint state constraints, global preset performance control and preset time disturbance observer are combined to realize tracking control of the flexible mechanical arm system, so as to improve the safety and control accuracy of the flexible mechanical arm during operation.

Description

Technical Field

[0001] This invention relates to the field of robotic arm control technology, and in particular to a method and apparatus for tracking and controlling a flexible robotic arm under constrained conditions. Background Technology

[0002] With the rapid development of industrial automation, intelligent manufacturing, and human-robot collaboration technologies, flexible robotic arms have become an important research direction in the field of robot control due to their advantages such as light weight, low energy consumption, high load-to-weight ratio, and good human-robot interaction safety. Compared with traditional rigid robotic arms, flexible robotic arms can effectively improve motion efficiency and reduce drive energy consumption, and are therefore widely used in material handling, industrial welding, precision assembly, medical surgery, and aerospace.

[0003] However, due to the elastic deformation of flexible links and complex electromechanical coupling characteristics, flexible robotic arms typically exhibit strong nonlinearity and strong disturbances, posing significant challenges to high-precision motion control and trajectory tracking. In actual operation, flexible robotic arms are inevitably affected by factors such as parameter uncertainties, joint flexibility, friction effects, actuator nonlinearity, external disturbances, and unmodeled dynamics. Furthermore, the joint angles and speeds of flexible robotic arms are often limited by physical structure and safety requirements; violations of these constraints can not only affect system performance but may even lead to equipment damage. Therefore, under external disturbances, model uncertainties, and complex operating environments, existing control methods struggle to simultaneously ensure that the system state meets constraint requirements and the tracking error meets preset performance indicators. Summary of the Invention

[0004] The main objective of this invention is to provide a method and apparatus for tracking and controlling a flexible robotic arm under state constraints, aiming to ensure that the system state meets the constraint requirements and the tracking error meets the preset performance indicators under external disturbances, model uncertainties and complex operating environments.

[0005] To achieve the above objectives, the present invention proposes a flexible robotic arm tracking control method under state constraints, comprising the following steps: Obtain the initial joint state of the flexible robotic arm; A nonlinear transformation mechanism is designed to perform coordinate transformation on the flexible robotic arm, and the system model of the flexible robotic arm is reconstructed based on the joint states and target signals obtained after the transformation; wherein, the nonlinear transformation mechanism combines state-constrained boundary functions and introduces adjustable parameters to perform nonlinear transformation; Based on the reconstructed flexible robotic arm system model, a global preset performance conversion mechanism and a preset time disturbance observer are designed. The global preset performance conversion mechanism is used to transform the tracking error to limit the tracking error within a pre-defined boundary. The preset time disturbance observer is used to estimate and compensate for external disturbances. Design a finite-time command filter, and recursively design a controller and adaptive law by combining it with the backstepping method; By utilizing a controller and a composite adaptive law, adaptive tracking control is performed on the flexible robotic arm system within a preset time control framework.

[0006] In the above-mentioned flexible robotic arm tracking control method under constrained conditions, the expression for the nonlinear conversion mechanism is: ; in, This represents the transformed joint state of the robotic arm. The target signal after conversion, and It is an adjustable parameter. ; , , and Let be a state-constrained boundary function, satisfying , This indicates the joint state of the robotic arm.

[0007] In the above-mentioned flexible robotic arm tracking control method under constrained conditions, the reconstructed flexible robotic arm system model is as follows: ; ; ; ; in, Represented as , , , , , , , , , , This indicates the angular position of the link in a flexible joint robotic arm. Indicates the angular position of the motor shaft; and Defined as a disturbance in the system. This represents the spring constant corresponding to the joint stiffness. This represents the moment of inertia of the connecting rod.

[0008] In the above-mentioned flexible robotic arm tracking control method under constrained conditions, the design of a globally preset performance conversion mechanism includes the following process: Define the preset time adjustment function as follows: ; in, It is a convergence constant set by an individual. It is an adjustable time that can be set manually. It is in A function that is continuously differentiable, monotonically increasing, and bounded within its inner boundary; The function to define the global preset performance is: ; in, , and These are artificially set global boundary constants. It is a constant that controls the convergence rate. For a pre-given time constant, Satisfying It is continuous and monotonically increasing within the interval, and its derivative is... Satisfying Continuous and bounded; The tracking error is defined as Taking the derivative with respect to the tracking error, we get: ; Using fuzzy logic systems Approximation is possible ; For the weights of the fuzzy logic system, For fuzzy basis functions, To approximate the error; ; in, It is a positive number. Let be the barrier function, when it satisfies hour, Unbounded if and only if satisfy At that time, the error boundary after transformation is: ; in, It is a strictly monotonically increasing odd function that satisfies ; This is the input to the function. Set up a global preset performance function.

[0009] In the above-mentioned flexible robotic arm tracking control method under constrained conditions, since unknown disturbances act on the second and fourth state equations of the flexible robotic arm system respectively, the preset time disturbance observer includes a second-order disturbance observer and a fourth-order disturbance observer. The second-order disturbance observer is as follows: ; in, This is an estimate of the composite disturbance. This is a second-order virtual error. For auxiliary functions, for The derivative with respect to time, and It is a constant. The output signal of the filter. These are estimates of the adaptive parameters. This is a preset time adjustment function; The fourth-order perturbation observer is: ; in, This is an estimate of the composite disturbance. It is a fourth-order virtual error. For auxiliary functions, for The derivative with respect to time, and It is a constant. The output signal of the filter. These are estimates of the adaptive parameters. This is a preset time adjustment function.

[0010] In the above-described flexible robotic arm tracking control method under constrained conditions, the finite-time command filter is: ; in, , and It is the output signal of the finite-time command filter. This serves as the virtual controller for the flexible robotic arm tracking controller, and also as the input signal for the finite-time command filter. and It is a positive number designed in the finite-time command filter, where the derivative signal of the virtual controller satisfies , satisfy and .

[0011] In the above-mentioned flexible robotic arm tracking control method under constrained conditions, the controller design includes the following process: The tracking error and virtual error are defined as follows: ; For the barrier function, For virtual controllers, To track errors, This is a virtual error; Taking the derivative of the tracking error, we get: ; in, and To simplify the calculation parameters, , ; The first step in constructing the Lyapunov function is as follows: ; in, This is the first step Lyapunov function. Design parameters for the adaptive law. For the error term of the adaptive parameters, For adaptive parameters The estimated value; Differentiating the Lyapunov function in the first step yields: ; yes The derivative of, is defined , , Indicates a second-order virtual error; Solving using the backstepping method, we obtain the first-order virtual controller and the adaptive law as follows: ; ; in, For controller gain, , It is a constant. , and Design parameters for the adaptive law. , ; Substituting the first-order virtual controller and the adaptive law back into the derivative of the first-step Lyapunov function, we get: ; Using Young's inequality for scaling, we get: ; Substituting the scaled inequality into the derivative of the first-order Lyapunov function, we get: ; Using fuzzy logic systems to analyze nonlinear terms To approach, , It is the weight of the fuzzy logic system. For fuzzy basis functions, To approximate the error; Differentiating the second-order virtual error yields: ; in, For the derivative of the first-order controller, This is the filter approximation error term; The second step of constructing the Lyapunov function is as follows: ; in, and These are design parameters, all of which are greater than 0; For the error term of the adaptive parameters, , This is the error term for the composite disturbance. ; It is a composite disturbance signal. , A constant greater than 0; Differentiating the Lyapunov function in the second step, we get: ; Solving using the backstepping method, the second-order virtual controller and the adaptive law are obtained as follows: ; in, For controller gain, , constant , and Design parameters for the adaptive law. , ; Substituting the second-order virtual controller and the adaptive law back into the derivative of the Lyapunov function in the second step, we get: ; Using Young's inequality for scaling, we get: ; Substituting the scaled inequality into the derivative of the Lyapunov function from the second step, we get: ; Using fuzzy logic systems to analyze nonlinear terms To approach, , It is the weight of the fuzzy logic system. For fuzzy basis functions, To approximate the error; Differentiating the third-order virtual error yields: ; in, The derivative of the second-order controller. This is the filter approximation error term; The third step, constructing the Lyapunov function, is as follows: ; in, For design parameters, , For the error term of the adaptive parameters, ; Differentiating the Lyapunov function in the third step yields: ; For the filter approximation error term, The output signal of the filter; Solving using the backstepping method, the third-order virtual controller and adaptive law are obtained as follows: ; in, For controller gain, , constant , and Design parameters for the adaptive law. , ; Substituting the third-order virtual controller and the adaptive law into the derivative of the Lyapunov function in the third step, we get: ; Using Young's inequality for scaling, we get: ; Substituting the scaled inequality into the derivative of the Lyapunov function from step three, we get: ; Using fuzzy logic systems to analyze nonlinear terms To approach, , It is the weight of the fuzzy logic system. For fuzzy basis functions, To approximate the error; Differentiating the fourth-order virtual error yields: ; in, For the derivative of the third-order controller, This is the filter approximation error term; The fourth step, the Lyapunov function, is constructed as follows: ; in, and These are design parameters, all greater than 0, among which... It is a fourth-order virtual error. It is the error term of the adaptive parameters. ; It is the error term of the composite disturbance. ; Differentiating the Lyapunov function in the fourth step yields: ; Solving using the backstepping method, the control input and adaptive law are obtained as follows: ; Substituting the control input and the adaptive law into the derivative of the Lyapunov function in the fourth step, we get: ; Using Young's inequality scaling, we obtain: ; Substituting the scaled inequality into the derivative of the Lyapunov function from step four, we get: .

[0012] A second aspect of the present invention also discloses a flexible robotic arm tracking control device under constrained conditions, comprising: The information acquisition module is configured to acquire the initial joint state of the flexible robotic arm; The nonlinear transformation module is configured to: design a nonlinear transformation mechanism to perform coordinate transformation on a flexible robotic arm with joint state constraints, and reconstruct the flexible robotic arm system model based on the transformed robotic arm joint states and target signals; wherein, the nonlinear transformation mechanism combines state-constrained boundary functions and introduces adjustable parameters to perform nonlinear transformation; The state estimation module is configured to: design a global preset performance conversion mechanism and a preset time disturbance observer based on the reconstructed flexible robotic arm system model. The global preset performance conversion mechanism is used to transform the tracking error to limit the tracking error within a pre-defined boundary. The preset time disturbance observer is used to estimate and compensate for external disturbances. The control design module is configured to: design a finite-time command filter, and recursively design a controller and adaptive law by combining the backstepping method; The tracking control module is configured to perform adaptive tracking control of the flexible robotic arm system within a preset time control framework using a controller and a composite adaptive law.

[0013] A third aspect of the present invention also discloses a flexible robotic arm tracking control device under state constraints, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the aforementioned flexible robotic arm tracking control method under state constraints.

[0014] The fourth aspect of the present invention also discloses a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the above-described flexible robotic arm tracking control method under state constraints.

[0015] The technical solution provided by this invention may include the following beneficial effects: This invention addresses state-constrained robotic arm systems. A nonlinear transformation mechanism, combined with state-constrained boundary functions and adjustable parameters, performs coordinate transformation on flexible robotic arms with joint state constraints. By incorporating state-constrained boundary functions, it can accommodate both state-constrained and state-free systems. Furthermore, by introducing manually adjustable parameters to alter the rate at which the transformed parameters tend towards infinity, it provides adjustability and better addresses complex state-constrained situations.

[0016] This application also incorporates a global preset performance conversion mechanism to control tracking errors and removes the restriction on initial values. Furthermore, through a preset time disturbance observer, it is possible to estimate composite disturbances at a manually preset time. This invention achieves tracking control of a flexible robotic arm system by combining joint state constraints, global preset performance control, and a preset time disturbance observer, thereby improving the safety and control accuracy of the flexible robotic arm during operation. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0018] Figure 1 A flowchart of a state-constrained flexible robotic arm tracking control method according to an embodiment of the present invention; Figure 2This is a simulation embodiment of the invention showing the motion trajectory of a flexible robotic arm joint under state constraints. Figure 3 This is a simulation embodiment of the present invention showing the joint motion trajectory of a flexible robotic arm under stateless constraints; Figure 4 This is a simulation embodiment of the present invention showing tracking error curves under different initial states; Figure 5 This is a composite disturbance error curve at different preset times in a simulation embodiment of the present invention; Figure 6 This is an adaptive parameter curve diagram in a simulation embodiment of the present invention; Figure 7 This is a control input curve of a flexible robotic arm system in a simulation embodiment of the present invention; Figure 8 This is a system framework diagram of a state-constrained flexible robotic arm tracking control device according to the present invention; Figure 9 This is a structural framework diagram of a flexible robotic arm tracking control device under state constraints according to the present invention. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0020] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present invention are only used to explain the relative positional relationship and movement of each component in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indication will also change accordingly.

[0021] In this invention, unless otherwise explicitly specified and limited, the terms "connection," "fixed," etc., should be interpreted broadly. For example, "fixed" can mean a fixed connection, a detachable connection, or an integral part; it can mean a mechanical connection or an electrical connection; it can mean a direct connection or an indirect connection through an intermediate medium; it can mean the internal communication of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0022] Furthermore, in this invention, descriptions involving "first," "second," etc., are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of those features. Additionally, the word "and / or" throughout the text means including three parallel solutions; taking "A and / or B" as an example, it includes solution A, solution B, or a solution that simultaneously satisfies A and B. Furthermore, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

[0023] This application provides a method and apparatus for tracking and controlling a flexible robotic arm under state constraints. State constraints refer to the fact that the system state of the flexible robotic arm is limited and always constrained within a limited range. This technical solution utilizes a fuzzy logic system, which is a nonlinear approximation model based on fuzzy rules, to approximate the nonlinear components of the system and unmodeled dynamics.

[0024] The following is combined with Figure 1 The present invention describes a state-constrained flexible robotic arm tracking control method according to an embodiment of the invention, comprising the following steps: Obtain the initial joint state of the flexible robotic arm; A nonlinear transformation mechanism is designed to perform coordinate transformation on the flexible robotic arm, and the system model of the flexible robotic arm is reconstructed based on the joint states and target signals obtained after the transformation; wherein, the nonlinear transformation mechanism combines state-constrained boundary functions and introduces adjustable parameters to perform nonlinear transformation; Based on the reconstructed flexible robotic arm system model, a global preset performance conversion mechanism and a preset time disturbance observer are designed. The global preset performance conversion mechanism is used to transform the tracking error to limit the tracking error within a pre-defined boundary. The preset time disturbance observer is used to estimate and compensate for external disturbances. Design a finite-time command filter, and recursively design a controller and adaptive law by combining it with the backstepping method; By utilizing a controller and a composite adaptive law, adaptive tracking control is performed on the flexible robotic arm system within a preset time control framework.

[0025] This invention addresses state-constrained robotic arm systems. A nonlinear transformation mechanism, combined with state-constrained boundary functions and adjustable parameters, performs coordinate transformation on flexible robotic arms with joint state constraints. By incorporating state-constrained boundary functions, it can accommodate both state-constrained and state-free systems. By introducing manually adjustable parameters to alter the rate at which the transformed parameters tend towards infinity, it provides adjustability and better addresses complex state-constrained situations.

[0026] This application also incorporates a global preset performance conversion mechanism to control tracking errors and removes the restriction on initial values. Furthermore, through a preset time disturbance observer, it is possible to estimate composite disturbances at a manually preset time. This invention achieves tracking control of a flexible robotic arm system by combining joint state constraints, global preset performance control, and a preset time disturbance observer, thereby improving the safety and control accuracy of the flexible robotic arm during operation.

[0027] Specifically, in one particular embodiment, the dynamic model of the flexible joint linkage robotic arm is established as follows: ; in, This indicates the angular position of the link in a flexible joint robotic arm. Indicates the angular position of the motor shaft. This represents the input torque of the control system. Indicates the mass of the connecting rod. Represents gravitational acceleration. This represents the moment of inertia of the connecting rod. This represents the moment of inertia of the motor. This represents the spring constant corresponding to the joint stiffness. This indicates the distance between the center of mass of the connecting rod and the joint axis of rotation. and This represents the dynamic disturbance term in the system. , This indicates unmodeled dynamics in the robotic arm system; By simplifying the structure of the flexible robotic arm, we obtain: ; in, , , , , For an uncertain Lipschitz continuous function, Defined as system state, Defined as the system output signal, Defined as system input signal, and For nonlinear dynamics in the system, and Defined as a disturbance in the system; The joint states of the flexible articulated robotic arm satisfy the following: ; in, , The target signal is a state-constrained boundary function, and is continuous, bounded, smooth, differentiable, and has a continuous derivative. satisfy ; The following text Represented as , Represented as , Represented as , Represented as ; To address the joint state problem, the nonlinear transformation mechanism is as follows: ; in, This represents the transformed joint state of the robotic arm. The target signal after conversion, and It is an adjustable parameter. ; , .

[0028] After the above transformation, the model of the flexible robotic arm system is as follows: ; in, Represented as , Represented as , , , , , The transformed coupling term parameters are expressed as follows: ; ; .

[0029] when hour, Approaching the state-constrained boundary ;when hour, Approaching the state-constrained boundary Furthermore, when When not constrained by state, Therefore, the state-constrained transformation method mentioned in this application is applicable to both state-constrained and non-state-constrained systems. Furthermore, the nonlinear transformation has adjustable parameters, which can better cope with complex state-constrained situations.

[0030] The design of a globally preset performance conversion mechanism includes the following process: Define the preset time adjustment function as follows: ; in, It is a convergence constant set by an individual. It is an adjustable time that can be set manually. It is in A function that is continuously differentiable, monotonically increasing, and bounded within its inner boundary; The function to define the global preset performance is: ; in, , and These are artificially set global boundary constants. It is a constant that controls the convergence rate. For a pre-given time constant, Satisfying It is continuous and monotonically increasing within the interval, and its derivative is... Satisfying Continuous and bounded; The tracking error is defined as Taking the derivative with respect to the tracking error, we get: ; Using fuzzy logic systems Approximation is possible ; For the weights of the fuzzy logic system, For fuzzy basis functions, To approximate the error; ; in, It is a positive number. Let be the barrier function, when it satisfies hour, Unbounded if and only if satisfy At that time, the error boundary after transformation is: ; in, It is a strictly monotonically increasing odd function that satisfies ; This is the input to the function. Set up a global preset performance function.

[0031] Design a finite-time command filter as follows: ; in, , and It is the output signal of the finite-time command filter. This serves as the virtual controller for the flexible robotic arm tracking controller, and also as the input signal for the finite-time command filter. and It is a positive number designed in the finite-time command filter, where the derivative signal of the virtual controller satisfies , satisfy and .

[0032] In the following text, Represented as , Represented as , Represented as , Represented as , Represented as , Represented as ; The controller and adaptive law are designed recursively as follows: Step 1: Define tracking error and virtual error as follows: ; For the barrier function, For virtual controllers, To track errors, This is a virtual error; Taking the derivative of the tracking error, we get: ; in, and To simplify the calculation parameters, , ; The first step in constructing the Lyapunov function is as follows: ; in, This is the first step Lyapunov function. Design parameters for the adaptive law. For the error term of the adaptive parameters, For adaptive parameters The estimated value; Differentiating the Lyapunov function in the first step yields: ; yes The derivative of, is defined , , Indicates a second-order virtual error; Solving using the backstepping method, we obtain the first-order virtual controller and the adaptive law as follows: ; ; in, For controller gain, , It is a constant. , and Design parameters for the adaptive law. , ; Substituting the first-order virtual controller and the adaptive law back into the derivative of the first-step Lyapunov function, we get: ; Using Young's inequality for scaling, we get: ; Substituting the scaled inequality into the derivative of the first-order Lyapunov function, we get: ; Step 2: Use a fuzzy logic system to process nonlinear terms. To approach, , It is the weight of the fuzzy logic system. For fuzzy basis functions, To approximate the error; Differentiating the second-order virtual error yields: ; in, For the derivative of the first-order controller, This is the filter approximation error term; The second step of constructing the Lyapunov function is as follows: ; in, and These are design parameters, all of which are greater than 0; For the error term of the adaptive parameters, , This is the error term for the composite disturbance. ; It is a composite disturbance signal. , It is a constant greater than 0.

[0033] To estimate the complex disturbances involved Design a pre-defined time perturbation observer: ; in, This is an estimate of the composite disturbance. This is a second-order virtual error. For auxiliary functions, for The derivative with respect to time, and It is a constant. The output signal of the filter. These are estimates of the adaptive parameters. This is a preset time adjustment function.

[0034] Differentiating the Lyapunov function in the second step, we get: ; Solving using the backstepping method, the second-order virtual controller and the adaptive law are obtained as follows: ; in, For controller gain, , constant , and Design parameters for the adaptive law. , ; Substituting the second-order virtual controller and the adaptive law back into the derivative of the Lyapunov function in the second step, we get: ; Using Young's inequality for scaling, we get: ; Substituting the scaled inequality into the derivative of the Lyapunov function from the second step, we get: ; Step 3: Use a fuzzy logic system to process nonlinear terms. To approach, , It is the weight of the fuzzy logic system. For fuzzy basis functions, To approximate the error; Differentiating the third-order virtual error yields: ; in, The derivative of the second-order controller. This is the filter approximation error term; The third step, constructing the Lyapunov function, is as follows: ; in, For design parameters, , For the error term of the adaptive parameters, ; Differentiating the Lyapunov function in the third step yields: ; For the filter approximation error term, The output signal of the filter; Solving using the backstepping method, the third-order virtual controller and adaptive law are obtained as follows: ; in, For controller gain, , constant , and Design parameters for the adaptive law. , ; Substituting the third-order virtual controller and the adaptive law into the derivative of the Lyapunov function in the third step, we get: ; Using Young's inequality for scaling, we get: ; Substituting the scaled inequality into the derivative of the Lyapunov function from step three, we get: ; Step 4: Use a fuzzy logic system to process nonlinear terms. To approach, , It is the weight of the fuzzy logic system. For fuzzy basis functions, To approximate the error; Differentiating the fourth-order virtual error yields: ; in, For the derivative of the third-order controller, This is the filter approximation error term; The fourth step, the Lyapunov function, is constructed as follows: ; in, and These are design parameters, all greater than 0, among which... It is a fourth-order virtual error. It is the error term of the adaptive parameters. ; It is the error term of the composite disturbance. ; In order to estimate the disturbances The preset time perturbation observer is designed as follows: ; in, This is an estimate of the composite disturbance. It is a fourth-order virtual error. For auxiliary functions, for The derivative with respect to time, and It is a constant. The output signal of the filter. These are estimates of the adaptive parameters. This is a preset time adjustment function.

[0035] Differentiating the Lyapunov function in the fourth step yields: ; Solving using the backstepping method, the control input and adaptive law are obtained as follows: ; Substituting the control input and the adaptive law into the derivative of the Lyapunov function in the fourth step, we get: ; Using Young's inequality scaling, we obtain: ; Substituting the scaled inequality into the derivative of the Lyapunov function from step four, we get: .

[0036] To perform stability analysis on the flexible robotic arm system, the overall Lyapunov function is constructed as follows: ; Differentiating the total Lyapunov function, we get: ; The external disturbance and its derivative have an upper bound that satisfies... , , , And satisfy , It is a positive number; Using Young's inequality, we obtain: ; Extract constant values; for simplicity, let ; Design the following constants as follows: ; Substituting the above equation into the derivative of the total Lyapunov function, we get: ; in, ; By solving the above first-order differential equation, we can obtain: ; and It is a constant. , It is a constant, and obviously, it always satisfies the following condition as it changes over time. ,therefore, There is an upper realm. The designed control system is semi-globally consistent and eventually bounded, thus satisfying stability requirements.

[0037] Specifically, Figures 2-7 Simulation results for one embodiment of this application are shown. In this simulation embodiment, the dynamic model of the flexible robotic arm system is as follows: ; Wherein, the constant is , , , , The tracking signal is Composite disturbance , The state constraints are designed as follows: , , , , , , , The initial state and adaptive parameters are designed as follows: , The remaining parameters are designed as shown in Table 1 below: Table 1 Simulation results are as follows Figure 2 — Figure 7 As shown, Figure 2 This is a diagram of the joint motion trajectory of a flexible robotic arm under constrained conditions. As can be seen, the joint state is located within the constraint boundary. Figure 3 This is a diagram of the joint motion trajectory of a flexible robotic arm under stateless constraints. It can be seen that, compared to... Figure 2 , Figure 3 The robotic arm joints are not limited by state. Figure 4 The design's global preset performance effect is displayed, showing that the tracking error is always limited within the set boundaries under different initial conditions. Figure 5 The estimation results of the disturbance observer under different preset times are shown. It can be seen that the settling time of the disturbance error is basically consistent with the preset time. Figure 6 It is the adaptive parameter curve of the flexible robotic arm system. Figure 7 This is the control input curve for the flexible robotic arm system.

[0038] like Figure 8 As shown, the second aspect of this application also discloses a flexible robotic arm tracking control device 200 under state constraints, comprising: The information acquisition module 201 is configured to acquire the initial joint state of the flexible robotic arm; The nonlinear transformation module 202 is configured to: design a nonlinear transformation mechanism to perform coordinate transformation on a flexible manipulator with joint state constraints, and reconstruct a flexible manipulator system model based on the transformed manipulator joint states and target signals; wherein, the nonlinear transformation mechanism combines state-constrained boundary functions and introduces adjustable parameters to perform nonlinear transformation; The state estimation module 203 is configured to: design a global preset performance conversion mechanism and a preset time disturbance observer based on the reconstructed flexible robotic arm system model. The global preset performance conversion mechanism is used to transform the tracking error to limit the tracking error within a pre-defined boundary. The preset time disturbance observer is used to estimate and compensate for external disturbances. The control design module 204 is configured to: design a finite-time command filter, and recursively design a controller and adaptive law by combining the backstepping method; The tracking control module 205 is configured to perform adaptive tracking control of the flexible robotic arm system within a preset time control framework using a controller and a composite adaptive law.

[0039] This invention addresses state-constrained robotic arm systems. A nonlinear transformation mechanism, combined with state-constrained boundary functions and adjustable parameters, performs coordinate transformation on flexible robotic arms with joint state constraints. By incorporating state-constrained boundary functions, it can accommodate both state-constrained and state-free systems. By introducing manually adjustable parameters to alter the rate at which the transformed parameters tend towards infinity, it provides adjustability and better addresses complex state-constrained situations.

[0040] This application also incorporates a global preset performance conversion mechanism to control tracking errors and removes the restriction on initial values. Furthermore, through a preset time disturbance observer, it is possible to estimate composite disturbances at a manually preset time. This invention achieves tracking control of a flexible robotic arm system by combining joint state constraints, global preset performance control, and a preset time disturbance observer, thereby improving the safety and control accuracy of the flexible robotic arm during operation.

[0041] like Figure 9 As shown, the third aspect of this application provides a flexible robotic arm tracking control device under state constraints, including a processor 301 and a memory 302 connected, such as via a bus 303. Further, the electronic device 300 may also include a transceiver 304. It should be noted that in practical applications, the transceiver 304 is not limited to one, and the structure of the electronic device 300 does not constitute a limitation on the embodiments of this application. The processor 301 is used in the embodiments of this application to implement a flexible robotic arm tracking control method under state constraints. The processor 301 can be a CPU, a general-purpose processor, a DSP, an ASIC, an FPGA, or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. It can implement or execute various exemplary logic blocks, modules, and circuits described in conjunction with the disclosure of this application. The processor 301 can also be a combination that implements computing functions, such as including one or more microprocessor combinations, a combination of a DSP and a microprocessor, etc. The bus 303 may include a path for transmitting information between the above components. The bus 303 can be a PCI bus or an EISA bus, etc. The bus 303 can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Figure 9The bus is represented by a single thick line, but this does not imply that there is only one bus or one type of bus. The memory 302 can be a ROM or other type of static storage device capable of storing static information and instructions, RAM or other type of dynamic storage device capable of storing information and instructions, or it can be an EEPROM, CD-ROM or other optical disc storage, optical disk storage (including compressed optical disks, laser discs, optical discs, digital universal optical discs, Blu-ray discs, etc.), magnetic disk storage media or other magnetic storage devices, or any other medium capable of carrying or storing desired program code in the form of instructions or data structures and accessible by a computer, but is not limited thereto. The memory 302 is used to store application code that executes the scheme of this application, and its execution is controlled by the processor 301. The processor 301 is used to execute the application code stored in the memory 302 to implement the steps of the state-constrained flexible robotic arm tracking control method provided by this invention.

[0042] This application also discloses a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the aforementioned method for tracking and controlling a flexible robotic arm under state constraints. This invention targets state-constrained robotic arm systems. A nonlinear transformation mechanism, combined with state-constrained boundary functions and adjustable parameters, performs coordinate transformation on a flexible robotic arm with joint state constraints. By incorporating state-constrained boundary functions, it can accommodate both state-constrained and state-unconstrained systems. By introducing manually adjustable parameters, the rate at which the transformed parameters tend towards infinity is changed, providing adjustability and better handling complex state-constrained situations. This application also incorporates a global preset performance transformation mechanism to control tracking errors and removes the restriction on initial values. Furthermore, a preset time disturbance observer enables estimation of composite disturbances at a manually preset time. This invention achieves tracking and control of a flexible robotic arm system by combining joint state constraints, global preset performance control, and a preset time disturbance observer, thereby improving the safety and control accuracy of the flexible robotic arm during operation.

[0043] The above description is only a preferred embodiment of the present invention and does not limit the patent scope of the present invention. All equivalent structural transformations made under the concept of the present invention using the contents of the present invention specification and drawings, or direct / indirect applications in other related technical fields, are included within the patent protection scope of the present invention.

Claims

1. A tracking control method for a flexible robotic arm under state constraints, characterized in that, Includes the following steps: Obtain the initial joint state of the flexible robotic arm; A nonlinear transformation mechanism is designed to perform coordinate transformation on the flexible robotic arm, and the system model of the flexible robotic arm is reconstructed based on the joint states and target signals obtained after the transformation; wherein, the nonlinear transformation mechanism combines state-constrained boundary functions and introduces adjustable parameters to perform nonlinear transformation; Based on the reconstructed flexible robotic arm system model, a global preset performance conversion mechanism and a preset time disturbance observer are designed. The global preset performance conversion mechanism is used to transform the tracking error to limit the tracking error within a pre-defined boundary. The preset time disturbance observer is used to estimate and compensate for external disturbances. Design a finite-time command filter, and recursively design a controller and adaptive law by combining it with the backstepping method; By utilizing a controller and a composite adaptive law, adaptive tracking control is performed on the flexible robotic arm system within a preset time control framework.

2. The method for tracking and controlling a flexible robotic arm under state constraints according to claim 1, characterized in that, The expression for the nonlinear conversion mechanism is: ； in, This represents the transformed joint state of the robotic arm. The target signal after conversion, and It is an adjustable parameter. ; , , and Let be a state-constrained boundary function, satisfying , This indicates the joint states of the robotic arm. For target signal.

3. The method for tracking and controlling a flexible robotic arm under state constraints according to claim 2, characterized in that, The reconstructed flexible robotic arm system model is as follows: ； ； ； ； in, Represented as , , , , , , , , , , This indicates the angular position of the link in a flexible joint robotic arm. Indicates the angular position of the motor shaft; and Defined as a disturbance in the system. This represents the spring constant corresponding to the joint stiffness. This represents the moment of inertia of the connecting rod.

4. The method for tracking and controlling a flexible robotic arm under state constraints according to claim 3, characterized in that, The design of a globally preset performance conversion mechanism includes the following process: Define the preset time adjustment function as follows: ； in, It is a convergence constant set by an individual. It is an adjustable time that can be set manually. It is in A function that is continuously differentiable, monotonically increasing, and bounded within its inner boundary; The function to define the global preset performance is: ； in, , and These are artificially set global boundary constants. It is a constant that controls the convergence rate. For a pre-given time constant, Satisfying It is continuous and monotonically increasing within the interval, and its derivative is... Satisfying Continuous and bounded; The tracking error is defined as Taking the derivative with respect to the tracking error, we get: ； Using fuzzy logic systems Approximation is possible ; For the weights of the fuzzy logic system, For fuzzy basis functions, To approximate the error; ； in, It is a positive number. Let be the barrier function, when it satisfies hour, Unbounded if and only if satisfy At that time, the error boundary after transformation is: ； in, It is a strictly monotonically increasing odd function that satisfies ; This is the input to the function. Set up a global preset performance function.

5. The method for tracking and controlling a flexible robotic arm under state constraints according to claim 4, characterized in that, The preset time disturbance observer includes a second-order disturbance observer and a fourth-order disturbance observer. The second-order disturbance observer is as follows: ； in, This is an estimate of the composite disturbance. This is a second-order virtual error. For auxiliary functions, for The derivative with respect to time, and It is a constant. The output signal of the filter. These are estimates of the adaptive parameters. This is a preset time adjustment function; The fourth-order perturbation observer is: ； in, This is an estimate of the composite disturbance. It is a fourth-order virtual error. For auxiliary functions, for The derivative with respect to time, and It is a constant. The output signal of the filter. These are estimates of the adaptive parameters. This is a preset time adjustment function.

6. The method for tracking and controlling a flexible robotic arm under state constraints according to claim 5, characterized in that, The finite-time command filter is: ； in, , and It is the output signal of the finite-time command filter. This serves as the virtual controller for the flexible robotic arm tracking controller, and also as the input signal for the finite-time command filter. and It is a positive number designed in the finite-time command filter, where the derivative signal of the virtual controller satisfies , satisfy and .

7. The method for tracking and controlling a flexible robotic arm under state constraints according to claim 6, characterized in that, Designing a controller involves the following process: The tracking error and virtual error are defined as follows: ； For the barrier function, For virtual controllers, To track errors, This is a virtual error; Taking the derivative of the tracking error, we get: ； in, and To simplify the calculation parameters, , ; The first step in constructing the Lyapunov function is as follows: ； in, This is the first step Lyapunov function. Design parameters for the adaptive law. For the error term of the adaptive parameters, For adaptive parameters The estimated value; Differentiating the Lyapunov function in the first step yields: ； yes The derivative of, is defined , , Indicates a second-order virtual error; Solving using the backstepping method, we obtain the first-order virtual controller and the adaptive law as follows: ； ； in, For controller gain, , It is a constant. , and Design parameters for the adaptive law. , ; Substituting the first-order virtual controller and the adaptive law back into the derivative of the first-step Lyapunov function, we get: ； Using Young's inequality for scaling, we get: ； Substituting the scaled inequality into the derivative of the first-order Lyapunov function, we get: ； Using fuzzy logic systems to analyze nonlinear terms To approach, , It is the weight of the fuzzy logic system. For fuzzy basis functions, To approximate the error; Differentiating the second-order virtual error yields: ； in, For the derivative of the first-order controller, This is the filter approximation error term; The second step of constructing the Lyapunov function is as follows: ； in, and These are design parameters, all of which are greater than 0; For the error term of the adaptive parameters, , This is the error term for the composite disturbance. ; It is a composite disturbance signal. , A constant greater than 0; Differentiating the Lyapunov function in the second step, we get: ； Solving using the backstepping method, the second-order virtual controller and the adaptive law are obtained as follows: ； in, For controller gain, , constant , and Design parameters for the adaptive law. , ; Substituting the second-order virtual controller and the adaptive law back into the derivative of the Lyapunov function in the second step, we get: ； Using Young's inequality for scaling, we get: ； Substituting the scaled inequality into the derivative of the Lyapunov function from the second step, we get: ； Using fuzzy logic systems to analyze nonlinear terms To approach, , It is the weight of the fuzzy logic system. For fuzzy basis functions, To approximate the error; Differentiating the third-order virtual error yields: ； in, The derivative of the second-order controller. This is the filter approximation error term; The third step, constructing the Lyapunov function, is as follows: ； in, For design parameters, , For the error term of the adaptive parameters, ; Differentiating the Lyapunov function in the third step yields: ； For the filter approximation error term, The output signal of the filter; Solving using the backstepping method, the third-order virtual controller and adaptive law are obtained as follows: ； in, For controller gain, , constant , and Design parameters for the adaptive law. , ; Substituting the third-order virtual controller and the adaptive law into the derivative of the Lyapunov function in the third step, we get: ； Using Young's inequality for scaling, we get: ； Substituting the scaled inequality into the derivative of the Lyapunov function from step three, we get: ； Using fuzzy logic systems to analyze nonlinear terms To approach, , It is the weight of the fuzzy logic system. For fuzzy basis functions, To approximate the error; Differentiating the fourth-order virtual error yields: ； in, For the derivative of the third-order controller, This is the filter approximation error term; The fourth step, the Lyapunov function, is constructed as follows: ； in, and These are design parameters, all greater than 0, among which... It is a fourth-order virtual error. It is the error term of the adaptive parameters. ; It is the error term of the composite disturbance. ; Differentiating the Lyapunov function in the fourth step yields: ； Solving using the backstepping method, the control input and adaptive law are obtained as follows: ； Substituting the control input and the adaptive law into the derivative of the Lyapunov function in the fourth step, we get: ； Using Young's inequality scaling, we obtain: ； Substituting the scaled inequality into the derivative of the Lyapunov function from step four, we get: 。 8. A flexible robotic arm tracking control device under state constraints, characterized in that, The method for tracking and controlling a flexible robotic arm under state constraints as described in any one of claims 1-7 includes: The information acquisition module is configured to acquire the initial joint state of the flexible robotic arm; The nonlinear transformation module is configured to: design a nonlinear transformation mechanism to perform coordinate transformation on a flexible robotic arm with joint state constraints, and reconstruct the flexible robotic arm system model based on the transformed robotic arm joint states and target signals; wherein, the nonlinear transformation mechanism combines state-constrained boundary functions and introduces adjustable parameters to perform nonlinear transformation; The state estimation module is configured to: design a global preset performance conversion mechanism and a preset time disturbance observer based on the reconstructed flexible robotic arm system model. The global preset performance conversion mechanism is used to transform the tracking error to limit the tracking error within a pre-defined boundary. The preset time disturbance observer is used to estimate and compensate for external disturbances. The control design module is configured to: design a finite-time command filter, and recursively design a controller and adaptive law by combining the backstepping method; The tracking control module is configured to perform adaptive tracking control of the flexible robotic arm system within a preset time control framework using a controller and a composite adaptive law.

9. A computer-readable storage medium, characterized in that: A computer-readable storage medium is used to store computer instructions that, when executed by a processor, implement the state-constrained flexible robotic arm tracking control method as described in any one of claims 1-7.

10. A flexible robotic arm tracking control device under state constraints, characterized in that, include: The system includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the state-constrained flexible robotic arm tracking control method according to any one of claims 1-7.

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