Single-connecting-rod mechanical arm dynamic memory event triggering fixed time control method and system

Abstract

The invention discloses a single-connecting-rod mechanical arm dynamic memory event triggering fixed time control method and system, and the method comprises the steps: describing a controlled system as a nonlinear system with state time lag and input time lag through modeling; introducing coordinate transformation based on a nonlinear system, and defining a tracking error; designing a virtual control law and an adaptive updating law through the defined tracking error; the stability of the control system is ensured by providing a dynamic memory event triggering mechanism, the system comprises a sensor module, a communication module, a control system and a man-machine interaction module, and the dynamic memory event triggering control mechanism in the method is used as a novel nonlinear control strategy, so that network resources and data transmission can be saved, and the system reliability is improved. The designed fixed time control strategy enables the system to achieve stable control within strictly specified time by accurately presetting the convergence time boundary, the response speed is remarkably improved, and the method is particularly suitable for industrial automation scenes with strict requirements for time precision.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of control theory and control engineering, and particularly relates to a single-link robot arm dynamic memory event-triggered fixed-time control method and system. BACKGROUND

[0002] With the continuous improvement of modern industrial automation level, the precise control problem of single-link robot arm system has been widely concerned. In actual industrial applications, the robot arm control system often needs to face multiple technical challenges such as complex nonlinear dynamics, significant joint drive time delay effect and strict communication resource limitation. These factors not only directly affect the trajectory tracking accuracy and operation stability of the robot arm, but also put higher requirements on the real-time and robustness of the control algorithm.

[0003] The traditional robot arm control method usually adopts a fixed-period PID control strategy. Although this scheme is simple to implement, it often shows obvious limitations when dealing with robot arm systems with strong nonlinear characteristics. Especially in high-precision trajectory tracking scenarios, a fixed sampling frequency may result in insufficient control accuracy or frequent actuator movement. Dynamic memory event-triggered control, as a new type of intelligent control strategy, can effectively balance the relationship between control performance and actuator energy consumption by dynamically triggering control updates based on real-time assessment of robot arm state changes.

[0004] Fixed-time control technology has the unique advantage of being able to accurately preset the convergence time, which has important application value in industrial robots and precision assembly. Compared with finite-time control, the convergence time of fixed-time control is independent of the initial state and is determined only by the controller parameters. Even if the system is subjected to a large range of disturbances, the convergence time can still be guaranteed. And the fixed time can be set in advance , which is convenient for system scheduling and optimization, suitable for industrial scenarios with high real-time requirements, and ensures that the system can be stabilized within a strictly specified time regardless of the initial error. However, existing research still faces many technical challenges when applying fixed-time control technology to single-link robot arm systems with nonlinear time delay characteristics.

[0005] The main technical bottlenecks in current robot arm control research are as follows: First, existing control methods have insufficient adaptability when dealing with robot arm nonlinear dynamics and joint time delay, making it difficult to guarantee both trajectory tracking accuracy and system stability. Second, under resource-limited conditions, traditional event-triggered mechanisms are often inefficient and cannot effectively reduce the communication and computational burden of the robot arm control system. Finally, the optimization balance between control performance and actuator energy consumption has not been fully addressed, making it difficult to meet the increasingly high energy efficiency requirements of industrial sites.

[0006] Adaptive control technology can effectively cope with load changes and external disturbances by adjusting the control parameters of the robot arm in real time. When combined with intelligent algorithms, its ability to handle complex nonlinear dynamics is significantly enhanced. However, existing research mainly focuses on the coordinated control of multi-joint robots, and there is a lack of systematic solutions and technical routes for adaptive event-triggered fixed-time control methods for single-link robots. This research status seriously restricts the popularization and application of related technologies in industrial automation.

[0007] The present invention proposes an innovative adaptive dynamic memory event-triggered fixed-time control method for single-link robots. This method introduces a dynamic memory event-triggering mechanism, uses historical information of the robot's motion state to optimize the triggering condition, and significantly improves the intelligence and execution efficiency of event triggering. At the same time, combined with advanced adaptive control strategies, it effectively solves the problem of nonlinear dynamics and joint time delay of the robot. More importantly, this method strictly guarantees the fixed-time convergence of the robot system, ensuring accurate trajectory tracking within a predetermined time, and the convergence time is independent of the initial state, meeting the real-time requirements of industrial scenarios. Through systematic theoretical analysis and detailed simulation verification, this method can significantly reduce the update frequency of control signals while ensuring excellent control performance, showing outstanding engineering application value. This research not only provides an innovative technical solution for precise control of single-link robots, but also lays an important theoretical foundation for the development of industrial robot control technology.

[0008] After searching, the Chinese invention patent with publication number CN119795200A proposes an event-triggered adaptive pre-defined time control method for single-link robots, including determining the parameters of the robot arm through modeling; designing an event-triggered control protocol that adapts to the measurement error of the system output; establishing a first virtual controller and a second virtual controller through coordinate transformation and designing an adaptive law, combining the event-triggered mechanism to build an event-triggered controller, achieving pre-defined time stability of the robot arm. This invention effectively improves the control accuracy and robustness of the robot arm through adaptive control and event-triggered mechanism, while reducing computational complexity, simplifying parameter estimation process and enhancing real-time performance, providing an efficient and stable solution for intelligent robots and automation technology control in actual industrial applications.

[0009] The technical comparison between the present invention and the above-mentioned patent is as follows:

[0010] 1. The patent "Adaptive Predefined Time Control Method for Single-Link Robotic Arm Based on Event Trigger" combines an event triggering mechanism with adaptive predefined time control. It achieves predefined time stability of the robotic arm through a virtual controller and adaptive law. Its control strategy is based on error threshold triggering, and the control signal update depends on the error magnitude.

[0011] This invention introduces a dynamic memory event triggering mechanism, which combines fixed-time control and time delay compensation. By dynamically adjusting the trigger threshold through historical control information, the communication frequency is significantly reduced, and active compensation for state time delay and input time delay is achieved. The core of the technical solution lies in processing the time delay system and optimizing the use of communication resources.

[0012] The two differ fundamentally in their technical solutions, particularly in their design philosophies regarding time delay handling methods and event triggering mechanisms.

[0013] 2. The patent "Adaptive Predefined Time Control Method for Single-Link Robotic Arm Based on Event Trigger" is applicable to robotic arm systems with no time delay or insignificant time delay, and focuses on error convergence within a predefined time.

[0014] This invention is specifically designed for robotic arm systems with state delay and input delay. Its applicable scenarios are more focused on high-precision control environments that are sensitive to time delay, such as precision assembly and high-speed grasping, where the control objectives are more stringent.

[0015] The two differ in the system models and application scenarios they target.

[0016] A search revealed Chinese invention patent CN113433825A, which discloses an adaptive fault-tolerant control method, system, and storage medium for a single-link robotic arm. The control method includes: establishing a failure nonlinear system model of the single-link robotic arm; determining a virtual controller model and an adaptive law based on the failure nonlinear system model, actual tracking error, and a transformation function; the parameters of the transformation function include a preset settling time; determining a trigger controller model and a parameter update law based on the failure nonlinear system model and a trigger event model; the parameters of the trigger event model include an update time; acquiring a control input signal and a preset settling time; and controlling the actuator of the single-link robotic arm according to the virtual controller model, the adaptive law, the trigger controller model, and the parameter update law. This invention can converge within a preset finite time, saves network bandwidth, and achieves globally unified bounded convergence, making it widely applicable in the field of industrial automatic control.

[0017] The technical comparison between this invention and the aforementioned patent is as follows:

[0018] 1. The core of the patent "Adaptive Fault-Tolerant Control Method, System and Storage Medium for Single-Link Robotic Arm" lies in fault-tolerant control. Its technical solution approximates the nonlinear system after the actuator fails completely or partially through a neural network, and combines it with an event triggering mechanism to achieve system stability and fault-tolerant tracking within a finite time.

[0019] This invention focuses on fixed-time control and dynamic memory event triggering, without involving actuator failure compensation. Instead, it improves the system response speed and stability by optimizing the triggering frequency of the control signal through time delay compensation and dynamic threshold optimization.

[0020] The two differ fundamentally in their core control objectives and functional focuses in their technical solutions.

[0021] 2. The patent "Adaptive Fault-Tolerant Control Method, System and Storage Medium for Single-Link Robotic Arm" is applicable to robotic arm systems where the actuator may fail partially or completely, emphasizing the robustness and fault tolerance of the system.

[0022] This invention is applicable to robotic arm systems with significant time delays and limited communication resources. It emphasizes achieving high-precision tracking within a fixed time period and optimizes the use of communication resources through a dynamic memory mechanism.

[0023] The two differ in the specific engineering problems they aim to solve and their application focus.

[0024] A search revealed that Chinese invention patent CN116000941A provides a fixed-time control method for a robotic arm system with output constraints, comprising the following steps: S1, modeling an n-degree-of-freedom robotic arm system to obtain a mathematical model of the robotic arm system; S2, designing a control law τi, a virtual control law ai, and an adaptive law based on the system error of the single-link robotic arm system; S3, designing an event-triggered mechanism for the robotic arm system; S4, simulation analysis. This invention addresses uncertain robotic arm systems with output constraints. Based on a backstepping design method, it utilizes RBFNN and obstacle Lyapunov functions to design an event-triggered fixed-time stable control method that can effectively track the desired trajectory. Simulation experiments show that this method enables the system to converge quickly under different initial conditions, and the system output meets the preset state constraint requirements. Simultaneously, it saves significant system communication resources and avoids the Zeno phenomenon.

[0025] The technology of this invention is compared with that of the aforementioned patent as follows:

[0026] 1. The patent "A Fixed-Time Control Method for a Robotic Arm System with Output Constraints" uses the obstacle Lyapunov function (BLF) to handle the output constraint problem of the system, and utilizes the RBF neural network to approximate the system uncertainty, combined with an event-triggered mechanism to achieve fixed-time control. Its event-triggered mechanism is based on a static threshold design.

[0027] This invention introduces a dynamic memory event triggering mechanism, the threshold of which can dynamically change based on historical information. Simultaneously, this patent uses the Pade approximation method to handle input time delay and employs a piecewise function to design the virtual control law; its technical solution utilizes different paths in handling time delay and triggering logic.

[0028] The two differ fundamentally in their technical approaches to handling system uncertainty and event triggering mechanisms.

[0029] 2. The patent "A Fixed-Time Control Method for a Robotic Arm System with Output Constraints" focuses on solving the problem of fixed-time control of robotic arm output (such as joint angle) under constraints.

[0030] While ensuring convergence within a fixed time, this invention focuses more on solving the state / input time delay problem caused by signal transmission and physical motion, and is suitable for high dynamic environments that are sensitive to time delay, such as high-speed and high-precision motion control.

[0031] The two differ fundamentally in their control objectives and applicability. Summary of the Invention

[0032] To address the aforementioned technical problems, this invention proposes a dynamic memory event-triggered fixed-time control method and system for a single-link robotic arm. By using adaptive control and an event-triggered mechanism, fixed-time control of the single-link robotic arm system is achieved.

[0033] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0034] A method for controlling a single-link robotic arm by triggering dynamic memory events at fixed times includes the following steps:

[0035] S1. By modeling, the controlled system is described as a nonlinear system with state time delay and input time delay;

[0036] S2. Based on nonlinear systems, coordinate transformation is introduced to define the tracking error;

[0037] S3. Design virtual control laws and adaptive update laws based on the defined tracking error;

[0038] S4. By providing a dynamic memory event triggering mechanism, the stability of the control system is guaranteed.

[0039] As a preferred technical scheme of the present application: in step S1, by modeling, the controlled single-link robot arm system is described as a nonlinear system with state time delay and input time delay, considering the actual operation factors of the robot arm, the dynamic model of which is:

[0040] (1);

[0041] wherein, is the position of the robot arm link, is the angular velocity of the robot arm link, is a piecewise continuous switching signal, is the total number of working modes representing significant changes in the dynamic characteristics of the robot arm, is a continuous time variable of system operation and all signal changes, is a nonlinear dynamic term dependent on transformations, is a time delay nonlinear function describing the influence of historical state on the current system dynamics, is the state time delay, is the input time delay, is the control input torque of the robot arm link joint;

[0042] (2);

[0043] wherein, is the moment of inertia of the motor rotor, is the link mass, is the torque constant, is the link length, is the load mass, is the load mass centroid offset, is the equivalent viscous friction coefficient of the motor shaft end, is the gravitational acceleration constant, is the gear box reduction ratio;

[0044] The single-link robot arm system model satisfies the following assumptions:

[0045] , wherein, is the minimum value of the equivalent inertia coefficient, is the minimum value of the damping coefficient;

[0046] The desired trajectory is second-order continuous and differentiable, and satisfies , is the first-order derivative of the desired trajectory, is the maximum value of the desired trajectory;

[0047] The time delay is bounded: , where is the maximum value of state time delay, is the maximum value of input time delay;

[0048] there exists a constant , , , , such that the Lyapunov function of the closed-loop system satisfies:

[0049] (3);

[0050] where is the first-order derivative of the Lyapunov function ;

[0051] At this time, the single-link robot system state converges within a fixed time , and the upper bound of the convergence time is :

[0052] (4);

[0053] where is the design margin, satisfying ;

[0054] Therefore, let , , the state of the controlled single-link robot system can be described as:

[0055] (5);

[0056] where is the derivative of with respect to time, i.e., the angular velocity, is the derivative of with respect to time, i.e., the angular acceleration, , is a time-delay nonlinear function that describes the influence of historical state on the current system dynamics, is the control input torque of the robot link joint, is the continuous-time variable of system operation and all signal changes, is the input time delay, , is the state time delay constant, representing the length of time delay for the state signal, is a nonlinear function that encapsulates part of the known dynamics of the system, which depends on the operating mode , is a bounded external disturbance, satisfying ;

[0057] (6).

[0058] As a preferred technical solution of the present invention, the time delay processing method includes using the Pade approximation method to transform the input time delay system into a time delay-free system, as follows:

[0059] (7);

[0060] in, Input torque for controlling the linkage joints of the robotic arm. For continuous time variables of system operation and all signal changes, For input time delay, For Laplace variables;

[0061] It also introduces intermediate variables constructed by approximating the input time delay using Pade. satisfy:

[0062] (8);

[0063] in, for The first derivative, For input time delay, Input torque for controlling the linkage joints of the robotic arm. It is a continuous time variable representing the system operation and all signal changes.

[0064] As a preferred embodiment of the present invention: in step S2, the tracking error is defined as:

[0065] (9);

[0066] in, , , This is an intermediate variable constructed to approximate the input time delay using Pade. For position tracking error, For angular velocity tracking error, To compensate for the tracking error of intermediate variables with time delay, For the desired trajectory, This is the first virtual control law.

[0067] As a preferred embodiment of the present invention: in step S3, the virtual control rate includes a first virtual control rate and a second virtual control rate.

[0068] The first virtual control law is designed as follows:

[0069] (10);

[0070] wherein, is a position error gain, is a position fixed-time control coefficient, is a position parameter adjustment gain, q is a fixed-time control high-order power parameter, and q>1 is satisfied;

[0071] is a piecewise function:

[0072] (11);

[0073] wherein, is a fixed-time control power parameter, and , is a preset position error accuracy threshold, and >0 is satisfied;

[0074] is an adaptive parameter, and an update law thereof is:

[0075] (12);

[0076] wherein, is a design parameter, is a damping coefficient;

[0077] the second virtual control law is designed as:

[0078] (13);

[0079] wherein, is an angular velocity error gain, is an angular velocity fixed-time coefficient, is an angular velocity parameter adjustment gain, q is a fixed-time control high-order power parameter, and q>1 is satisfied;

[0080] is a piecewise function:

[0081] (14);

[0082] wherein, is a fixed-time control power parameter, and , is a preset angular velocity error accuracy threshold, and >0 is satisfied;

[0083] is an adaptive parameter, and an update law thereof is:

[0084] (15);

[0085] wherein, is a design parameter, is a damping coefficient.

[0086] As a preferred technical solution of the present application: in step 4, the dynamic memory event triggering mechanism is set as:

[0087] (16);

[0088] wherein, is the time of event triggering, is the time of kth event triggering, is the time of k+1th event triggering, is a triggering margin coefficient, is a measurement error;

[0089] is a continuous-time controller, is a dynamic threshold, whose initial value satisfies:

[0090] (17);

[0091] wherein, r is a decay rate, is a dynamic memory function, is a natural constant, is an exponential decay coefficient, is an error weight coefficient, satisfying , , , , is an inertial time delay term of the dynamic memory event triggering mechanism.

[0092] As a preferred technical solution of the present application: the controller of the control system is designed in the form of dynamic memory event triggering:

[0093] (18);

[0094] wherein, is the time of event triggering, is the time of kth event triggering, is the time of k+1th event triggering;

[0095] The continuous-time controller is:

[0096] (19);

[0097] wherein, is a triggering margin coefficient, 0 is a smoothing factor, is an angular velocity tracking error, is a second virtual control law, is a normalized dynamic threshold, satisfying , tanh is a hyperbolic tangent function.

[0098] The single-link robot arm dynamic memory event-triggered fixed-time control system comprises:

[0099] A sensor module is responsible for real-time monitoring of the state of each actuator of the single-link robot arm system, and transmitting these data to the communication module and the control system, the sensor module real-time collects the position, speed, angular velocity and high-order state quantity of the robot arm, and marks the time delay state quantity through time stamp;

[0100] A communication module is responsible for receiving a trigger signal, when the event trigger condition is met, transmitting the control quantity to the control system through a dedicated channel, and controlling the position, speed, angular velocity and high-order state quantity of the single-link robot arm system through the control system, thereby controlling the position, speed, angular velocity and high-order state quantity of the single-link robot arm system;

[0101] A control system is responsible for receiving the data of the sensor module and the communication module, and calculating the first and second virtual control laws and the actual control quantity in real time according to the preset control algorithm, updating the parameter estimation value online, the update frequency is synchronized with the controller, and the condition response time is continuously monitored;

[0102] A human-computer interaction module is responsible for interacting with the operator, displaying the state information, error signal and trigger event statistics of the single-link robot arm system in real time, supporting online adjustment of parameters, receiving control instructions of the operator, and realizing human-computer collaborative control.

[0103] Compared with the prior art, the beneficial effects of the present application are:

[0104] Through the organic integration of multiple innovative technologies, the present application realizes significant comprehensive performance improvement. The method adopts a fixed-time control strategy, and through accurate presetting of the convergence time boundary, the system can realize stable control within a strictly specified time. Compared with finite time control, the convergence time of fixed-time control is independent of the initial state, and is only determined by the controller parameters, so that even if the system is disturbed in a large range, the convergence time can be guaranteed, and the fixed time can be set in advance It is convenient for system scheduling and optimization, suitable for industrial scenes with high real-time requirements, and ensures that the system can be stable within the strictly specified time regardless of the initial error. The designed dynamic memory event triggering mechanism integrates the current state and historical control information, and dynamically adjusts the intelligent triggering threshold, effectively reduces the update frequency of the control signal under the premise of ensuring control accuracy, and greatly reduces the communication bandwidth occupation and actuator energy consumption. In terms of anti-interference ability, the method realizes real-time online compensation for the nonlinear dynamics of the manipulator, time-varying load and external disturbance through the deep integration of adaptive control technology, and significantly improves the robustness of the system. BRIEF DESCRIPTION OF DRAWINGS

[0105] Figure 1 A single-link manipulator adaptive dynamic memory event triggering fixed time control method flowchart in the application;

[0106] Figure 2 A single-link manipulator adaptive dynamic memory event triggering fixed time control system position tracking performance graph in the application;

[0107] Figure 3 A single-link manipulator system angular velocity change graph of the single-link manipulator adaptive dynamic memory event triggering fixed time control method in the application;

[0108] Figure 4 A single-link manipulator system angular velocity change graph of the single-link manipulator adaptive dynamic memory event triggering fixed time control method in the application;

[0109] Figure 5 A single-link manipulator adaptive dynamic memory event triggering fixed time control method flowchart in the application;

[0110] Figure 6 A single-link manipulator adaptive dynamic memory event triggering fixed time control method flowchart in the application;

[0111] Figure 7 A single-link manipulator adaptive dynamic memory event triggering fixed time control system module schematic diagram in the application. DETAILED DESCRIPTION

[0112] The application will be further described in detail below in combination with the drawings and specific embodiments:

[0113] Referring to Figure 1 The single-link manipulator dynamic memory event triggering fixed time control method provided by the application includes:

[0114] S1: Considering the actual factors such as physical transmission and signal transmission delay of the manipulator, the controlled system is described as a nonlinear system with state time delay and input time delay through modeling.

[0115] Further, the controlled single-link manipulator system is described as a nonlinear system, including: the controlled single-link manipulator system is described as a nonlinear system with state time delay and input time delay through modeling, considering the actual factors such as physical transmission and signal transmission delay of the manipulator, and the dynamic model thereof is:

[0116] (1);

[0117] wherein, is the position of the manipulator link, is the angular velocity of the manipulator link, is a piecewise continuous switching signal, is the total number of working modes representing significant changes in the dynamic characteristics of the manipulator, is a continuous time variable of system operation and all signal changes, is a nonlinear dynamic term dependent on transformations, is a time delay nonlinear function describing the influence of historical state on the current system dynamics, is a state time delay, is an input time delay, is the control input torque of the manipulator link joint;

[0118] (2);

[0119] wherein, is the moment of inertia of the motor rotor, is the link mass, is the torque constant, is the link length, is the load mass, is the load mass centroid offset, is the equivalent viscous friction coefficient of the motor shaft end, is the gravitational acceleration constant, is the gear box reduction ratio;

[0120] The single-link manipulator system model satisfies the following assumptions:

[0121] , wherein, is the minimum value of the equivalent inertia coefficient, is the minimum value of the damping coefficient;

[0122] The desired trajectory is twice continuously differentiable, and satisfies , is the first derivative of the desired trajectory, is the maximum value of the desired trajectory;

[0123] is bounded by a time delay: , where is the maximum value of the state time delay, is the maximum value of the input time delay;

[0124] there exists a constant , , , , such that the Lyapunov function of the closed-loop system satisfies:

[0125] (3);

[0126] where is the first derivative of the Lyapunov function ;

[0127] The state of the single-link robot system converges within a fixed time and the upper bound of the convergence time is :

[0128] (4);

[0129] where is the design margin, satisfying ;

[0130] Therefore, let , the state of the controlled single-link robot system can be described as:

[0131] (5);

[0132] where is the derivative of with respect to time, i.e. the angular velocity, is the derivative of with respect to time, i.e. the angular acceleration, , is a time delay nonlinear function that describes the influence of historical state on the current system dynamics, is the control input torque of the robot link joint, is a continuous-time variable for system operation and all signal changes, , is a state time delay constant, representing the length of time delay for the state signal, For work mode It encapsulates nonlinear functions of some known dynamics of the system. For a bounded external disturbance, satisfying ;

[0133] (6).

[0134] Furthermore, time-delay processing methods include using the Pade approximation method to transform the input time-delay system into a time-delay-free system:

[0135] (7);

[0136] in, Input torque for controlling the linkage joints of the robotic arm. For continuous time variables of system operation and all signal changes, For Laplace variables;

[0137] It also introduces intermediate variables constructed by approximating the input time delay using Pade. satisfy:

[0138] (8);

[0139] in, for The first derivative, Input torque for controlling the linkage joints of the robotic arm. It is a continuous time variable representing the system operation and all signal changes.

[0140] S2: Based on the nonlinear system, coordinate transformation is introduced to define the tracking error.

[0141] Furthermore, the tracking error is defined as:

[0142] (9);

[0143] in, , , This is an intermediate variable constructed to approximate the input time delay using Pade. For position tracking error, For angular velocity tracking error, To compensate for the tracking error of intermediate variables with time delay, For the desired trajectory, This is the first virtual control law.

[0144] S3: Design virtual control laws and adaptive update laws based on the defined tracking error.

[0145] Further, the virtual control law includes a first virtual control law and a second virtual control law,

[0146] The first virtual control law is designed as:

[0147] (10);

[0148] wherein, is a position error gain, is a position fixed-time control coefficient, is a position parameter adjustment gain, and q is a fixed-time control high-order power parameter satisfying q>1;

[0149] is a piecewise function:

[0150] (11);

[0151] wherein, is a fixed-time control power parameter satisfying , is a preset position error accuracy threshold satisfying >0;

[0152] is an adaptive parameter, and an update law thereof is:

[0153] (12);

[0154] wherein, is a design parameter, is a damping coefficient;

[0155] The second virtual control law is designed as:

[0156] (13)

[0157] wherein, is an angular velocity error gain, is an angular velocity fixed-time coefficient, is an angular velocity parameter adjustment gain, and q is a fixed-time control high-order power parameter satisfying q>1;

[0158] is a piecewise function:

[0159] (14);

[0160] wherein, is a preset angular velocity error accuracy threshold satisfying >0;

[0161] is an adaptive parameter, and its update law is

[0162] (15);

[0163] wherein, is a design parameter, is a damping coefficient.

[0164] S4: By giving a dynamic memory event triggering mechanism, the stability of the control system is ensured.

[0165] Further, the dynamic memory event triggering mechanism is set as:

[0166] (16);

[0167] wherein, is the time of event triggering, is the time of the kth event triggering, is the time of the k+1th event triggering, is a triggering margin coefficient, is a measurement error;

[0168] is a continuous-time controller, is a dynamic threshold, whose initial value satisfies:

[0169] (17);

[0170] wherein, r is a decay rate, is a dynamic memory function, is a natural constant, approximately equal to 2.71828, is an exponential decay coefficient, is an error weight coefficient, satisfying , , , , is an inertial time delay term of the dynamic memory event triggering mechanism.

[0171] The actual controller is designed in the form of dynamic memory event triggering:

[0172] (18);

[0173] wherein, is the time of event triggering, is the time of the kth event triggering, is the time of the k+1th event triggering;

[0174] The continuous-time controller is:

[0175] (19);

[0176] wherein, is a trigger margin coefficient, >0 is a smoothing factor, is an angular velocity tracking error, is a second virtual control law, is a normalized dynamic threshold, satisfying , and tanh is a hyperbolic tangent function.

[0177] Referring to Figures 2-5 , in order to verify the effect of the single-link robot arm dynamic memory event-triggered fixed-time control method provided by the application, scientific demonstration is carried out through experiments.

[0178] For a single-link robot arm system, the application provides an adaptive dynamic memory event-triggered fixed-time control method. The fixed-time control method ensures that the robot arm system converges within a preset time, which meets the real-time requirement of the industrial scene. After adding the dynamic memory event-triggered control, the overall task completion efficiency of the system can be effectively improved with the good robustness and the simplicity of the design. The dynamic memory event-triggered control can effectively save the communication resources of the system.

[0179] The expected trajectory in the embodiment is :

[0180] .

[0181] Figure 2 is a single-link robot arm system position tracking performance graph, Figure 3 is a single-link robot arm system angular velocity change graph, Figure 4 a trajectory diagram of the controller input, Figure 5 is a trigger time diagram, Figure 6 is a tracking error time domain characteristic graph.

[0182] As Figures 2-4 can be seen, the controller designed by the application can ensure that the nonlinear multi-agent system is stable, while saving communication resources. As Figure 5 can be seen, in the test experiment, the adaptive dynamic memory event-triggered fixed-time control method of the application is adopted, and the system triggers the control signal 2028 times within 10 seconds. As Figure 6 can be seen, the tracking error of the system is less than 0.02 within 10 seconds, indicating that the overall tracking precision of the system controller is excellent. These data fully verify the comprehensive advantages of the application in reducing communication burden, improving control precision and ensuring stable convergence time.

[0183] Reference is made to Figure 7 The single-link robot adaptive dynamic memory event-triggered fixed-time control system provided by the application comprises a sensor module, a communication module, a control system and a human-computer interaction module.

[0184] The sensor module is responsible for real-time monitoring of the state of each actuator of the single-link robot system and transmitting these data to the communication module and the control system. The sensor module collects the position, speed, angular velocity and high-order state quantity of the robot in real time and marks the time delay state quantity through a time stamp.

[0185] The communication module is responsible for receiving a trigger signal and transmitting a control quantity to the control system through a dedicated channel when the event trigger condition is met, so as to control the position, speed, angular velocity and high-order state quantity of the single-link robot system through the control system.

[0186] The control system is responsible for receiving the data of the sensor module and the communication module and calculating the first and second virtual control laws and the actual control quantity in real time according to a preset control algorithm, updating the parameter estimation value online, and monitoring the condition response time continuously.

[0187] The human-computer interaction module is responsible for interacting with the operator, displaying the state information, error signal and trigger event statistics of the single-link robot system in real time, supporting online adjustment of parameters, receiving the control instructions of the operator and realizing human-computer collaborative control.

[0188] Fixed-time control technology has the unique advantage of precise preset convergence time and important application value in the fields of industrial robots and precision assembly. However, the existing research still faces many technical problems to be solved when applying fixed-time control technology to the single-link robot system with nonlinear time delay characteristics.

[0189] The present application realizes significant comprehensive performance improvement through the organic integration of multiple innovative technologies, the method adopts a fixed time control strategy, and through accurate preset convergence time boundary, the system can realize stable control within a strictly specified time. Compared with finite time control, the convergence time of fixed time control is irrelevant to the initial state, and is only determined by the controller parameters, so that even if the system is disturbed in a large range, the convergence time can still be guaranteed, and the fixed time can be set in advance, facilitating system scheduling and optimization, suitable for high real-time requirement industrial scenes, and ensuring that no matter how large the initial error is, the system can be stabilized within a strictly specified time. The designed dynamic memory event triggering mechanism integrates the current state and historical control information, and through intelligent triggering threshold dynamic adjustment, the control signal update frequency is effectively reduced under the premise of ensuring control accuracy, and the communication bandwidth occupation and actuator energy consumption are greatly reduced. In terms of anti-interference ability, the present method realizes real-time online compensation for the nonlinear dynamics of the manipulator, the time-varying load and external disturbance through the deep integration of adaptive control technology, and significantly improves the robustness of the system.

[0190] The above is only a preferred embodiment of the present application, not any other form of limitation on the present application, and any modification or equivalent change made according to the technical essence of the present application still belongs to the scope of the present application.

Claims

1. A method for controlling a single-link robotic arm with dynamic memory event triggering at a fixed time, characterized in that, Includes the following steps: S1. By modeling, the controlled system is described as a nonlinear system with state time delay and input time delay; S2. Based on nonlinear systems, coordinate transformation is introduced to define the tracking error; S3. Design virtual control laws and adaptive update laws based on the defined tracking error; S4. By providing a dynamic memory event triggering mechanism, the stability of the control system is guaranteed.

2. The method for controlling the fixed-time dynamic memory event triggering of a single-link robotic arm according to claim 1, characterized in that, In step S1, the controlled single-link robotic arm system is described as a nonlinear system with state time delay and input time delay through modeling. Considering the actual operating factors of the robotic arm, its dynamic model is as follows: （1）； in, Position of the robotic arm link. The angular velocity of the robotic arm link. For segmented continuous switching signals, To represent the total number of working modes in which the dynamic characteristics of the robotic arm change significantly, For continuous time variables of system operation and all signal changes, For dependence The nonlinear dynamic term of the transformation, A time-delay nonlinear function describing the impact of historical states on the current system dynamics. State delay, For input time delay, Input torque for controlling the linkage joints of the robotic arm; （2）； in, The moment of inertia of the motor rotor. For the mass of the connecting rod, It is the torque constant. The length of the link. For load quality, This is the offset of the load centroid. The equivalent viscous friction coefficient at the motor shaft end is... The acceleration due to gravity is constant. This refers to the gearbox reduction ratio; The single-link robotic arm system model satisfies the following assumptions: , ,in, This represents the minimum value of the equivalent inertia coefficient. This represents the minimum damping coefficient. Expected trajectory It is twice continuously differentiable and satisfies , The first derivative of the desired trajectory, The maximum value of the expected trajectory; Bounded time delay: , ,in This represents the maximum state time delay. Input the maximum time delay; There exists a constant , , , , This makes the Lyapunov function of the closed-loop system... satisfy: （3）； in, For Lyapunov functions The first derivative; At this time, the single-link robotic arm system is in a state that lasts for a fixed period of time. It converges internally, and the upper bound of the convergence time is... : （4）； in, To provide design margin, to meet ; Therefore, let , The state of a controlled single-link robotic arm system can be described as follows: （5）； in, for The derivative with respect to time, i.e., angular velocity, for The derivative with respect to time, i.e., angular acceleration, , To describe the influence of historical states on the current system dynamics, a time-delay nonlinear function is used. Input torque for controlling the linkage joints of the robotic arm. For continuous time variables of system operation and all signal changes, For input time delay, , The state delay constant represents the time delay of the state signal. For work mode It encapsulates nonlinear functions of some known dynamics of the system. For a bounded external disturbance, satisfying ; （6）。 3. The method for controlling the fixed-time dynamic memory event triggering of a single-link robotic arm according to claim 2, characterized in that, Time-delay processing methods include using the Pade approximation method to transform the input time-delay system into a time-delay-free system, as detailed below: （7）； in, Input torque for controlling the linkage joints of the robotic arm. For continuous time variables of system operation and all signal changes, For input time delay, For Laplace variables; It also introduces intermediate variables constructed by approximating the input time delay using Pade. satisfy: （8）； in, for The first derivative, For input time delay, Input torque for controlling the linkage joints of the robotic arm. It is a continuous time variable representing the system operation and all signal changes.

4. The method for controlling the fixed-time dynamic memory event triggering of a single-link robotic arm according to claim 1, characterized in that, In step S2, the tracking error is defined as: （9）； in, , , This is an intermediate variable constructed to approximate the input time delay using Pade. For position tracking error, For angular velocity tracking error, To compensate for the tracking error of intermediate variables with time delay, For the desired trajectory, This is the first virtual control law.

5. The method for controlling the fixed-time dynamic memory event triggering of a single-link robotic arm according to claim 1, characterized in that, In step S3, the virtual control law includes a first virtual control law and a second virtual control law. The first virtual control law is designed as follows: （10）； in, For position error gain, For fixed-position time control coefficients, The gain is adjusted by the position parameter, and q is a high-order power parameter controlled for a fixed time, satisfying q>1; For piecewise functions: （11）； in, To control the power parameter at a fixed time, satisfying , The preset position error accuracy threshold is satisfied. >0; For adaptive parameters, its update law is: （12）； in, For design parameters, The damping coefficient; The second virtual control law is designed as follows: （13）； in, For angular velocity error gain, For a fixed time coefficient of angular velocity, The gain is adjusted for the angular velocity parameter, and q is a high-order power parameter controlled for a fixed time, satisfying q>1; For piecewise functions: （14）； in, To control the power parameter at a fixed time, satisfying , The preset angular velocity error accuracy threshold is satisfied. >0; For adaptive parameters, its update law is: （15）； in, For design parameters, is the damping coefficient.

6. The method for controlling a fixed-time dynamic memory event triggering of a single-link robotic arm according to claim 1, characterized in that, In step 4, the dynamic memory event triggering mechanism is set as follows: （16）； in, The moment the event is triggered. The time when the k-th event is triggered. The time when the (k+1)th event is triggered. To trigger the margin factor, For measurement error; It is a continuous-time controller. This is a dynamic threshold, with its initial value... ,satisfy: （17）； Where r is the attenuation rate, It is a dynamic memory function. It is a natural constant. The exponential decay coefficient is... Let be the error weighting coefficient, satisfying , , , , This is the inertial delay term for the dynamic memory event triggering mechanism.

7. The method for controlling a single-link robotic arm with dynamic memory event triggering at a fixed time according to claim 6, characterized in that, The controller of the control system is designed to be dynamically memory-triggered. （18）； in, The moment the event is triggered. The time when the k-th event is triggered. This refers to the time when the (k+1)th event is triggered. Continuous Time Controller for: （19）； in, To trigger the margin factor, >0 is a smoothing factor. For angular velocity tracking error, This is the second virtual control law. The normalized dynamic threshold satisfies tanh is the hyperbolic tangent function.

8. A dynamic memory event-triggered fixed-time control system for a single-link robotic arm, characterized in that: include: Sensor module: Responsible for real-time monitoring of the status of each actuator in the single-link robotic arm system and transmitting this data to the communication module and control system. The sensor module collects the position, speed, angular velocity and higher-order state variables of the robotic arm in real time and marks the time-delayed state variables with timestamps. Communication module: Responsible for receiving trigger signals. When the event triggering conditions are met, it transmits control quantities to the control system through a dedicated channel. The control system controls the position, speed, angular velocity, and higher-order state quantities of the single-link robotic arm system. Control system: Responsible for receiving data from sensor modules and communication modules, and calculating the first and second virtual control laws and actual control quantities in real time according to the preset control algorithm, updating parameter estimates online, updating frequency synchronized with the controller, and continuously monitoring condition response time; Human-machine interaction module: Responsible for interacting with the operator, displaying the status information, error signals and trigger event statistics of the single-link robotic arm system in real time, supporting online parameter adjustment, receiving control commands from the operator, and realizing human-machine collaborative control.

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