Single-link robot dynamic memory event-triggered fixed-time control method and system

Abstract

The application discloses a single-link mechanical arm dynamic memory event trigger fixed time control method and system, the method comprises the following steps: by modeling, the controlled system is described as a nonlinear system with state time delay and input time delay; based on the nonlinear system, a coordinate transformation is introduced, and a tracking error is defined; by the defined tracking error, a virtual control law and an adaptive update law are designed; by giving a dynamic memory event trigger mechanism, the stability of the control system is ensured, the system comprises a sensor module, a communication module, a control system and a man-machine interaction module, in the method, the dynamic memory event trigger control mechanism is a new type of nonlinear control strategy, which can save network resources and data transmission, the designed fixed time control strategy can realize stable control within a strictly specified time by accurately presetting the convergence time boundary, the response speed is significantly improved, and the method is especially suitable for industrial automation scenes with strict time accuracy requirements.

Description

Technical Field

[0001] This invention relates to the fields of control theory and control engineering technology, and in particular to a method and system for controlling fixed-time dynamic memory event triggering of a single-link robotic arm. Background Technology

[0002] With the continuous improvement of modern industrial automation, the precise control of single-link robotic arm systems has received increasing attention. In practical industrial applications, robotic arm control systems often face multiple technical challenges, including complex nonlinear dynamic characteristics, significant joint drive time delays, and strict communication resource limitations. These factors not only directly affect the trajectory tracking accuracy and operational stability of the robotic arm, but also place higher demands on the real-time performance and robustness of the control algorithm.

[0003] Traditional robotic arm control methods typically employ fixed-cycle PID control strategies. While simple to implement, this approach often exhibits significant limitations when handling robotic arm systems with highly nonlinear characteristics. Particularly in high-precision trajectory tracking scenarios, a fixed sampling frequency can lead to insufficient control accuracy or cause frequent actuator movements. Dynamic memory event-triggered control, as a novel intelligent control strategy, dynamically triggers control updates by assessing changes in the robotic arm's state in real time, effectively balancing control performance with actuator energy consumption.

[0004] Fixed-time control technology, with its unique advantage of precisely preset convergence time, has demonstrated significant application value in fields such as industrial robots and precision assembly. Compared to finite-time control, the convergence time of fixed-time control is independent of the initial state and is determined solely by the controller parameters. Even under large disturbances, the convergence time can still be guaranteed. Furthermore, a fixed time can be preset. This facilitates system scheduling and optimization, making it suitable for industrial scenarios with high real-time requirements, ensuring system stability within a strictly defined timeframe regardless of initial error. However, existing research still faces numerous unresolved technical challenges when applying fixed-time control technology to single-link robotic arm systems with nonlinear time-delay characteristics.

[0005] The main technical bottlenecks in current robotic arm control research are concentrated in the following aspects: First, existing control methods are not adaptable enough to handle the nonlinear dynamics and joint time delay of robotic arms, making it difficult to simultaneously ensure trajectory tracking accuracy and system stability; second, under resource-constrained conditions, traditional event-triggered mechanisms are often inefficient and cannot effectively reduce the communication and computing burden of the robotic arm control system; finally, the optimization balance between control performance and actuator energy consumption has not been fully resolved, making it difficult to meet the increasingly stringent energy efficiency requirements of industrial sites.

[0006] Adaptive control technology effectively responds to load changes and external disturbances by adjusting the control parameters of a robotic 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 robotic arms, while research on adaptive event-triggered fixed-time control methods for single-link robotic arms is relatively scarce, lacking systematic solutions and technical approaches. This research status quo severely restricts the widespread application of related technologies in industrial automation.

[0007] This invention addresses the aforementioned technical challenges by proposing an innovative adaptive dynamic memory event-triggered fixed-time control method for single-link robotic arms. This method introduces a dynamic memory event triggering mechanism, utilizing historical information about the robotic arm's motion state to optimize triggering conditions, significantly improving the intelligence and execution efficiency of event triggering. Simultaneously, combined with advanced adaptive control strategies, it effectively solves the problems of nonlinear dynamic characteristics and joint time delay in robotic arms. More importantly, this method strictly guarantees the fixed-time convergence characteristics of the robotic arm 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 significantly reduces the update frequency of control signals while maintaining excellent control performance, demonstrating outstanding engineering application value. This research result not only provides an innovative technical solution for the precise control of single-link robotic arms but also lays an important theoretical foundation for the technological development of industrial robot control.

[0008] A search revealed Chinese invention patent CN119795200A, which discloses an adaptive predefined time control method for a single-link robotic arm based on event triggering. This method includes determining the robotic arm's parameters through modeling; designing a control protocol with an event triggering mechanism to adapt to measurement errors in the system output; establishing a first and second virtual controller through coordinate transformation and designing an adaptive law; and constructing an event triggering controller in conjunction with the event triggering mechanism to achieve predefined time stability of the robotic arm. This invention effectively improves the control accuracy and robustness of the robotic arm through adaptive control and an event triggering mechanism, while reducing computational complexity, simplifying the parameter estimation process, and enhancing real-time performance. It provides an efficient and stable solution for the control of intelligent robots and automation technologies in practical industrial applications.

[0009] The technology of this invention is compared with that of the aforementioned patent 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 technology of this invention is compared with that of the aforementioned patent 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 solution of the present invention: 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:

[0040] (1);

[0041] 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. For state time delay, For input time delay, Input torque for controlling the linkage joints of the robotic arm;

[0042] (2);

[0043] 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;

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

[0045] , ,in, This represents the minimum value of the equivalent inertia coefficient. This represents the minimum damping coefficient.

[0046] Expected trajectory It is twice continuously differentiable and satisfies , The first derivative of the desired trajectory, The maximum value of the expected trajectory;

[0047] Bounded time delay: , ,in This represents the maximum state time delay. Input the maximum time delay;

[0048] There exists a constant , , , , This makes the Lyapunov function of the closed-loop system... satisfy:

[0049] (3);

[0050] in, For Lyapunov functions The first derivative;

[0051] 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... :

[0052] (4);

[0053] in, To ensure design margin and meet ;

[0054] Therefore, let , The state of a controlled single-link robotic arm system can be described as follows:

[0055] (5);

[0056] 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 ;

[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] 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;

[0071] For piecewise functions:

[0072] (11);

[0073] in, To control the power parameter at a fixed time, satisfying , The preset position error accuracy threshold is satisfied. >0;

[0074] For adaptive parameters, its update law is:

[0075] (12);

[0076] in, For design parameters, The damping coefficient;

[0077] The second virtual control law is designed as follows:

[0078] (13);

[0079] 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;

[0080] For piecewise functions:

[0081] (14);

[0082] in, To control the power parameter at a fixed time, satisfying , The preset angular velocity error accuracy threshold is satisfied. >0;

[0083] For adaptive parameters, its update law is:

[0084] (15);

[0085] in, For design parameters, is the damping coefficient.

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

[0087] (16);

[0088] 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;

[0089] It is a continuous-time controller. This is a dynamic threshold, with its initial value... ,satisfy:

[0090] (17);

[0091] 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.

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

[0093] (18);

[0094] 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.

[0095] Continuous Time Controller for:

[0096] (19);

[0097] 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.

[0098] A dynamic memory event-triggered fixed-time control system for a single-link robotic arm includes:

[0099] 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.

[0100] 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.

[0101] 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;

[0102] 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.

[0103] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0104] This invention achieves a significant improvement in overall performance through the organic integration of multiple innovative technologies. The method employs a fixed-time control strategy, which, by precisely presetting the convergence time boundary, enables the system to achieve stable control within a strictly defined time. Compared to finite-time control, the convergence time of fixed-time control is independent of the initial state and is determined solely by the controller parameters. Even if the system is subjected to large-scale disturbances, the convergence time can still be guaranteed, and the fixed time can be preset in advance. This approach facilitates system scheduling and optimization, making it suitable for industrial scenarios with high real-time requirements. It ensures system stability within a strictly defined timeframe regardless of initial error. The designed dynamic memory event triggering mechanism integrates current state and historical control information. Through intelligent dynamic adjustment of trigger thresholds, it effectively reduces the update frequency of control signals while maintaining control accuracy, significantly decreasing communication bandwidth usage and actuator energy consumption. Regarding anti-interference capabilities, this method achieves real-time online compensation for nonlinear dynamics of the robotic arm, time-varying loads, and external disturbances through deep integration of adaptive control technology, significantly improving system robustness. Attached Figure Description

[0105] Figure 1 This is a schematic diagram of the adaptive dynamic memory event triggering fixed-time control method for a single-link robotic arm in this invention;

[0106] Figure 2 This is a performance diagram of the position tracking of the adaptive dynamic memory event-triggered fixed-time control system for the single-link robotic arm in this invention.

[0107] Figure 3 This is a graph showing the change in angular velocity of the single-link robotic arm system in the adaptive dynamic memory event triggering fixed-time control method of the single-link robotic arm in this invention;

[0108] Figure 4 This is a schematic diagram of the trajectory input to the controller of the adaptive dynamic memory event-triggered fixed-time control method for a single-link robotic arm in this invention.

[0109] Figure 5 This is a schematic diagram of the triggering time of the adaptive dynamic memory event triggering fixed-time control method for a single-link robotic arm in this invention;

[0110] Figure 6 This is a time-domain characteristic diagram of the tracking error of the adaptive dynamic memory event-triggered fixed-time control method for a single-link robotic arm in this invention;

[0111] Figure 7 This is a schematic diagram of the module of the adaptive dynamic memory event triggering fixed-time control system for the single-link robotic arm in this invention. Detailed Implementation

[0112] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0113] Reference Figure 1 As shown, the single-link robotic arm dynamic memory event triggering fixed-time control method provided by the present invention includes:

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

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

[0116] (1);

[0117] in, Position of the robotic arm link. The angular velocity of the robotic arm link. It is a segmented continuous switching signal. 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;

[0118] (2);

[0119] 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;

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

[0121] , ,in, This represents the minimum value of the equivalent inertia coefficient. This represents the minimum damping coefficient.

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

[0123] Bounded time delay: , ,in This represents the maximum state time delay. Input the maximum time delay;

[0124] There exists a constant , , , , This makes the Lyapunov function of the closed-loop system... satisfy:

[0125] (3);

[0126] in, For Lyapunov functions The first derivative;

[0127] 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... :

[0128] (4);

[0129] in, To provide design margin, to meet ;

[0130] Therefore, let , The state of a controlled single-link robotic arm system can be described as follows:

[0131] (5);

[0132] 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, , 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 ;

[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] Furthermore, the virtual control rate includes a first virtual control rate and a second virtual control rate.

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

[0147] (10);

[0148] 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;

[0149] For piecewise functions:

[0150] (11);

[0151] in, To control the power parameter at a fixed time, satisfying , The preset position error accuracy threshold is satisfied. >0;

[0152] For adaptive parameters, its update law is:

[0153] (12);

[0154] in, For design parameters, The damping coefficient;

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

[0156] (13)

[0157] 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;

[0158] For piecewise functions:

[0159] (14);

[0160] in, The preset angular velocity error accuracy threshold is satisfied. >0;

[0161] For adaptive parameters, its update law is:

[0162] (15);

[0163] in, For design parameters, is the damping coefficient.

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

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

[0166] (16);

[0167] 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;

[0168] It is a continuous-time controller. This is a dynamic threshold, with its initial value... ,satisfy:

[0169] (17);

[0170] Where r is the attenuation rate, It is a dynamic memory function. It is a natural constant, approximately equal to 2.71828. 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.

[0171] The actual controller is designed to be dynamically memory-triggered.

[0172] (18);

[0173] 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.

[0174] Continuous Time Controller for:

[0175] (19);

[0176] 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.

[0177] Reference Figures 2-5 To verify the effectiveness of the dynamic memory event triggering fixed-time control method for the single-link robotic arm provided by this invention, scientific demonstration was conducted through experiments.

[0178] For single-link robotic arm systems, this invention proposes an adaptive dynamic memory event-triggered fixed-time control method. This fixed-time control method ensures the robotic arm system converges within a preset time, a characteristic that meets the real-time requirements of industrial scenarios. Furthermore, by incorporating dynamic memory event-triggered control, its robustness and ease of design effectively improve the overall task completion efficiency of the system. Dynamic memory event-triggered control also effectively saves system communication resources.

[0179] The desired trajectory in this embodiment for:

[0180] .

[0181] Figure 2 This is a performance diagram of the position tracking of a single-link robotic arm system. Figure 3 This is a graph showing the change in angular velocity of a single-link robotic arm system. Figure 4 A schematic diagram of the trajectory input to the controller. Figure 5 This is a diagram illustrating the triggering time. Figure 6 This is a time-domain characteristic diagram of the tracking error.

[0182] Depend on Figure 2-4 It can be seen that the controller designed in this invention can ensure the stability of the nonlinear multi-agent system while saving communication resources. Figure 5 As can be seen, in the test experiment, using the adaptive dynamic memory event triggering fixed-time control method of the present invention, the system only triggered the control signal 2028 times within 10 seconds. Figure 6 As can be seen, the system's tracking error is less than 0.02 within 10 seconds, indicating that the overall tracking accuracy of the system controller is excellent. These data fully verify the comprehensive advantages of this invention in reducing communication burden, improving control accuracy, and ensuring stable convergence time.

[0183] Reference Figure 7 The single-link robotic arm adaptive dynamic memory event-triggered fixed-time control system provided by this invention includes: a sensor module, a communication module, a control system, and a human-machine interaction module, wherein:

[0184] The sensor module is 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, velocity, angular velocity, and higher-order state variables of the robotic arm in real time and marks the time-delayed state variables with timestamps.

[0185] The communication module is 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.

[0186] The control system is responsible for receiving data from the sensor module and the communication module, calculating the first and second virtual control laws and actual control quantities in real time according to the preset control algorithm, updating the parameter estimates online, updating the frequency in sync with the controller, and continuously monitoring the condition response time.

[0187] The human-machine interaction module is 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.

[0188] Fixed-time control technology, with its unique advantage of precisely preset convergence time, has demonstrated significant application value in fields such as industrial robots and precision assembly. However, existing research still faces many unresolved technical challenges when applying fixed-time control technology to single-link robotic arm systems with nonlinear time-delay characteristics.

[0189] This invention achieves a significant improvement in overall performance through the organic integration of multiple innovative technologies. The method employs a fixed-time control strategy, precisely presetting the convergence time boundary to ensure stable control of the system within a strictly defined timeframe. Compared to finite-time control, the convergence time of fixed-time control is independent of the initial state and determined solely by the controller parameters. Even under large-scale disturbances, the convergence time is guaranteed, and the fixed time can be pre-set, facilitating system scheduling and optimization. It is suitable for industrial scenarios with high real-time requirements, ensuring system stability within a strictly defined timeframe regardless of initial error. The designed dynamic memory event triggering mechanism integrates current state and historical control information. Through intelligent dynamic adjustment of the trigger threshold, it effectively reduces the update frequency of control signals while maintaining control accuracy, significantly reducing communication bandwidth usage and actuator energy consumption. Regarding anti-interference capabilities, this method, through deep integration of adaptive control technology, achieves real-time online compensation for nonlinear dynamics of the robotic arm, time-varying loads, and external disturbances, significantly improving the system's robustness.

[0190] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any modifications or equivalent changes made based on the technical essence of the present invention shall still fall within the scope of protection claimed by the present invention.

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; 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. It is a segmented continuous switching signal. 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 ; make , ; 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. For continuous time variables of system operation and all signal changes; S2. Based on nonlinear systems, coordinate transformation is introduced to define the tracking error; 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; 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 dynamic memory event triggering fixed time 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.

3. 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 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.

4. The method for controlling the fixed-time dynamic memory event triggering of a single-link robotic arm according to claim 3, 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.

5. A single-link robotic arm dynamic memory event-triggered fixed-time control system using the single-link robotic arm dynamic memory event-triggered fixed-time control method as described in any one of claims 1-4, 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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