Robotic arm control method and device with preset performance and predefined time

Abstract

This application relates to a robotic arm control method and device with preset performance and predefined time. The method includes: converting a first error to obtain an unconstrained error; designing a first control law based on the unconstrained error and predefined time; determining a second error based on the first control law and the real-time angular velocities of each joint; determining a first unknown function based on the derivative of the synthesized Lyapunov function; processing the first unknown function; and updating the derivative of the synthesized Lyapunov function using the processed first unknown function; the synthesized Lyapunov function is determined by the unconstrained error, the second error, and design weight parameters; designing a synthesized control law based on the updated derivative of the synthesized Lyapunov function; and constructing a time-varying threshold triggering mechanism based on a dynamic error threshold and the synthesized control law to regulate the real-time control parameters of the dual-joint robotic arm. This method can meet the time constraints and preset performance constraints of a fixed production cycle, improving industrial production efficiency.

Description

Technical Field

[0001] This application relates to the field of industrial automation technology, and in particular to a robotic arm control method and device with preset performance and predefined time. Background Technology

[0002] With the development of industrial automation technology, dual-joint robotic arms are widely used in industrial scenarios such as precision assembly, material handling, and welding. Dual-joint robotic arms achieve tracking and high-precision positioning of complex trajectories through the coordinated movement of two or more joints.

[0003] However, the convergence time of a dual-joint robotic arm system is heavily dependent on its initial state error; that is, the settling time of the dual-joint robotic arm system depends on the distance of the system from the target at the start. This means that when the dual-joint robotic arm starts performing a task from different actual positions each time, the time required for it to reach and stabilize at the target position varies and is uncertain. Consequently, the dual-joint robotic arm system cannot meet the time constraints of fixed industrial production cycles, thus reducing industrial production efficiency. Summary of the Invention

[0004] Therefore, it is necessary to provide a robotic arm control method and device with preset performance and predefined time that can meet the time constraints of fixed industrial production cycles and thus improve industrial production efficiency, in order to address the above-mentioned technical problems.

[0005] In a first aspect, this application provides a robotic arm control method with preset performance and predefined time, including:

[0006] For the first error Unconstrained transformation is performed to obtain unconstrained error. According to unconstrained error The first control law is obtained by designing with a predefined time. And based on the first control law And the second error in determining the real-time angular velocity of each joint. First error Determined based on the real-time and desired positions of each joint. The first joint of the dual-joint robotic arm Unconstrained error of each joint ;

[0007] Derivatives based on synthetic Lyapunov functions The first unknown function is determined, estimated using a fuzzy system, and then scaled to obtain a scaled first unknown function. The Lyapunov function is then synthesized based on the unconstrained error... Second error and design weight parameters Sure;

[0008] Using the derivative of the first unknown function after scaling with respect to the synthesized Lyapunov function The update is performed based on the derivative of the updated synthesized Lyapunov function. Design Adaptive Law And based on the derivative of the updated synthesized Lyapunov function. and adaptive law The design yielded a comprehensive control law. ;

[0009] Based on the dynamic error threshold and the comprehensive control law Defined target virtual control law A time-varying threshold triggering mechanism is constructed, and the real-time control parameters of the dual-joint robotic arm are dynamically adjusted based on the time-varying threshold triggering mechanism. The dynamic error threshold is determined based on the current control parameters of the dual-joint robotic arm.

[0010] In one embodiment, the first error Unconstrained transformation is performed to obtain unconstrained error. According to unconstrained error The first control law is obtained by designing with a predefined time. ,include:

[0011] Based on real-time joint position and desired location Determine the first error For the first error Perform an unconstrained transformation to obtain the unconstrained error. ;in, The first error of the first joint of the dual-joint robotic arm. The first error of the second joint of the dual-joint robotic arm is an unconstrained error. Depend on The transformation yields, For the first The first error of each joint For the first dual-joint robotic arm Error boundary function for each joint, , As the initial first error boundary, This is the first error boundary in steady state. For boundary decay rate, For joint indexing;

[0012] For unconstrained errors By performing differentiation, we obtain the unconstrained error after differentiation. In the formula, , ,in, For the first The second error of each joint For the first The first control law of each joint. For the first The derivative of the expected position of each joint, For the first The derivative of the error boundary function of each joint;

[0013] Based on the unconstrained error after differentiation and predefined time For the first control law Design, ,get In the formula, This is the first control law for the first joint. This is the first control law for the second joint. Scaling factor , For the unconstrained error of the first joint, This represents the unconstrained error of the second joint.

[0014] In one embodiment, the method further includes:

[0015] According to unconstrained error Define the first Lyapunov function ;

[0016] Based on the first control law Determine the first Lyapunov function The derivative is ,in, , Let be the error boundary function of the first joint. This is the error boundary function for the second joint.

[0017] In one embodiment, the method further includes:

[0018] According to the first Lyapunov function Second error and design weight parameters Determine the synthetic Lyapunov function ,in, , The second error of the first joint. This is the second error of the second joint. , For optimal weight parameters, To design weight parameters, For the real-time angular velocity of the joint, The inertia matrix of the two-joint robotic arm. For pre-set constants;

[0019] Synthetic Lyapunov functions Taking the derivative yields In the formula, For the first unknown function, The expression is , To utilize fuzzy systems to determine the first unknown function The input vector for estimation, First control law The derivative, For intersecting terms, The matrix of Coriolis force and centrifugal force is given by the following specific form: , Let the mass of the second link corresponding to the second joint be denoted as . The length of the second link. This is the distance between the center of mass of the first link corresponding to the first joint. The angle of the first joint, For the angle of the second joint, Let be the angular velocity of the first joint. The angular velocity of the second joint; Let be the derivative of the inertia matrix of the two-joint robotic arm. The derivative of the second error. It is a bounded external disturbance.

[0020] In one embodiment, a fuzzy system is used to estimate a first unknown function, and the estimated first unknown function is then scaled to obtain a scaled first unknown function, including:

[0021] Using fuzzy systems to study the first unknown function Estimation is performed to obtain the first unknown function after estimation. ,in, , Let be the first unknown function of the first joint. Let be the first unknown function of the second joint. To estimate the error, satisfy the following conditions: , To estimate the upper bound of the error, As basis vectors, , Let be the basis vector of the first joint. Let be the basis vector of the second joint. This is the optimal weight vector before scaling. , This is the optimal weight vector for the first joint before scaling. This is the optimal weight vector of the second joint before scaling.

[0022] The derivative of the synthetic Lyapunov function In Scaling process:

[0023] ,

[0024] , ····

[0025] In the formula, For a pre-defined constant, To estimate and scale the unknown function using a fuzzy system, , ,use As the optimal estimate of the unknown function after estimation and scaling using fuzzy systems, .

[0026] In one embodiment, the derivative of the scaled first unknown function with respect to the synthesized Lyapunov function is used. The update is performed based on the derivative of the updated synthesized Lyapunov function. Design Adaptive Law And based on the derivative of the updated synthesized Lyapunov function. and adaptive law The design yielded a comprehensive control law. ,include:

[0027] After scaling Substituting the derivative of the synthetic Lyapunov function The derivative of the synthetic Lyapunov function The result is an update, yielding the derivative of the updated synthetic Lyapunov function. for:

[0028] In the formula, ;

[0029] Derivatives based on the updated synthetic Lyapunov function Design the adaptive law as follows: ,in, , , , The design weight parameters for the first joint, The design weight parameters for the second joint;

[0030] Derivatives based on the updated synthetic Lyapunov function and adaptive law The design yielded a comprehensive control law. , The inertial matrix of a two-joint robotic arm The upper boundary.

[0031] In one embodiment, the method further includes:

[0032] According to the comprehensive control law Determine the target virtual control law ,in, The coefficient used to adjust the trigger sensitivity, For smoothing parameters, , Let be the scaling factor tanh of the first joint. denoted by tanh, which is the scaling factor for the second joint.

[0033] Based on target virtual control law Calculate the current target virtual control parameters of the dual-joint robotic arm. And calculate the current target virtual control parameters. Current control parameters of the dual-joint robotic arm Current control error between The current formula for calculating control error is: The current control error includes the current control error of each joint of the dual-joint robotic arm;

[0034] When the current control error of any joint in a two-joint robotic arm is determined When the error exceeds the dynamic error threshold corresponding to that joint, adjust the current control parameters of each joint of the dual-joint robotic arm to... The formula for calculating the dynamic error threshold is as follows: ,in, For the pre-set number The minimum error threshold for each joint, For the first Current control error of each joint For the first Current control parameters for each joint. For the first The current target virtual control parameters for each joint.

[0035] Secondly, this application also provides a robotic arm control device with preset performance and predefined time, comprising:

[0036] The determination module is used to determine the first error. Unconstrained transformation is performed to obtain unconstrained error. According to unconstrained error The first control law is obtained by designing with a predefined time. And based on the first control law And the second error in determining the real-time angular velocity of each joint. First error Determined based on the real-time and desired positions of each joint. The first joint of the dual-joint robotic arm Unconstrained error of each joint ;

[0037] Scaling module for derivatives based on synthesized Lyapunov functions The first unknown function is determined, estimated using a fuzzy system, and then scaled to obtain a scaled first unknown function. The Lyapunov function is then synthesized based on the unconstrained error... Second error and design weight parameters Sure;

[0038] The design module is used to utilize the derivative of the scaled first unknown function with respect to the synthesized Lyapunov function. The update is performed based on the derivative of the updated synthesized Lyapunov function. Design Adaptive Law And based on the derivative of the updated synthesized Lyapunov function. and adaptive law The design yielded a comprehensive control law. ;

[0039] The control module is used to determine the dynamic error threshold and the comprehensive control law. Defined target virtual control law A time-varying threshold triggering mechanism is constructed, and the real-time control parameters of the dual-joint robotic arm are dynamically adjusted based on the time-varying threshold triggering mechanism. The dynamic error threshold is determined based on the current control parameters of the dual-joint robotic arm.

[0040] Thirdly, this application also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to perform the following steps:

[0041] For the first error Unconstrained transformation is performed to obtain unconstrained error. According to unconstrained error The first control law is obtained by designing with a predefined time. And based on the first control law And the second error in determining the real-time angular velocity of each joint. First error Determined based on the real-time and desired positions of each joint. The first joint of the dual-joint robotic arm Unconstrained error of each joint ;

[0042] Derivatives based on synthetic Lyapunov functions The first unknown function is determined, estimated using a fuzzy system, and then scaled to obtain a scaled first unknown function. The Lyapunov function is then synthesized based on the unconstrained error... Second error and design weight parameters Sure;

[0043] Using the derivative of the first unknown function after scaling with respect to the synthesized Lyapunov function The update is performed based on the derivative of the updated synthesized Lyapunov function. Design Adaptive Law And based on the derivative of the updated synthesized Lyapunov function. and adaptive law The design yielded a comprehensive control law. ;

[0044] Based on the dynamic error threshold and the comprehensive control law Defined target virtual control law A time-varying threshold triggering mechanism is constructed, and the real-time control parameters of the dual-joint robotic arm are dynamically adjusted based on the time-varying threshold triggering mechanism. The dynamic error threshold is determined based on the current control parameters of the dual-joint robotic arm.

[0045] Fourthly, this application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, performs the following steps:

[0046] For the first error Unconstrained transformation is performed to obtain unconstrained error. According to unconstrained error The first control law is obtained by designing with a predefined time. And based on the first control law And the second error in determining the real-time angular velocity of each joint. First error Determined based on the real-time and desired positions of each joint. The first joint of the dual-joint robotic arm Unconstrained error of each joint ;

[0047] Derivatives based on synthetic Lyapunov functions The first unknown function is determined, estimated using a fuzzy system, and then scaled to obtain a scaled first unknown function. The Lyapunov function is then synthesized based on the unconstrained error... Second error and design weight parameters Sure;

[0048] Using the derivative of the first unknown function after scaling with respect to the synthesized Lyapunov function The update is performed based on the derivative of the updated synthesized Lyapunov function. Design Adaptive Law And based on the derivative of the updated synthesized Lyapunov function. and adaptive law The design yielded a comprehensive control law. ;

[0049] Based on the dynamic error threshold and the comprehensive control law Defined target virtual control law A time-varying threshold triggering mechanism is constructed, and the real-time control parameters of the dual-joint robotic arm are dynamically adjusted based on the time-varying threshold triggering mechanism. The dynamic error threshold is determined based on the current control parameters of the dual-joint robotic arm.

[0050] Fifthly, this application also provides a computer program product, including a computer program that, when executed by a processor, performs the following steps:

[0051] For the first error Unconstrained transformation is performed to obtain unconstrained error. According to unconstrained error The first control law is obtained by designing with a predefined time. And based on the first control law And the second error in determining the real-time angular velocity of each joint. First error Determined based on the real-time and desired positions of each joint. The first joint of the dual-joint robotic arm Unconstrained error of each joint ;

[0052] Derivatives based on synthetic Lyapunov functions The first unknown function is determined, estimated using a fuzzy system, and then scaled to obtain a scaled first unknown function. The Lyapunov function is then synthesized based on the unconstrained error... Second error and design weight parameters Sure;

[0053] Using the derivative of the first unknown function after scaling with respect to the synthesized Lyapunov function The update is performed based on the derivative of the updated synthesized Lyapunov function. Design Adaptive Law And based on the derivative of the updated synthesized Lyapunov function. and adaptive law The design yielded a comprehensive control law. ;

[0054] Based on the dynamic error threshold and the comprehensive control law Defined target virtual control law A time-varying threshold triggering mechanism is constructed, and the real-time control parameters of the dual-joint robotic arm are dynamically adjusted based on the time-varying threshold triggering mechanism. The dynamic error threshold is determined based on the current control parameters of the dual-joint robotic arm.

[0055] Compared with the prior art, the beneficial effects achieved by the present invention are as follows: The present invention addresses the first error... Unconstrained transformation is performed to obtain unconstrained error. According to unconstrained error The first control law is obtained by designing with a predefined time. And based on the first control law And the second error in determining the real-time angular velocity of each joint. First error Determined based on the real-time and desired positions of each joint. The first joint of the dual-joint robotic arm Unconstrained error of each joint In this method, the first error Perform an unconstrained error transformation based on preset performance to obtain the unconstrained error. So that when the first error When approaching the error threshold boundary, the unconstrained error This will increase to some extent, thereby increasing the control parameters to mitigate the first error. The error is always constrained within a preset error range and meets preset performance constraints, ensuring no overshoot during the control of the dual-joint robotic arm and guaranteeing the steady-state accuracy of the dual-joint robotic arm control within the preset performance range. This is based on unconstrained error. The first control law is obtained by designing with a predefined time. Based on the first control law And the second error in determining the real-time angular velocity of each joint. And based on unconstrained error Second error and design weight parameters Determine the synthetic Lyapunov function; based on the derivative of the synthetic Lyapunov function We obtain the first unknown function after scaling; we then use the derivative of the first unknown function with respect to the synthesized Lyapunov function. The update is performed based on the derivative of the updated synthesized Lyapunov function. Design Adaptive Law and comprehensive control law This method enables the dual-joint robotic arm to converge within a user-preset convergence time, ensuring that the control of the dual-joint robotic arm meets the time constraints of fixed industrial production cycles, thereby improving industrial production efficiency. Furthermore, compared to traditional methods where fixed threshold event triggering mechanisms are prone to over-triggering and wasting communication bandwidth in the transient phase, and insufficiently responding to accumulated small errors in the steady-state phase, making it difficult to balance control performance and communication resource efficiency, this method addresses the issue by using a dynamic error threshold determined by the current control parameters of the dual-joint robotic arm and a comprehensive control law. Defined target virtual control law A time-varying threshold triggering mechanism is constructed, and the real-time control parameters of the dual-joint robotic arm are dynamically adjusted based on the time-varying threshold triggering mechanism. It can solve the problems of excessive triggering and wasted communication bandwidth and insufficient response to accumulated small errors in the fixed threshold event triggering mechanism of traditional technology, thereby ensuring the control accuracy of the dual-joint robotic arm and reducing the waste of communication resources. Attached Figure Description

[0056] To more clearly illustrate the technical solutions in the embodiments or related technologies of this application, the accompanying drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0057] Figure 1 This is an application environment diagram of a robotic arm control method with preset performance and predefined time in one embodiment;

[0058] Figure 2 This is a flowchart illustrating a robotic arm control method with preset performance and predefined time in one embodiment.

[0059] Figure 3 This is a schematic diagram comparing the convergence of position errors at different predefined times in one embodiment;

[0060] Figure 4 This is a schematic diagram of the position error response in one embodiment;

[0061] Figure 5 This is a schematic diagram illustrating the adaptive capability of a fuzzy logic system in one embodiment;

[0062] Figure 6 This is a schematic diagram illustrating the event-triggered control input update of a joint in one embodiment;

[0063] Figure 7 This is a structural block diagram of a robotic arm control device with preset performance and predefined time in one embodiment;

[0064] Figure 8 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0065] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0066] The robotic arm control method with preset performance and predefined time provided in this application embodiment can be applied to, for example... Figure 1 In the application environment shown, terminal 102 communicates with server 104 via a network. A data storage system can store the data that server 104 needs to process. The data storage system can be integrated onto server 104 or located in the cloud or on another network server. Terminal 102 sends the real-time positions and angular velocities of each joint of the dual-joint robotic arm to server 104. Server 104 controls the dual-joint robotic arm in terminal 102 based on the received real-time joint positions and angular velocities. Terminal 102 is a machine including a dual-joint robotic arm, and can be, but is not limited to, various robots and robotic arms. Server 104 can be implemented using a standalone server or a server cluster consisting of multiple servers.

[0067] In one exemplary embodiment, such as Figure 2 As shown, a robotic arm control method with preset performance and predefined time is provided, which can be applied to... Figure 1 The following steps, from step 202 to step 208, will be used as an example to illustrate the process.

[0068] Step 202: Perform an unconstrained transformation on the first error to obtain an unconstrained error. Design a first control law based on the unconstrained error and a predefined time. Determine a second error based on the first control law and the real-time angular velocity of each joint. The first error is determined based on the real-time position and desired position of each joint.

[0069] Among them, for the first error Unconstrained transformation is performed to obtain unconstrained error. , The first joint of the dual-joint robotic arm Unconstrained error of each joint Specifically, regarding the first error Performing an unconstrained transformation refers to converting the constrained tracking error (i.e., the first error) into a single, unconstrained tracking error. This is converted into an unconstrained error to avoid transient overshoot during the control of the dual-joint robotic arm, thereby ensuring that the error in the control of the dual-joint robotic arm always remains within the preset error boundary. The predefined time refers to the maximum allowable time set in advance for the dual-joint robotic arm during its control process, from the initial posture (including position, angle, velocity, etc.) after receiving the control command until each joint stably reaches the target posture. The real-time position of each joint refers to the real-time angle of each joint.

[0070] Optionally, in this embodiment, a dynamic model of the dual-joint robotic arm is first established to clarify the state variables required for the control process, providing a foundation for subsequent control law design. The dynamic equation of the dual-joint robotic arm is as follows: ,in, , This represents the actual angle (real-time position) of the two joints, measured in rad. The angle of the first joint, The angle of the second joint. , ω represents the angular velocity of the two joints (unit: rad / s). Let be the angular velocity of the first joint. The angular velocity of the second joint. ω represents the angular acceleration of the two joints (unit: rad / s²). Let be the angular acceleration of the first joint. This is the angular acceleration of the second joint; The inertia matrix of the two-joint robotic arm. It is a symmetric positive definite inertial matrix, and has positive constants. and satisfy , The specific form of the symmetric positive definite inertia matrix is ​​a 2x2 identity matrix. ,in , , Let be the mass of the first link corresponding to the first joint. Let the mass of the second link corresponding to the second joint be denoted as . The length of the first link. The length of the second link. This is the distance between the center of mass of the first link; The matrix of Coriolis force and centrifugal force is given by the following specific form: ; and satisfy , for The derivative; For bounded external disturbances. ( , (For unknown constants) The control torque (unit: N·m), which is the final control parameter output by this application, The control torque of the first joint. This is the control torque for the second joint; This is the output (i.e., the angles of each joint).

[0071] To accommodate the recursive design of backstep control, state variables are defined. , , and The dynamic model of the two-joint robotic arm is transformed into a cascaded form (to facilitate subsequent phased design of the control law):

[0072] ,

[0073] in It is the inverse of the inertia matrix (because) If a matrix is ​​positive definite, then its inverse matrix exists and is bounded. for The derivative, for The derivative of .

[0074] The desired trajectory is preset (i.e., the desired position of the joint), and Continuous and bounded, , They are respectively The first and second derivatives), where, The desired position of the first joint. This represents the desired position of the second joint.

[0075] Based on the actual trajectory of the dual-joint robotic arm (i.e., the real-time position of each joint) and the preset desired trajectory (i.e., the desired position of each joint), the first error is determined. And for the first error Unconstrained transformation is performed to obtain unconstrained error. According to unconstrained error The first control law is obtained by designing with a predefined time. Therefore, based on the first control law And the second error in determining the real-time angular velocity of each joint. .

[0076] Step 204: Determine the first unknown function based on the derivative of the synthesized Lyapunov function, estimate the first unknown function using a fuzzy system, and perform scaling on the estimated first unknown function to obtain the scaled first unknown function; the synthesized Lyapunov function is determined based on the unconstrained error, the second error, and the design weight parameters.

[0077] Optionally, based on unconstrained error Define the first Lyapunov function According to the second error Define the second Lyapunov function And according to the design weight parameters Define the third Lyapunov function This leads to the determination of the synthetic Lyapunov function. For synthesizing Lyapunov functions Taking the derivative, we get Derivatives based on synthetic Lyapunov functions Determine the first unknown function The first unknown function Given an unknown nonlinear function, a fuzzy logic system (FLS) is used to approximate this function without model control. The fuzzy logic system operates by constructing a mapping using fuzzy IF-THEN rules, which maps the input vector... With output Connected. For example, the specific working principle of a fuzzy logic system is as follows.

[0078] First, select appropriate membership functions for the input variables to map the clear input values ​​to fuzzy distributions. This involves calculating the degree to which the input belongs to each fuzzy set using the membership functions, thus converting precise numerical values ​​into a fuzzy language description. The fuzzy system contains N rules, and the nth rule (denoted as...) ) is expressed as is THEN is ( ),in, Represents a fuzzy set. This represents the fuzzy single value corresponding to the output of the nth rule. Next, a product inference engine is used to operate on the fuzzy system, multiplying the membership degrees of each input variable to obtain the trigger strength of each rule, thus generating a fuzzy basis vector. This vector comprehensively reflects the activation status of all rules. Finally, combining the single-valued fuzzifier and the center-average defuzzifier, the fuzzy basis vector is combined with the weight vector to complete the transformation from fuzzy quantities to sharp quantities, ultimately obtaining the output of the fuzzy logic system, which is an approximation of the unknown function. Therefore, the FLS output... (An approximate value of the unknown function) can be written as

[0079] ,

[0080] In the above formula, Represents fuzzy basis vectors. Represents the weight vector. express right The degree of membership.

[0081] According to the general approximation theorem, when for When N is large enough, It can efficiently estimate any given nonlinear function. Let X be a compact set of input X. This yields the expression... ,in, It is a 2*1 vector. As basis vectors, , Let be the basis vector of the first joint. Let be the basis vector of the second joint. To estimate the error, satisfy the following conditions: , This is the upper bound of the estimation error; This is the optimal weight vector before scaling. , This is the optimal weight vector for the first joint before scaling. This is the optimal weight vector for the second joint before scaling.

[0082] Based on the above fuzzy logic system, the first unknown function is estimated, and the estimated first unknown function is scaled to obtain the scaled first unknown function.

[0083] Step 206: Update the derivative of the synthesized Lyapunov function using the scaled first unknown function, design an adaptive law based on the updated derivative of the synthesized Lyapunov function, and design the synthesized control law based on the updated derivative of the synthesized Lyapunov function and the adaptive law.

[0084] Determine the derivative of the synthesized Lyapunov function After determining the unknown function (i.e., the first unknown function), substitute this determined first unknown function into the derivative of the synthesized Lyapunov function. The derivative of the synthetic Lyapunov function The function is updated, and the derivative of the updated synthetic Lyapunov function is used. Design Adaptive Law and comprehensive control law .

[0085] Step 208: Based on the dynamic error threshold and the target virtual control law determined by the comprehensive control law, a time-varying threshold triggering mechanism is constructed, and the real-time control parameters of the dual-joint robotic arm are dynamically adjusted according to the time-varying threshold triggering mechanism; the dynamic error threshold is determined based on the current control parameters of the dual-joint robotic arm.

[0086] Based on the comprehensive control law determined above Determine the target virtual control law And according to the target virtual control law The current target virtual control parameters of the dual-joint robotic arm are determined. Furthermore, based on these current control parameters, the dynamic error threshold of the dual-joint robotic arm at the current moment is determined. This is done by comparing the current target virtual control parameters with the current actual control parameters of the dual-joint robotic arm. The difference is calculated to obtain the control error at the current moment. This control error is then compared with the dynamic error threshold at the current moment. If the control error at the current moment is greater than the dynamic error threshold, the current control parameters of the dual-joint robotic arm are adjusted. Adjustments are made; specifically, the current control parameters of the dual-joint robotic arm are adjusted to the current target virtual control parameters.

[0087] In the aforementioned robotic arm control method with preset performance and predefined time, the first error... Unconstrained transformation is performed to obtain unconstrained error. According to unconstrained error The first control law is obtained by designing with a predefined time. And based on the first control law And the second error in determining the real-time angular velocity of each joint. First error Determined based on the real-time and desired positions of each joint; in this method, the first error... Perform an unconstrained error transformation based on preset performance to obtain the unconstrained error. So that when the first error When approaching the error threshold boundary, the unconstrained error This will increase to some extent, thereby increasing the control parameters to mitigate the first error. The error is always constrained within a preset error range and meets preset performance constraints, ensuring no overshoot during the control of the dual-joint robotic arm and guaranteeing the steady-state accuracy of the dual-joint robotic arm control within the preset performance range. This is based on unconstrained error. The first control law is obtained by designing with a predefined time. Based on the first control law And the second error in determining the real-time angular velocity of each joint. And based on unconstrained error Second error and design weight parameters Determine the synthetic Lyapunov function; based on the derivative of the synthetic Lyapunov function We obtain the first unknown function after scaling; we then use the derivative of the first unknown function with respect to the synthesized Lyapunov function. The update is performed based on the derivative of the updated synthesized Lyapunov function. Design Adaptive Law and comprehensive control law This method enables the dual-joint robotic arm to converge within a user-preset convergence time, ensuring that the control of the dual-joint robotic arm meets the time constraints of fixed industrial production cycles, thereby improving industrial production efficiency. Furthermore, compared to traditional methods where fixed threshold event triggering mechanisms are prone to over-triggering and wasting communication bandwidth in the transient phase, and insufficiently responding to accumulated small errors in the steady-state phase, making it difficult to balance control performance and communication resource efficiency, this method addresses the issue by using a dynamic error threshold determined by the current control parameters of the dual-joint robotic arm and a comprehensive control law. Defined target virtual control law A time-varying threshold triggering mechanism is constructed, and the real-time control parameters of the dual-joint robotic arm are dynamically adjusted based on the time-varying threshold triggering mechanism. It can solve the problems of excessive triggering and wasted communication bandwidth and insufficient response to accumulated small errors in the fixed threshold event triggering mechanism of traditional technology, thereby ensuring the control accuracy of the dual-joint robotic arm and reducing the waste of communication resources.

[0088] In an exemplary embodiment, for the first error Unconstrained transformation is performed to obtain unconstrained error. According to unconstrained error The first control law is obtained by designing with a predefined time. This includes: based on the real-time position of the joint and desired location Determine the first error For the first error Perform an unconstrained transformation to obtain the unconstrained error. ;in, The first error of the first joint of the dual-joint robotic arm. The first error of the second joint of the dual-joint robotic arm is an unconstrained error. Depend on The transformation yields, For the first The first error of each joint For the first dual-joint robotic arm Error boundary function for each joint, , As the initial first error boundary, This is the first error boundary in steady state. For boundary decay rate, For joint indexes; for unconstrained errors By performing differentiation, we obtain the unconstrained error after differentiation. for:

[0089] ,

[0090] In the formula, , ,in, For the first The second error of each joint For the first The first control law of each joint. For the first The derivative of the expected position of each joint, For the first The derivative of the error boundary function of each joint; based on the unconstrained error after differentiation. and predefined time For the first control law Design, ,get In the formula, This is the first control law for the first joint. This is the first control law for the second joint. Scaling factor , For the unconstrained error of the first joint, This represents the unconstrained error of the second joint.

[0091] For example, based on the actual trajectory of the dual-joint robotic arm (i.e., the real-time position of each joint) ) and the preset desired trajectory (i.e., the desired position of each joint). ), determine the first error (original error) ,in, For the tracking error of the first joint, For the second joint tracking error, the goal is to reduce... The constraints are within the preset boundaries.

[0092] The specific form of the error constraint is as follows: Design an exponential performance function. , Let be the error boundary function of the first joint. Define the error boundary function for the second joint, and clarify the transient and steady-state constraints of the error. .in, As the initial error boundary, it must satisfy... (Ensure that the initial error is within the boundaries and there is no startup overshoot). For the first The initial first error of each joint; This serves as the steady-state error boundary, limiting the final error magnitude. The boundary decay rate is used to control the boundary tightening speed and ensure fast transient convergence.

[0093] Introducing the inverse hyperbolic tangent function will constrain the... Transform into a new unconstrained error :

[0094] ,

[0095] After transformation, the explicit expression for the new error is obtained as follows: The advantage of the above transformation is that when near When the error reaches the boundary, Approaching It will automatically enhance subsequent control and suppress overshoot; when When the error reaches the boundary (Unconstrained), which simplifies controller design; the transformation is reversible and has consistent sign. and (Same sign) to ensure that error characteristics are not lost.

[0096] right Take the derivative and combine it with the formula for calculating the second error. And the cascaded form obtained from the transformation of the dynamic model of the dual-joint robotic arm ,Sure , sorted out The derivative is:

[0097] ,

[0098] In the formula, , (The derivative of the performance function, because) (Ensure the boundary tightens monotonously).

[0099] The first stage is to allow unconstrained errors Satisfying predefined time convergence, based on the unconstrained error after differentiation. and predefined time For the first control law The design yielded the following:

[0100] ,

[0101] In the formula, Scaling factor For predefined time.

[0102] In this embodiment, the first error By performing unconstrained error transformation with preset performance, the preset performance constraints on the error can be achieved.

[0103] In the previous exemplary embodiment, the method further includes: based on the unconstrained error Define the first Lyapunov function Based on the first control law Determine the first Lyapunov function The derivative is ,in, .

[0104] Optionally, for the stability analysis of the first subsystem, based on the transformed unconstrained error... Define a positive definite Lyapunov function ; and based on the determined first control law Determine the first Lyapunov function The derivative is:

[0105] ,

[0106] in, .

[0107] In this embodiment, the first error Perform an unconstrained transformation such that when the first error When approaching the error threshold boundary, the unconstrained error This will increase to some extent, thereby increasing the control parameters to mitigate the first error. The error is always constrained within a preset error range, thereby ensuring that there is no overshoot during the control of the dual-joint robotic arm and guaranteeing that the steady-state accuracy of the dual-joint robotic arm control is within the preset performance range.

[0108] In one exemplary embodiment, the method further includes: according to a first Lyapunov function Second error and design weight parameters Determine the synthetic Lyapunov function ,in, , The second error of the first joint. This is the second error of the second joint. , For optimal weight parameters, To design weight parameters, For the real-time angular velocity of the joint, The inertia matrix of the two-joint robotic arm. For pre-set constants; for synthesized Lyapunov functions Taking the derivative, the derivative of the synthesized Lyapunov function is: In the formula, For the first unknown function, The expression is , To utilize fuzzy systems to determine the first unknown function The input vector for estimation, First control law The derivative, For intersecting terms, The matrix of Coriolis force and centrifugal force is given by the following specific form: , Let the mass of the second link corresponding to the second joint be denoted as . The length of the second link. This is the distance between the center of mass of the first link corresponding to the first joint. The angle of the first joint, For the angle of the second joint, Let be the angular velocity of the first joint. The angular velocity of the second joint; Let be the derivative of the inertia matrix of the two-joint robotic arm. The derivative of the second error. It is a bounded external disturbance.

[0109] Second error This is the second state (i.e., the real-time angular velocity of the joint). With the first control law The deviation between them is expressed as follows: ,in, This is the first control law of the above design. This is the first control law for the first joint. The first control law for the second joint has the goal of passing through the first control law. Let unconstrained error It converges within the time specified by the user.

[0110] For controller design (i.e., target virtual control law) This paper analyzes the stability of the entire system during the control process of a dual-joint robotic arm. First, a synthetic Lyapunov function is defined, which integrates the subsystem and design weight parameters. Its function is constructed as follows: .in, For the first Lyapunov function of the first subsystem; To be based on the second error The second Lyapunov function is defined. The inertia matrix of the dual-joint robotic arm; Related to the design weight parameters, which are based on the third error The third Lyapunov function is defined, and the third error is... This represents the error between the designed weight parameters and the optimal weight parameters. , This is the third error of the first joint. This is the third error of the second joint.

[0111] Based on the dynamic model of the dual-joint robotic arm, Taking the derivative, we get , combined The derivative of the second Lyapunov function can be calculated. for:

[0112] .

[0113] Next, calculate the third Lyapunov function. The derivative, This reflects the variation law of the error between the design weight parameters and the optimal weight parameters, and its derivative is... Combining the first Lyapunov function The second Lyapunov function and the third Lyapunov function The derivative of the synthetic Lyapunov function is obtained. The derivative is:

[0114] ,

[0115] in, ( (where the cross term is an unknown nonlinear function) is approximated by a fuzzy logic system (FLS) in the absence of model control.

[0116] In this embodiment, based on unconstrained error The first control law obtained from the predefined time design And the second error in determining the real-time angular velocity of each joint. And based on unconstrained error Second error and the third error Determine the synthetic Lyapunov function based on its derivative. We obtain the first unknown function after scaling, and then, based on the derivative of the synthesized Lyapunov function... And designing an adaptive law for the first unknown function after scaling. and comprehensive control law This enables the dual-joint robotic arm to converge within a user-preset convergence time, allowing the dual-joint robotic arm control to meet the time constraints of fixed industrial production cycles, thereby improving industrial production efficiency.

[0117] In an exemplary embodiment, step 204 involves the fuzzy system estimating the first unknown function and scaling the estimated first unknown function to obtain a scaled first unknown function. This includes: using the fuzzy system to estimate the first unknown function... Estimation is performed to obtain the first unknown function after estimation. ,in, , Let be the first unknown function of the first joint. Let be the first unknown function of the second joint. To estimate the error, satisfy the following conditions: , To estimate the upper bound of the error, As basis vectors, , Let be the basis vector of the first joint. Let be the basis vector of the second joint. This is the optimal weight vector before scaling. , This is the optimal weight vector for the first joint before scaling. The optimal weight vector of the second joint before scaling; the derivative with respect to the synthesized Lyapunov function. In Scaling process:

[0118] ,

[0119] ,

[0120] In the formula, For a pre-defined constant, To estimate and scale the unknown function using a fuzzy system, , ,use As the optimal estimate of the unknown function after estimation and scaling using fuzzy systems, .

[0121] For example, the first unknown function Two-dimensional vector function The input is ,in and These are two components of a vector (both unknown nonlinear functions with respect to the input). The goal is to simultaneously estimate these two unknown components. and The specific design is as follows.

[0122] Using a Gaussian function as the membership function, the input is mapped to a fuzzy distribution. Both components use the same fuzzy system, and the fuzzy basis vectors are obtained through a product inference engine. To prevent over-parameterization, use... Instead of updating the weight vector element-wise, use the derivative of the synthesized Lyapunov function. In Scaling process:

[0123] ,

[0124] ,

[0125] Among them, can be used This represents the optimal estimate of the unknown function after scaling using fuzzy system estimation. To estimate and scale the unknown function using a fuzzy system, , , It is a pre-defined constant.

[0126] In the previous exemplary embodiment, the scaled-up Substituting the derivative of the synthetic Lyapunov function The derivative of the synthetic Lyapunov function The result is an update, yielding the derivative of the updated synthetic Lyapunov function. for:

[0127] In the formula, ;Derivatives based on the updated synthetic Lyapunov functions Design the adaptive law as follows: ,in, , , , The design weight parameters for the first joint, The design weight parameters for the second joint; based on the derivative of the updated synthetic Lyapunov function. and adaptive law The design yielded a comprehensive control law. , The inertial matrix of a two-joint robotic arm The upper boundary.

[0128] For example, the above-mentioned scaling Substituting the derivative of the synthetic Lyapunov function And simplifying, we get:

[0129] .

[0130] Next is the design. The adaptive law is obtained. Approaching .

[0131] Considering the convergence within a predefined time and the overall system stability of the dual-joint robotic arm control process, an adaptive law is designed. and comprehensive control law (Intermediate control law) is as follows:

[0132] ,

[0133] ,

[0134] In the above formula, , , ; The inertial matrix of a two-joint robotic arm The upper boundary.

[0135] In this embodiment, the derivative of the scaled first unknown function with respect to the synthesized Lyapunov function is used. The update is performed based on the derivative of the updated synthesized Lyapunov function. Design Adaptive Law and comprehensive control law This enables the dual-joint robotic arm to converge within a user-preset convergence time, allowing the dual-joint robotic arm control to meet the time constraints of fixed industrial production cycles, thereby improving industrial production efficiency.

[0136] In one exemplary embodiment, the method further includes: according to the comprehensive control law Determine the target virtual control law ,in, The coefficient used to adjust the trigger sensitivity, For smoothing parameters, , Let be the scaling factor tanh of the first joint. The scaling factor for tanh of the second joint; based on the target virtual control law. Calculate the current target virtual control parameters of the dual-joint robotic arm. And calculate the current target virtual control parameters. Current control parameters of the dual-joint robotic arm Current control error between The current formula for calculating control error is: The current control error includes the current control error of each joint of the dual-joint robotic arm; when determining the current control error of any joint in the dual-joint robotic arm... When the error exceeds the dynamic error threshold corresponding to that joint, adjust the current control parameters of each joint of the dual-joint robotic arm to... The formula for calculating the dynamic error threshold is as follows: ,in, For the pre-set number The minimum error threshold for each joint, For the first Current control error of each joint For the first Current control parameters for each joint. For the first The current target virtual control parameters for each joint.

[0137] According to the comprehensive control law Design the controller (determine the target virtual control law) )for:

[0138] ,

[0139] In the formula, It is a 2*1 vector. The coefficient used to adjust the trigger sensitivity, For smoothing parameters, , Let be the scaling factor tanh of the first joint. is the scaling factor of tanh for the second joint.

[0140] Current control parameters of the dual-joint robotic arm Only in control error Update when the dynamic error threshold is exceeded, i.e.:

[0141] ,

[0142] ,

[0143] In the formula, For the first dual-joint robotic arm Current control error of each joint This is the current control error, that is, the deviation between the current target virtual control parameter and the current control parameter; For the pre-set number Minimum error threshold for each joint; The time when the control parameters are adjusted for the kth time (initial) ); The next trigger time is determined by the trigger condition, which is the [number]th trigger condition. Current control error of each joint Greater than the current dynamic error threshold , For the first Current control parameters for each joint.

[0144] In this embodiment, replacing the traditional "periodic triggering of control parameter adjustment" with "on-demand triggering of control parameter adjustment" reduces the number of control parameter updates, saves communication resources, and ensures the control performance of the dual-joint robotic arm. Furthermore, this embodiment implements a time-varying threshold triggering mechanism for each joint of the dual-joint robotic arm; that is, as long as the control error of any joint exceeds its corresponding dynamic error threshold, the control parameters are updated and adjusted, further ensuring the control accuracy of the dual-joint robotic arm. Moreover, compared to the traditional method where the fixed threshold event triggering mechanism is prone to over-triggered and wastes communication bandwidth in the transient phase, and insufficiently responds to accumulated small errors in the steady-state phase, making it difficult to balance control performance and communication resource efficiency, this method addresses the problem of the dynamic error threshold determined by the current control parameters of the dual-joint robotic arm and the comprehensive control law... Defined target virtual control law A time-varying threshold triggering mechanism is constructed, and the real-time control parameters of the dual-joint robotic arm are dynamically adjusted based on the time-varying threshold triggering mechanism. It can solve the problems of excessive triggering and wasted communication bandwidth and insufficient response to accumulated small errors in the fixed threshold event triggering mechanism of traditional technology, thereby ensuring the control accuracy of the dual-joint robotic arm and reducing the waste of communication resources.

[0145] In one exemplary embodiment, the target virtual control law designed in this invention is demonstrated through the following proof process. The constructed time-varying threshold triggering mechanism can prevent Zeno behavior (system crash due to infinite triggering) from occurring.

[0146] Specifically, due to the boundedness of the system state and control law components, there exist positive constants. satisfy , For the first The derivative of the current control error of each joint. For the first The derivative of the current target virtual control law for each joint.

[0147] from arrive Integrate and utilize We got .

[0148] From the perspective of the time-varying threshold triggering mechanism, at time... There exists at least one Make:

[0149] ,

[0150] in, It is the lower bound of the trigger threshold (dynamic error threshold). for .

[0151] but, Therefore, there is a lower limit to the interval between adjacent trigger control parameter adjustments:

[0152] ,

[0153] In the formula, and for The upper realm, The derivative of the control error of the first joint. The derivative of the control error of the second joint. This is the lower limit of the time interval between adjustments to adjacent trigger control parameters.

[0154] This proves the target virtual control law designed in this invention. Furthermore, the constructed time-varying threshold triggering mechanism ensures a limited number of triggers within a finite time period, thus proving the target virtual control law designed in this invention. The constructed time-varying threshold triggering mechanism can prevent Zeno behavior from occurring.

[0155] In one exemplary embodiment, the target virtual control law designed in this invention is demonstrated through the following proof process. It can ensure that the control error converges within a predefined time.

[0156] Specifically, define a continuous time-varying vector. It has the following characteristics: , or ,and For this coefficient, the following relationship holds:

[0157] ,

[0158] In the formula, This represents the value of the first element of the time-varying vector at time t. This represents the value of the second element of the time-varying vector at time t. express The value of the first element of the time-varying vector at time t. express The value of the second element of the time-varying vector at time t. and They represent The values ​​of the first and second elements of the time-varying vector at time 1. Let represent the value of the i-th element of the time-varying vector at time t, defined as follows: , For the first The current target virtual control law for each joint. Given, and Then there is This will The expression simplifies to:

[0159] ,

[0160] in, and By rearranging the solution, the control parameters can be obtained. The expression is:

[0161] ,

[0162] Then the following vector inequality holds:

[0163] ,

[0164] in, .

[0165] In addition, due to , ,and , , and thus .

[0166] definition ,Will Expression Substitution And apply the above inequality:

[0167] ,

[0168] In the formula, The minimum error threshold is set in advance. , The minimum error threshold for the first joint is set in advance. The minimum error threshold for the pre-set second joint is determined by... Substituting into the above expression, we get:

[0169] ,

[0170] ,

[0171] ,

[0172] By Lemma achievable

[0173] ,

[0174] Substitute it into the previous expression:

[0175] ,

[0176] in, .

[0177] Based on the previous derivation, we obtain:

[0178] ,

[0179] Using Young's inequality, we obtain .

[0180] Next, consider the lemma. ,right , , , as well as By making the substitutions, we arrive at:

[0181] ,

[0182] therefore, The derivative can be simplified to:

[0183] .

[0184] Using lemmas ,available:

[0185] ,

[0186] Applying the merging lemma We can obtain:

[0187] ,

[0188] therefore:

[0189] ,

[0190] in, Defined as .

[0191] In order to merge and For the terms, we continue to apply the lemma of union, which gives two key inequalities:

[0192] ,

[0193] ,

[0194] Substituting into the previous equation, we get:

[0195] .

[0196] Finally, by applying the lemma of union, we can... and Combined into a total Lyapunov function :

[0197] ,

[0198] Using the predefined time stability lemma, this verifies that the system possesses actual predefined time stability (PPTS), where the final bound of the state is expressed as:

[0199] ,

[0200] In the formula, Indicates the adjustment time, which satisfies ,in This is the upper limit of the convergence time. This conclusion directly supports the time limit of this invention. The technical goal is to achieve state convergence internally, which is different from the infinite convergence time defect of traditional asymptotically stable schemes.

[0201] In this embodiment, by measuring the first error Unconstrained transformation ensures no overshoot throughout the entire process, and steady-state accuracy remains within the preset performance range; predefined time. User-specified upper limit This invention meets the fixed-cycle requirements of industry; moreover, the time-varying threshold triggering mechanism of the present invention can save communication resources. Specifically, the time-varying threshold triggering mechanism of the present invention controls only 1824 updates within 30 seconds, saving 87.9% of communication resources compared with 500Hz periodic sampling, and saving 60.7% compared with fixed threshold triggering (5896 updates).

[0202] In another embodiment, the specific implementation of the present invention employs Matlab simulation. The simulation process is based on the dynamic model of the dual-joint robotic arm in step 202, and incorporates the adaptive laws of subsequent related designs. and comprehensive control law The corresponding parameters were determined and selected.

[0203]

[0204] The table above summarizes all the key parameters used in the simulation. These parameters cover the robot arm's dynamic parameters, performance constraint parameters, event triggering mechanism parameters, and predefined time parameters, providing a clear and complete parameter basis for simulation verification.

[0205] Firstly, at different predefined times The strategy was evaluated at 2, 4, and 6 seconds to demonstrate its convergence properties, and then... A detailed analysis was performed at t=6 seconds to demonstrate tracking accuracy and operational efficiency. Disturbances were injected at t=15 seconds. Figures 3 to 5 The dashed line in the correlation diagram represents the interference to assess robustness.

[0206] Figure 3 Figures (a) and (b) show the first and second joints at different predefined times, respectively. A comparison of position error convergence at 2, 4, and 6 seconds. Clearly, the position error converges within its specified time range, indicating that the strategy, by adjusting... It was able to achieve convergence as designed. Except for this comparison chart, all subsequent results use... =6 seconds for unified analysis.

[0207] Figure 4 Figures (a) and (b) focus on the position error response of the first and second joints, respectively, highlighting the pre-defined performance characteristics. Throughout the simulation, including the stage after the disturbance injection at t=15 seconds, the position error was strictly limited to the predefined range, verifying the effectiveness of the pre-defined performance design in ensuring bounded tracking error.

[0208] Figure 5Figures (a) and (b) illustrate the adaptive capabilities of the fuzzy logic systems corresponding to the first and second joints, respectively. Even after a disturbance at t=15 seconds, the dynamically adjusted weight norm of the fuzzy system closely matches the actual dynamic terms of the robot joints. This highlights the ability of a carefully designed adaptive law to accurately fit and compensate for complex time-varying robot dynamics without relying on an exact system model.

[0209] Figure 6 Figures (a) and (b) depict the updates of event-triggered control inputs for the first and second joints, respectively. Control updates are infrequent in the steady-state phase, but occur intensively in transient phases (such as the initial phase and the period following disturbance injection). This behavior aligns with the design goal of event-triggered mechanisms: minimizing unnecessary control transmissions to conserve communication resources while ensuring control performance remains unaffected. This event-triggered drive effectively balances control accuracy and communication efficiency, which is crucial for networked robot systems with limited bandwidth.

[0210] Overall, these numerical simulation results confirm the effectiveness of the controller in achieving preset performance-based tracking, accurate adaptive dynamic compensation, and efficient communication event-triggered control, even under external disturbances.

[0211] It should be understood that although the steps in the flowcharts of the above embodiments are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the above embodiments may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0212] Based on the same inventive concept, this application also provides a robotic arm control device with preset performance and predefined time for implementing the robotic arm control method with preset performance and predefined time described above. The solution provided by this device is similar to the solution described in the above method. Therefore, the specific limitations of one or more robotic arm control device embodiments with preset performance and predefined time provided below can be found in the limitations of the robotic arm control method with preset performance and predefined time described above, and will not be repeated here.

[0213] In one exemplary embodiment, such as Figure 7As shown, a robotic arm control device with preset performance and predefined time is provided, including: a determination module 702, a scaling module 704, a design module 706, and a control module 708, wherein:

[0214] Determining module 702, used for determining the first error Unconstrained transformation is performed to obtain unconstrained error. According to unconstrained error The first control law is obtained by designing with a predefined time. And based on the first control law And the second error in determining the real-time angular velocity of each joint. First error Determined based on the real-time and desired positions of each joint. The first joint of the dual-joint robotic arm Unconstrained error of each joint ;

[0215] Scaling module 704 is used for derivatives based on synthesized Lyapunov functions. The first unknown function is determined, estimated using a fuzzy system, and then scaled to obtain a scaled first unknown function. The Lyapunov function is then synthesized based on the unconstrained error... Second error and design weight parameters Sure;

[0216] Design module 706 is used to utilize the derivative of the scaled first unknown function with respect to the synthesized Lyapunov function. The update is performed based on the derivative of the updated synthesized Lyapunov function. Design Adaptive Law And based on the derivative of the updated synthesized Lyapunov function. and adaptive law The design yielded a comprehensive control law. ;

[0217] Control module 708 is used to determine the dynamic error threshold and the integrated control law. Defined target virtual control law A time-varying threshold triggering mechanism is constructed, and the real-time control parameters of the dual-joint robotic arm are dynamically adjusted based on the time-varying threshold triggering mechanism. The dynamic error threshold is determined based on the current control parameters of the dual-joint robotic arm.

[0218] In one exemplary embodiment, the determining module 702 is further configured to determine based on the real-time position of the joint. and desired location Determine the first error For the first error Perform an unconstrained transformation to obtain the unconstrained error. ;in, The first error of the first joint of the dual-joint robotic arm. The first error of the second joint of the dual-joint robotic arm is an unconstrained error. Depend on The transformation yields, For the first The first error of each joint For the first dual-joint robotic arm Error boundary function for each joint, , Initial first error boundary, This is the first error boundary in steady state. For boundary decay rate, For joint indexes; for unconstrained errors By performing differentiation, we obtain the unconstrained error after differentiation. In the formula, , ,in, For the first The second error of each joint For the first The first control law of each joint. For the first The derivative of the expected position of each joint, For the first The derivative of the error boundary function of each joint; based on the unconstrained error after differentiation. and predefined time For the first control law Design, ,get In the formula, This is the first control law for the first joint. This is the first control law for the second joint. Scaling factor , For the unconstrained error of the first joint, This represents the unconstrained error of the second joint.

[0219] In one exemplary embodiment, the robotic arm control device having preset performance and predefined time further includes:

[0220] The first derivative determination module is used to determine the unconstrained error. Define the first Lyapunov function Based on the first control law Determine the first Lyapunov function The derivative is ,in, , Let be the error boundary function of the first joint. This is the error boundary function for the second joint.

[0221] In one exemplary embodiment, the robotic arm control device having preset performance and predefined time further includes:

[0222] The comprehensive derivative determination module is used to determine the derivative based on the first Lyapunov function. Second error and design weight parameters Determine the synthetic Lyapunov function ,in, , The second error of the first joint. This is the second error of the second joint. , For optimal weight parameters, To design weight parameters, For the real-time angular velocity of the joint, The inertia matrix of the two-joint robotic arm. For pre-set constants; for synthesized Lyapunov functions Taking the derivative yields In the formula, For the first unknown function, The expression is , To utilize fuzzy systems to determine the first unknown function The input vector for estimation, First control law The derivative, For intersecting terms, The matrix of Coriolis force and centrifugal force is given by the following specific form: , Let the mass of the second link corresponding to the second joint be denoted as . The length of the second link. This is the distance between the center of mass of the first link corresponding to the first joint. The angle of the first joint, For the angle of the second joint, Let be the angular velocity of the first joint. The angular velocity of the second joint; Let be the derivative of the inertia matrix of the two-joint robotic arm. The derivative of the second error. It is a bounded external disturbance.

[0223] In one exemplary embodiment, the scaling module 704 is further configured to utilize a fuzzy system to scale the first unknown function. Estimation is performed to obtain the first unknown function after estimation. ,in, , Let be the first unknown function of the first joint. Let be the first unknown function of the second joint. To estimate the error, satisfy the following conditions: , To estimate the upper bound of the error, As basis vectors, , Let be the basis vector of the first joint. The basis vector of the second joint This is the optimal weight vector before scaling. , This is the optimal weight vector for the first joint before scaling. The optimal weight vector of the second joint before scaling; the derivative with respect to the synthesized Lyapunov function. In Scaling process:

[0224] ,

[0225] ,

[0226] In the formula, For a pre-defined constant, To estimate and scale the unknown function using a fuzzy system, , ,use As the optimal estimate of the unknown function after estimation and scaling using fuzzy systems, .

[0227] In one exemplary embodiment, the design module 706 is further configured to scale the design module. Substituting the derivative of the synthetic Lyapunov function The derivative of the synthetic Lyapunov function The result is an update, yielding the derivative of the updated synthetic Lyapunov function. for:

[0228] In the formula, ;Derivatives based on the updated synthetic Lyapunov functions Design the adaptive law as follows: ,in, , , , The design weight parameters for the first joint, The design weight parameters for the second joint; based on the derivative of the updated synthetic Lyapunov function. and adaptive law The designed comprehensive control law is as follows: , The inertial matrix of a two-joint robotic arm The upper boundary.

[0229] In an exemplary embodiment, the control module 708 is further configured to, according to the comprehensive control law Determine the target virtual control law ,in, The coefficient used to adjust the trigger sensitivity, For smoothing parameters, , Let be the scaling factor tanh of the first joint. The scaling factor for tanh of the second joint; based on the target virtual control law. Calculate the current target virtual control parameters of the dual-joint robotic arm. And calculate the current target virtual control parameters. Current control parameters of the dual-joint robotic arm Current control error between The current formula for calculating control error is: The current control error includes the current control error of each joint of the dual-joint robotic arm; when determining the current control error of any joint in the dual-joint robotic arm... When the error exceeds the dynamic error threshold corresponding to that joint, adjust the current control parameters of each joint of the dual-joint robotic arm to... The formula for calculating the dynamic error threshold is as follows: ,in, For the pre-set number The minimum error threshold for each joint, For the first Current control parameters for each joint. For the first The current target virtual control parameters for each joint.

[0230] Each module in the aforementioned robotic arm control device with preset performance and predefined time can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device in hardware form, or stored in the memory of a computer device in software form, so that the processor can call and execute the operations corresponding to each module.

[0231] In one exemplary embodiment, a computer device is provided, which may be a server, and its internal structure diagram may be as follows: Figure 8 As shown, the computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The database stores the real-time positions and angular velocities of each joint of the dual-joint robotic arm. The I / O interfaces are used for information exchange between the processor and external devices. The communication interface is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements a robotic arm control method with preset performance and predefined time.

[0232] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps in the above method embodiments.

[0233] In one embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above method embodiments.

[0234] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0235] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0236] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0237] The above embodiments are merely illustrative of several implementation methods of this application, and their descriptions are relatively specific and detailed. However, they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A robotic arm control method with preset performance and predefined time, characterized in that, The method includes: For the first error Unconstrained transformation is performed to obtain unconstrained error. According to the unconstrained error The first control law is obtained by designing with a predefined time. And based on the first control law And the second error in determining the real-time angular velocity of each joint. The first error Determined based on the real-time and desired positions of each joint. The first joint of the dual-joint robotic arm Unconstrained error of each joint The first error Unconstrained transformation is performed to obtain unconstrained error. According to the unconstrained error The first control law is obtained by designing with a predefined time. This includes: based on the real-time position of the joint and desired location Determine the first error Regarding the first error Perform an unconstrained transformation to obtain the unconstrained error. ;in, The first error of the first joint of the dual-joint robotic arm. The first error of the second joint of the dual-joint robotic arm is an unconstrained error. Depend on The transformation yields, For the first The first error of each joint For the first dual-joint robotic arm Error boundary function for each joint, , As the initial first error boundary, This is the first error boundary in steady state. For boundary decay rate, For joint index; for the unconstrained error By performing differentiation, we obtain the unconstrained error after differentiation. In the formula, , ,in, For the first The second error of each joint For the first The first control law of each joint. For the first The derivative of the expected position of each joint, For the first The derivative of the error boundary function of each joint; based on the unconstrained error after differentiation. and predefined time For the first control law Design, ,get In the formula, This is the first control law for the first joint. This is the first control law for the second joint. Scaling factor , The unconstrained error of the first joint is... This represents the unconstrained error of the second joint; Derivatives based on synthetic Lyapunov functions A first unknown function is determined, estimated using a fuzzy system, and then scaled to obtain a scaled first unknown function. The Lyapunov function is then synthesized based on the unconstrained error. Second error and design weight parameters Sure; Using the derivative of the first unknown function after scaling with respect to the synthesized Lyapunov function The update is performed based on the derivative of the updated synthesized Lyapunov function. Design Adaptive Law And based on the derivative of the updated synthesized Lyapunov function. and adaptive law The design yielded a comprehensive control law. ; Based on the dynamic error threshold and the comprehensive control law Defined target virtual control law A time-varying threshold triggering mechanism is constructed, and the real-time control parameters of the dual-joint robotic arm are dynamically adjusted according to the time-varying threshold triggering mechanism. The dynamic error threshold is determined based on the current control parameters of the dual-joint robotic arm. The method further includes: According to the unconstrained error Define the first Lyapunov function ; Based on the first control law Determine the first Lyapunov function The derivative is ,in, , Let be the error boundary function of the first joint. is the error boundary function for the second joint.

2. The robotic arm control method with preset performance and predefined time according to claim 1, characterized in that, The method further includes: According to the first Lyapunov function Second error and design weight parameters Determine the synthetic Lyapunov function ,in, , This is the second error of the first joint. This is the second error of the second joint. , For optimal weight parameters, To design weight parameters, For the real-time angular velocity of the joint, The inertia matrix of the two-joint robotic arm. For pre-set constants; For the synthesized Lyapunov function Taking the derivative yields In the formula, For the first unknown function, The expression is , To utilize fuzzy systems to determine the first unknown function The input vector for estimation, where, First control law The derivative of For intersecting terms, The matrix of Coriolis force and centrifugal force is given by the following specific form: , Let be the mass of the second link corresponding to the second joint. The length of the second link. This is the distance between the center of mass of the first link corresponding to the first joint. The angle of the first joint. The angle of the second joint. Let be the angular velocity of the first joint. The angular velocity of the second joint; Let be the derivative of the inertia matrix of the two-joint robotic arm. The derivative of the second error. It is a bounded external disturbance.

3. The robotic arm control method with preset performance and predefined time according to claim 2, characterized in that, The step of estimating the first unknown function using a fuzzy system and then scaling the estimated first unknown function to obtain a scaled first unknown function includes: Using a fuzzy system to study the first unknown function Estimation is performed to obtain the first unknown function after estimation. ,in, , Let be the first unknown function of the first joint. Let be the first unknown function of the second joint. To estimate the error, satisfy the following conditions: , To estimate the upper bound of the error, As basis vectors, , Let be the basis vector of the first joint. Let be the basis vector of the second joint. This is the optimal weight vector before scaling. , This is the optimal weight vector of the first joint before scaling. This is the optimal weight vector of the second joint before scaling. The derivative of the synthetic Lyapunov function In Scaling process: ， ， In the formula, For a pre-defined constant, To estimate and scale the unknown function using a fuzzy system, , ,use As the optimal estimate of the unknown function after estimation and scaling using fuzzy systems, .

4. The robotic arm control method with preset performance and predefined time according to claim 3, characterized in that, The derivative of the first unknown function after scaling with respect to the synthesized Lyapunov function is described. The update is performed based on the derivative of the updated synthesized Lyapunov function. Design Adaptive Law And based on the derivative of the updated synthesized Lyapunov function. and adaptive law The design yielded a comprehensive control law. ,include: After scaling Substituting the derivative of the synthesized Lyapunov function The derivative of the synthetic Lyapunov function The result is an update, yielding the derivative of the updated synthetic Lyapunov function. for: In the formula, ; Derivative based on the updated synthetic Lyapunov function Design the adaptive law as follows: ,in, , , , The design weight parameters for the first joint are... The design weight parameters for the second joint; Derivative based on the updated synthetic Lyapunov function and adaptive law The design yielded a comprehensive control law. , The inertial matrix of a two-joint robotic arm The upper boundary.

5. The robotic arm control method with preset performance and predefined time according to claim 4, characterized in that, The method further includes: According to the comprehensive control law Determine the target virtual control law ,in, The coefficient used to adjust the trigger sensitivity, For smoothing parameters, , Let be the scaling factor tanh of the first joint. is the scaling factor of tanh for the second joint; Based on target virtual control law Calculate the current target virtual control parameters of the dual-joint robotic arm. And calculate the current target virtual control parameters. Current control parameters of the dual-joint robotic arm Current control error between The formula for calculating the current control error is as follows: The current control error includes the current control error of each joint of the dual-joint robotic arm; When the current control error of any joint in a two-joint robotic arm is determined When the error exceeds the dynamic error threshold corresponding to that joint, adjust the current control parameters of each joint of the dual-joint robotic arm to... The formula for calculating the dynamic error threshold is as follows: ,in, For the pre-set number The minimum error threshold for each joint, For the first Current control error of each joint For the first Current control parameters for each joint. For the first The current target virtual control parameters for each joint.

6. A robotic arm control device with preset performance and predefined time, characterized in that, The device is used to implement the robotic arm control method with preset performance and predefined time as described in any one of claims 1 to 5; the device includes: The determination module is used to determine the first error. Unconstrained transformation is performed to obtain unconstrained error. According to the unconstrained error The first control law is obtained by designing with a predefined time. And based on the first control law And the second error in determining the real-time angular velocity of each joint. The first error Determined based on the real-time and desired positions of each joint. The first joint of the dual-joint robotic arm Unconstrained error of each joint ; Scaling module for derivatives based on synthesized Lyapunov functions A first unknown function is determined, estimated using a fuzzy system, and then scaled to obtain a scaled first unknown function. The Lyapunov function is then synthesized based on the unconstrained error. Second error and design weight parameters Sure; The design module is used to utilize the derivative of the scaled first unknown function with respect to the synthesized Lyapunov function. The update is performed based on the derivative of the updated synthesized Lyapunov function. Design Adaptive Law And based on the derivative of the updated synthesized Lyapunov function. and adaptive law The design yielded a comprehensive control law. ; The control module is used to determine the dynamic error threshold and the comprehensive control law. Defined target virtual control law A time-varying threshold triggering mechanism is constructed, and the real-time control parameters of the dual-joint robotic arm are dynamically adjusted according to the time-varying threshold triggering mechanism. The dynamic error threshold is determined based on the current control parameters of the dual-joint robotic arm.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the robotic arm control method with preset performance and predefined time as described in any one of claims 1 to 5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the robotic arm control method with preset performance and predefined time as described in any one of claims 1 to 5.

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