Multi-mechanical-arm system self-adaptive control method and equipment based on DMET and composite learning control framework

Abstract

The invention relates to a multi-mechanical-arm system self-adaptive control method based on a DMET and a composite learning control framework, and the method comprises the steps: building a nonlinear dynamic model of a multi-mechanical-arm system, and converting the nonlinear dynamic model into a state space model; the tracking error of each slave mechanical arm relative to the leader is defined; a composite learning adaptive law is obtained; designing an actual controller of the multi-mechanical-arm system; and designing a final controller. According to the method, a dynamic memory event triggering mechanism is designed, the triggering threshold value is adaptively adjusted by introducing an internal dynamic variable containing historical information, and compared with a static event triggering mechanism, the average triggering interval can be more effectively prolonged, so that on the premise that the system control performance is ensured, the system reliability is improved. The updating frequency of the controller and the network communication resource consumption are obviously reduced; instantaneous tracking errors are utilized to ensure the stability of the system, and prediction errors are generated by constructing a dynamic data model to make full use of historical operation data of the system.

Description

Technical Field

[0001] This invention relates to the field of multi-agent cooperative control technology, and in particular to an adaptive control method and device for a multi-manipulator system based on DMET and a composite learning control framework. Background Technology

[0002] Multi-arm robotic systems are widely used in industrial assembly, collaborative material handling, and other fields. Their core objective is to achieve coordinated tracking of the leader's trajectory by each robotic arm under conditions of modeling uncertainty and external disturbances. However, existing control methods have significant limitations:

[0003] First, unknown nonlinearities in system dynamics usually rely on neural networks for approximation, but traditional weight updates are based only on instantaneous errors and fail to make full use of historical operating data, resulting in the approximation capability not being effectively explored and the parameters converging slowly, which limits the final control accuracy.

[0004] Second, system communication resources are often limited: traditional time-triggered mechanisms have a heavy communication burden, while existing event-triggered methods, although able to reduce frequency, mostly use fixed trigger thresholds and cannot be dynamically adjusted according to errors, still causing unnecessary communication waste during stable system phases. In addition, most control strategies can only achieve asymptotic or finite-time convergence, and the convergence time is affected by the initial value, making it difficult to meet the application scenarios with precise requirements for system response time.

[0005] Therefore, there is an urgent need for a new cooperative control method that can converge within a fixed time while possessing both high approximation accuracy and low communication load. Summary of the Invention

[0006] To address the problems of low accuracy in neural network approximation, slow parameter convergence, significant waste of communication resources, and convergence time dependence on initial conditions in existing technologies, the primary objective of this invention is to provide an adaptive control method for multi-manipulator systems based on DMET and composite learning control framework. This method ensures that the cooperative tracking error of a multi-manipulator system converges to near the equilibrium point within a predetermined time independent of the initial state, greatly improving the system response speed and determinism in engineering applications, and significantly reducing the controller update frequency and network communication resource consumption.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: an adaptive control method for a multi-manipulator system based on DMET and a composite learning control framework, the method comprising the following sequential steps:

[0008] (1) Use graph theory to construct the communication topology of the multi-manipulator system, establish the nonlinear dynamic model of the multi-manipulator system, and transform the nonlinear dynamic model into a state-space model;

[0009] (2) Based on the state space model, set the leader robot trajectory and calculate the coordination error, and define the tracking error of each slave robot relative to the leader;

[0010] (3) Update the weight vector by combining prediction error and tracking error. The estimated value The composite learning adaptive law is obtained. This enables online approximation of uncertain nonlinear terms in multi-robotic arm systems;

[0011] (4) Design dynamic memory event triggering conditions and design the actual controller of the multi-robotic arm system;

[0012] (5) Design the final controller based on the actual controller to ensure that the tracking error of all robotic arms converges within a fixed time and that all closed-loop signals of the multi-robotic arm system are bounded.

[0013] Step (1) specifically includes the following steps in sequence:

[0014] (1a) The nonlinear dynamic model of the multi-manipulator system is established according to the Euler-Lagrange method as follows:

[0015] (1);

[0016] in, Indicates mechanical inertia; Acceleration representing the angle of rotation; This represents the coefficient of viscous friction at the joint. The speed representing the rotation angle; Indicates the mass of the robotic arm; Represents gravitational acceleration; Indicates the length of the robotic arm; This indicates the position of the link angle, i.e., the rotation angle of the robotic arm joint; Indicates control input, Indicates system output;

[0017] (1b) Let , Then equation (1) can be reconstructed into a state-space model:

[0018] ;

[0019] In the formula, Indicates the angle of the follower robotic arm joint; Indicates the speed of the follower robotic arm joints; This represents the acceleration at the joint angle; Indicates the actual control input; Indicates the length of the robotic arm; Indicates due to The introduced nonlinear term of gravity; due to ,so It also indicates the speed of the follower robotic arm joints;

[0020] Step (2) specifically includes the following steps in sequence:

[0021] (2a) Set the trajectory of the leader robotic arm :

[0022] ;

[0023] in, Indicates the independent variable of time;

[0024] (2b) Obtain the communication status between each agent in the multi-arm system, and use the following formula to calculate the first-order cooperative tracking error between the i-th follower arm and the other arms in the system. :

[0025] ;

[0026] in, To indicate the first The trajectory of a robotic arm Indicates the first The output trajectory of the robotic arm Indicates the total number of robotic arms. In a multi-arm robotic system, the intelligent agent is represented. With intelligent agents Communication status between them; Indicates the first The connection weights between the follower robotic arm and the leader robotic arm;

[0027] (2c) Based on the error between the state of the follower robotic arm and the state of the leader robotic arm, the following formula is used to construct a representation of the state of the first robotic arm. The second-order cooperative error of the multi-arm system between the follower robotic arm and the other follower robotic arms in the system. :

[0028] ;

[0029] in, Indicates the first The first-order virtual controller input for the robotic arm;

[0030] The first-order cooperative tracking error and second-order cooperative error Together they constitute the tracking error.

[0031] Step (3) specifically includes the following steps in sequence:

[0032] (3a) Use the following formula to determine the radial basis function neural network model in the set Approximately bounded unknown functions on:

[0033] ;

[0034] in, Let represent an approximately bounded unknown function, and The input vector; Represents a set of possible values; express 3D real space; Represents a weight vector. belong 3D real space, It is the number of hidden layer nodes in the radial basis function neural network model; Represents the radial basis function vector; Indicates error;

[0035] In any time interval Multiply both sides by the basis function vector , After integration, we get:

[0036] ;

[0037] In the formula, The first The online integral excitation matrix of the first and second subsystems of the robotic arm; The first The integral approximation error of the first and second subsystems of the robotic arm; The integral time window length is a positive design constant used to construct the prediction error and the integral excitation matrix; Indicates the current time; Indicates the speed of the follower robotic arm joints; This represents the acceleration at the joint angle; Indicates the actual control input; express arrive The set of states, ; Indicates the speed of the follower robotic arm joints;

[0038] (3b) Construct a dynamic data model, considering the first The dynamics of the first subsystem of the robotic arm are as follows:

[0039] ;

[0040] In the formula, Indicates the first The ideal weight vector of the first subsystem of the robotic arm. express Transpose of; Indicate the first The NN error of the first subsystem of the robotic arm; The dynamics of the second subsystem of the robotic arm are as follows:

[0041] ;

[0042] In the formula, Indicates the first The ideal weight vector of the second subsystem of the robotic arm. express Transpose of; Indicates the first The NN error of the second subsystem of the robotic arm, where:

[0043] ;

[0044] ;

[0045] For a multi-arm robotic system, given any initial conditions: ,in, Indicates the system at the initial moment The initial state vector at time, Indicates the initial set of values ​​to be taken. If the integer is a positive constant, then there exists a constant. ,in, , , making ,in The state vector of the multi-arm robotic system at time t represents the state vector of the system at time t. The value of , express The set of possible values; assume there exists a constant. and ,in , This makes it possible to achieve the following within the time interval: Above, the windowed regression matrix satisfies the persistent excitation IE condition, that is... , It is the identity matrix;

[0046] (3c) Based on the dynamic data model, construct a prediction error that can be used for weight updates:

[0047] ;

[0048] ;

[0049] in, and Indicates prediction error; for The estimate, for The estimate;

[0050] (3d) Design based on prediction error Composite learning adaptive law:

[0051] ;

[0052] in, All are positive parameters of the design; It is a projection operator; The first The composite learning adaptive law of the first and second subsystems of the robotic arm.

[0053] Step (4) specifically includes the following steps in sequence:

[0054] (4a) Design dynamic memory event triggering conditions:

[0055] ;

[0056] ;

[0057] in, It is the first The actual control input for a robotic arm; Indicates a virtual controller; Indicates time as the independent variable; Indicates the first The next trigger moment; Indicates the first The next trigger moment; Indicates control input deviation. ; and For design parameters, , ; This is an internal dynamic variable used to adaptively adjust the trigger threshold. ; Indicates the first Virtual control input for a robotic arm;

[0058] (4b) Design internal dynamic variables The renewal law:

[0059] ;

[0060] in, All are design parameters and satisfy the following:

[0061] ;

[0062] in, It is a small positive constant; Indicates the time span of memory; As initial conditions, ,in Indicates the initial time variable. ; For the initial function, ;

[0063] (4c) Based on the dynamic memory event triggering conditions, design the actual controller of the multi-robotic arm system. :

[0064] ;

[0065] in, and They are two unknown time-varying continuous functions that satisfy... .

[0066] Step (5) specifically includes the following steps in sequence:

[0067] (5a) Suppose there exists a smooth positive definite function. , so that:

[0068] ;

[0069] in, All are design constants. ,and If the state-space model is stable at a fixed time, then the maximum convergence time of the system is... satisfy: for The time derivative;

[0070] ;

[0071] in, All are systematic errors. To adjust the parameters, ;

[0072] The virtual controller of the system is designed in the following form:

[0073] ;

[0074] ;

[0075] in, , , , All are positive parameters of the design; For the first The total weight of each agent's neighbors All are parameters of the NN compensation term; This represents the first-order cooperative tracking error. This is a second-order cooperative error; For design parameters; , Both are basis function vectors; Indicates the first The connection weights between the follower robotic arm and the leader robotic arm;

[0076] (5b) Select the first Lyapunov candidate equation for:

[0077] ;

[0078] in, For positive parameters of the design; express and The error between them ; Indicates the first The ideal weight vector of the first subsystem of the robotic arm; Indicates the first The ideal weight vector of the second subsystem of the robotic arm; for The estimate, for The estimate;

[0079] right Taking the derivative with respect to time, we get:

[0080] ;

[0081] In the formula, Indicates the first The input vector of the radial basis function neural network model of the first subsystem of the robotic arm. , Indicates the angle of the follower robotic arm joints. This indicates the trajectory of the leader's robotic arm. This represents the time derivative of the reference signal; Indicates the first The approximate bounded unknown function of the first subsystem of the robotic arm; Indicate the first The NN error of the first subsystem of the robotic arm;

[0082] (5c) Take the second Lyapunov candidate equation for:

[0083] ;

[0084] in, For positive parameters of the design; Represents the weight estimate Compared with actual value The error between them ;

[0085] right Taking the derivative with respect to time, we get:

[0086] ;

[0087] In the formula, The first step is the estimation of the virtual control signal. Time derivative, Indicates the first The input vector of the god-like network of the second subsystem of the robotic arm. , Indicates the angle of the follower robotic arm joint; Indicates the first The approximate bounded unknown function of the second subsystem of the robotic arm; and They are two unknown time-varying continuous functions. and These are all design parameters. , ; This is an internal dynamic variable used to adaptively adjust the trigger threshold. ; Indicates the first Virtual control input for a robotic arm; Indicate the first The NN error of the second subsystem of the robotic arm; and Indicates prediction error;

[0088] (5d) The first Lyapunov candidate equation Take the second Lyapunov candidate equation To form the complete Lyapunov equations as follows:

[0089] ;

[0090] (5e) Based on the complete Lyapunov equations Design the final controller, which includes a virtual controller. and , No. The composite learning adaptive law of the first subsystem of the robotic arm , No. The composite learning adaptive law of the second subsystem of the robotic arm :

[0091] ;

[0092] In the formula, The first The composite learning adaptive law of the first and second subsystems of the robotic arm; It is a projection operator.

[0093] Another object of the present invention is to provide an electronic device comprising:

[0094] Processor; and

[0095] The memory stores computer program instructions that, when executed by the processor, cause the processor to perform the adaptive control method for a multi-manipulator system based on the DMET and composite learning control framework as described above.

[0096] The present invention also provides a computer-readable storage medium storing computer program instructions thereon, which, when executed by a processor, cause the processor to execute the adaptive control method for a multi-manipulator system based on the DMET and composite learning control framework as described above.

[0097] As can be seen from the above technical solution, the beneficial effects of the present invention are as follows: First, by introducing fractional power terms into the controller design and designing a virtual controller containing fixed-time convergence terms, and by conducting rigorous stability analysis based on the fixed-time Lyapunov equation, the present invention ensures that the cooperative tracking error of the multi-manipulator system converges to near the equilibrium point within a predetermined time independent of the initial state. This overcomes the limitation that the convergence time of traditional finite-time control depends on the initial conditions, greatly improving the system response speed and the determinism of engineering applications. Second, the present invention designs a dynamic memory event triggering mechanism. By introducing internal dynamic variables containing historical information to adaptively adjust the triggering threshold, compared with the static event triggering mechanism, it can more effectively extend the average triggering interval, thereby significantly reducing the controller update frequency and network communication resource consumption while ensuring system control performance, solving the bottleneck problem of resource constraints in multi-agent systems. Third, the present invention innovatively combines a composite learning mechanism with a radial basis function neural network. The composite learning mechanism not only uses instantaneous tracking errors to ensure system stability, but also generates prediction errors by constructing a dynamic data model to fully utilize the historical operating data of the system. Attached Figure Description

[0098] Figure 1 This is a communication network topology diagram of the multi-robotic arm system in this invention;

[0099] Figure 2 This is a flowchart of the method of the present invention;

[0100] Figure 3 This is a schematic diagram of the positional trajectories of the navigator and follower in this invention;

[0101] Figure 4 This is a tracking error curve diagram of the present invention;

[0102] Figure 5 This is a control input curve diagram of the multi-robotic arm system in this invention;

[0103] Figure 6 This is a graph showing the approximate error curve of the radial basis neural network of the present invention;

[0104] Figure 7 This is a schematic diagram showing the trigger count of three followers in the multi-robotic arm system utilizing the dynamic memory event triggering mechanism in this invention;

[0105] Figure 8 This is a schematic diagram showing the time interval between adjacent triggered events for each agent under DMET in this invention. Detailed Implementation

[0106] like Figure 2 As shown, an adaptive control method for a multi-manipulator system based on DMET and a composite learning control framework is presented. This method includes the following sequential steps:

[0107] (1) Use graph theory to construct the communication topology of the multi-manipulator system, establish the nonlinear dynamic model of the multi-manipulator system, and transform the nonlinear dynamic model into a state-space model;

[0108] (2) Based on the state space model, set the leader robot trajectory and calculate the coordination error, and define the tracking error of each slave robot relative to the leader;

[0109] (3) Update the weight vector by combining prediction error and tracking error. The estimated value The composite learning adaptive law is obtained. This enables online approximation of uncertain nonlinear terms in multi-robotic arm systems;

[0110] (4) Design dynamic memory event triggering conditions and design the actual controller of the multi-robotic arm system;

[0111] (5) Design the final controller based on the actual controller to ensure that the tracking errors of all robotic arms converge within a fixed time and keep all closed-loop signals of the multi-robotic arm system bounded. DMET indicates dynamic memory event triggering.

[0112] Step (1) specifically includes the following steps in sequence:

[0113] (1a) The nonlinear dynamic model of the multi-manipulator system is established according to the Euler-Lagrange method as follows:

[0114] (1);

[0115] in, Indicates mechanical inertia; Acceleration representing the angle of rotation; This represents the coefficient of viscous friction at the joint. The speed representing the rotation angle; Indicates the mass of the robotic arm; Represents gravitational acceleration; Indicates the length of the robotic arm; This indicates the position of the link angle, i.e., the rotation angle of the robotic arm joint; Indicates control input, Indicates system output;

[0116] (1b) Let , Then equation (1) can be reconstructed into a state-space model:

[0117] ;

[0118] In the formula, Indicates the angle of the follower robotic arm joint; Indicates the speed of the follower robotic arm joints; This represents the acceleration at the joint angle; Indicates the actual control input; Indicates the length of the robotic arm; Indicates due to The introduced nonlinear term of gravity; due to ,so It also indicates the speed of the follower robotic arm joints;

[0119] Step (2) specifically includes the following steps in sequence:

[0120] (2a) Set the trajectory of the leader robotic arm :

[0121] ;

[0122] in, Indicates the independent variable of time;

[0123] (2b) Obtain the communication status between each agent in the multi-arm system, and use the following formula to calculate the first-order cooperative tracking error between the i-th follower arm and the other arms in the system. :

[0124] ;

[0125] in, To indicate the first The trajectory of a robotic arm Indicates the first The output trajectory of the robotic arm Indicates the total number of robotic arms. In a multi-arm robotic system, the intelligent agent is represented. With intelligent agents Communication status between them; Indicates the first The connection weights between the follower robotic arm and the leader robotic arm;

[0126] (2c) Based on the error between the state of the follower robotic arm and the state of the leader robotic arm, the following formula is used to construct a representation of the state of the first robotic arm. The second-order cooperative error of the multi-arm system between the follower robotic arm and the other follower robotic arms in the system. :

[0127] ;

[0128] in, Indicates the first The first-order virtual controller input for the robotic arm;

[0129] The first-order cooperative tracking error and second-order cooperative error Together they constitute the tracking error.

[0130] Step (3) specifically includes the following steps in sequence:

[0131] (3a) Use the following formula to determine the radial basis function neural network model in the set Approximately bounded unknown functions on:

[0132] ;

[0133] in, Let represent an approximately bounded unknown function, and The input vector; Represents a set of possible values; express 3D real space; Represents a weight vector. belong 3D real space, It is the number of hidden layer nodes in the radial basis function neural network model; Represents the radial basis function vector; Indicates error;

[0134] In any time interval Multiply both sides by the basis function vector , After integration, we get:

[0135] ;

[0136] In the formula, The first The online integral excitation matrix of the first and second subsystems of the robotic arm; The first The integral approximation error of the first and second subsystems of the robotic arm; The integral time window length is a positive design constant used to construct the prediction error and the integral excitation matrix; Indicates the current time; Indicates the speed of the follower robotic arm joints; This represents the acceleration at the joint angle; Indicates the actual control input; express arrive The set of states, ; Indicates the speed of the follower robotic arm joints;

[0137] (3b) Construct a dynamic data model, considering the first The dynamics of the first subsystem of the robotic arm are as follows:

[0138] ;

[0139] In the formula, Indicates the first The ideal weight vector of the first subsystem of the robotic arm. express Transpose of; Indicate the first The NN error of the first subsystem of the robotic arm; The dynamics of the second subsystem of the robotic arm are as follows:

[0140] ;

[0141] In the formula, Indicates the first The ideal weight vector of the second subsystem of the robotic arm. express Transpose of; Indicates the first The NN error of the second subsystem of the robotic arm, where:

[0142] ;

[0143] ;

[0144] For a multi-arm robotic system, given any initial conditions: ,in, Indicates the system at the initial moment The initial state vector at time, Indicates the initial set of values ​​to be taken. If the integer is a positive constant, then there exists a constant. ,in, , , making ,in The state vector of the multi-arm robotic system at time t represents the state vector of the system at time t. The value of , express The set of possible values; assume there exists a constant. and ,in , This makes it possible to achieve the following within the time interval: Above, the windowed regression matrix satisfies the persistent excitation IE condition, that is... , It is the identity matrix;

[0145] (3c) Based on the dynamic data model, construct a prediction error that can be used for weight updates:

[0146] ;

[0147] ;

[0148] in, and Indicates prediction error; for The estimate, for The estimate;

[0149] (3d) Design based on prediction error Composite learning adaptive law:

[0150] ;

[0151] in, All are positive parameters of the design; It is a projection operator; The first The composite learning adaptive law of the first and second subsystems of the robotic arm.

[0152] Step (4) specifically includes the following steps in sequence:

[0153] (4a) Design dynamic memory event triggering conditions:

[0154] ;

[0155] ;

[0156] in, It is the first The actual control input for a robotic arm; Indicates a virtual controller; Indicates time as the independent variable; Indicates the first The next trigger moment; Indicates the first The next trigger moment; Indicates control input deviation. ; and For design parameters, , ; This is an internal dynamic variable used to adaptively adjust the trigger threshold. ; Indicates the first Virtual control input for a robotic arm;

[0157] (4b) Design internal dynamic variables The renewal law:

[0158] ;

[0159] in, All are design parameters and satisfy the following:

[0160] ;

[0161] in, It is a small positive constant; Indicates the time span of memory; As initial conditions, ,in Indicates the initial time variable. ; For the initial function, ;

[0162] (4c) Based on the dynamic memory event triggering conditions, design the actual controller of the multi-robotic arm system. :

[0163] ;

[0164] in, and They are two unknown time-varying continuous functions that satisfy... .

[0165] Step (5) specifically includes the following steps in sequence:

[0166] (5a) Suppose there exists a smooth positive definite function. , so that:

[0167] ;

[0168] in, All are design constants. ,and If the state-space model is stable at a fixed time, then the maximum convergence time of the system is... satisfy: for The time derivative;

[0169] ;

[0170] in, All are systematic errors. To adjust the parameters, ;

[0171] The virtual controller of the system is designed in the following form:

[0172] ;

[0173] ;

[0174] in, , , , All are positive parameters of the design; For the first The total weight of each agent's neighbors All are parameters of the NN compensation term; This represents the first-order cooperative tracking error. This is a second-order cooperative error; For design parameters; , Both are basis function vectors; Indicates the first The connection weights between the follower robotic arm and the leader robotic arm;

[0175] (5b) Select the first Lyapunov candidate equation for:

[0176] ;

[0177] in, For positive parameters of the design; express and The error between them ; Indicates the first The ideal weight vector of the first subsystem of the robotic arm; Indicates the first The ideal weight vector of the second subsystem of the robotic arm; for The estimate, for The estimate;

[0178] right Taking the derivative with respect to time, we get:

[0179] ;

[0180] In the formula, Indicates the first The input vector of the radial basis function neural network model of the first subsystem of the robotic arm. , Indicates the angle of the follower robotic arm joints. This indicates the trajectory of the leader's robotic arm. This represents the time derivative of the reference signal; Indicates the first The approximate bounded unknown function of the first subsystem of the robotic arm; Indicate the first The NN error of the first subsystem of the robotic arm;

[0181] (5c) Take the second Lyapunov candidate equation for:

[0182] ;

[0183] in, For positive parameters of the design; Represents the weight estimate Compared with actual value The error between them ;

[0184] right Taking the derivative with respect to time, we get:

[0185] ;

[0186] In the formula, The first step is the estimation of the virtual control signal. Time derivative, Indicates the first The input vector of the god-like network of the second subsystem of the robotic arm. , Indicates the angle of the follower robotic arm joint; Indicates the first The approximate bounded unknown function of the second subsystem of the robotic arm; and They are two unknown time-varying continuous functions. and These are all design parameters. , ; This is an internal dynamic variable used to adaptively adjust the trigger threshold. ; Indicates the first Virtual control input for a robotic arm; Indicate the first The NN error of the second subsystem of the robotic arm; and Indicates prediction error;

[0187] (5d) The first Lyapunov candidate equation Take the second Lyapunov candidate equation To form the complete Lyapunov equations as follows:

[0188] ;

[0189] (5e) Based on the complete Lyapunov equations Design the final controller, which includes a virtual controller. and , No. The composite learning adaptive law of the first subsystem of the robotic arm , No. The composite learning adaptive law of the second subsystem of the robotic arm :

[0190] ;

[0191] In the formula, The first The composite learning adaptive law of the first and second subsystems of the robotic arm; It is a projection operator.

[0192] like Figure 1 As shown, the rectangular nodes represent the leader robotic arm trajectory. As a reference signal, the goal of all follower robotic arms is to collaboratively track the trajectory of the leader robotic arm. Circular nodes 1, 2, and 3 represent the three follower robotic arms.

[0193] Figure 3 The horizontal axis represents time in seconds; the vertical axis represents position in radians, corresponding to the joint angle position of the robotic arm; the dashed line... The leader's robotic arm trajectory is represented by the following expression: ; solid blue line solid red line solid green line These represent the first state components of the three following robotic arms. The three follower curves rapidly approach the reference signal from the initial moment and remain consistent with it throughout the time interval. The results show a high degree of overlap, with no significant lag or divergence. Simulation results clearly demonstrate that this invention can achieve precise collaborative tracking of a reference signal by multiple robotic arms within a fixed time, verifying the tracking performance and consistency of the controller of this invention.

[0194] Figure 4 The horizontal axis represents time in seconds; the vertical axis represents tracking error. The unit is radians. The blue, red, and green curves correspond to the first component of the tracking error of the three following robotic arms, respectively. That is, each follower relative to the dotted line The error curve represents the deviation of the leader's robotic arm trajectory. Initially, the error curve exhibits small transient fluctuations, then rapidly converges and stabilizes within a very small neighborhood, oscillating without divergence or significant deviation throughout the simulation. The results demonstrate that this invention can achieve convergence of the cooperative tracking error to a sufficiently small residual set within a fixed time, even under conditions of modeling uncertainty and external disturbances, fully reflecting the fixed-time convergence characteristics and the robustness of the method.

[0195] Figure 5 The horizontal axis represents time in seconds; the vertical axis represents the actual control input. The unit is usually Newton-meter (N·m), which represents the torque input of the robotic arm. The blue, red, and green curves correspond to the three control inputs of the following robotic arm, respectively. The control input exhibits significant fluctuations in the initial stage to quickly compensate for initial errors and uncertainties. These fluctuations then rapidly decay and stabilize within a small range of oscillations, exhibiting overall smoothness without sustained high-amplitude jitter. This demonstrates that the present invention can dynamically adjust the torque based on the tracking error, and the input signal is smooth. While ensuring tracking accuracy, it significantly suppresses drastic fluctuations in the control input, verifying the feasibility of the invention in engineering applications.

[0196] Figure 6 The horizontal axis represents time in seconds; the vertical axis represents the neural network approximation error. The first sub-figure (above) shows the... NN error of the first subsystem of the robotic arm The second subgraph (below) shows the first... NN error of the second subsystem of the robotic arm Each error curve exhibited some oscillations in the initial stage, then gradually decreased and stabilized within a small bounded range, without showing sustained divergence or a trend of increase. The results indicate that the composite learning mechanism effectively utilizes historical data and prediction errors, enabling rapid convergence of neural network weights and a significant improvement in approximation accuracy. This provides high-quality uncertainty compensation, validating the crucial role of composite learning in enhancing approximation capability and control accuracy.

[0197] Figure 7The horizontal axis represents time in seconds; the vertical axis represents the cumulative count or trigger intensity of event triggers (indicated by the height of the dot). The three subgraphs correspond to the trigger event distribution for Agent 1, Agent 2, and Agent 3, respectively. Blue dots (Agent 1), red dots (Agent 2), and green dots (Agent 3) mark the position and interval of each event trigger. Trigger events are relatively dense in the initial stage, then become significantly sparse. The distribution shows that DMET can adaptively adjust the trigger threshold based on error dynamics and historical information, effectively extending the average trigger interval, significantly reducing the number of controller updates and communications, while still maintaining system stability and tracking performance.

[0198] Figure 8 The horizontal axis represents time in seconds; the vertical axis displays the trigger event timelines for Agent1, Agent2, and Agent3 in a layered format. Blue dots represent the trigger times for Agent1, red dots for Agent2, and green dots for Agent3. A zoom-in window further clarifies the density and intervals of the trigger events. Overall, the trigger events for each Agent are initially frequent, then become sparse and irregularly distributed, with a relatively long average trigger interval. Figure 8 The paper intuitively demonstrates the asynchronicity and sparsity of events triggered by each agent under DMET, indicating that the DMET mechanism can significantly reduce the communication and computation burden while ensuring the performance of cooperative control. It also verifies the efficiency and practical value of dynamic memory event triggering in resource-constrained scenarios of multi-robotic arm systems.

[0199] In summary, this invention, by introducing fractional power terms into the controller design, designing a virtual controller with fixed-time convergence terms, and conducting rigorous stability analysis based on the fixed-time Lyapunov equations, ensures that the cooperative tracking error of the multi-manipulator system converges to near the equilibrium point within a predetermined time independent of the initial state. This overcomes the limitation of traditional finite-time control where convergence time depends on initial conditions, greatly improving system response speed and determinism in engineering applications. Furthermore, this invention designs a dynamic memory event triggering mechanism. By introducing internal dynamic variables containing historical information to adaptively adjust the triggering threshold, compared to static event triggering mechanisms, it can more effectively extend the average triggering interval. This significantly reduces the controller update frequency and network communication resource consumption while ensuring system control performance, solving the bottleneck problem of resource constraints in multi-agent systems. Finally, this invention innovatively combines a composite learning mechanism with a radial basis function neural network. The composite learning mechanism not only utilizes instantaneous tracking errors to ensure system stability but also generates prediction errors by constructing dynamic data models to fully utilize historical system operation data.

[0200] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention. The scope of protection claimed by the appended claims and their equivalents is defined.

Claims

1. An adaptive control method for a multi-manipulator system based on DMET and a composite learning control framework, characterized in that: The method includes the following steps in sequence: (1) Use graph theory to construct the communication topology of the multi-manipulator system, establish the nonlinear dynamic model of the multi-manipulator system, and transform the nonlinear dynamic model into a state-space model; (2) Based on the state space model, set the leader robot trajectory and calculate the coordination error, and define the tracking error of each slave robot relative to the leader; (3) Update the weight vector by combining prediction error and tracking error. The estimated value The composite learning adaptive law is obtained. This enables online approximation of uncertain nonlinear terms in multi-robotic arm systems; (4) Design dynamic memory event triggering conditions and design the actual controller of the multi-robotic arm system; (5) Design the final controller based on the actual controller to ensure that the tracking error of all robotic arms converges within a fixed time and that all closed-loop signals of the multi-robotic arm system are bounded.

2. The adaptive control method for a multi-manipulator system based on DMET and a composite learning control framework according to claim 1, characterized in that: Step (1) specifically includes the following steps in sequence: (1a) The nonlinear dynamic model of the multi-manipulator system is established according to the Euler-Lagrange method as follows: （1）； in, Indicates mechanical inertia; Acceleration representing the angle of rotation; This represents the coefficient of viscous friction at the joint. The speed representing the rotation angle; Indicates the mass of the robotic arm; Represents gravitational acceleration; Indicates the length of the robotic arm; This indicates the position of the link angle, i.e., the rotation angle of the robotic arm joint; Indicates control input, Indicates system output; (1b) Let , Then equation (1) can be reconstructed into a state-space model: ； In the formula, Indicates the angle of the follower robotic arm joint; Indicates the speed of the follower robotic arm joints; This represents the acceleration at the joint angle; Indicates the actual control input; Indicates the length of the robotic arm; Indicates due to The introduced nonlinear term of gravity; due to ,so It also indicates the speed of the follower robotic arm joints.

3. The adaptive control method for a multi-manipulator system based on DMET and a composite learning control framework according to claim 1, characterized in that: Step (2) specifically includes the following steps in sequence: (2a) Set the trajectory of the leader robotic arm : ； in, Indicates the independent variable of time; (2b) Obtain the communication status between each agent in the multi-arm system, and use the following formula to calculate the first-order cooperative tracking error between the i-th follower arm and the other arms in the system. : ； in, To indicate the first The trajectory of a robotic arm Indicates the first The output trajectory of the robotic arm Indicates the total number of robotic arms. In a multi-arm robotic system, the intelligent agent is represented. With intelligent agents Communication status between them; Indicates the first The connection weights between the follower robotic arm and the leader robotic arm; (2c) Based on the error between the state of the follower robotic arm and the state of the leader robotic arm, the following formula is used to construct a representation of the state of the first robotic arm. The second-order cooperative error of the multi-arm system between the follower robotic arm and the other follower robotic arms in the system. : ； in, Indicates the first The first-order virtual controller input for the robotic arm; The first-order cooperative tracking error and second-order cooperative error Together they constitute the tracking error.

4. The adaptive control method for a multi-manipulator system based on DMET and a composite learning control framework according to claim 1, characterized in that: Step (3) specifically includes the following steps in sequence: (3a) Use the following formula to determine the radial basis function neural network model in the set Approximately bounded unknown functions on: ； in, Let represent an approximately bounded unknown function, and The input vector; Represents a set of possible values; express 3D real space; Represents a weight vector. belong 3D real space, It is the number of hidden layer nodes in the radial basis function neural network model; Represents the radial basis function vector; Indicates error; In any time interval Multiply both sides by the basis function vector , After integration, we get: ； In the formula, The first The online integral excitation matrix of the first and second subsystems of the robotic arm; The first The integral approximation error of the first and second subsystems of the robotic arm; The integral time window length is a positive design constant used to construct the prediction error and the integral excitation matrix; Indicates the current time; Indicates the speed of the follower robotic arm joints; This represents the acceleration at the joint angle; Indicates the actual control input; express arrive The set of states, ; Indicates the speed of the follower robotic arm joints; (3b) Construct a dynamic data model, considering the first The dynamics of the first subsystem of the robotic arm are as follows: ； In the formula, Indicates the first The ideal weight vector of the first subsystem of the robotic arm. express Transpose of; Indicate the first The NN error of the first subsystem of the robotic arm; The dynamics of the second subsystem of the robotic arm are as follows: ； In the formula, Indicates the first The ideal weight vector of the second subsystem of the robotic arm. express Transpose of; Indicates the first The NN error of the second subsystem of the robotic arm, where: ； ； For a multi-arm robotic system, given any initial conditions: ,in, Indicates the system at the initial moment The initial state vector at time, Indicates the initial set of values ​​to be taken. If the integer is a positive constant, then there exists a constant. ,in, , , making ,in The state vector of the multi-arm robotic system at time t represents the state vector of the system at time t. The value of , express The set of possible values; assume there exists a constant. and ,in , This makes it possible to achieve the following within the time interval: Above, the windowed regression matrix satisfies the persistent excitation IE condition, that is... , It is the identity matrix; (3c) Based on the dynamic data model, construct a prediction error that can be used for weight updates: ； ； in, and Indicates prediction error; for The estimate, for The estimate; (3d) Design based on prediction error Composite learning adaptive law: ； in, All are positive parameters of the design; It is a projection operator; The first The composite learning adaptive law of the first and second subsystems of the robotic arm.

5. The adaptive control method for a multi-manipulator system based on DMET and a composite learning control framework according to claim 1, characterized in that: Step (4) specifically includes the following steps in sequence: (4a) Design dynamic memory event triggering conditions: ； ； in, It is the first The actual control input for a robotic arm; Indicates a virtual controller; Indicates time as the independent variable; Indicates the first The next trigger moment; Indicates the first The next trigger moment; Indicates control input deviation. ; and For design parameters, , ; This is an internal dynamic variable used to adaptively adjust the trigger threshold. ; Indicates the first Virtual control input for a robotic arm; (4b) Design internal dynamic variables The renewal law: ； in, All are design parameters and satisfy the following: ； in, It is a small positive constant; Indicates the time span of memory; As initial conditions, ,in Indicates the initial time variable. ; For the initial function, ; (4c) Based on the dynamic memory event triggering conditions, design the actual controller of the multi-robotic arm system. : ； in, and They are two unknown time-varying continuous functions that satisfy... .

6. The adaptive control method for a multi-manipulator system based on DMET and a composite learning control framework according to claim 1, characterized in that: Step (5) specifically includes the following steps in sequence: (5a) Assume there exists a smooth positive definite function. , so that: ； in, All are design constants. ,and If the state-space model is stable at a fixed time, then the maximum convergence time of the system is... satisfy: for The time derivative; ； in, All are systematic errors. To adjust the parameters, ; The virtual controller of the system is designed in the following form: ； ； in, , , , All are positive parameters of the design; For the first The total weight of each agent's neighbors All are parameters of the NN compensation term; This represents the first-order cooperative tracking error. This is a second-order cooperative error; For design parameters; , Both are basis function vectors; Indicates the first The connection weights between the follower robotic arm and the leader robotic arm; (5b) Select the first Lyapunov candidate equation for: ； in, For positive parameters of the design; express and The error between them ; Indicates the first The ideal weight vector of the first subsystem of the robotic arm; Indicates the first The ideal weight vector of the second subsystem of the robotic arm; for The estimate, for The estimate; right Taking the derivative with respect to time, we get: ； In the formula, Indicates the first The input vector of the radial basis function neural network model of the first subsystem of the robotic arm. , Indicates the angle of the follower robotic arm joints. This indicates the trajectory of the leader's robotic arm. This represents the time derivative of the reference signal; Indicates the first The approximate bounded unknown function of the first subsystem of the robotic arm; Indicate the first The NN error of the first subsystem of the robotic arm; (5c) Take the second Lyapunov candidate equation for: ； in, For positive parameters of the design; Represents the weight estimate Compared with actual value The error between them ; right Taking the derivative with respect to time, we get: ； In the formula, The first step is the estimation of the virtual control signal. Time derivative, Indicates the first The input vector of the god-like network of the second subsystem of the robotic arm. , Indicates the angle of the follower robotic arm joint; Indicates the first The approximate bounded unknown function of the second subsystem of the robotic arm; and They are two unknown time-varying continuous functions. and These are all design parameters. , ; This is an internal dynamic variable used to adaptively adjust the trigger threshold. ; Indicates the first Virtual control input for a robotic arm; Indicate the first The NN error of the second subsystem of the robotic arm; and Indicates prediction error; (5d) The first Lyapunov candidate equation Take the second Lyapunov candidate equation To form the complete Lyapunov equations as follows: ； (5e) Based on the complete Lyapunov equations Design the final controller, which includes a virtual controller. and , No. The composite learning adaptive law of the first subsystem of the robotic arm , No. The composite learning adaptive law of the second subsystem of the robotic arm : ； In the formula, The first The composite learning adaptive law of the first and second subsystems of the robotic arm; It is a projection operator.

7. An electronic device, comprising: processor; as well as A memory storing computer program instructions, which, when executed by the processor, cause the processor to perform the adaptive control method for a multi-manipulator system based on the DMET and composite learning control framework as described in any one of claims 1-6.

8. A computer-readable storage medium having stored thereon computer program instructions, which, when executed by a processor, cause the processor to perform the adaptive control method for a multi-manipulator system based on the DMET and composite learning control framework as described in any one of claims 1-6.

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