Multi-mechanical-arm specified time event triggering sliding mode control method

Abstract

The invention discloses a multi-mechanical-arm specified time event triggering sliding mode control method, and relates to the technical field of mechanical arm processing, and the method comprises the following steps: S1, building a kinematics model and a dynamics model for a leader and a follower of a plurality of mechanical arms, and determining a specified time control criterion; s2, the consistency error of the mechanical arm is determined; s3, determining an error conversion function; s4, determining a nonsingular terminal sliding mode surface; s5, constructing a first self-construction neural network, and determining a self-construction neural network disturbance observer in the specified time; and S6, a second self-construction neural network is constructed, a specified time controller is determined, and consistency tracking of the multiple mechanical arms is completed. According to the method, the formation control precision in continuous time when disturbance exists is improved through introduction of an error function and proper adjustment of a sliding mode gain parameter; the event triggering mechanism avoids unnecessary continuous monitoring through periodic monitoring, reduces repeated periodic calculation, reduces system hardware requirements, and further improves physical realizability of the method.

Description

Technical Field

[0001] The present invention relates to the technical field of robot arm processing, and in particular to a sliding mode control method for triggering a specified time event of multiple robot arms. Background Art

[0002] In the past few decades, distributed cooperative control of multi-agent systems has been widely used due to its advantages such as stronger robustness, stability and high fault tolerance. In particular, as the most important branch of distributed cooperative control, consistency control plays a vital role in practical engineering applications such as ship formation control, underwater robot cooperative control and UAV formation flight. In view of the fact that the dynamic characteristics of complex mechanical systems in practical engineering applications are often difficult to describe by simple linear system models, the research focus of consistency problems has gradually shifted to the field of more complex nonlinear systems. At the same time, as a special nonlinear case, multi-agent systems with Lagrangian dynamics have been favored by researchers because they can model some practical industrial systems, such as the cooperative control of multiple robotic arms.

[0003] Compared with traditional linear or nonlinear systems, multi-manipulator systems show higher uncertainty and nonlinear characteristics, especially in complex scenarios involving unmodeled dynamics and strong parameter coupling. Some existing studies use methods such as adaptive control, neural network control and fuzzy control to deal with this model uncertainty. However, when considering the problem of time consistency, all three methods have certain shortcomings. As an alternative, a time-limited self-constructed neural network disturbance observer can be introduced to estimate model uncertainty and external disturbances.

[0004] For these systems with high model uncertainty, the current control methods have shown obvious limitations. Therefore, it is particularly important to develop an innovative control algorithm. Considering that the sliding mode control strategy has shown excellent results in weakening the negative effects of model uncertainty and unknown disturbances in the control process, it has become a strong candidate for us to explore new control schemes. Therefore, how to apply sliding mode control to solve the problem of cooperative control of multi-manipulator systems is a very interesting topic. On the one hand, the fixed time stability theory has been widely used in the field of sliding mode control due to its many advantages. However, the determination process of its convergence upper bound involves complex system parameter adjustment, which may cause the upper bound set to be too conservative. In order to overcome this limitation, subsequent studies introduced the predefined time stability theory, whose upper bound of convergence time can be more closely approximated to the user-specified adjustment parameters, but still has a certain ambiguity. Therefore, the study of prescribed time stability has received widespread attention and has been applied to sliding mode control, adaptive control and optimal control. Its convergence time can be specified in advance and is independent of initial conditions and other parameters, ensuring the timeliness of the control process. On the other hand, compared with the traditional linear sliding mode control, the terminal sliding mode control can ensure that once the system state reaches the sliding surface, it can converge to zero within the specified time, and has a faster response speed. However, the tracking error is usually unstable and fluctuates significantly, and a transfer function based on the performance function is introduced to limit the range of the error.

[0005] In order to effectively reduce the load pressure of the closed-loop system communication network and maintain a high level of control performance satisfaction, a distributed event-triggered control strategy with efficient resource utilization was developed. This strategy achieves optimal allocation and utilization of resources by reasonably managing the timing of triggering events. It is worth noting that the important idea of ​​event-triggered control is that when the constant magnitude of the measurement error exceeds the preset allowable threshold or the norm of the system state reaches a specific condition, the event trigger mechanism will be activated and the controller will be updated. This process ensures that the system maintains a certain performance level while also ensuring that the internal execution time has a positive minimum limit. Therefore, it is necessary to study the distributed event-triggered formation control of multiple manipulators. Summary of the invention

[0006] In order to solve the above problems, the present invention proposes a sliding mode control method for triggering a multi-manipulator specified time event.

[0007] The technical solution of the present invention is: a sliding mode control method for triggering a multi-manipulator specified time event comprises the following steps:

[0008] S1. Establish kinematic and dynamic models for the leader and follower of the multi-manipulator, and determine the specified time control criteria;

[0009] S2, determining the consistency error of the robot arm according to the specified time control criterion, the kinematic model and the dynamic model of the leader, and the kinematic model and the dynamic model of the follower;

[0010] S3, determining an error conversion function according to the consistency error and performance function of the robot arm;

[0011] S4, determining a non-singular terminal sliding surface according to the error transfer function;

[0012] S5. constructing a first self-constructed neural network according to the non-singular terminal sliding surface, and determining a self-constructed neural network observer at a specified time;

[0013] S6. According to the specified time, the neural network observer is self-constructed, a second self-constructed neural network is constructed, and the specified time controller is determined to complete the consistency tracking of multiple robotic arms.

[0014] Furthermore, in S1, the expression of the follower's kinematic model is:

[0015]

[0016] Where M i,11 represents the first symmetric positive definite inertia matrix of the i-th dual-joint manipulator, M i,12 represents the second symmetric positive definite inertia matrix of the i-th dual-joint manipulator, M i,21 represents the third symmetric positive definite inertia matrix of the i-th dual-joint manipulator, M i,22 represents the fourth symmetric positive definite inertia matrix of the i-th dual-joint manipulator, represents the first speed of the i-th dual-joint robot, represents the second speed of the i-th dual-joint robot arm, represents the first acceleration of the i-th dual-joint robotic arm, represents the second acceleration of the i-th dual-joint robotic arm, C i,11 represents the first Coriolis force of the i-th dual-joint robot, C i,12 represents the first centrifugal force of the i-th dual-joint robot, C i,21 represents the second Coriolis force of the i-th dual-joint robot arm, C i,22 represents the second centrifugal force of the i-th dual-joint robotic arm, G i,1 represents the first gravity of the i-th dual-joint robotic arm, G i,2 represents the second gravity of the i-th dual-joint robotic arm, w i,1 represents the first control signal of the i-th dual-joint robot after event triggering processing, w i,2 represents the second control signal of the i-th dual-joint robot after event triggering processing, τ di,1represents the external disturbance of the i-th dual-joint robot, τ di,2 represents the second external disturbance suffered by the i-th dual-joint robot;

[0017] In S1, the expression of the follower's dynamic model is:

[0018]

[0019] In the formula, x i,λ represents the position of the λth joint of the i-th robot, v i,λ represents the velocity of the λth joint of the ith robot arm, represents the first-order derivative of the velocity of the λth joint of the i-th robot, represents the first-order derivative of the position of the λth joint of the i-th robot, f i,λ (x i,λ ) represents the set of model uncertainties of the λth joint of the i-th robot, w i,λ represents the control signal of the λth joint of the i-th robot after event triggering processing, τ di,λ represents the external time-varying disturbance of the λth joint of the i-th robot arm, M i,λ represents the moment of inertia of the motor and connecting rod of the λth joint of the i-th robot;

[0020] In S1, the kinematic model of the leader is expressed as:

[0021]

[0022] In the formula, represents the first-order derivative of the position of the leader manipulator, v 0,λ represents the velocity of the λth joint of the leader robot;

[0023] In S1, the leader’s dynamic model is expressed as:

[0024]

[0025] In the formula, represents the first-order derivative of the velocity of the leader robot, u 0,λ represents the control signal of the λth joint of the leader robot arm;

[0026] In S1, the expression of the time control criterion is specified as:

[0027]

[0028] Where V i,λ (t) represents a continuously differentiable function, μ(t) represents a time-varying function, is the first-order derivative of the time-varying function, t represents the time of the control process, κ1 represents the first positive real constant, κ2 represents the second positive real constant, and T represents the specified time.

[0029] Further, in S2, the consistency error includes the position consistency error of the λth joint of the i-th robotic arm, the velocity consistency error of the λth joint of the i-th robotic arm, and the acceleration consistency error of the λth joint of the i-th robotic arm;

[0030] The position consistency error e of the λth joint of the i-th robot arm xi,λ The expression is:

[0031]

[0032] In the formula, N represents the number of robotic arms, a ij represents the communication link between the i-th follower robot and the j-th follower robot, b i represents the communication link between the leader robot and the ith follower robot, x i,λ represents the position of the λth joint of the ith robot arm, x j,λ represents the position of the λth joint of the jth follower robot, x 0,λ represents the position of the leader's robotic arm;

[0033] The velocity consistency error e of the λth joint of the i-th robot arm vi,λ The expression is:

[0034]

[0035] In the formula, v i,λ represents the velocity of the λth joint of the ith robot arm, v j,λ represents the velocity of the λth joint of the jth robot, v 0,λ represents the speed of the leader's robotic arm;

[0036] The acceleration consistency error e of the λth joint of the i-th robot arm ai,λ The expression is:

[0037]

[0038] In the formula, a i,λ represents the acceleration of the λth joint of the i-th robot, a j,λ represents the acceleration of the λth joint of the jth robot, a 0,λ Represents the acceleration of the leader's robot arm.

[0039] Furthermore, in S3, the error conversion function δ i,λ The expression is:

[0040]

[0041] In the formula, e xi,λ represents the position consistency error, Φ a Represents a performance function.

[0042] Furthermore, in S4, the non-singular terminal sliding surface s i,λ The expression is:

[0043]

[0044] In the formula, δ i,λ represents the error transfer function, represents the first-order derivative of the error transfer function, κ 1i,λ represents the first positive real constant of the λth joint of the ith robot, κ 2i,λ represents the second positive real constant of the λth joint of the i-th robot, μ(t) represents the time variation function, Represents the first derivative of a time-varying function.

[0045] Furthermore, in S5, the self-constructed neural network f i,λ (σ i,λ ) is:

[0046] f i,λ (σ i,λ )=W i,λ h i,λ (σ i,λ )+ε i,λ ;

[0047] In the formula, σ i,λ represents the input of the self-constructed neural network, ε i,λ represents the estimation error of the self-constructed neural network, W i,λ represents the optimal weight, h i,λ (σ i,λ ) represents Gaussian basis function;

[0048] In S5, the neural network disturbance observer is constructed at a specified time The expression is:

[0049]

[0050] In the formula, represents the estimated value of the neural network approximation error, represents the estimated value of uncertainty, M i,λ represents the moment of inertia of the motor and connecting rod of the λth joint of the i-th robot arm, u ai,λ represents the control signal after input saturation, κ 7i,λrepresents the seventh positive real constant of the λth joint of the i-th robot arm, κ 8i,λ represents the eighth positive real constant of the λth joint of the i-th robot, μ(t) represents the time variation function, represents the first-order derivative of the time-varying function, ψ i,λ represents the state variable, Indicates an adjustable parameter.

[0051] Furthermore, S6 includes the following sub-steps:

[0052] S61, constructing a second self-constructed neural network according to the specified time self-constructed neural network observer, and determining the specified time controller;

[0053] S62, determining the auxiliary system and event triggering mechanism;

[0054] S63. Using the specified time controller, auxiliary system and event trigger mechanism, the consistency error is converged to the zero domain within the specified time, and the consistency tracking of the multi-manipulator is completed.

[0055] Further, in S61, the time controller u is specified i,λ The expression is:

[0056]

[0057] Where M i,λ represents the moment of inertia of the motor and connecting rod of the λth joint of the i-th robot arm, represents the conversion error function, represents the derivative of the conversion error function, N represents the number of robotic arms, a ij represents the communication link between the i-th follower robot and the j-th follower robot, b i represents the communication link between the leader robot and the i-th follower robot, Φ a represents the performance function, represents the first derivative of the performance function, represents the second-order derivative of the performance function, represents the first-order derivative of the velocity of the λth joint of the i-th robot, represents the first-order derivative of the velocity of the leader robot, e xi,λ represents the position consistency error, represents the first-order derivative of the position consistency error, κ 1i,λ represents the first positive real constant of the λth joint of the ith robot, κ 2i,λ represents the second positive real constant of the λth joint of the ith robot arm, κ 11i,λ represents the eleventh positive real constant of the λth joint of the ith robot arm, κ 12i,λrepresents the twelfth positive real constant of the λth joint of the i-th robot, μ(t) represents the time variation function, Represents the first derivative of the time-varying function, s i,λ represents the non-singular terminal sliding surface, represents the estimated value of the first optimal weight, h ai,λ represents the first Gaussian basis function, ξ i,λ represents the first approximation error, represents the estimated value of the external disturbance of the λth joint of the i-th robot.

[0058] Further, in S62, the auxiliary system update rate expression is:

[0059]

[0060] Where M i,λ represents the moment of inertia of the motor and connecting rod of the λth joint of the i-th robot arm, represents the conversion error, represents the derivative of the conversion error, N represents the number of robotic arms, a ij represents the communication link between the i-th follower robot and the j-th follower robot, b i represents the communication link between the leader robot and the i-th follower robot, Δu i,λ represents the control input difference after input saturation, ξ i,λ represents the first approximation error, θ α represents the auxiliary system, κ 13i,λ represents the thirteenth positive real constant of the λth joint of the ith robot arm, κ 14i,λ represents the fourteenth positive real constant of the λth joint of the ith robot arm;

[0061] In S62, the event trigger mechanism w i,λ The expression of (t) is:

[0062]

[0063] In the formula, μ c represents the first positive design parameter, represents the second positive design parameter, m a represents the third positive design parameter, represents the fourth positive design parameter, t represents the time of the control process, u ai,λ represents the control signal after input saturation, represents the transpose of the non-singular terminal sliding surface, Γ represents a natural number, θ represents the monitoring period, and w i,λ (t k-1 ) represents the control signal at the next triggering time after the event is triggered, wi,λ (t k ) represents the control signal at the current triggering moment after the event is triggered, t k Indicates the current triggering time, t k-1 Indicates the next triggering time, t k+1 Indicates the last triggering time, E i,λ (t) represents the trigger condition defined by the measurement error.

[0064] The beneficial effects of the present invention are:

[0065] (1) The present invention determines a specified time disturbance observer based on a self-constructed neural network to approximate uncertain external disturbances. Compared with the existing technology, the proposed observer can achieve more accurate disturbance estimation within the specified time and further improve the convergence speed of the observer. The introduction of the adaptive structure neural network can continuously adjust the number of neurons according to the segmentation strategy under the premise of ensuring good approximation accuracy, and finally obtain the optimal number;

[0066] (2) Aiming at the consistency control of a multi-manipulator system, the present invention has determined a multi-manipulator specified time event triggered sliding mode control method based on a disturbance observer. Compared with the existing technology, the proposed sliding mode controller achieves specified time convergence, and improves the formation control accuracy in continuous time when there is a disturbance by introducing an error function and appropriately adjusting the sliding mode gain parameters. The event trigger mechanism avoids unnecessary continuous monitoring through periodic monitoring, reduces repeated periodic calculations, reduces the system hardware requirements, and further improves the physical feasibility of the method. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 Flow chart of a sliding mode control method for multi-manipulators with time event triggering;

[0068] Figure 2 A schematic diagram of the structure of a sliding mode control system triggered by a time event for multiple manipulators;

[0069] Figure 3 A schematic diagram of the topological communication relationship of a multi-manipulator system;

[0070] Figure 4 is a first schematic diagram of the variation of the position tracking errors of joints 1 and 2 in the multi-manipulator system over time;

[0071] Figure 5 is a second schematic diagram of the change of the position tracking errors of joints 1 and 2 in the multi-manipulator system over time;

[0072] Figure 6is a first schematic diagram of the variation of the velocity tracking errors of joints 1 and 2 in the multi-manipulator system over time;

[0073] Figure 7 is a second schematic diagram of the change of the velocity tracking errors of joints 1 and 2 in the multi-manipulator system over time;

[0074] Figure 8 Schematic diagram of the error changes of joints 1 and 2 of all manipulators during the disturbance observation process;

[0075] Fig. 9 This is a schematic diagram of the distribution of event triggering times of all robot joints 1 and 2;

[0076] Fig.10 This is a schematic diagram of the event triggering times of joints 1 and 2 of all robot arms;

[0077] Fig.11 The first schematic diagram is a diagram showing the change in the number of neurons of a self-constructed neural network;

[0078] Fig.12 A second schematic diagram showing the change in the number of neurons of the self-constructed neural network;

[0079] Fig.13 is a first schematic diagram of saturated control signals of joints 1 and 2 of all robot arms after being processed by the event trigger mechanism;

[0080] Fig.14 This is a second schematic diagram of the saturated control signals of joints 1 and 2 of all robot arms after being processed by the event trigger mechanism. DETAILED DESCRIPTION

[0081] The embodiments of the present invention will be further described below in conjunction with the accompanying drawings.

[0082] like Figure 1 As shown, the present invention provides a sliding mode control method for triggering a multi-manipulator specified time event, comprising the following steps:

[0083] S1. Establish kinematic and dynamic models for the leader and follower of the multi-manipulator, and determine the specified time control criteria;

[0084] S2, determining the consistency error of the robot arm according to the specified time control criterion, the kinematic model and the dynamic model of the leader, and the kinematic model and the dynamic model of the follower;

[0085] S3, determining an error conversion function according to the consistency error and performance function of the robot arm;

[0086] S4, determining a non-singular terminal sliding surface according to the error transfer function;

[0087] S5. constructing a first self-constructed neural network according to the non-singular terminal sliding surface, and determining a self-constructed neural network observer at a specified time;

[0088] S6. According to the specified time, the neural network observer is self-constructed, a second self-constructed neural network is constructed, and the specified time controller is determined to complete the consistency tracking of multiple robotic arms.

[0089] In the embodiment of the present invention, in S1, the expression of the kinematic model of the follower is:

[0090]

[0091] Where M i,11 represents the first symmetric positive definite inertia matrix of the i-th dual-joint manipulator, M i,12 represents the second symmetric positive definite inertia matrix of the i-th dual-joint manipulator, M i,21 represents the third symmetric positive definite inertia matrix of the i-th dual-joint manipulator, M i,22 represents the fourth symmetric positive definite inertia matrix of the i-th dual-joint manipulator, represents the first speed of the i-th dual-joint robot, represents the second speed of the i-th dual-joint robot arm, represents the first acceleration of the i-th dual-joint robotic arm, represents the second acceleration of the i-th dual-joint robotic arm, C i,11 represents the first Coriolis force of the i-th dual-joint robot, C i,12 represents the first centrifugal force of the i-th dual-joint robot, C i,21 represents the second Coriolis force of the i-th dual-joint robot arm, C i,22 represents the second centrifugal force of the i-th dual-joint robotic arm, G i,1 represents the first gravity of the i-th dual-joint robotic arm, G i,2 represents the second gravity of the i-th dual-joint robotic arm, w i,1 represents the first control signal of the i-th dual-joint robot after event triggering processing, w i,2 represents the second control signal of the i-th dual-joint robot after event triggering processing, τ di,1 represents the external disturbance of the i-th dual-joint robot, τ di,2 represents the second external disturbance suffered by the i-th dual-joint robot;

[0092] In S1, the expression of the follower's dynamic model is:

[0093]

[0094] In the formula, x i,λ represents the position of the λth joint of the i-th robot, v i,λ represents the velocity of the λth joint of the ith robot arm, represents the first-order derivative of the velocity of the λth joint of the i-th robot, represents the first-order derivative of the position of the λth joint of the i-th robot, f i,λ (x i,λ ) represents the set of model uncertainties of the λth joint of the i-th robot, w i,λ represents the control signal of the λth joint of the i-th robot after event triggering processing, τ di,λ represents the external time-varying disturbance of the λth joint of the i-th robot arm, M i,λ represents the moment of inertia of the motor and connecting rod of the λth joint of the i-th robot;

[0095] In S1, the kinematic model of the leader is expressed as:

[0096]

[0097] In the formula, represents the first-order derivative of the position of the leader manipulator, v 0,λ represents the velocity of the λth joint of the leader robot;

[0098] In S1, the leader’s dynamic model is expressed as:

[0099]

[0100] In the formula, represents the first-order derivative of the velocity of the leader robot, u 0,λ represents the control signal of the λth joint of the leader robot arm;

[0101] In S1, specifically, a time-varying function μ(t)=(T / Tt) ω , t∈[t0,t0+T);μ(t)=1,t∈[t0+T,∞)Determine the specified time control criterion:

[0102]

[0103] Where V i,λ (t) represents a continuously differentiable function, μ(t) represents a time-varying function, is the first-order derivative of the time-varying function, t represents the time of the control process, κ1 represents the first positive real constant, κ2 represents the second positive real constant, and T represents the specified time.

[0104] In the embodiment of the present invention, in S2, it is assumed that the communication topology between the follower manipulators is described by graph theory θ(L,Π), Y=[y1,K,y n ] represents the vertex set, Π∈y×y represents the edge set (y i ,y j ), i represents the number of robotic arms, the directed graph A = [a ij ]∈R n The incident adjacency matrix of is defined as Ω, where a ij =1. ij =1, j≠i means that the i-th follower robot arm has communication with the j-th follower robot arm; otherwise, a ij = 0. The exponential correlation matrix is ​​defined as C = diag (c i )∈R n ,in Denotes node i. Define Y'=CA as the Laplacian matrix. The adjacency matrix of the leader robot is defined as B=diag(b i )∈R n , where b i =1 indicates that the leader robot arm has communication connection with the i-th follower robot arm; otherwise, the leader robot arm has no communication connection with the i-th follower robot arm, which is defined as b i =0.

[0105] In the embodiment of the present invention, in S2, the consistency error includes the position consistency error of the λth joint of the ith robotic arm, the velocity consistency error of the λth joint of the ith robotic arm, and the acceleration consistency error of the λth joint of the ith robotic arm;

[0106] The position consistency error e of the λth joint of the i-th robot arm xi,λ The expression is:

[0107]

[0108] In the formula, N represents the number of robotic arms, a ij represents the communication link between the i-th follower robot and the j-th follower robot, b i represents the communication link between the leader robot and the ith follower robot, x i,λ represents the position of the λth joint of the ith robot arm, x j,λ represents the position of the λth joint of the jth follower robot, x 0,λ represents the position of the leader's robotic arm;

[0109] The velocity consistency error e of the λth joint of the i-th robot arm vi,λ The expression is:

[0110]

[0111] In the formula, v i,λ represents the velocity of the λth joint of the ith robot arm, v j,λ represents the velocity of the λth joint of the jth robot, v 0,λ represents the speed of the leader's robotic arm;

[0112] The acceleration consistency error e of the λth joint of the i-th robot arm ai,λ The expression is:

[0113]

[0114] In the formula, a i,λ represents the acceleration of the λth joint of the i-th robot, a j,λ represents the acceleration of the λth joint of the jth robot, a 0,λ Represents the acceleration of the leader's robot arm.

[0115] In the embodiment of the present invention, in S3, a performance function Φ a∞ ,t≥T determines the error conversion function δ i,λ :

[0116]

[0117] In the formula, e xi,λ represents the position consistency error, Φ a Represents a performance function.

[0118] In S3, the first-order derivative of the error transfer function The expression is:

[0119]

[0120] In the formula, e xi,λ represents the position consistency error, Represents the first-order derivative of the position consistency error, Φ a represents the performance function, represents the first derivative of the performance function,

[0121] In S3, the second derivative of the error transfer function is The expression is:

[0122]

[0123] In the formula, represents the conversion error, represents the derivative of the conversion error, represents the second-order derivative of the position consistency error, Represents the second derivative of the performance function.

[0124] In the embodiment of the present invention, in S4, the non-singular terminal sliding surface s i,λ The expression is:

[0125]

[0126] In the formula, δ i,λ represents the error transfer function, represents the first-order derivative of the error transfer function, κ 1i,λ represents the first positive real constant of the λth joint of the ith robot, κ 2i,λ represents the second positive real constant of the λth joint of the i-th robot, μ(t) represents the time variation function, Represents the first derivative of a time-varying function.

[0127] In S4, the first-order derivative of the non-singular terminal sliding surface The expression is:

[0128]

[0129] In the formula, represents the first-order derivative of the error transfer function, Represents the second derivative of the error transfer function.

[0130] In S4, the first-order derivative of the non-singular terminal sliding surface It can be further expressed as:

[0131]

[0132] In the formula, represents the conversion error, represents the derivative of the conversion error, e xi,λ represents the position consistency error, represents the first-order derivative of the position consistency error, Represents the second-order derivative of the position consistency error, Φ a represents the performance function, represents the first derivative of the performance function, Represents the second derivative of the performance function.

[0133] In the embodiment of the present invention, in S5, the self-constructed neural network f i,λ (σ i,λ ) is:

[0134] f i,λ (σ i,λ )=W i,λ h i,λ (σ i,λ )+εi,λ ;

[0135] In the formula, σ i,λ represents the input of the self-constructed neural network, ε i,λ represents the estimation error of the self-constructed neural network, W i,λ represents the optimal weight, h i,λ (σ i,λ ) represents Gaussian basis function;

[0136] In S5, specifically, the first self-constructed neural network update rate and adaptive rate Determine the specified time to self-construct the neural network disturbance observer:

[0137]

[0138] In the formula, represents the estimated value of the neural network approximation error, represents the estimated value of the first optimal weight, h ai,λ represents the Gaussian basis function of the first self-constructed neural network, ξ i,λ represents the first approximation error, M i,λ represents the moment of inertia of the motor and connecting rod of the λth joint of the i-th robot arm, u ai,λ represents the control signal after input saturation, κ 7i,λ represents the seventh positive real constant of the λth joint of the i-th robot arm, κ 8i,λ represents the eighth positive real constant of the λth joint of the i-th robot, μ(t) represents the time variation function, represents the first-order derivative of the time-varying function, ψ i,λ represents the state variable, Indicates an adjustable parameter.

[0139] In this embodiment of the present invention, S6 includes the following sub-steps:

[0140] S61, constructing a second self-constructed neural network according to the specified time self-constructed neural network observer, and determining the specified time controller;

[0141] S62, determining the auxiliary system and event triggering mechanism;

[0142] S63. Using the specified time controller, auxiliary system and event trigger mechanism, the consistency error is converged to the zero domain within the specified time, and the consistency tracking of the multi-manipulator is completed.

[0143] In the embodiment of the present invention, in S61, specifically, the second self-constructed neural network update rate Determine the external disturbance estimate of the λth joint of the i-th manipulator Then specify the time controller u i,λ The expression is:

[0144]

[0145] Where M i,λ represents the moment of inertia of the motor and connecting rod of the λth joint of the i-th robot arm, represents the conversion error function, represents the derivative of the conversion error function, N represents the number of robotic arms, a ij represents the communication link between the i-th follower robot and the j-th follower robot, b i represents the communication link between the leader robot and the i-th follower robot, Φ a represents the performance function, represents the first derivative of the performance function, represents the second-order derivative of the performance function, represents the first-order derivative of the velocity of the λth joint of the i-th robot, represents the first-order derivative of the velocity of the leader robot, e xi,λ represents the position consistency error, represents the first-order derivative of the position consistency error, κ 1i,λ represents the first positive real constant of the λth joint of the ith robot, κ 2i,λ represents the second positive real constant of the λth joint of the ith robot arm, κ 11i,λ represents the eleventh positive real constant of the λth joint of the ith robot arm, κ 12i,λ represents the twelfth positive real constant of the λth joint of the i-th robot, μ(t) represents the time variation function, Represents the first derivative of the time-varying function, s i,λ represents the non-singular terminal sliding surface, represents the estimated value of the first optimal weight, h ai,λ represents the first Gaussian basis function, ξ i,λ represents the first approximation error, represents the estimated value of the external disturbance of the λth joint of the i-th robot.

[0146] In the embodiment of the present invention, in S62, the auxiliary system update rate expression is:

[0147]

[0148] Where M i,λ represents the moment of inertia of the motor and connecting rod of the λth joint of the i-th robot arm, represents the conversion error, represents the derivative of the conversion error, N represents the number of robotic arms, a ijrepresents the communication link between the i-th follower robot and the j-th follower robot, b i represents the communication link between the leader robot and the i-th follower robot, Δu i,λ represents the control input difference after input saturation, ξ i,λ represents the first approximation error, θ α represents the auxiliary system, κ 13i,λ represents the thirteenth positive real constant of the λth joint of the ith robot arm, κ 14i,λ represents the fourteenth positive real constant of the λth joint of the ith robot arm;

[0149] In S62, the event trigger mechanism w i,λ The expression of (t) is:

[0150]

[0151] In the formula, μ c represents the first positive design parameter, represents the second positive design parameter, m a represents the third positive design parameter, represents the fourth positive design parameter, t represents the time of the control process, u ai,λ represents the control signal after input saturation, represents the transpose of the non-singular terminal sliding surface, Γ represents a natural number, θ represents the monitoring period, and w i,λ (t k-1 ) represents the control signal at the next triggering time after the event is triggered, w i,λ (t k ) represents the control signal at the current triggering moment after the event is triggered, t k Indicates the current triggering time, t k-1 Indicates the next triggering time, t k+1 Indicates the last triggering time, E i,λ (t) represents the trigger condition defined by the measurement error.

[0152] In the embodiment of the present invention, Figure 2 As shown, the multi-manipulator specified time event triggered sliding mode control system based on disturbance observer should include a leader trajectory generator module, an error conversion module, a performance constraint module, a specified time controller module, an auxiliary system module, an event trigger mechanism module, a multi-manipulator system module, a specified time self-constructed neural network disturbance observer module, a self-constructed neural network module and an adaptive rate module.

[0153] The leader trajectory generator module is used to generate the desired position, desired velocity and desired acceleration of the control system, and input the desired position, desired velocity and desired acceleration of the control system into the error conversion module and the self-constructed neural network module respectively.

[0154] The error conversion module is used to obtain the expected trajectory input by the leader trajectory generator module, the follower state information input by the multi-robotic arm system module, and the performance function input by the performance constraint module, and calculate the errors between each follower and between the leader and each follower according to the communication topology relationship. Then, the performance function input by the performance constraint module is combined with the errors between each follower and between the leader and each follower to solve the error conversion function, and the non-singular terminal sliding surface of the specified time is solved by the calculated error conversion function.

[0155] The performance constraint module is used to generate the performance function applied to the multi-manipulator system and input it into the error conversion module.

[0156] The specified time controller module is used to obtain the non-singular terminal sliding surface input by the error conversion module, the errors between each follower and the leader and each follower, and the performance function, and further obtain the product of the optimal weight and the Gaussian basis function and the sum of the approximate errors (i.e., the estimated value of the model uncertainty) input by the self-constructed neural network module and the external disturbance estimate input by the specified time self-constructed neural network disturbance observer module. The output signal of the specified time controller is obtained by solving the non-singular terminal sliding surface, the errors between each follower and the leader and each follower, the performance function, the product of the optimal weight and the Gaussian basis function and the sum of the approximate errors, and the external disturbance estimate.

[0157] The auxiliary system module is used to obtain the output signal of the specified time controller module, and according to the output signal of the specified time controller module, perform saturation suppression processing on the control signal and calculate the processed control signal.

[0158] The event trigger mechanism module is used to obtain the control signal of the auxiliary system module and design the event trigger mechanism according to the control signal. The event trigger mechanism is used to limit the transmission frequency of the continuous control signal sent from the auxiliary system to the multi-robotic arm system.

[0159] The multi-robotic arm system module is used to obtain the control signal of the event trigger mechanism module, and perform differential solution based on the actual control signal to obtain the position, velocity and acceleration of the follower, and then adjust the follower state information based on the obtained position, velocity and acceleration information.

[0160] The specified time self-constructed neural network disturbance observer module is used to obtain the position, velocity and acceleration information of the follower of the multi-robotic arm system module, the control signal of the auxiliary system module, the product of the optimal weight and Gaussian basis function of the self-constructed neural network module input and the sum of the approximate error (i.e., the estimated value of the model uncertainty) and the product of the optimal weight and Gaussian basis function and the sum of the approximate error (i.e., the estimated value of the external disturbance) and the adaptive rate of the adaptive rate module.

[0161] The self-constructed neural network module is used to obtain the expected position, expected speed and expected acceleration of the leader trajectory generator module, the position, speed and acceleration of the follower of the multi-robotic arm system module, and the state variables of the self-constructed neural network disturbance observer module at a specified time. According to the characteristics of the expected position, expected speed and expected acceleration of the leader trajectory generator module, the position, speed and acceleration of the follower of the multi-robotic arm system module, and the state variable data of the self-constructed neural network disturbance observer module at a specified time, the internal structure is automatically adjusted and optimized, the neural network neurons with poor effects are automatically removed, and the neural network neurons with better effects are split.

[0162] The adaptive rate module is used to obtain the state variables of the self-constructed neural network module, and the adaptive rate is obtained by differential solution.

[0163] The input end of the error conversion module is connected to the output end of the leader trajectory generator module, the input end of the error conversion module is connected to the output end of the multi-manipulator system, the input end of the error conversion module is connected to the output end of the performance constraint module, the input end of the specified time controller module is connected to the output end of the self-constructed neural network module, the input end of the specified time controller module is connected to the output end of the specified time self-constructed neural network disturbance observer module, the input end of the auxiliary system module is connected to the output end of the specified time controller module, the input end of the event trigger mechanism module is connected to the output end of the auxiliary system module, the input end of the multi-manipulator system module is connected to the output end of the event trigger mechanism module, and the specified time self-constructed neural network The input end of the network disturbance observer module is connected to the output end of the multi-robotic arm system module, the input end of the specified time self-constructed neural network disturbance observer module is connected to the output end of the auxiliary system module, the input end of the specified time self-constructed neural network disturbance observer module is connected to the output end of the self-constructed neural network module, the input end of the specified time self-constructed neural network disturbance observer module is connected to the output end of the adaptive rate module, the input end of the self-constructed neural network module is connected to the output end of the leader trajectory generator module, the input end of the self-constructed neural network module is connected to the output end of the multi-robotic arm system, the input end of the self-constructed neural network module is connected to the output end of the specified time self-constructed neural network disturbance observer module, and the input end of the adaptive rate module is connected to the output end of the self-constructed neural network module.

[0164] In order to verify the effectiveness of the method of the present invention, a simulation experiment was carried out using the following model, as follows.

[0165] Through the selected model parameters, simulation experiments were carried out on five dual-joint manipulator systems to verify the effectiveness of the designed multi-manipulator specified time event triggered sliding mode control method based on disturbance observer. The multi-manipulator system parameters are shown in Table 1, the controller parameters are shown in Table 2, and the other parameters are shown in Table 3.

[0166] Table 1

[0167] Parameter name Parameter Value Parameter name Parameter Value Parameter name Parameter Value <![CDATA[J 1,1 ]]> 0.21 <![CDATA[m 4,1 ]]> 0.98 <![CDATA[l 3,2 ]]> 0.88 <![CDATA[J 2,1 ]]> 0.28 <![CDATA[m 1,2 ]]> 1.06 <![CDATA[l 4,2 ]]> 0.97 <![CDATA[J 3,1 ]]> 0.19 <![CDATA[m 2,2 ]]> 1.66 <![CDATA[τ d1,1 ]]> 2+1.6sin(0.5t) <![CDATA[J 4,1 ]]> 0.41 <![CDATA[m 3,2 ]]> 1.86 <![CDATA[τ d2,1 ]]> 1-0.5sin(0.3t) <![CDATA[J 1,2 ]]> 0.42 <![CDATA[m 4,2 ]]> 2.16 <![CDATA[τ d3,1 ]]> 2-0.6sin(0.5t) <![CDATA[J 2,2 ]]> 0.4 <![CDATA[l 1,1 ]]> 1.54 <![CDATA[τ d4,1 ]]> 2+0.5sin(0.3t) <![CDATA[J 3,2 ]]> 0.33 <![CDATA[l 2,1 ]]> 1.34 <![CDATA[τ d1,2 ]]> 1.5-0.5cos(0.4t) <![CDATA[J 4,2 ]]> 0.21 <![CDATA[l 3,1 ]]> 1.39 <![CDATA[τ d2,2 ]]> 1.8+0.3cos(0.2t) <![CDATA[m 1,1 ]]> 0.86 <![CDATA[l 4,1 ]]> 1.59 <![CDATA[τ d3,2 ]]> 0.9-0.8cos(0.6t) <![CDATA[m 2,1 ]]> 0.91 <![CDATA[l 1,2 ]]> 0.94 <![CDATA[τ d4,2 ]]> 1.2+0.6cos(0.7t) <![CDATA[m 3,1 ]]> 1.34 <![CDATA[l 2,2 ]]> 0.78 g 9.81

[0168] In Table 1, J 1,1 represents the moment of inertia of the first joint of the first robot arm, J 2,1 represents the moment of inertia of the first joint of the second robot arm, J 3,1 represents the moment of inertia of the first joint of the third robot arm, J 4,1 represents the moment of inertia of the first joint of the fourth robot arm, J 1,2 represents the moment of inertia of the second joint of the first robotic arm, J 2,2represents the moment of inertia of the second joint of the second robot arm, J 3,2 represents the moment of inertia of the second joint of the third robotic arm, J 4,2 represents the moment of inertia of the second joint of the fourth robotic arm, m 1,1 Indicates the weight of the connecting rod of the first joint of the first robot arm, m 2,1 Indicates the weight of the connecting rod of the first joint of the second robot arm, m 3,1 Indicates the weight of the connecting rod of the first joint of the third robot arm, m 4,1 Indicates the weight of the connecting rod of the first joint of the fourth robot arm, m 1,2 Indicates the weight of the connecting rod of the second joint of the first robot arm, m 2,2 Indicates the weight of the connecting rod of the second joint of the second robot arm, m 3,2 Indicates the weight of the connecting rod of the second joint of the third robot arm, m 4,2 represents the weight of the connecting rod of the second joint of the fourth robot arm, l 1,1 Indicates the weight of the connecting rod of the first joint of the first robot arm, l 2,1 represents the weight of the connecting rod of the first joint of the second robot arm, l 3,1 represents the weight of the connecting rod of the first joint of the third robot arm, l 4,1 represents the weight of the connecting rod of the first joint of the fourth robot arm, l 1,2 Indicates the weight of the connecting rod of the second joint of the first robot arm, l 2,2 represents the weight of the connecting rod of the second joint of the second robot arm, l 3,2 represents the weight of the connecting rod of the second joint of the third robot arm, l 4,2 represents the weight of the connecting rod of the second joint of the fourth robot arm, τ d1,1 represents the disturbance variable of the first joint of the first robot arm, τ d2,1 represents the disturbance variable of the first joint of the second robot arm, τ d3,1 represents the disturbance variable of the first joint of the third robot arm, τ d4,1 represents the disturbance variable of the first joint of the fourth robot arm, τ d1,2 represents the disturbance variable of the second joint of the first robot arm, τ d2,2 represents the disturbance variable of the second joint of the second robot arm, τ d3,2 represents the disturbance variable of the second joint of the third robot arm, τ d4,2 represents the disturbance variable of the second joint of the fourth robotic arm, and g represents the gravity.

[0169] Table 2

[0170] Parameter name Parameter Value Parameter name Parameter Value Parameter name Parameter Value T 1.5 <![CDATA[κ 1i,λ ]]> 1.2 <![CDATA[κ 12i,λ ]]> 0.75 <![CDATA[t0]]> 0 <![CDATA[κ 2i,λ ]]> 1.5 ω 1 <![CDATA[κ 11i,λ ]]> 1.35

[0171] In Table 2, T represents the time of the control process, t0 represents the initial time, ω represents the adjustable parameter set by the time variation function, and κ 1i,λ represents the first positive real constant of the λth joint of the ith robot, κ 2i,λ represents the second positive real constant of the λth joint of the ith robot arm, κ 11i,λ represents the eleventh positive real constant of the λth joint of the ith robot arm, κ 12i,λ represents the twelfth positive real constant of the λth joint of the ith robot arm.

[0172] Table 3

[0173]

[0174]

[0175] In Table 3, κ 3i,λ represents the third positive real constant of the λth joint of the ith robot, κ 4i,λ represents the fourth positive real constant of the λth joint of the i-th robot arm, Γ ai,λ ,Ξ i,λ and represents an adjustable parameter, κ 5i,λ represents the fifth positive real constant of the λth joint of the ith robot, κ 6i,λ represents the sixth positive real constant of the λth joint of the ith robot, κ 7i,λ represents the seventh positive real constant of the λth joint of the i-th robot arm, κ 8i,λ represents the eighth positive real constant of the λth joint of the ith robot arm, Γ bi,λ represents an adjustable parameter, κ 9i,λ represents the ninth positive real constant of the λth joint of the ith robot, κ 10i,λ represents the tenth positive real constant of the λth joint of the i-th robot arm, κ 13i,λ represents the thirteenth positive real constant of the λth joint of the ith robot arm, κ 14i,λ represents the fourteenth positive real constant of the λth joint of the ith robot arm, c ai,λ represents the center range of the Gaussian basis function of the first self-constructed neural network, b ai,λ represents the width of the Gaussian basis function of the first self-constructed neural network, Ψ a,s Denotes the segmentation threshold of the first self-constructed neural network, Ψ a,d Denotes the deletion threshold of the first self-constructed neural network, h a,e Represented as the boundary value of the first self-constructed neural network, c bi,λ represents the center range of the Gaussian basis function of the second self-constructed neural network, b bi,λ It is represented as the width of the Gaussian basis function of the second self-constructed neural network, Ψ b,sDenotes the segmentation threshold of the second self-constructed neural network, Ψ b,d Denotes the deletion threshold of the second self-constructed neural network, h b,e Represented as the boundary value of the second self-constructed neural network, u i,1max Indicates the maximum value allowed by the control signal of all robot joints 1, u i,1min Indicates the minimum value allowed by the control signal of all robot joints 1, u i,2max Indicates the maximum value allowed by the control signal of all robot joints 2, u i,2min Indicates the minimum value allowed by the control signal of all robot joints 2, Φ a0 represents the initial value of the performance function, Φ a∞ Represents the final value of the performance function.

[0176] The initial value of the multi-manipulator system in this simulation experiment is [x d1,1 ,x d1,2 ,x d2,1 ,x d2,2 ,x d3,1 ,x d3,2 ,x d4,1 ,x d4,2 ] T =[1,1.7,0.5,2,-0.5,0.5,-1,1] T and [v d1,1 ,v d1,2 ,v d2,1 ,v d2,2 ,v d3,1 ,v d3,2 ,v d4,1 ,v d4,2 ] T =[0.2,1,-0.2,-1,0.8,7,1,8] T The desired trajectory of the multi-manipulator system is set to s d1,1 = sin(0.5t), s d1,2 =2cos(0.5t),s d2,1 =0.5cos(0.5t),s d2,2 = -sin(0.5t), s d3,1 =-0.25sin(0.5t) and s d3,2 =-0.5cos(0.5t). Where x d1,1 represents the initial position of the first joint of the first robot arm, x d1,2 represents the initial position of the second joint of the first robot arm, x d2,1 represents the initial position of the first joint of the second robot arm, x d2,2 represents the initial position of the second joint of the second robot arm, xd3,1 represents the initial position of the first joint of the third robot arm, x d3,2 represents the initial position of the second joint of the third robot arm, x d4,1 represents the initial position of the first joint of the fourth robot arm, x d4,2 represents the initial position of the second joint of the fourth robot arm, v d1,1 Indicates the initial velocity of the first joint of the first robot arm, v d1,2 Indicates the initial velocity of the second joint of the first robot arm, v d2,1 represents the initial velocity of the first joint of the second robot arm, v d2,2 represents the initial velocity of the second joint of the second robot arm, v d3,1 represents the initial velocity of the first joint of the third robot arm, v d3,2 represents the initial velocity of the second joint of the third robot arm, v d4,1 represents the initial velocity of the first joint of the fourth robot arm, v d4,2 Indicates the initial velocity of the second joint of the fourth robot arm. s d1,1 represents the expected position of the first joint of all robotic arms, s d1,2 represents the expected position of the second joint of all robotic arms, s d2,1 represents the expected speed of the first joint of all robotic arms, s d2,2 represents the expected speed of the second joint of all robotic arms, s d3,1 represents the expected acceleration of the first joint of all robotic arms, s d3,2 represents the expected acceleration of the second joint of all robot arms.

[0177] Figure 3 Represents the topological communication relationship of the multi-manipulator system. The simulation results are as follows Figure 4 shown. Figure 5 The position tracking errors of joints 1 and 2 of all the manipulators are shown. It can be clearly observed from the figure that the performance constraint curve effectively defines the fluctuation range of the error, ensuring that the error remains within a controllable level. In particular, at the preset time t = 1.5s, the positions of the four follower manipulators can accurately match the expected trajectory of the leader manipulator, fully verifying the high precision and fast response capabilities of the system. Figure 6-7The variation of the velocity tracking error of joint 1 and joint 2 in the multi-manipulator system over time is presented. Before t = 1.5s, the error curve shows a certain degree of overshoot, which reflects the system's initial rapid response and adjustment process to the target speed. However, it is worth noting that at t = 1.5s, these errors converged and stabilized quickly. In the subsequent control process, the error continued to remain in the range close to zero, and there was no obvious fluctuation or jitter, which reflects the good stability and precise control performance of the system. Figure 8 The error changes of joints 1 and 2 of all manipulators during the disturbance observation process are clearly shown. From the figure, we can see that before t = 1.5s, the error value experienced a gradual attenuation stage from high to low, which reflects the system's initial perception and response process to external disturbances. When it reaches the preset time point t = 1.5s, the error has a short peak. However, after that, the error quickly and effectively converges to near zero, fully demonstrating the excellent fitting ability and control accuracy of the proposed self-constructed neural network observer in accurately capturing and compensating for disturbances. Fig. 9 The distribution of event triggering times for all robot joints 1 and 2 is shown in the form of a scatter plot. By adopting the proposed periodic monitoring event triggering algorithm, the figure clearly shows that the algorithm can significantly reduce the number of communications with the actuators, thereby effectively reducing the consumption of communication resources. This result not only reflects the advantage of the algorithm in optimizing the communication efficiency of the system, but also proves its practical application value in the coordinated control of multiple robot arms. Fig.10 It shows the number of times the event is triggered for joint 1 and joint 2 of all robot arms. Figure 11-12 The figure shows the change in the number of neurons of the self-constructed neural network, where the number of neurons in joint 1 of the first, second, third and fourth robotic arms decreases from 41 to 2, 4, 6 and 3 respectively, and the number of neurons in joint 2 of the first, second, third and fourth robotic arms decreases from 41 to 2, 3, 4 and 5 respectively. Figure 13-14 The saturated control signals of joints 1 and 2 of all manipulators after being processed by the event trigger mechanism are shown in the figure. It is not difficult to see from the figure that before t = 1.5s, the amplitude of the control signal was limited to a certain range due to the constraint of the saturation function. The introduction of the auxiliary system significantly improved the performance of the control system. At t = 1.5s, the control signal reached its peak state, and then quickly and steadily approached the zero value area. In the subsequent control process, the control signal was segmented and remained consistent. This change shows that the system has achieved good stability and controllability at this stage.

[0178] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A sliding mode control method for triggering a multi-manipulator specified time event, characterized in that: The following steps are involved: S1. Establish kinematic and dynamic models for the leader and follower of the multi-manipulator, and determine the specified time control criteria; S2, determining the consistency error of the robot arm according to the specified time control criterion, the kinematic model and the dynamic model of the leader, and the kinematic model and the dynamic model of the follower; S3, determining an error conversion function according to the consistency error and performance function of the robot arm; S4, determining a non-singular terminal sliding surface according to the error transfer function; S5. constructing a first self-constructed neural network according to the non-singular terminal sliding surface, and determining a self-constructed neural network observer at a specified time; S6. According to the specified time, the neural network observer is self-constructed, a second self-constructed neural network is constructed, and the specified time controller is determined to complete the consistency tracking of multiple robotic arms.

2. The sliding mode control method triggered by a specified time event of a multi-manipulator according to claim 1, characterized in that: In S1, the expression of the kinematic model of the follower is: Where M i,11 represents the first symmetric positive definite inertia matrix of the i-th dual-joint manipulator, M i,12 represents the second symmetric positive definite inertia matrix of the i-th dual-joint manipulator, M i,21 represents the third symmetric positive definite inertia matrix of the i-th dual-joint manipulator, M i,22 represents the fourth symmetric positive definite inertia matrix of the i-th dual-joint manipulator, represents the first speed of the i-th dual-joint robot, represents the second speed of the i-th dual-joint robot arm, represents the first acceleration of the i-th dual-joint robotic arm, represents the second acceleration of the i-th dual-joint robotic arm, C i,11 represents the first Coriolis force of the i-th dual-joint robot, C i,12 represents the first centrifugal force of the i-th dual-joint robot, C i,21 represents the second Coriolis force of the i-th dual-joint robot arm, C i,22 represents the second centrifugal force of the i-th dual-joint robotic arm, G i,1 represents the first gravity of the i-th dual-joint robotic arm, G i,2 represents the second gravity of the i-th dual-joint robotic arm, w i,1 represents the first control signal of the i-th dual-joint robot after event triggering processing, w i,2 represents the second control signal of the i-th dual-joint robot after event triggering processing, τ di,1 represents the external disturbance of the i-th dual-joint robot, τ di,2 represents the second external disturbance suffered by the i-th dual-joint robot; In S1, the expression of the follower's dynamic model is: In the formula, x i,λ represents the position of the λth joint of the i-th robot, v i,λ represents the velocity of the λth joint of the ith robot arm, represents the first-order derivative of the velocity of the λth joint of the i-th robot, represents the first-order derivative of the position of the λth joint of the i-th robot, f i,λ (x i,λ ) represents the set of model uncertainties of the λth joint of the i-th robot, w i,λ represents the control signal of the λth joint of the i-th robot after event triggering processing, τ di,λ represents the external time-varying disturbance of the λth joint of the i-th robot arm, M i,λ represents the moment of inertia of the motor and connecting rod of the λth joint of the i-th robot; In S1, the expression of the leader's kinematic model is: In the formula, represents the first-order derivative of the position of the leader manipulator, v 0,λ represents the velocity of the λth joint of the leader robot; In S1, the leader's dynamic model is expressed as: In the formula, represents the first-order derivative of the velocity of the leader robot arm, u 0,λ represents the control signal of the λth joint of the leader robot arm; In S1, the expression of the time control criterion is specified as: Where V i,λ (t) represents a continuously differentiable function, μ(t) represents a time-varying function, is the first-order derivative of the time-varying function, t represents the time of the control process, κ1 represents the first positive real constant, κ2 represents the second positive real constant, and T represents the specified time.

3. The sliding mode control method triggered by a specified time event of a multi-manipulator according to claim 1, characterized in that: In S2, the consistency error includes the position consistency error of the λth joint of the ith robotic arm, the velocity consistency error of the λth joint of the ith robotic arm, and the acceleration consistency error of the λth joint of the ith robotic arm; The position consistency error e of the λth joint of the i-th robot arm xi,λ The expression is: In the formula, N represents the number of robotic arms, a ij represents the communication link between the i-th follower robot and the j-th follower robot, b i represents the communication link between the leader robot and the i-th follower robot, x i,λ represents the position of the λth joint of the ith robot arm, x j,λ represents the position of the λth joint of the jth follower robot, x 0,λ represents the position of the leader's robotic arm; The velocity consistency error e of the λth joint of the i-th robot arm vi,λ The expression is: In the formula, v i,λ represents the velocity of the λth joint of the ith robot arm, v j,λ represents the velocity of the λth joint of the jth robot, v 0,λ represents the speed of the leader's robotic arm; The acceleration consistency error e of the λth joint of the i-th manipulator ai,λ The expression is: In the formula, a i,λ represents the acceleration of the λth joint of the i-th robot, a j,λ represents the acceleration of the λth joint of the jth robot, a 0,λ Represents the acceleration of the leader's robot arm.

4. The sliding mode control method triggered by a specified time event of a multi-manipulator according to claim 1, characterized in that: In S3, the error conversion function δ i,λ The expression is: In the formula, e xi,λ represents the position consistency error, Φ a Represents a performance function.

5. The sliding mode control method for triggering a multi-manipulator specified time event according to claim 1, characterized in that: In S4, the non-singular terminal sliding surface s i,λ The expression is: In the formula, δ i,λ represents the error transfer function, represents the first-order derivative of the error transfer function, κ 1i,λ represents the first positive real constant of the λth joint of the ith robot arm, κ 2i,λ represents the second positive real constant of the λth joint of the i-th robot, μ(t) represents the time variation function, Represents the first derivative of a time-varying function.

6. The sliding mode control method triggered by a specified time event of a multi-manipulator according to claim 1, characterized in that: In S5, the self-constructed neural network f i,λ (σ i,λ ) is: f i,λ (s i,λ )=W i,λ h i,λ (s i,λ )+e i,λ ; In the formula, σ i,λ represents the input of the self-constructed neural network, ε i,λ represents the estimation error of the self-constructed neural network, W i,λ represents the optimal weight, h i,λ (σ i,λ ) represents Gaussian basis function; In S5, a neural network disturbance observer is constructed at a predetermined time. The expression is: In the formula, represents the estimated value of the neural network approximation error, represents the estimated value of uncertainty, M i,λ represents the moment of inertia of the motor and connecting rod of the λth joint of the i-th robot arm, u ai,λ represents the control signal after input saturation, κ 7i,λ represents the seventh positive real constant of the λth joint of the i-th robot arm, κ 8i,λ represents the eighth positive real constant of the λth joint of the i-th robot, μ(t) represents the time variation function, represents the first-order derivative of the time-varying function, ψ i,λ represents the state variable, Indicates an adjustable parameter.

7. The sliding mode control method triggered by a specified time event of a multi-manipulator according to claim 1, characterized in that: The S6 comprises the following sub-steps: S61, constructing a second self-constructed neural network according to the specified time self-constructed neural network observer, and determining the specified time controller; S62, determining the auxiliary system and event triggering mechanism; S63. Using the specified time controller, auxiliary system and event trigger mechanism, the consistency error is converged to the zero domain within the specified time, and the consistency tracking of the multi-manipulator is completed.

8. The sliding mode control method triggered by a specified time event of a multi-manipulator according to claim 7, characterized in that: In S61, the time controller u is specified i,λ The expression is: Where M i,λ represents the moment of inertia of the motor and connecting rod of the λth joint of the i-th robot arm, represents the conversion error function, represents the derivative of the conversion error function, N represents the number of robotic arms, a ij represents the communication link between the i-th follower robot and the j-th follower robot, b i represents the communication link between the leader robot and the i-th follower robot, Φ a represents the performance function, represents the first derivative of the performance function, represents the second-order derivative of the performance function, represents the first-order derivative of the velocity of the λth joint of the i-th robot, represents the first-order derivative of the velocity of the leader robot, e xi,λ represents the position consistency error, represents the first-order derivative of the position consistency error, κ 1i,λ represents the first positive real constant of the λth joint of the ith robot arm, κ 2i,λ represents the second positive real constant of the λth joint of the ith robot arm, κ 11i,λ represents the eleventh positive real constant of the λth joint of the ith robot arm, κ 12i,λ represents the twelfth positive real constant of the λth joint of the i-th robot, μ(t) represents the time variation function, Represents the first derivative of the time-varying function, s i,λ represents the non-singular terminal sliding surface, represents the estimated value of the first optimal weight, h ai,λ represents the first Gaussian basis function, ξ i,λ represents the first approximation error, represents the estimated value of the external disturbance of the λth joint of the i-th robot.

9. The sliding mode control method triggered by a specified time event of a multi-manipulator according to claim 7, characterized in that: In S62, the auxiliary system update rate expression is: Where M i,λ represents the moment of inertia of the motor and connecting rod of the λth joint of the i-th robot arm, represents the conversion error, represents the derivative of the conversion error, N represents the number of robotic arms, a ij represents the communication link between the i-th follower robot and the j-th follower robot, b i represents the communication link between the leader robot and the i-th follower robot, Δu i,λ represents the control input difference after input saturation, ξ i,λ represents the first approximation error, θ α represents the auxiliary system, κ 13i,λ represents the thirteenth positive real constant of the λth joint of the ith robot arm, κ 14i,λ represents the fourteenth positive real constant of the λth joint of the ith robot arm; In S62, the event trigger mechanism w i,λ The expression of (t) is: In the formula, μ c represents the first positive design parameter, represents the second positive design parameter, m a represents the third positive design parameter, represents the fourth positive design parameter, t represents the time of the control process, u ai,λ represents the control signal after input saturation, represents the transpose of the non-singular terminal sliding surface, Γ represents a natural number, θ represents the monitoring period, and w i,λ (t k-1 ) represents the control signal at the next triggering time after the event is triggered, w i,λ (t k ) represents the control signal at the current triggering time after the event is triggered, t k Indicates the current triggering time, t k-1 Indicates the next triggering time, t k+1 Indicates the last triggering time, E i,λ (t) represents the trigger condition defined by the measurement error.

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