A method and system for controlling multi-arm pre-set time super-helical sliding mode

Abstract

This invention belongs to the field of robot control technology and provides a multi-arm preset-time superspiral sliding mode control method and system. The method includes establishing a dynamic model of the multiple robotic arms, determining the network communication topology between the robotic arms during the inclusion control process, and defining the inclusion error of the multi-arm system. Based on sliding mode variable structure theory and preset-time control theory, a nonlinear sliding surface function is designed, and a preset-time superspiral sliding mode control law is constructed. A dynamic event triggering mechanism is established, and a preset-time superspiral sliding mode control law based on dynamic event triggering is constructed. Each robotic arm is controlled according to the obtained control law. This disclosure not only ensures that the joint positions of all follower robotic arms can enter the convex hull formed by multiple leader robotic arms within a preset expected time, but also significantly reduces controller chattering and effectively reduces actuator mechanical wear.

Description

Technical Field

[0001] This disclosure relates to the field of robot control technology, specifically to a multi-arm preset-time super-helical sliding mode control method and system. Background Technology

[0002] The statements in this section are merely background information relating to this disclosure and do not necessarily constitute prior art.

[0003] In the new era of intelligent industrial manufacturing, robotic arm systems have become an indispensable part. However, in practical applications, robotic arm cluster control faces many challenges, one of which is the system's susceptibility to external disturbances. These external disturbances may stem from uncertainties in environmental factors, such as load changes and power fluctuations, or from motion interference from other mechanical equipment. These factors can negatively impact the accuracy, stability, and overall performance of the robotic arm system control. Furthermore, with the continuous improvement of industrial automation, the requirements for the real-time performance and response speed of robotic arm cluster control are becoming increasingly stringent. Especially in collaborative operations or complex tasks, multiple robotic arms are required to work together efficiently to complete tasks and avoid collisions or conflicts. In such cases, the control system needs to make rapid and accurate responses within a very short time to adapt to rapidly changing working environments and task requirements. Therefore, research on how to improve the robustness of robotic arm cluster control in disturbed environments and under increasingly stringent requirements for settling-time performance has become crucial. This research aims to provide reliable control algorithms to ensure the stable operation of robotic arms in complex and dynamic environments and to make rapid responses in a short time, thereby better meeting the needs of industrial production and automation applications.

[0004] Currently, many robotic arm control algorithms only achieve asymptotic stability of the control system, which means that the convergence time tends to be infinite, making it difficult to meet high real-time requirements. Even if some algorithms use finite-time or fixed-time control, the convergence time cannot be simply and arbitrarily set due to the complexity of parameter design. Summary of the Invention

[0005] To address the aforementioned shortcomings, this disclosure proposes a multi-manipulator preset-time super-helical sliding mode control method and system. The proposed preset-time super-helical sliding mode control scheme drives each manipulator, which can reduce the impact of internal nonlinearity and external disturbances on the manipulator cluster. It not only ensures that the joint positions of all follower manipulators can enter the convex hull formed by multiple leader manipulators within a preset expected time, but also significantly reduces controller chattering and effectively reduces actuator mechanical wear.

[0006] To achieve the above objectives, the present disclosure adopts the following technical solution:

[0007] The first aspect of this disclosure provides a method for controlling a multi-manipulator with a preset time super-helical sliding mode, comprising the following steps:

[0008] Establish a dynamic model of the multi-manipulator system, determine the network communication topology between each manipulator in the inclusion control process of the multi-manipulator cluster, and define the inclusion error of the multi-manipulator system.

[0009] Based on sliding mode variable structure theory and preset time control theory, a nonlinear sliding mode surface function is designed, and a preset time super-helical sliding mode control law for multiple robotic arms is constructed.

[0010] Establish a dynamic event triggering mechanism and construct a multi-robot arm preset time super spiral sliding mode control law based on dynamic event triggering;

[0011] Each robotic arm is controlled according to the preset time super-spiral sliding mode control law.

[0012] As a further implementation method, a dynamic model of the multi-robotic arm system is established, specifically as follows:

[0013] A dynamic model of a multi-manipulator system is established by utilizing the generalized coordinate position state of the robotic arm, the symmetric positive definite inertia matrix, the Coriolis force, the centrifugal torque, the gravitational torque, the control input, and the external disturbances it suffers, based on the Euler-Lagrange equations.

[0014] As a further implementation method, the network communication topology between the robotic arms in the multi-robotic arm cluster, including the control process, is determined as follows:

[0015] An undirected graph is used to describe a robotic arm cluster, including the communication connections between the individual robotic arms during the control process.

[0016] When the i-th robotic arm receives the position and velocity information of the j-th robotic arm, it determines the Laplacian matrix element l associated with the adjacency matrix of the undirected graph. ij ;

[0017] Assuming the leader in the robotic arm cluster has no neighboring nodes, update the Laplace matrix associated with the adjacency matrix of the undirected graph.

[0018] As a further implementation, the inclusion error of the multi-robotic arm system is defined as follows:

[0019]

[0020] Where, q i and q j ρ represents the generalized coordinate vectors of the i-th and j-th robotic arms, respectively. ijrepresents the communication weight between the $i$-th and $j$-th robotic arms, $n$ represents $n$ follower robotic arms, $m$ represents $m$ leader robotic arms, and $t$ represents time.

[0021] As a further implementation method, based on the sliding mode variable structure theory and the preset time control theory, a nonlinear sliding mode surface function is designed, specifically as follows:

[0022] Based on the preset time control theory, a time-varying function is set. Based on the time-varying function, the sliding mode variable structure theory, and the included error, a nonlinear sliding mode surface function is designed, where the time-varying function is as follows:

[0023]

[0024]

[0025] where $T_1$ is the preset time required to reach the sliding mode surface, $T_2$ is the preset time for the system state to slide and converge on the sliding mode surface, $t_0$ is the initial time, $h_1$ and $h_2$ are any positive numbers greater than 2, and satisfy:

[0026]

[0027]

[0028] where is the derivative of $\zeta_1(t)$ with respect to time, is the derivative of $\zeta_2(t)$ with respect to time.

[0029] As a further implementation method, based on the time-varying function, the sliding mode variable structure theory, and the included error, the nonlinear sliding mode surface function is set as follows:

[0030]

[0031] where $\psi_2(t)$ is a time-varying function, is the derivative of $J$ i (t), the constant $\eta_2 > 0$. When $t < t_0 + T_1 + T_2$, the function $\psi_2(t)$ is in a极小邻域 of zero. When $t \geq t_0 + T_1 + T_2$, $\psi_2(t)$ can be set to any value greater than zero, and is constructed as follows:

[0032]

[0033] where when $t \geq t_0 + T_1 + T_2$, set to determine the value of $\psi_2(t)$.

[0034] As a further implementation method, a multi-robotic arm preset time super-twisting sliding mode control law is constructed, specifically as follows:

[0035]

[0036] where, ψ1(t) is a time-varying function, η1 and η2 are attenuation coefficients, and the constant β 1i >0, β2i satisfies Sgn(a) = [sign(a1), …, sign(a n )] T , sig γ (a) = [|a1| γ sign(a1), …, |a n | γ sign(a n )] T , sign(·) is the sign function, and the constant γ > 0;

[0037] When t < t0 + T1, the function ψ1(t) is in a极小neighborhood of zero. When t ≥ t0 + T1, ψ1(t) can be set to any value greater than zero and is constructed as follows:

[0038]

[0039] where, when t ≥ t0 + T1, set to determine the value of ψ1(t).

[0040] The second aspect of the present disclosure provides a multi-manipulator preset-time super-twisting sliding mode control system, including:

[0041] A model construction module, configured to: establish a dynamic model of the multi-manipulator system, determine the network communication topology among the manipulators during the inclusion control process of the multi-manipulator cluster, and define the inclusion error of the multi-manipulator system;

[0042] An instruction generation module, configured to: design a non-linear sliding mode surface function and construct a multi-manipulator preset-time super-twisting sliding mode control law based on the sliding mode variable structure theory and the preset-time control theory;

[0043] An instruction trigger module, configured to: establish a dynamic event trigger mechanism and construct a multi-manipulator preset-time super-twisting sliding mode control law based on the dynamic event trigger;

[0044] An execution module, configured to: control each manipulator according to the obtained preset-time super-twisting sliding mode control law.

[0045] The third aspect of the present disclosure provides a medium on which a program is stored, and when the program is executed by a processor, it implements the steps in the multi-manipulator preset-time super-twisting sliding mode control method described in the first aspect of the present disclosure.

[0046] It should be noted that the Chinese character "极小" in the original text seems to be an incorrect or incomplete expression. I translated it as "极小" as it is, but it might need to be verified and corrected in the original context. Also, there are some consecutive tags without content which might be an error in the original input. If possible, it would be beneficial to check and clarify those aspects.The fourth aspect of this disclosure provides an electronic device, including a memory, a processor, and a program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the multi-manipulator preset-time super-helical sliding mode control method described in the first aspect of this disclosure.

[0047] Compared with the prior art, the beneficial effects of this disclosure are as follows:

[0048] This disclosure presents a multi-arm preset-time superspiral sliding mode control method and system. Within a distributed preset-time superspiral sliding mode control framework based on dynamic event triggering, it controls the motors of each joint on each robotic arm to ensure that the joint positions of all follower robotic arms enter the convex hull formed by the leader robotic arm within a preset time. This reduces the impact of internal nonlinearity and external disturbances on the robotic arm cluster, ensuring stable operation of the multi-arm system. Based on preset-time theory, this disclosure constructs a nonlinear sliding surface with a time-varying function, guaranteeing that the robotic arm cluster's error converges to zero within the preset time. The controller is designed based on the superspiral sliding mode algorithm, effectively reducing controller chattering and facilitating practical engineering applications. Establishing a dynamic event triggering mechanism between the controller and actuators, and updating the controller based on trigger conditions, reduces wear on the robotic arm actuators.

[0049] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0050] The accompanying drawings, which form part of this disclosure, are used to provide a further understanding of this disclosure. The illustrative embodiments of this disclosure and their descriptions are used to explain this disclosure and do not constitute an undue limitation of this disclosure.

[0051] Figure 1 This is a schematic diagram of the structure of the robotic arm disclosed herein;

[0052] Figure 2 This is a schematic diagram of the generalized coordinate trajectory of the first joint of the robotic arm cluster disclosed herein;

[0053] Figure 3 This is a schematic diagram of the generalized coordinate trajectory of the second joint of the robotic arm cluster disclosed herein;

[0054] Figure 4 This is a schematic diagram of the controller variation curve of the first joint of the robotic arm cluster disclosed herein;

[0055] Figure 5 This is a schematic diagram of the controller variation curve of the second joint of the robotic arm cluster disclosed herein;

[0056] Figure 6This is a diagram showing the comparison of event trigger counts for the publicly disclosed follower robotic arm system. Detailed Implementation

[0057] The present disclosure will be further described below with reference to the accompanying drawings and embodiments.

[0058] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure pertains.

[0059] Where there is no conflict, the embodiments and features described herein can be combined with each other.

[0060] Example 1

[0061] like Figure 1-6 As shown, Embodiment 1 of this disclosure provides a multi-robotic arm preset-time super-spiral sliding mode control method, including the following steps:

[0062] S1 establishes a dynamic model of the multi-manipulator system, determines the network communication topology between each manipulator in the inclusion control process of the multi-manipulator cluster, and defines the inclusion error of the multi-manipulator system.

[0063] Based on sliding mode variable structure theory and preset time control theory, S2 designs a nonlinear sliding surface function and constructs a preset time super-helical sliding mode control law for multiple robotic arms.

[0064] S3 establishes a dynamic event triggering mechanism and constructs a multi-robot arm preset time super spiral sliding mode control law based on dynamic event triggering;

[0065] S4 controls each robotic arm according to the preset time super-spiral sliding mode control law.

[0066] Specifically, the dynamic model of the multi-manipulator system established in step S1 is as follows:

[0067] The dynamic model is used to describe the relationship between joint torques and the positions, velocities, and accelerations of each joint in a robotic arm system. Utilizing the generalized coordinate position state of the robotic arm, the symmetric positive definite inertia matrix, Coriolis force, centrifugal torque, gravitational torque, control inputs, and external disturbances, a dynamic model of the multi-robotic arm system is established based on the Euler-Lagrange equations. Its description is as follows:

[0068]

[0069] Where, q i Represents the generalized coordinate vector of the robotic arm. This represents the generalized velocity vector of the robotic arm. M represents the generalized acceleration vector of the robotic arm.i (q i ) represents a symmetric positive definite inertia matrix. G represents the Coriolis force and centrifugal torque. i (q i ) represents gravitational torque, u i and d i Let these represent the control input and the external disturbance, respectively, where the external disturbance is bounded and satisfies the following condition: It is a known constant, and d i (t0) = 0, where t0 is the initial time.

[0070] The network communication topology between the individual robotic arms in the robotic arm cluster, including the control process, is as follows:

[0071] An undirected graph G = {W, E, A} is used to describe the communication connections between individual robotic arms in a robotic arm cluster, including the control process. Where W = {w1, w2, ..., w...} n ,w n+1 ,…,w n+m} represents the set of nodes in graph G. Let A represent the set of edges in graph G, where A = [ρ ij ]∈R (n+m)×(n+m) Let G be the adjacency matrix of an undirected graph.

[0072] If the i-th robotic arm can receive the position, speed, and other status information of the j-th robotic arm, then ρ ij =1 (i≠j), otherwise, ρ ij =0, ρ ij This represents the communication weights between robotic arms i and j, which is the communication state between the robotic arms. The Laplace matrix associated with A is represented as L = [l ij ]∈R (n+m)×(n+m) .in, And l ij =-ρ ij ,j≠i,i,j=1,2,…,n+m.

[0073] Assume the leader has no neighboring nodes. Therefore, the Laplace matrix L associated with A and G can be expressed as: Where L1∈R n×n L2∈R n×m .

[0074] L1∈R n×n The L1 matrix consists of n×n elements, representing the communication topology between n follower robotic arms.

[0075] L2∈R n×mThe L2 matrix consists of n×m elements, representing the communication topology between n follower robotic arms and m leader robotic arms.

[0076] For multi-robotic arm systems, the following error is defined:

[0077]

[0078] Where, q i and q j ρ represents the generalized coordinate vectors of the i-th and j-th robotic arms, respectively. ij Let represent the communication weights between the i-th and j-th robotic arms, n represent the number of n follower robotic arms, m represent the number of m leader robotic arms, and t represent time. If the error converges to zero, the joint positions of all follower robotic arms will fall within the convex hull formed by the multiple leader robotic arms.

[0079] In step S2, based on sliding mode variable structure theory and preset time control theory, a nonlinear sliding surface function is designed, and a preset time super-helical sliding mode control law for multiple robotic arms is constructed. This eliminates the influence of coupling nonlinearity and external disturbances on the stability of the robotic arm system, ensuring that the joint positions of the follower robotic arm can be driven into the convex hull formed by the leader robotic arm within a preset time. Specifically:

[0080] A time-varying function is set based on a preset time control theory. Based on the time-varying function, sliding mode variable structure theory, and error inclusion, a nonlinear sliding surface function is designed. The time-varying function is as follows:

[0081]

[0082]

[0083] Where T1 is the preset time required to reach the sliding surface, T2 is the preset time for the system state to converge on the sliding surface, t0 is the initial time, and h1 and h2 are any positive numbers greater than 2, satisfying the following condition:

[0084]

[0085]

[0086] in, Let ζ1(t) be the derivative with respect to time. Let ζ2(t) be the derivative of ζ2(t) with respect to time.

[0087] Based on time-varying functions, sliding mode variable structure theory, and inclusion error, the nonlinear sliding mode surface function is designed as follows:

[0088]

[0089] Among them, ψ2(t) is a time-varying function. By reasonably adjusting its values before and after the preset time T1+T2, the stability of the system is strengthened. is the derivative of J i (t), the constant η2>0. When t<t0+T1+T2, the function ψ2(t) is in a very small neighborhood of zero. When t≥t0+T1+T2, ψ2(t) can be set to any value greater than zero, and it is constructed as follows:

[0090]

[0091] Among them, when t≥t0+T1+T2, set to determine the value of ψ2(t).

[0092] Construct the preset-time super-twisting sliding mode control law for multiple robotic arms as follows:

[0093]

[0094] Among them, ψ1(t) is a time-varying function. By reasonably adjusting its values before and after the preset time T1, the sliding of the system state on the sliding surface is better guaranteed. η1 and η2 are attenuation coefficients to adjust the attenuation of the system state. The constant β 1i >0, β 2i satisfies Sgn(a) = [sign(a1),…,sign(a n )] T , sig γ (a) = [|a1| γ sign(a1),…,|a n | γ sign(a n )] T , sign(·) is the sign function, and the constant γ>0.

[0095] When t<t0+T1, the function ψ1(t) is in a very small neighborhood of zero. When t≥t0+T1, ψ1(t) can be set to any value greater than zero, and it is constructed as follows:

[0096]

[0097] Among them, when t≥t0+T1, set to determine the value of ψ1(t).

[0098] Step S3 is specifically as follows:

[0099] For the i-th follower robotic arm, a suitable dynamic event triggering mechanism is established based on a time-varying function. A multi-robotic arm preset-time super-spiral sliding mode control law based on dynamic event triggering is constructed. Compared with existing time-triggered control strategies and static event-triggered control strategies, the control method based on dynamic event triggering can further reduce the controller update frequency and reduce actuator losses in the multi-robotic arm system, thus possessing higher practical value. As shown in the following equation:

[0100]

[0101] in, The dynamic event triggering mechanism designed for the triggering time of the i-th robotic arm state is as follows:

[0102]

[0103]

[0104] in, For χ i The derivative of (t) gives χ i The update form of (t) makes χ i (t) converges. i , ι i All are constants greater than zero.

[0105] Under the distributed preset time super spiral sliding mode control framework based on dynamic event triggering, by controlling the motors of each joint on each robotic arm, it is ensured that the joint positions of all follower robotic arms enter the convex hull formed by the leader robotic arm within a preset time, and the mechanical wear of the actuators is effectively reduced.

[0106] The effectiveness of the theoretical design of this disclosure is verified through the following simulation experiments.

[0107] The goal of this simulation experiment is to design a distributed, preset-time superspiral sliding mode control law based on dynamic event triggering, ensuring that the positions of each joint of the follower robotic arm can be driven into the convex hull formed by multiple leader robotic arms within a preset time. The model parameters used in this example are as follows:

[0108]

[0109]

[0110] in, M 3i (q i ) = M 2i (q i ), g 1i(q i )=(m 1i l 1i +m 2i )gsin(q 1i )+m 2i l 2i gsin(q 1i +q 2i ), g 2i (q i ) = m 2i l 2i gsin(q 1i +q 2i ), q i =[q 1i ,q 2i ] T For the i-th follower robotic arm, some specific physical parameters are selected, with specific values ​​of l. 1i =0.25m, l 2i =0.3m, m 1i =m 2i =0.7kg, g = 9.8 m / s 2 The interference is given as d. i (t) = [5sin(0.5t), 5sin(0.5t)] T The leader trajectory selection is q. d1 (t) = [3sin(t), 3cos(t)] T q d2 (t) = [3sin(t) + 1, 3cos(t) + 1] T .

[0111] Set the Laplacian matrix L as follows:

[0112]

[0113] For the i-th follower robotic arm, the parameters in the time-varying function are chosen as h1 = h2 = 10, T1 = 2s, T2 = 0.5s, and the parameter in the controller is β. 1i =12.0, β 2i =3, eta1=0.5, eta2=0.6, The parameters in the dynamic event triggering function are selected as ι respectively. i =0.001, μ i =0.1.

[0114] The initial values ​​for the position, velocity, and acceleration of the robotic arm joints are given as follows:

[0115]

[0116]

[0117]

[0118] The Lyapunov function is selected as follows:

[0119]

[0120] Taking the derivative with respect to time, we get:

[0121]

[0122] Based on the pre-defined time control lemma and Lyapunov's stability theorem, appropriate parameters are selected to satisfy β. 1i >γ, Ensure that the state of the i-th robotic arm can reach the constructed sliding surface within a preset time.

[0123] The stability analysis of the multi-robotic arm system is as follows:

[0124] The closed-loop system error state satisfies the following when sliding on the sliding surface:

[0125]

[0126] The Lyapunov function is selected as follows:

[0127]

[0128] Taking the derivative with respect to time, we get:

[0129]

[0130] That is, the inclusion error J of the closed-loop system i It converges to zero within a preset time.

[0131] Experimental results are as follows Figures 2-6 As shown. Figure 2 and Figure 3 The trajectories of the generalized coordinates of the first and second joints of the multi-arm robotic system are shown respectively. Figure 4 and Figure 5 The control signal changes for the first and second joints are shown in the diagrams. Figure 6The paper compares the update frequency of five follower robotic arm controllers under three triggering mechanisms: Time-Triggered Mechanism (TTM), Static Event-Triggered Mechanism (SETM), and Dynamic Event-Triggered Mechanism (DETM). Therefore, the distributed preset-time super-helical sliding mode control law based on dynamic event triggering proposed in this embodiment can ensure preset-time control of the multi-robotic arm system even under conditions of simultaneous coupling nonlinearity and external disturbances, while also reducing controller chattering and actuator losses.

[0132] This case study presents a distributed preset-time superspiral sliding mode control technique based on dynamic event triggering, applicable to multi-robot collaborative operations in industrial production. Complex disturbances and coupling nonlinearities often exist in multi-robot collaborative operation environments. To achieve preset-time inclusion control for multi-robot systems, a distributed preset-time superspiral sliding mode control strategy based on dynamic event triggering is proposed. Based on the network communication topology and robot state information, the inclusion error dynamic equation of the multi-robot system is established. Introducing the superspiral sliding mode control algorithm into the controller design significantly reduces controller chattering. Based on sliding mode variable structure theory and preset-time control theory, a distributed preset-time superspiral sliding mode control law is designed, effectively solving the preset-time inclusion control problem of robot clusters with coupling nonlinearities and external disturbances. Simultaneously, an event-triggered detection mechanism is established and deployed in the controller-actuator channel, reducing the controller update frequency and effectively reducing actuator mechanical wear in the robot cluster. Finally, the designed distributed preset-time superspiral sliding mode control scheme based on dynamic event triggering is applied to a robot cluster system simulation, verifying the effectiveness of the control scheme.

[0133] Example 2

[0134] Embodiment 2 of this disclosure provides a multi-robotic arm preset-time super-spiral sliding mode control system, including:

[0135] The model building module is configured to: establish a dynamic model of the multi-manipulator system, determine the network communication topology between the manipulators in the multi-manipulator cluster during the inclusion control process, and define the inclusion error of the multi-manipulator system.

[0136] The instruction generation module is configured to: design a nonlinear sliding surface function based on sliding mode variable structure theory and preset time control theory, and construct a preset time super-helical sliding mode control law for multiple robotic arms;

[0137] The instruction triggering module is configured to: establish a dynamic event triggering mechanism and construct a multi-robot arm preset time super spiral sliding mode control law based on dynamic event triggering;

[0138] The execution module is configured to control each robotic arm according to the preset time super-helical sliding mode control law.

[0139] The more detailed steps are the same as in Example 1, and will not be repeated here.

[0140] Example 3

[0141] This disclosure provides a medium on which a program is stored, which, when executed by a processor, implements the steps of a multi-manipulator preset-time super-helical sliding mode control method as described in this disclosure, embodiment one.

[0142] The more detailed steps are the same as in Example 1, and will not be repeated here.

[0143] Example 4

[0144] This disclosure provides an electronic device, including a memory, a processor, and a program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the multi-manipulator preset-time super-helical sliding mode control method described in this disclosure.

[0145] The more detailed steps are the same as in Example 1, and will not be repeated here.

[0146] The above description is merely a preferred embodiment of this disclosure and is not intended to limit this disclosure. Various modifications and variations can be made to this disclosure by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this disclosure should be included within the scope of protection of this disclosure.

Claims

1. A multi-robotic arm preset-time super-spiral sliding mode control method, characterized in that, Includes the following steps: Establish a dynamic model of the multi-manipulator system, determine the network communication topology between each manipulator in the inclusion control process of the multi-manipulator cluster, and define the inclusion error of the multi-manipulator system. Based on sliding mode variable structure theory and preset time control theory, a nonlinear sliding mode surface function is designed, and a preset time super-helical sliding mode control law for multiple robotic arms is constructed. Establish a dynamic event triggering mechanism and construct a multi-robot arm preset time super spiral sliding mode control law based on dynamic event triggering; Each robotic arm is controlled according to the preset time super-helical sliding mode control law; Based on sliding mode variable structure theory and preset time control theory, a nonlinear sliding mode surface function is designed, specifically as follows: A time-varying function is set based on a preset time control theory. Based on the time-varying function, sliding mode variable structure theory, and error inclusion, a nonlinear sliding surface function is designed. The time-varying function is as follows: in, T 1 represents the preset time required to reach the sliding surface. T 2 represents the preset time for the system state to converge on the sliding surface. t 0 represents the initial time. , Let be any positive number greater than 2, and satisfy: in, for The derivative with respect to time, for The derivative with respect to time; Based on time-varying functions, sliding mode variable structure theory, and inclusion error, the nonlinear sliding mode surface function is set as follows: in, It is a time-varying function. for The derivative of the constant ,when When, function In the smallest neighborhood of zero, when hour, It can be set to any value greater than zero, and is constructed as follows: Among them, when When, set To decide The value; The pre-set time super-helical sliding mode control law for multiple robotic arms is constructed as follows: in, It is a time-varying function. η 1 and η 2 is the attenuation coefficient, a constant. , satisfy , , , For symbolic functions, constants ; when When, function In the smallest neighborhood of zero, when hour, It can be set to any value greater than zero, and is constructed as follows: Among them, when When, set To decide The value of .

2. The multi-robotic arm preset-time super-spiral sliding mode control method as described in claim 1, characterized in that, Establish the dynamic model of the multi-robotic arm system, specifically as follows: A dynamic model of a multi-manipulator system is established by utilizing the generalized coordinate position state of the robotic arm, the symmetric positive definite inertia matrix, the Coriolis force, the centrifugal torque, the gravitational torque, the control input, and the external disturbances it suffers, based on the Euler-Lagrange equations.

3. The multi-robotic arm preset-time super-spiral sliding mode control method as described in claim 1, characterized in that, The network communication topology between the robotic arms in a multi-robotic arm cluster, including the control process, is determined as follows: An undirected graph is used to describe a robotic arm cluster, including the communication connections between the individual robotic arms during the control process. When the i The robotic arm received the first... j The position and velocity information of each robotic arm are used to determine the Laplacian matrix elements associated with the adjacency matrix of the undirected graph. ; Assuming the leader in the robotic arm cluster has no neighboring nodes, update the Laplace matrix associated with the adjacency matrix of the undirected graph.

4. The multi-arm preset-time super-spiral sliding mode control method as described in claim 1, characterized in that, The inclusion error of a multi-robotic arm system is defined as follows: in, and Representing the first The and the first The generalized coordinate vector of a robotic arm, Representing the The and the first Communication weights between robotic arms express A follower robotic arm, express A leader robotic arm, t Indicates time.

5. A multi-robotic arm preset-time super-spiral sliding mode control system, characterized in that, The multi-robot arm preset-time super-spiral sliding mode control method according to any one of claims 1-4 includes: The model building module is configured to: establish a dynamic model of the multi-manipulator system, determine the network communication topology between the manipulators in the multi-manipulator cluster during the inclusion control process, and define the inclusion error of the multi-manipulator system. The instruction generation module is configured to: design a nonlinear sliding surface function based on sliding mode variable structure theory and preset time control theory, and construct a preset time super-helical sliding mode control law for multiple robotic arms; The instruction triggering module is configured to: establish a dynamic event triggering mechanism and construct a multi-robot arm preset time super spiral sliding mode control law based on dynamic event triggering; The execution module is configured to control each robotic arm according to the preset time super-helical sliding mode control law.

6. A medium having a program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps in the multi-manipulator preset time super-helical sliding mode control method as described in any one of claims 1-4.

7. An electronic device comprising a memory, a processor, and a program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the multi-manipulator preset time super-helical sliding mode control method as described in any one of claims 1-4.

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