Multi-mechanical-arm cooperative control method oriented to unknown disturbance

Abstract

The invention belongs to the technical field of multi-agent cooperative intelligent control, and particularly relates to a multi-mechanical-arm cooperative control method under unknown disturbance, which comprises the following steps: establishing a dynamic model of a strict feedback nonlinear multi-mechanical-arm cooperative system; constructing a communication topological structure of the system through a virtual coupling mechanism; constructing a unified system collaborative error model; introducing a preset time function and a global preset performance function, mapping errors to an adjustable constraint performance space, and ensuring that all error signals are dynamically converged in a performance range set by a user; a task layer shape control force and a pose control force are designed under a distributed gradient descent method framework, a task layer overall control force is constructed, and multiple mechanical arms are driven to move cooperatively and keep a stable formation in a task space; designing a joint layer distributed adaptive control law under unknown disturbance through passive characteristics of a nonlinear system; according to the method, cooperative convergence and stable control of the multi-mechanical-arm system within the preset time can be achieved under unknown disturbance.

Description

Technical Field

[0001] This invention belongs to the field of multi-agent cooperative intelligent control technology, specifically relating to a multi-manipulator cooperative control method for unknown disturbances. Background Technology

[0002] In practical engineering applications, multiple intelligent agents are often required to collaborate to complete complex tasks. For example, in industrial manufacturing, multiple robots can be controlled to perform high-precision, complex welding operations along specific paths or postures; in the military field, multiple autonomous vehicles can be used to perform tasks such as border patrol, mine clearance, and geographic exploration; and in the 3C manufacturing field, multi-fingered, flexible, dexterous hands can be used to perform collaborative grasping and assembly operations in a human-like manner. Currently, distributed control methods for multi-agent systems mainly include: consistency control based on behavioral differences between neighboring agents as feedback information; finite-time distributed control using sliding mode control technology, which has good anti-disturbance capabilities; and adaptive distributed trajectory tracking control based on preset performance functions. For multi-input multi-output nonlinear systems, existing technologies have been able to achieve asymptotic convergence and finite-time convergence of the state variables of Lagrange systems, exhibiting high steady-state performance. However, the following technical bottlenecks still exist: First, the consistency control between adjacent agents lags in the transient response phase. Insufficient response of individual agents to external disturbances can easily lead to disordered production line operation, thereby reducing the overall consistency of the system. Second, although traditional preset performance functions can ensure that system errors converge within preset boundaries, their boundary performance is constrained by the initial conditions of the system and lacks adaptive adjustment capability in the transient process, making it difficult to simultaneously optimize convergence speed and dynamic performance.

[0003] To address these challenges, there is an urgent need to develop a multi-agent distributed cooperative control method suitable for unknown disturbance environments. This method aims to improve the transient response capability and disturbance robustness of agents such as robotic arms, drones, dexterous hands, and mobile robots under complex working conditions, thereby achieving rapid, stable, and coordinated convergence of the system's global performance. Summary of the Invention

[0004] To address the above problems, this invention provides a multi-manipulator cooperative control method for unknown disturbances, comprising:

[0005] S1. Establish a dynamic model for a strictly feedback nonlinear multi-manipulator cooperative system;

[0006] S2. A communication topology for a nonlinear multi-manipulator collaborative system is constructed through a virtual coupling mechanism to realize information and state interaction between manipulators;

[0007] S3. Construct a unified system cooperative error model based on the communication topology, wherein the system cooperative error model includes cooperative working error and target pose error;

[0008] S4. Introduce a preset time function and a global preset performance function to map the collaborative working error and the target pose error to the performance space of adjustable constraints, thereby obtaining a scaled system collaborative error model, ensuring that all error signals converge dynamically within the performance range set by the user.

[0009] S5. Based on the scaled system cooperative error model, the shape control force and pose control force of the task layer are designed under the framework of distributed gradient descent method, and the overall control force of the task layer is constructed to drive the cooperative motion and stable formation maintenance of multiple robotic arms in the task space.

[0010] S6. Based on the overall control force of the task layer, a distributed adaptive control law for the joint layer under unknown disturbances is designed through the passive characteristics of the nonlinear system, enabling multiple robotic arms to achieve coordinated control within a preset time.

[0011] The beneficial effects of this invention are:

[0012] This invention proposes a control method for the cooperative control problem of multi-agent systems under unknown external disturbances. By establishing a distributed robotic arm dynamics model and combining a global preset performance function (GPPF), a preset time function (PTF), gradient descent (GDF), and adaptive theory, a distributed adaptive controller is designed. This controller enables cooperative convergence and stable control of the multi-agent system within a preset time under unknown disturbances. Compared to traditional finite-time and fixed-time control methods, the introduced preset time control offers precise and controllable convergence time, independent of initial system conditions and control parameters. Compared to traditional preset energy functions, the proposed global preset performance function ensures dynamic iteration of system state errors within user-defined performance boundaries. The performance boundary curve can be flexibly customized according to task requirements, independent of initial conditions, and allows for active control of convergence time and rate through parameter adjustment to meet practical needs. Through a distributed virtual coupling architecture, cooperative parallel computation and state interaction of the multi-agent system are achieved, effectively reducing communication load. Attached Figure Description

[0013] Figure 1 This is a flowchart of the collaborative control method of the present invention;

[0014] Figure 2 This is a virtual coupling communication topology diagram of the multi-robotic arm system of the present invention;

[0015] Figure 3 This is a schematic diagram of the collaborative working error and preset performance boundary of multiple robotic arms in an embodiment of the present invention;

[0016] Figure 4 This is a schematic diagram of the target pose error and preset performance boundary of the multi-robotic arm in an embodiment of the present invention;

[0017] Figure 5 This is a simulation diagram of the joint angles and velocities of the multi-arm robotic system according to an embodiment of the present invention.

[0018] Figure 6 This is a schematic diagram of the control inputs for each joint of the multi-robotic arm in an embodiment of the present invention;

[0019] Figure 7 This is a schematic diagram of the collaborative working trajectory of multiple robotic arms in an embodiment of the present invention. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] Figure 1 This is a flowchart of a multi-robotic arm cooperative control method under unknown disturbances, as shown in some embodiments of the present invention.

[0022] This invention specification provides a method for cooperative control of multiple robotic arms under unknown disturbances, such as... Figure 1 As shown, it includes:

[0023] S1. Establish a dynamic model for a strictly feedback nonlinear multi-manipulator cooperative system.

[0024] In some embodiments, step S1 constructs a multi-manipulator cooperative system with Euler-Lagrange multi-input multi-output characteristics, wherein the dynamic model of each manipulator with strict feedback can be expressed as:

[0025] (1)

[0026] In the formula, M i (q i ) This represents the positive definite inertia matrix of the i=1,…,N robotic arm. Let the Coriolis force matrix of the i-th robotic arm be represented. Let i represent the gravity term of the i-th robotic arm; This represents the joint control input torque of the i-th robotic arm; This represents an unknown external disturbance or malicious attack on the i-th robotic arm under actual working conditions; Let represent the rotation angle, velocity, and acceleration of the i-th robotic arm joint, respectively; n represents the number of joints in the i-th robotic arm; N represents the number of robotic arms; and R represents the set of real numbers.

[0027] S2. A communication topology for a nonlinear multi-manipulator collaborative system is constructed through a virtual coupling mechanism to realize information and status interaction between manipulators.

[0028] In some embodiments, the communication topology of the nonlinear multi-manipulator cooperative system is represented by an undirected graph G:={V,ε}, where the undirected graph G satisfies minimum rigidity or infinitesimal rigidity; vertex set |V|=N represents the number of robotic arms in a nonlinear multi-robotic arm collaborative system; Let |ε| be the set of edges used to represent the communication connections between robotic arms, and |ε| represent the total number of edges in the entire multi-robotic arm system; the neighbor set of the i-th robotic arm is defined as... The incidence matrix of an undirected graph G element b ik The relationship between the i-th robotic arm and the k∈ε edge is represented as follows:

[0029] (2)

[0030] In the formula, This represents the tail vertex of the k-th edge. This represents the head vertex of the k-th edge.

[0031] Figure 2 This is based on virtual coupling as shown in some embodiments of the present invention. Virtual coupling communication topology diagram of a multi-robotic arm system.

[0032] In some embodiments, constructing as Figure 2 The virtual coupling communication topology diagram of the multi-arm robotic system shown can realize information interaction and position sharing between robotic arms, avoiding the need for pairwise interaction between robotic arms and greatly reducing the amount of information interaction.

[0033] S3. Construct a unified system cooperative error model based on the communication topology, wherein the system cooperative error model includes cooperative working error and target pose error.

[0034] In some embodiments, based on the edges in an undirected graph G Construct a system cooperative error model. This represents the connection between the i-th robotic arm and the i-th robotic arm in an undirected graph G. The first robotic arm Edge; where, the collaborative working error e of the i-th robotic arm is defined. i (t) is represented as:

[0035] (3)

[0036] In the formula, Let |z| represent the error corresponding to the k-th edge in the undirected graph G. k || represents the actual Euclidean distance corresponding to the k-th edge in the undirected graph G. b represents the expected distance corresponding to the k-th edge in an undirected graph G, where |ε| represents the number of edges; ik Let || ...

[0037] Define the target pose error e of the i-th robotic arm pos,i (t) is represented as:

[0038] (4)

[0039] In the formula, This represents the position vector of the end effector of the i-th robotic arm in the task space. Let m represent the target position vector of the i-th robotic arm in the task space, where m∈{2,3} represents the dimension of the task space (i.e., the dimension of the Cartesian coordinate system). When m=2, it means that the task space adopts a two-dimensional coordinate system; when m=3, it means that the task space adopts a three-dimensional coordinate system.

[0040] In some embodiments, the actual Euclidean distance and the expected Euclidean distance corresponding to the k-th edge in an undirected graph G can be expressed as:

[0041] (5)

[0042] In the formula, Let represent the end effector position vectors of the i-th and j-th robotic arms in the task space at the current time t, respectively. Let represent the expected target position vectors of the i-th and j-th robotic arms in the task space, respectively. Let represent the dimension of the task space; where represents the position vector of the end effector of the i-th robotic arm in the task space. It is obtained by mapping from joint space using a positive kinematic model, and its expression is:

[0043] (6)

[0044] In the formula, This represents the positive kinematic mapping function of the robotic arm, used to describe the joint rotation angle q. i A linear mapping to the spatial position of the robotic arm's end effector in the task space. Let represent the base position vector of the i-th robotic arm in the task space.

[0045] S4. Introduce a Prescribed Time Function (PTF) and a Global Prescribed Performance Function (GPPF) to map the collaborative working error and the target pose error to the performance space of adjustable constraints, thereby obtaining a scaled system collaborative error model, ensuring that all error signals dynamically converge within the user-defined performance range.

[0046] In some embodiments, to ensure that all errors converge within a preset performance boundary, the following constraints should be met:

[0047] (7)

[0048] To achieve the above conditions, the following processing is performed:

[0049] Define global preset performance functions The specific expression is:

[0050] (8)

[0051] In the formula, b s >0 indicates a positive integer. This represents the preset time scaling function, and its expression is:

[0052] (9)

[0053] Within the interval [0,T] It is a monotonically decreasing and continuously differentiable function that satisfies the initial conditions. , and have v>0 indicates the contraction rate coefficient, b f ∈[0,1) represents the lower bound parameter for contraction, T represents the user-preset system convergence time; μ(t) represents the preset time function, the specific expression of which is:

[0054] (10)

[0055] In the formula, within the interval t∈[0,T), μ(t) is a monotonically increasing and continuously differentiable function, satisfying μ(0)=1, and has λ>0 indicates a constant approaching zero.

[0056] The collaborative working error e of robotic arm i i (t) is normalized to obtain:

[0057] (11)

[0058] Where, η i (ei (t))∈(-1,1) represents the normalized dimensionless cooperative working error signal;

[0059] A global preset performance function in the form of a barrier function is used to evaluate the cooperative working error e. i (t) is transformed to obtain the scaled collaborative working error s. i (t):

[0060] (12)

[0061] In the formula, , ;

[0062] The target pose error e of robotic arm i pos,i (t) is normalized to obtain:

[0063] (13)

[0064] In the formula, η pos,i (e pos,i (t))∈(-1,1) represents the normalized dimensionless target pose error signal;

[0065] The target pose error e is evaluated using a globally preset performance function in the form of an obstacle function. pos,i (t) is transformed to obtain the scaled target pose error s. pos,i (t):

[0066] (14)

[0067] In the formula, , .

[0068] S5. Based on the scaled system cooperative error model, the shape control force and pose control force of the task layer are designed under the framework of distributed gradient descent method, and the overall control force of the task layer is constructed to drive multiple robotic arms to cooperate in motion and maintain stable formation in the task space.

[0069] In subsequent processes, to avoid complex calculation expressions, some parameter representations are simplified. For example, the scaled collaborative working error s of the i-th robotic arm is represented. i (t) represents s s i The original collaborative working error e of the i-th robotic arm i (t) represents simplification to e i Although (t) is simplified, the meaning and calculation process are the same.

[0070] In some embodiments, the task layer shape control force is represented as:

[0071] (15)

[0072] In the formula, s represents the shape control force of the i-th robotic arm at the task level; i This represents the scaled collaborative work error variable of the i-th robotic arm. The scaled collaborative error s of the i-th robotic arm represents the error in the collaborative operation of the i-th robotic arm. i For the original collaborative working error e i gradient, Indicates the original collaborative working error e i For the position vector x of the end effector of the i-th robotic arm in the task space i The gradient; where,

[0073] (16)

[0074] (17)

[0075] In the formula, , , , b s >0 indicates a positive integer. This indicates the preset time scaling function. b represents the normalized dimensionless cooperative working error signal; ik Let ||z| represent the relationship between the i-th robotic arm and the k∈ε-th edge. k || represents the actual Euclidean distance corresponding to the k-th edge in the undirected graph G;

[0076] To achieve precise position tracking and dynamic stability control of multiple robotic arms in the task space, the task-level pose control force is represented as:

[0077] (18)

[0078] In the formula, k represents the pose control force of the i-th robotic arm at the task layer; 1,i >0, k 2,i >0 indicates the control gain of the i-th robotic arm, s pos,i Let e ​​represent the target pose error variable of the i-th robotic arm after scaling. pos,i Let represent the original target pose error variable of the i-th robotic arm; The velocity vector of the i-th robotic arm in the task space is represented by the following expression:

[0079] (19)

[0080] In the formula, Let the Jacobian matrix of the i-th robotic arm be denoted as . This represents the joint velocity vector of the i-th robotic arm. Let m represent the positive kinematic mapping function of the i-th robotic arm, m represent the dimension of the task space, and n represent the number of joints of the i-th robotic arm.

[0081] In some embodiments, the task layer shape control force and pose control force are weighted and fused to form the overall task layer control force, which is expressed as:

[0082] (20)

[0083] In the formula, f i w represents the overall control force of the i-th robotic arm at the task level. s >0、w p >0 represents the weighting coefficients of shape control force and pose control force, respectively.

[0084] S6. Based on the overall control force of the task layer, a distributed adaptive control law for the joint layer under unknown disturbances is designed through the passive characteristics of the nonlinear system, enabling multiple robotic arms to achieve coordinated control within a preset time.

[0085] In some embodiments, based on the passive characteristics of the robotic arm, the joint-layer distributed adaptive control law under unknown disturbances is as follows:

[0086] (twenty one)

[0087] In the formula, u i Let J represent the joint layer control law of the i-th robotic arm. i (q i ) Let f be the Jacobian matrix of the i-th robotic arm. i k represents the overall control force of the i-th robotic arm at the task level. d Indicates joint velocity gain. Let G represent the joint velocity vector of the i-th robotic arm. i Let n represent the gravity vector of the i-th robotic arm, and n represent the number of joints of the i-th robotic arm.

[0088] By incorporating the overall control force of the task layer into the robotic arm's dynamics model, a closed-loop control system is obtained, represented as:

[0089] (twenty two)

[0090] In the formula, Let these represent the velocity and acceleration vectors of the i-th robotic arm joint, respectively. Let represent the positive definite inertia matrix of the i-th robotic arm. Let the Coriolis force matrix of the i-th robotic arm be represented. η represents an unknown external disturbance or malicious attack on the i-th robotic arm under actual working conditions. i (e i (t) represents the normalized dimensionless cooperative working error signal. , e i Let b represent the collaborative working error of the i-th robotic arm. s b represents a positive constant. ik Let ||z| represent the relationship between the i-th robotic arm and the k∈ε-th edge. k || represents the actual Euclidean distance corresponding to the k-th edge in the undirected graph G. , This indicates the preset time scaling factor. This indicates the preset time scaling function. The derivative of the preset time scaling factor with respect to time is given by , where T represents the system's preset convergence time, and b... f ∈[0,1) represents the lower bound parameter of contraction, v>0 represents the contraction rate coefficient, and μ(t) represents the preset time function. Indicates the first The scaling error of the collaborative work of the robotic arms affects time. The derivative of .

[0091] Furthermore, consider a group of N robotic arms facing unknown disturbances, whose undirected graph G satisfies minimum stiffness or infinitesimal stiffness. Choose an appropriate gain parameter. For the reference configuration The desired collaborative working state formed can realize all system state variables by integrating the global performance function and the preset time adaptive control law (21). , , , At the user's preset time The convergence is zero.

[0092] In some embodiments, to verify the effectiveness of the method of the present invention, simulation verification is performed using Matlab 2024a, as follows:

[0093] The simulation object is four sets of two-degree-of-freedom robotic arm systems. The dynamic models and parameters of each robotic arm system are consistent (as shown in Table 1). The total simulation time is set to t=10s, and the sampling period is [missing information]. Other relevant simulation parameters are shown in Tables 1 and 2. The specific expression for a single dynamic model is:

[0094] Inertia matrix for:

[0095]

[0096] Coriolis force and centripetal force matrix for:

[0097]

[0098] Gravity vector for:

[0099]

[0100] In the formula, , , ; They represent the first The angular positions of joints 1 and 2 of the robotic arm; They represent the first The angular velocities of joints 1 and 2 of a robotic arm; It represents the acceleration due to gravity.

[0101] Table 1 Dynamic parameters of the i-th robotic arm system

[0102]

[0103] Table 1 lists only the system dynamics parameters of a single two-degree-of-freedom robotic arm; the system parameters of other robotic arms are exactly the same as those listed above.

[0104] Table 2 Control Parameters

[0105]

[0106] in, , , , These represent the initial joint angles of the robotic arm. This indicates that the initial angular velocity of each robotic arm joint is zero. , , This represents the globally preset performance control parameters. , , These represent the control gain parameters of the robotic arm. , , , These represent the desired target positions of the four robotic arms, , These represent the weights of formation control and pose control at the task level, respectively.

[0107] To further illustrate, the kinematic model of each two-joint robotic arm can be represented as:

[0108]

[0109] The Jacobian matrix of the i-th robotic arm can be represented as:

[0110]

[0111] in, , , , The base positions of the four robotic arms are represented by the following values. The corresponding incidence matrix B of the undirected graph G is:

[0112]

[0113] Unknown external disturbance is defined as Assume the system's preset convergence time is... .

[0114] Simulation results are as follows Figure 3-6 As shown, Figure 3 The collaborative working error of each robotic arm was demonstrated, and all iterations were rapid within a preset performance range and within a preset time. It converges globally. Figure 4 For each robotic arm's target pose error, the results show that, under unknown disturbances, the designed adaptive controller can still make the error converge precisely to zero within a preset time and always meet the preset performance constraints. Figure 5 The two images above and below show the joint rotation angle and joint velocity curves of each robotic arm, respectively. It can be seen that within the preset time... At that time, the velocities of all joints converge to zero. Figure 6 The input torque for the two joints of each robotic arm is reasonable in amplitude and without severe jitter, which meets the engineering feasibility requirements of actual system control applications.

[0115] Figure 7 The collaborative motion trajectory of the end effectors in a multi-manipulator system is clearly presented, showing the convergence process from the initial pose (marked as a dot) to the target pose (marked as a square). Simulation results show that the closed-loop system achieves the desired collaborative working formation in a two-dimensional workspace, verifying the effectiveness of the proposed control method.

[0116] In summary, from the joint level, the control precision of each joint is high, all converging to zero within the preset time, and the control torque does not exhibit significant overshoot or saturation, verifying the transient response performance of the multi-arm system. From the task level, the collaborative working error and pose error of each arm remain within the preset performance boundaries, maintaining global boundedness, and the end effectors of all arms reach the desired target position within the preset time, forming the desired collaborative working formation. Overall, the results verify that the adaptive controller proposed in this invention exhibits excellent performance in terms of control precision, transient performance, and robustness to unknown disturbances.

[0117] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "setting," "connection," "fixing," "rotation," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Unless otherwise explicitly limited, those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0118] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A multi-robotic arm cooperative control method for unknown disturbances, characterized in that, include: S1. Establish a dynamic model for a strictly feedback nonlinear multi-manipulator cooperative system; S2. A communication topology for a nonlinear multi-manipulator collaborative system is constructed through a virtual coupling mechanism to realize information and state interaction between manipulators; S3. Construct a unified system cooperative error model based on the communication topology, wherein the system cooperative error model includes cooperative working error and target pose error; S4. Introduce a preset time function and a global preset performance function to map the collaborative working error and the target pose error to the performance space of adjustable constraints, thereby obtaining a scaled system collaborative error model, ensuring that all error signals converge dynamically within the performance range set by the user. S5. Based on the scaled system cooperative error model, the shape control force and pose control force of the task layer are designed under the framework of distributed gradient descent method, and the overall control force of the task layer is constructed to drive the cooperative motion and stable formation maintenance of multiple robotic arms in the task space. S6. Based on the overall control force of the task layer, a distributed adaptive control law for the joint layer under unknown disturbances is designed through the passive characteristics of the nonlinear system, enabling multiple robotic arms to achieve coordinated control within a preset time.

2. The multi-robotic arm cooperative control method for unknown disturbances according to claim 1, characterized in that, Step S1 constructs a multi-manipulator cooperative system with Eulerian-Lagrange multi-input multi-output characteristics, where the dynamic model of each manipulator is represented as: In the formula, M i (q i ) This represents the positive definite inertia matrix of the i=1,2,…,N robotic arm. Let the Coriolis force matrix of the i-th robotic arm be represented. Let i represent the gravity term of the i-th robotic arm; This represents the joint control input torque of the i-th robotic arm; This represents an unknown external disturbance or malicious attack on the i-th robotic arm under actual working conditions; Let represent the rotation angle, velocity, and acceleration of the i-th robotic arm joint, respectively; n represents the number of joints of the i-th robotic arm; N represents the number of robotic arms; and R represents the set of real numbers.

3. The multi-robotic arm cooperative control method for unknown disturbances according to claim 1, characterized in that, The communication topology of a nonlinear multi-manipulator cooperative system is represented by an undirected graph G:={V,ε}, where G satisfies minimum rigidity or infinitesimal rigidity; vertex set |V|=N represents the number of robotic arms in a nonlinear multi-robotic arm collaborative system; Let ε be the set of edges used to represent the communication connections between robotic arms, where |ε| represents the total number of edges in the system. The neighbor set of the i-th robotic arm is defined as follows: The incidence matrix of an undirected graph G element b ik The relationship between the i-th robotic arm and the k∈ε edge is represented as follows: In the formula, This represents the tail vertex of the k-th edge. This represents the head vertex of the k-th edge.

4. The multi-robotic arm cooperative control method for unknown disturbances according to claim 1, characterized in that, In the system cooperative error model, the cooperative working error e of the i-th robotic arm is defined. i (t) is represented as: In the formula, Let |z| represent the error corresponding to the k-th edge in the undirected graph G. k || represents the actual Euclidean distance corresponding to the k-th edge in the undirected graph G. b represents the expected distance corresponding to the k-th edge in an undirected graph G, where |ε| represents the number of edges; ik Let || ... Define the target pose error e of the i-th robotic arm pos,i (t) is represented as: In the formula, This represents the position vector of the end effector of the i-th robotic arm in the task space. Let m represent the target position vector of the i-th robotic arm in the task space, and m represent the dimension of the task space.

5. The multi-robotic arm cooperative control method for unknown disturbances according to claim 4, characterized in that, The actual Euclidean distance and expected Euclidean distance corresponding to the k-th edge in an undirected graph G can be expressed as: In the formula, Let represent the end effector position vectors of the i-th and j-th robotic arms in the task space at the current time t, respectively. Let represent the desired target position vectors of the i-th and j-th robotic arms in the task space, respectively; where represents the end effector position vector of the i-th robotic arm in the task space. It is obtained by mapping from joint space using a positive kinematic model, and its expression is: In the formula, This represents the positive kinematic mapping function of the robotic arm, used to describe the joint rotation angle q. i A linear mapping to the spatial position of the robotic arm's end effector in the task space. Let represent the base position vector of the i-th robotic arm in the task space.

6. The multi-robotic arm cooperative control method for unknown disturbances according to claim 1, characterized in that, Global preset performance functions The specific expression is: In the formula, b s Represents positive numbers. This represents the preset time scaling function, and its expression is: Within the interval [0,T] It is a monotonically decreasing and continuously differentiable function that satisfies the initial conditions. , and have v>0 indicates the contraction rate coefficient, b f ∈[0,1) represents the lower bound parameter for contraction, T represents the user-preset system convergence time; μ(t) represents the preset time function, the specific expression of which is: In the formula, within the interval t∈[0,T), μ(t) is a monotonically increasing and continuously differentiable function, satisfying μ(0)=1, and has λ>0 indicates a constant approaching zero.

7. A multi-robotic arm cooperative control method for unknown disturbances according to claim 6, characterized in that, Based on a preset time function and a global preset performance function, the scaled system cooperative error model is obtained as follows: The collaborative working error e of robotic arm i i (t) is normalized to obtain: Where, η i (e i (t))∈(-1,1) represents the normalized dimensionless cooperative working error signal; A global preset performance function in the form of a barrier function is used to evaluate the cooperative working error e. i (t) is transformed to obtain the scaled collaborative working error s. i (t): In the formula, , ; The target pose error e of robotic arm i pos,i (t) is normalized to obtain: In the formula, η pos,i (e pos,i (t))∈(-1,1) represents the normalized dimensionless target pose error signal; The target pose error e is evaluated using a globally preset performance function in the form of an obstacle function. pos,i (t) is transformed to obtain the scaled target pose error s. pos,i (t): In the formula, , .

8. The multi-robotic arm cooperative control method for unknown disturbances according to claim 1, characterized in that, The shape control force of the task layer is represented as: In the formula, s represents the shape control force of the i-th robotic arm at the task level; i This represents the scaled collaborative error of the i-th robotic arm. The scaled collaborative error s of the i-th robotic arm represents the error in the collaborative operation of the i-th robotic arm. i For the original collaborative working error e i gradient, Indicates the original collaborative working error e i For the position vector x of the end effector of the i-th robotic arm in the task space i The gradient; where, In the formula, , , , b s >0 indicates a positive integer. This indicates the preset time scaling function. b represents the normalized dimensionless cooperative working error signal; ik This represents the relationship between the i-th robotic arm and the k-th edge, ||z k || represents the actual Euclidean distance corresponding to the k-th edge in the undirected graph G; The task-level pose control force is represented as: In the formula, k represents the pose control force of the i-th robotic arm at the task layer; 1,i k 2,i s represents the control gain of the i-th robotic arm. pos,i Let e ​​represent the target pose error variable of the i-th robotic arm after scaling. pos,i Let represent the original target pose error variable of the i-th robotic arm; The velocity vector of the i-th robotic arm in the task space is represented by the following expression: In the formula, Let the Jacobian matrix of the i-th robotic arm be denoted as . This represents the joint velocity vector of the i-th robotic arm. Let m represent the positive kinematic mapping function of the i-th robotic arm, m represent the dimension of the task space, and n represent the number of joints of the i-th robotic arm.

9. A multi-robotic arm cooperative control method for unknown disturbances according to claim 8, characterized in that, The shape control force and pose control force of the task layer are weighted and fused to form the overall control force of the task layer, which is expressed as: In the formula, f i w represents the overall control force of the i-th robotic arm at the task level. s w p These represent the weighting coefficients for shape control force and pose control force, respectively.

10. A multi-robotic arm cooperative control method for unknown disturbances according to claim 1, characterized in that, The joint-layer distributed adaptive control law under unknown disturbances is expressed as: In the formula, This represents the joint layer control law of the i-th robotic arm. Let f be the Jacobian matrix of the i-th robotic arm. i k represents the overall control force of the i-th robotic arm at the task level. d Indicates joint velocity gain. This represents the joint velocity vector of the i-th robotic arm. Let n represent the gravity vector of the i-th robotic arm, and n represent the number of joints of the i-th robotic arm. By incorporating the overall control force of the task layer into the robotic arm's dynamics model, a closed-loop control system is obtained, represented as: In the formula, Let these represent the velocity and acceleration vectors of the i-th robotic arm joint, respectively. Let represent the positive definite inertia matrix of the i-th robotic arm. Let the Coriolis force matrix of the i-th robotic arm be represented. η represents an unknown external disturbance or malicious attack on the i-th robotic arm under actual working conditions. i (e i (t) represents the normalized dimensionless cooperative working error signal. , e i (t) represents the collaborative working error of the i-th robotic arm, b s b represents a positive constant. ik This represents the relationship between the i-th robotic arm and the k-th edge, ||z k || represents the actual Euclidean distance corresponding to the k-th edge in the undirected graph G. , This indicates the preset time scaling factor. This indicates the preset time scaling function. The derivative of the preset time scaling factor with respect to time is given by , where T represents the system's preset convergence time, and b... f ∈[0,1) represents the lower bound parameter of contraction, v>0 represents the contraction rate coefficient, and μ(t) represents the preset time function. Indicates the first The scaling error of the collaborative work of the robotic arms affects time. The derivative of .

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