Cooperative control method and system for multiple robots

Abstract

The invention relates to the technical field of multi-robot cooperative control, and discloses a cooperative control method and system for multiple robots, and the method comprises the steps: building a first mathematical model of a multi-robot system, building a second mathematical model of a moving target, building a communication topology of the multi-robot system and the moving target, and carrying out the communication of the multi-robot system and the moving target. Establishing a third mathematical model of cooperative rotation of the multi-robot system based on the first mathematical model and the second mathematical model, constructing a distributed fixed time estimator, determining the internal state of the moving target based on the distributed fixed time estimator, and determining the real-time position of the moving target based on the internal state. And control input of the multi-robot system is determined according to the distributed fixed time estimator and based on the fixed time controller, and the control input is substituted into the multi-robot system to complete fixed time cooperative rotation consistency control. According to the invention, the reliability and stability of cooperative control of multiple robots within a fixed time are ensured.

Description

Technical Field

[0001] This invention relates to the field of multi-robot cooperative control technology, and more specifically, to a cooperative control method and system for multiple robots. Background Technology

[0002] With the rapid development of industries such as manufacturing, robots have been widely used. Compared to single robots, multi-robot systems, through distributed information interaction and collaborative control, can efficiently complete complex tasks that single robots cannot handle, thereby improving the industry's ability to cope with large-scale operations. Rotational consistency control is a specific manifestation of collaborative control in multi-robot systems. However, existing rotational consistency control can only achieve asymptotic stability or finite-time stability of multi-robot systems. In some practical scenarios, multi-robot systems need to achieve coordinated rotational motion around a moving target within a preset time. For example, in the field of warehousing and logistics, when shelves are dynamically transferred as moving targets, multiple robots need to complete coordinated rotation around the shelves within a preset time to achieve precise docking. Failure to achieve stable coordination within the specified time will lead to delays in shelf loading and unloading, thus posing a challenge to the collaborative control of multi-robot systems.

[0003] Therefore, it is necessary to design a cooperative control method and system for multiple robots to solve the problems existing in the current technology. Summary of the Invention

[0004] In view of this, the present invention proposes a cooperative control method and system for multiple robots, aiming to solve the above problems.

[0005] In one aspect, the present invention proposes a cooperative control method for multiple robots, comprising: A first mathematical model of the multi-robot system and a second mathematical model of the moving target are established, and the communication topology between the multi-robot system and the moving target is constructed. A third mathematical model for the cooperative rotation of a multi-robot system is established based on the first and second mathematical models. A distributed fixed-time estimator is constructed, the internal state of the moving target is determined based on the distributed fixed-time estimator, and the real-time position of the moving target is determined based on the internal state; The control input of the multi-robot system is determined based on the distributed fixed-time estimator and the fixed-time controller, and the control input is substituted into the multi-robot system to complete the fixed-time cooperative rotation consistency control.

[0006] Furthermore, in establishing the first mathematical model of the multi-robot system, the following are included: The first mathematical model of the multi-robot system is determined according to the following formula: ; ; in, express The derivative with respect to time, This represents the position of the i-th robot in two-dimensional space. This represents the velocity input of the i-th robot in two-dimensional space. express The derivative with respect to time, Let i represent the control input of the i-th robot in two-dimensional space, i∈{1,2,···,n}, and n represent the number of robots in the multi-robot system.

[0007] Furthermore, in establishing the second mathematical model of the moving target, the following are included: The second mathematical model of the moving target is determined according to the following formula: ; ; in, express The derivative with respect to time, This represents the state vector of the moving target. Represents the location information of a moving target; matrices A and E are constant matrices. Based on the second mathematical model of the moving target, the velocity and acceleration of the moving target are determined as follows: and The constant matrix pair (E,A) of the moving target satisfies the observability condition.

[0008] Furthermore, in constructing the communication topology between the multi-robot system and the moving target, the following is included: The communication topology of the multi-robot system is determined based on an undirected graph, which is determined according to the following formula: G={V,ε}; Where G represents an undirected graph, V represents a set of points, and each point represents a robot. The number of points is the same as the number of robots in the multi-robot system. Let ε represent the set of edges, and let N be the set of neighbor nodes of the i-th robot. i , , (j, i) ∈ ε means that the i-th robot is used to receive information from the j-th robot.

[0009] Furthermore, the construction of the communication topology between the multi-robot system and the moving target also includes: Based on the undirected graph, determine the adjacency matrix Q, Q=[a ij ], aij Let a represent the element in the i-th row and j-th column of the adjacency matrix Q, where a is the element in the i-th row and j-th column when (j, i) ∈ E. ij >0, otherwise a ij =0; Determine the Laplacian matrix based on the undirected graph. , , l ij Represents the Laplace matrix The element in the i-th row and j-th column, where When i≠j, l ij =-a ij ; when a i0 When = 1, it indicates that at least one robot has acquired the position information of the moving target, then the diagonal matrix , .

[0010] Furthermore, when establishing a third mathematical model for the cooperative rotation of a multi-robot system based on the first and second mathematical models, it includes: When a third mathematical model of the cooperative rotation of a multi-robot system is established, it satisfies the fixed-time position consistency convergence condition, the fixed-time velocity consistency convergence condition, and the fixed-time rotational motion condition.

[0011] Furthermore, when the fixed-time position uniformity convergence condition, the fixed-time velocity uniformity convergence condition, and the fixed-time rotational motion condition are satisfied, the following conditions are included: The condition for fixed-time position consistency convergence is expressed as follows: the multi-robot system meets the requirement of fixed-time T position consistency convergence based on the control input. ; The condition for consistent velocity convergence over a fixed time is expressed as follows: the multi-robot system meets the requirement for consistent velocity convergence over a fixed time T based on the control input. ; The condition for satisfying the fixed-time rotational motion is expressed as follows: the multi-robot system, based on the control input, satisfies the requirement of performing rotational motion around the moving target for a fixed time T. ; in, , Let represent the acceleration of the i-th robot relative to the moving target. , Let S represent the velocity of the i-th robot relative to the moving target, and let S denote the antisymmetric matrix. ω represents the angular velocity of the multi-robot system rotating around the moving target.

[0012] Furthermore, when constructing a distributed fixed-time estimator, the following is included: The distributed fixed-time estimator is determined according to the following formula: ; ; ; ; in, express The derivative with respect to time, This indicates that the i-th robot is interacting with the moving target. The estimated value, c 1、 c 2、 c3 and Denotes the estimator parameters, and >0, c1>0, c2>0, , , ,matrix ,matrix H represents the largest eigenvalue of matrix A. -1 H represents the inverse matrix of matrix H. -T H represents -1 The transpose of A T Describe the transpose of matrix A. Let i represent the auxiliary error variable for the i-th robot. This represents the state auxiliary variable of a distributed fixed-time estimator. This represents the derivative of the state auxiliary variable with respect to time. P(0) = P0 = 0 m×m m represents the moving target Dimensions Represents the auxiliary matrix. Let L denote the derivative of the auxiliary matrix with respect to time. We choose a matrix L such that -A+LE satisfies the Herwitz condition.

[0013] Furthermore, the fixed-time controller is determined according to the following formula: ; ; ; Where, k 1、 k 2、 γ, b1, and b2 are positive constants, α1 and α2 are weighting coefficients, and 0 < α1 < 1, α2 > 1. And i∈{1,2}, R represents the radius of rotation of the robot around the moving target. Indicates a fixed-time controller. This represents the derivative of the velocity auxiliary variable with respect to time. Represents the auxiliary variable of velocity. This is to ensure that the fixed-time controller does not require speed information. Represents a time-varying rotation vector. , Indicates the position consistency parameter. Used to achieve positional consistency for robots.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows: By constructing a distributed fixed-time estimator and a fixed-time controller, the multi-robot system is ensured to complete the cooperative rotation consistency control within a preset time. Furthermore, the perception of the moving target by multiple robots is easily affected by measurement errors or untimely information exchange, leading to coordination deviations. Based on the distributed fixed-time estimator, the internal state of the moving target is determined in real time, providing reliable information support for the cooperative rotation of multiple robots. The communication topology, the third mathematical model of cooperative rotation, and the fixed-time controller ensure that the position and velocity of multiple robots achieve consistent convergence within a preset time, ensuring the synchronization of the rotation trajectory around the moving target and avoiding the failure of robot tasks due to individual deviations. Thus, the reliability and stability of the cooperative control of multiple robots within a fixed time are ensured.

[0015] On the other hand, this application also provides a cooperative control system for multiple robots, for applying the above-described cooperative control method for multiple robots, including: The model building module is configured to build a first mathematical model of the multi-robot system and a second mathematical model of the moving target, and to construct the communication topology between the multi-robot system and the moving target. The model control module is configured to establish a third mathematical model for the cooperative rotation of the multi-robot system based on the first and second mathematical models. The location determination module is configured to construct a distributed fixed-time estimator, determine the internal state of the moving target based on the distributed fixed-time estimator, and determine the real-time location of the moving target based on the internal state. The collaborative control module is configured to determine the control input of the multi-robot system based on the distributed fixed-time estimator and the fixed-time controller, and substitute the control input into the multi-robot system to complete fixed-time collaborative rotation consistency control.

[0016] It is understandable that the above-mentioned cooperative control method and system for multiple robots have the same beneficial effects, and will not be elaborated further here. Attached Figure Description

[0017] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1 A flowchart of a collaborative control method for multiple robots provided in an embodiment of the present invention.

[0018] Figure 2 This is a trajectory diagram of the cooperative rotation consistency control provided in the embodiments of the present invention.

[0019] Figure 3 This is a schematic diagram of the error time response between the state of a moving target estimated by a distributed fixed-time estimator and a fixed-time controller and the actual state, provided in an embodiment of the present invention.

[0020] Figure 4 This is a schematic diagram of the robot's relative position signal time response provided in an embodiment of the present invention.

[0021] Figure 5 This is a schematic diagram of the time response of the robot's relative velocity signal provided in an embodiment of the present invention.

[0022] Figure 6 This is a schematic diagram of the error time response between the robot speed and the moving target speed provided in an embodiment of the present invention.

[0023] Figure 7 This is a schematic diagram of the error time response between the robot acceleration and the moving target acceleration provided in an embodiment of the present invention.

[0024] Figure 8 This is a functional block diagram of a collaborative control system for multiple robots provided in an embodiment of the present invention. Detailed Implementation

[0025] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the disclosure to those skilled in the art. It should be noted that, unless otherwise specified, embodiments and features in the embodiments of the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0026] In some embodiments of this application, see Figure 1 As shown, a cooperative control method for multiple robots includes: S100: Establish the first mathematical model of the multi-robot system and the second mathematical model of the moving target, and construct the communication topology between the multi-robot system and the moving target.

[0027] S200: A third mathematical model for the cooperative rotation of a multi-robot system is established based on the first and second mathematical models.

[0028] S300: Construct a distributed fixed-time estimator, determine the internal state of the moving target based on the distributed fixed-time estimator, and determine the real-time position of the moving target based on the internal state; S400: Determines the control input of the multi-robot system based on the distributed fixed-time estimator and the fixed-time controller, and substitutes the control input into the multi-robot system to complete the fixed-time cooperative rotation consistency control.

[0029] In some embodiments of this application, establishing the first mathematical model of the multi-robot system includes: The first mathematical model of the multi-robot system is determined according to the following formula: ; ; in, express The derivative with respect to time, This represents the position of the i-th robot in two-dimensional space. This represents the velocity input of the i-th robot in two-dimensional space. express The derivative with respect to time, Let i represent the control input of the i-th robot in two-dimensional space, i∈{1,2,···,n}, and n represent the number of robots in the multi-robot system.

[0030] In some embodiments of this application, when establishing a second mathematical model of a moving target, the second mathematical model of the moving target is determined according to the following formula: ; ; in, express The derivative with respect to time, This represents the state vector of the moving target. Represents the location information of a moving target; matrices A and E are constant matrices. Based on the second mathematical model of the moving target, the velocity and acceleration of the moving target are determined as follows: and The constant matrix pair (E,A) of the moving target satisfies the observability condition.

[0031] In some embodiments of this application, the communication topology of the multi-robot system and the moving target is constructed by: determining the communication topology of the multi-robot system based on an undirected graph, wherein the undirected graph is determined according to the following formula: G={V,ε}; Where G represents an undirected graph, V represents a set of points, and each point represents a robot. The number of points is the same as the number of robots in the multi-robot system. Let ε represent the set of edges, and let N be the set of neighbor nodes of the i-th robot. i , , (j, i) ∈ ε means that the i-th robot is used to receive information from the j-th robot.

[0032] In some embodiments of this application, when constructing the communication topology of the multi-robot system and the moving target, the method further includes: determining the adjacency matrix Q based on an undirected graph, where Q = [a ij ], a ij Let a represent the element in the i-th row and j-th column of the adjacency matrix Q, where a is the element in the i-th row and j-th column when (j, i) ∈ E. ij >0, otherwise a ij =0; Determine the Laplacian matrix based on the undirected graph. , , l ij Represents the Laplace matrix The element in the i-th row and j-th column, where When i≠j, l ij =-a ij ; when a i0 When = 1, it indicates that at least one robot has acquired the position information of the moving target, then the diagonal matrix , .

[0033] In some embodiments of this application, when establishing a third mathematical model for the cooperative rotation of a multi-robot system based on a first mathematical model and a second mathematical model, the following is included: when establishing a third mathematical model for the cooperative rotation of a multi-robot system, the fixed-time position consistency convergence condition, the fixed-time velocity consistency convergence condition, and the fixed-time rotational motion condition are satisfied.

[0034] In some embodiments of this application, when the fixed-time position consistency convergence condition, the fixed-time velocity consistency convergence condition, and the fixed-time rotational motion condition are satisfied, the following is included: satisfying the fixed-time position consistency convergence condition is expressed as: the multi-robot system satisfies the requirement of fixed-time T position consistency convergence based on the control input; ; The condition for consistent velocity convergence over a fixed time is expressed as follows: the multi-robot system meets the requirement for consistent velocity convergence over a fixed time T based on the control input. ; The condition for satisfying the fixed-time rotational motion is expressed as follows: the multi-robot system, based on the control input, satisfies the requirement of performing rotational motion around the moving target for a fixed time T. ; in, , Let represent the acceleration of the i-th robot relative to the moving target. , Let S represent the velocity of the i-th robot relative to the moving target, and let S denote the antisymmetric matrix. ω represents the angular velocity of the multi-robot system rotating around the moving target.

[0035] In some embodiments of this application, constructing a distributed fixed-time estimator includes: the distributed fixed-time estimator being determined according to the following formula: ; ; ; ; in, express The derivative with respect to time, This indicates that the i-th robot is interacting with the moving target. The estimated value, c 1、 c 2、 c3 and Denotes the estimator parameters, and >0, c1>0, c2>0, , , ,matrix ,matrix H represents the largest eigenvalue of matrix A. -1 H represents the inverse matrix of matrix H. -T H represents -1 The transpose of AT Describe the transpose of matrix A. Let i represent the auxiliary error variable for the i-th robot. This represents the state auxiliary variable of a distributed fixed-time estimator. This represents the derivative of the state auxiliary variable with respect to time. P(0) = P0 = 0 m×m m represents the moving target Dimensions Represents the auxiliary matrix. Let L denote the derivative of the auxiliary matrix with respect to time. We choose a matrix L such that -A+LE satisfies the Herwitz condition.

[0036] In some embodiments of this application, the fixed-time controller is determined according to the following formula: ; ; ; Where, k 1、 k 2、 γ, b1, and b2 are positive constants, α1 and α2 are weighting coefficients, and 0 < α1 < 1, α2 > 1. And i∈{1,2}, R represents the radius of rotation of the robot around the moving target. Indicates a fixed-time controller. This represents the derivative of the velocity auxiliary variable with respect to time. Represents the auxiliary variable of velocity. This is to ensure that the fixed-time controller does not require speed information. Represents a time-varying rotation vector. , Indicates the position consistency parameter. Used to achieve positional consistency for robots.

[0037] Specifically, the multi-robot system is used as an example with four robots. The simulation is used for verification, and the initialization of all parameters and parameter matrices is shown in Table 1:

[0038] Specifically, according to Figure 2 It can be seen that the first mathematical model, the second mathematical model, the third mathematical model, the distributed fixed-time estimator, the fixed-time controller, and the communication topology between the multi-robot system and the moving target enable the four robots to complete coordinated rotational consistency control at a fixed time (set time). Figure 3This represents the error between the state information of the moving target estimated by each robot and the actual state. It initially presents a large error but gradually approaches zero, ensuring the accuracy and reliability of the distributed fixed-time estimator. Figure 4 This indicates the robot's relative position signal, which also initially has a large error but gradually approaches zero. Figure 5 The signal representing the robot's relative velocity also initially showed a large error before gradually approaching zero. Figure 6 This represents the error between the robot's position and the position of the moving target, and its value gradually approaches the rotation radius R=2. Figure 7 This represents the acceleration of each robot relative to the moving target. and the speed of each robot relative to the moving target satisfy This indicates that the robot rotates around the moving target, while existing technologies can only achieve asymptotic stability (without a definite convergence time) or finite-time stability (convergence time increases with the initial error). The accuracy and reliability of cooperative control are improved through the use of a first mathematical model, a second mathematical model, a third mathematical model, a distributed fixed-time estimator, a fixed-time controller, and the communication topology between the multi-robot system and the moving target. The communication topology between the multi-robot system and the moving target determines the interactive positions, velocities, and estimated values ​​of the moving target between robots through edge sets and adjacency matrices, providing a foundation for state synchronization among the multiple robots. Internal states are variables that fully describe the motion characteristics of the moving target, and are represented by state vectors.

[0039] In summary, the beneficial effects of this invention are as follows: By constructing a distributed fixed-time estimator and a fixed-time controller, the invention ensures that the multi-robot system completes coordinated rotation consistency control within a preset time. Furthermore, the perception of the moving target by multiple robots is susceptible to measurement errors or untimely information exchange, leading to coordination deviations. Based on the distributed fixed-time estimator, the internal state of the moving target is determined in real time, providing reliable information support for the coordinated rotation of multiple robots. The communication topology, the third mathematical model of coordinated rotation, and the fixed-time controller ensure that the position and velocity of multiple robots achieve consistent convergence within a preset time, ensuring the synchronization of the rotation trajectory around the moving target and avoiding the failure of robot tasks due to individual deviations. This ensures the reliability and stability of the coordinated control of multiple robots within a fixed time.

[0040] In another preferred embodiment based on the above embodiments, see [reference] Figure 8 As shown, this embodiment provides a cooperative control system for multiple robots, used to apply the above-described cooperative control method for multiple robots, including: The model building module is configured to build a first mathematical model of the multi-robot system and a second mathematical model of the moving target, and to construct the communication topology between the multi-robot system and the moving target.

[0041] The model control module is configured to establish a third mathematical model for the cooperative rotation of the multi-robot system based on the first and second mathematical models.

[0042] The location determination module is configured to build a distributed fixed-time estimator, determine the internal state of the moving target based on the distributed fixed-time estimator, and determine the real-time location of the moving target based on the internal state.

[0043] The collaborative control module is configured to determine the control input of the multi-robot system based on the distributed fixed-time estimator and the fixed-time controller, and then substitute the control input into the multi-robot system to complete the fixed-time collaborative rotation consistency control.

[0044] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program goods. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program goods embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0045] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program goods according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0046] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0047] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0048] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A cooperative control method for multiple robots, characterized in that, include: A first mathematical model of the multi-robot system and a second mathematical model of the moving target are established, and the communication topology between the multi-robot system and the moving target is constructed. A third mathematical model for the cooperative rotation of a multi-robot system is established based on the first and second mathematical models. A distributed fixed-time estimator is constructed, the internal state of the moving target is determined based on the distributed fixed-time estimator, and the real-time position of the moving target is determined based on the internal state; The control input of the multi-robot system is determined based on the distributed fixed-time estimator and the fixed-time controller, and the control input is substituted into the multi-robot system to complete the fixed-time cooperative rotation consistency control.

2. The cooperative control method for multiple robots according to claim 1, characterized in that, The first mathematical model of the multi-robot system includes: The first mathematical model of the multi-robot system is determined according to the following formula: ； ； in, express The derivative with respect to time, This represents the position of the i-th robot in two-dimensional space. This represents the velocity input of the i-th robot in two-dimensional space. express The derivative with respect to time, Let i represent the control input of the i-th robot in two-dimensional space, i∈{1,2,···,n}, and n represent the number of robots in the multi-robot system.

3. The cooperative control method for multiple robots according to claim 2, characterized in that, The second mathematical model for the moving target includes: The second mathematical model of the moving target is determined according to the following formula: ； ； in, express The derivative with respect to time, This represents the state vector of the moving target. Represents the location information of a moving target; matrices A and E are constant matrices. Based on the second mathematical model of the moving target, the velocity and acceleration of the moving target are determined as follows: and The constant matrix pair (E,A) of the moving target satisfies the observability condition.

4. The cooperative control method for multiple robots according to claim 3, characterized in that, When constructing the communication topology between the multi-robot system and the moving target, the following is included: The communication topology of the multi-robot system is determined based on an undirected graph, which is determined according to the following formula: G={V,ε}; Where G represents an undirected graph, V represents a set of points, and each point represents a robot. The number of points is the same as the number of robots in the multi-robot system. Let ε represent the set of edges, and let N be the set of neighbor nodes of the i-th robot. i , , (j, i) ∈ ε means that the i-th robot is used to receive information from the j-th robot.

5. The cooperative control method for multiple robots according to claim 4, characterized in that, The construction of the communication topology between the multi-robot system and the moving target also includes: Based on the undirected graph, determine the adjacency matrix Q, Q=[a ij ], a ij Let a represent the element in the i-th row and j-th column of the adjacency matrix Q, where a is the element in the i-th row and j-th column when (j, i) ∈ E. ij >0, otherwise a ij =0; Determine the Laplacian matrix based on the undirected graph. , , l ij Represents the Laplace matrix The element in the i-th row and j-th column, where When i≠j, l ij =-a ij ; when a i0 When = 1, it indicates that at least one robot has acquired the position information of the moving target, then the diagonal matrix , .

6. The cooperative control method for multiple robots according to claim 5, characterized in that, When establishing a third mathematical model for the cooperative rotation of a multi-robot system based on the first and second mathematical models, the following are included: When a third mathematical model of the cooperative rotation of a multi-robot system is established, it satisfies the fixed-time position consistency convergence condition, the fixed-time velocity consistency convergence condition, and the fixed-time rotational motion condition.

7. The cooperative control method for multiple robots according to claim 6, characterized in that, When the following conditions are met: fixed-time position uniformity convergence condition, fixed-time velocity uniformity convergence condition, and fixed-time rotational motion condition, the following conditions are included: The condition for fixed-time position consistency convergence is expressed as follows: the multi-robot system meets the requirement of fixed-time T position consistency convergence based on the control input. ； The condition for consistent velocity convergence over a fixed time is expressed as follows: the multi-robot system meets the requirement for consistent velocity convergence over a fixed time T based on the control input. ； The condition for satisfying the fixed-time rotational motion is expressed as follows: the multi-robot system, based on the control input, satisfies the requirement of performing rotational motion around the moving target for a fixed time T. ； in, , Let represent the acceleration of the i-th robot relative to the moving target. , Let S represent the velocity of the i-th robot relative to the moving target, and let S denote the antisymmetric matrix. ω represents the angular velocity of the multi-robot system rotating around the moving target.

8. The cooperative control method for multiple robots according to claim 7, characterized in that, When constructing a distributed fixed-time estimator, the following are included: The distributed fixed-time estimator is determined according to the following formula: ； ； ； ； in, express The derivative with respect to time, This indicates that the i-th robot is interacting with the moving target. The estimated value, c 1、 c 2、 c3 and Denotes the estimator parameters, and >0, c1>0, c2>0, , , ,matrix ,matrix H represents the largest eigenvalue of matrix A. -1 H represents the inverse matrix of matrix H. -T H represents -1 The transpose of A T Describe the transpose of matrix A. Let i represent the auxiliary error variable for the i-th robot. This represents the state auxiliary variable of a distributed fixed-time estimator. This represents the derivative of the state auxiliary variable with respect to time. P(0) = P0 = 0 m×m m represents the moving target Dimensions Represents the auxiliary matrix. Let L denote the derivative of the auxiliary matrix with respect to time. We choose a matrix L such that -A+LE satisfies the Herwitz condition.

9. The cooperative control method for multiple robots according to claim 8, characterized in that, The fixed-time controller is determined according to the following formula: ； ； ； Where, k 1、 k 2、 γ, b1, and b2 are positive constants, α1 and α2 are weighting coefficients, and 0 < α1 < 1, α2 > 1. And i∈{1,2}, R represents the radius of rotation of the robot around the moving target. Indicates a fixed-time controller. This represents the derivative of the velocity auxiliary variable with respect to time. Represents the auxiliary variable of velocity. This is to ensure that the fixed-time controller does not require speed information. Represents a time-varying rotation vector. , Indicates the position consistency parameter. Used to achieve positional consistency for robots.

10. A cooperative control system for multiple robots, used to apply the cooperative control method for multiple robots as described in any one of claims 1-9, characterized in that, include: The model building module is configured to build a first mathematical model of the multi-robot system and a second mathematical model of the moving target, and to construct the communication topology between the multi-robot system and the moving target. The model control module is configured to establish a third mathematical model for the cooperative rotation of the multi-robot system based on the first and second mathematical models. The location determination module is configured to construct a distributed fixed-time estimator, determine the internal state of the moving target based on the distributed fixed-time estimator, and determine the real-time location of the moving target based on the internal state. The collaborative control module is configured to determine the control input of the multi-robot system based on the distributed fixed-time estimator and the fixed-time controller, and substitute the control input into the multi-robot system to complete fixed-time collaborative rotation consistency control.

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