A method and system for cooperative control of multiple robots

Abstract

The application relates to the technical field of multi-robot cooperative control, and discloses a cooperative control method and system for a multi-robot, which comprises the following steps: establishing a first mathematical model of a multi-robot system, establishing a second mathematical model of a moving target, constructing a communication topology 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 an internal state of the moving target based on the distributed fixed-time estimator, determining a real-time position of the moving target based on the internal state, determining a control input of the multi-robot system according to the distributed fixed-time estimator and based on a fixed-time controller, and substituting the control input into the multi-robot system to complete fixed-time cooperative rotation consistency control. The application ensures the reliability and stability of cooperative control of the multi-robot within a fixed time.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of multi-robot cooperative control, in particular to a multi-robot cooperative control method and system. BACKGROUND

[0002] With the rapid development of industries, manufacturing industries and the like, robots have been widely applied. Compared with single robots, multi-robot systems can efficiently complete complex tasks that single robots cannot undertake through distributed information interaction and cooperative control, thereby improving the ability of the industry to cope with large-scale operations. Rotational consistency control is a specific embodiment of multi-robot system cooperative control. However, the existing rotational consistency control can only achieve asymptotic stability or finite time stability of the multi-robot system. In some actual scenarios, the multi-robot system needs to achieve cooperative rotational motion around a moving target within a preset time. For example, in the field of warehouse logistics, when shelves are used as moving targets for dynamic transfer, the multi-robot needs to complete cooperative rotation around the shelves within a preset time to achieve precise docking. If stable cooperation cannot be achieved within the specified time, it will cause delay in loading and unloading of the shelves, thereby challenging the cooperative control of the multi-robot.

[0003] Therefore, it is necessary to design a multi-robot cooperative control method and system to solve the problems existing in the prior art. SUMMARY

[0004] In view of this, the present application provides a multi-robot cooperative control method and system to solve the above problems.

[0005] In one aspect, the present application provides a multi-robot cooperative control method, comprising:

[0006] establishing a first mathematical model of a multi-robot system and a second mathematical model of a moving target, and constructing a communication topology of the multi-robot system and the moving target;

[0007] establishing a third mathematical model of cooperative rotation of the multi-robot system based on the first mathematical model and the second mathematical model;

[0008] constructing a distributed fixed-time estimator, determining an internal state of the moving target based on the distributed fixed-time estimator, and determining a real-time position of the moving target based on the internal state;

[0009] determining a control input of the multi-robot system based on the distributed fixed-time estimator and a fixed-time controller, and substituting the control input into the multi-robot system to complete fixed-time cooperative rotational consistency control.

[0010] Further, in establishing the first mathematical model of the multi-robot system, comprising:

[0011] The first mathematical model of the multi-robot system is determined according to the following formula:

[0012] ;

[0013] ;

[0014] wherein, denotes derivative with respect to time, denotes position input of the i-th robot in two-dimensional space, denotes velocity input of the i-th robot in two-dimensional space, denotes derivative with respect to time, denotes control input of the i-th robot in two-dimensional space, i∈{1,2,···,n}, n represents the number of robots in the multi-robot system.

[0015] Further, in establishing the second mathematical model of the moving target, comprising:

[0016] The second mathematical model of the moving target is determined according to the following formula:

[0017] ;

[0018] ;

[0019] wherein, denotes derivative with respect to time, denotes state vector of the moving target, denotes position information of the moving target, matrix A and E are constant matrices,

[0020] Based on the second mathematical model of the moving target, the velocity and acceleration of the moving target are determined as and respectively, and the constant matrix pair (E, A) of the moving target satisfies the observability condition.

[0021] Further, in constructing the communication topology of the multi-robot system and the moving target, comprising:

[0022] The communication topology of the multi-robot system is determined based on an undirected graph, and the undirected graph is determined according to the following formula:

[0023] G={V,ε};

[0024] Wherein, G represents an undirected graph, V represents a point set, and each point represents a robot, the number of points is the same as the number of robots in the multi-robot system, , ε represents an edge set, and the neighbor node set of the i th robot is N i , , (j, i) ∈ ε represents that the i th robot is used to receive the information of the j th robot.

[0025] Further, when constructing the communication topology of the multi-robot system and the moving target, it further includes:

[0026] Determine the adjacency matrix Q based on the undirected graph, Q = [a ij ], a ij represents the element of the i th row and the j th column in the adjacency matrix Q, when (j, i) ∈ E, then a ij > 0, otherwise a ij = 0;

[0027] Determine the Laplacian matrix based on the undirected graph, l ij represents the element of the i th row and the j th column in the Laplacian matrix , wherein , when i ≠ j, l ij = -a ij ;

[0028] When a i0 = 1, it means that at least one robot obtains the position information of the moving target, and the diagonal matrix , .

[0029] Further, when establishing the third mathematical model of the multi-robot system cooperative rotation based on the first mathematical model and the second mathematical model, it includes:

[0030] When establishing the third mathematical model of the multi-robot system cooperative rotation, it satisfies the fixed-time position consensus convergence condition, the fixed-time velocity consensus convergence condition and the fixed-time rotational motion condition.

[0031] Further, when satisfying the fixed-time position consensus convergence condition, the fixed-time velocity consensus convergence condition and the fixed-time rotational motion condition, it includes:

[0032] Satisfying the fixed-time position consensus convergence condition is expressed as: the multi-robot system based on the control input satisfies the requirement of fixed-time T position consensus convergence;

[0033] ;

[0034] Satisfying the fixed-time velocity consistency convergence condition means that the multi-robot system satisfies the requirement of fixed-time T velocity consistency convergence based on the control input;

[0035] ;

[0036] Satisfying the fixed-time rotational motion condition means that the multi-robot system satisfies the requirement of fixed-time T rotational motion around the moving target based on the control input;

[0037] ;

[0038] wherein, , denotes the acceleration of the i-th robot relative to the moving target, , denotes the velocity of the i-th robot relative to the moving target, S denotes a skew-symmetric matrix, , and ω denotes the angular velocity of the multi-robot system in rotational motion around the moving target.

[0039] Further, in constructing the distributed fixed-time estimator, comprising:

[0040] The distributed fixed-time estimator is determined according to the following formula:

[0041] ;

[0042] ;

[0043] ;

[0044] ;

[0045] wherein, denotes the derivative with respect to time, denotes the estimation value of the i-th robot to , denotes the estimation value of the j-th robot to , 1、 c 2、 c3 and denote estimator parameters, and > 0, c1 > 0, c2 > 0, , , , the matrix , the matrix denotes the maximum eigenvalue of the matrix A, H -1 denotes the inverse matrix of the matrix H, H -T denotes H-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.

[0046] Furthermore, the fixed-time controller is determined according to the following formula:

[0047] ;

[0048] ;

[0049] ;

[0050] 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 speed. This is to ensure that the fixed-time controller does not require speed information. Represents a time-varying rotation vector. , This indicates the position consistency parameter. Used to achieve positional consistency for robots.

[0051] Compared with the prior art, the application has the beneficial effects that: 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, and the multi-robot perception of the moving target is susceptible to measurement errors or untimely information interaction, which leads to cooperative deviation, the internal state of the moving target is determined in real time based on the distributed fixed-time estimator, which provides reliable information support for the cooperative rotation of the multi-robot, the communication topology, the third mathematical model of the cooperative rotation, and the fixed-time controller are combined to ensure that the multi-robot realizes the consistency convergence of the position and the speed within a preset time, ensures the synchronization of the rotation track around the moving target, avoids the failure of the robot task caused by individual deviation, and thus ensures the reliability and stability of the multi-robot completing the cooperative control within a fixed time.

[0052] In another aspect, the application also provides a cooperative control system for a multi-robot, which is used for applying the cooperative control method for the multi-robot.

[0053] The model establishing module is configured to establish a first mathematical model of the multi-robot system and a second mathematical model of the moving target, and construct a communication topology of the multi-robot system and the moving target.

[0054] The model control module is configured to establish a third mathematical model of the cooperative rotation of the multi-robot system based on the first mathematical model and the second mathematical model.

[0055] The position determining 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 position of the moving target based on the internal state.

[0056] The cooperative control module is configured to determine the control input of the multi-robot system according to the distributed fixed-time estimator and based on a fixed-time controller, and substitute the control input into the multi-robot system to complete the fixed-time cooperative rotation consistency control.

[0057] It can be understood that the cooperative control method and system for the multi-robot have the same beneficial effects, which will not be described here. BRIEF DESCRIPTION OF DRAWINGS

[0058] Various other advantages and benefits will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The accompanying drawings are included to provide a description of preferred embodiments, and are not meant to limit the present application. Moreover, the same reference numerals in the attached drawings indicate the same or similar components. In the drawings:

[0059] Figure 1A flow chart of a method for cooperative control of multiple robots is provided in embodiments of the present application.

[0060] Figure 2 A trajectory diagram of cooperative rotation consistency control is provided in embodiments of the present application.

[0061] Figure 3 A diagram of error time response between the estimated state of the moving target and the actual state of the moving target based on a distributed fixed-time estimator and a fixed-time controller is provided in embodiments of the present application.

[0062] Figure 4 A diagram of robot relative position signal time response is provided in embodiments of the present application.

[0063] Figure 5 A diagram of robot relative velocity signal time response is provided in embodiments of the present application.

[0064] Figure 6 A diagram of error time response between the robot velocity and the moving target velocity is provided in embodiments of the present application.

[0065] Figure 7 A diagram of error time response between the robot acceleration and the moving target acceleration is provided in embodiments of the present application.

[0066] Figure 8 A functional block diagram of a cooperative control system for multiple robots is provided in embodiments of the present application. DETAILED DESCRIPTION

[0067] Exemplary embodiments of the present disclosure will be described below in greater detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it is to be understood that the present disclosure can be embodied in various forms without being limited by the embodiments set forth herein. Rather, these embodiments are provided so that the present disclosure can be thoroughly and completely understood, and so that the scope of the present disclosure can be accurately conveyed to those skilled in the art. It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict. The present application will be described in detail below with reference to the accompanying drawings and in conjunction with the embodiments.

[0068] In some embodiments of the present application, referring to Figure 1 A method for cooperative control of multiple robots is provided, comprising:

[0069] S100: Establish a first mathematical model of a multiple robot system, and establish a second mathematical model of a moving target, and construct a communication topology of the multiple robot system and the moving target.

[0070] S200: establishing a third mathematical model of the cooperative rotation of the multi-robot system based on the first mathematical model and the second mathematical model.

[0071] S300: 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;

[0072] S400: determining the control input of the multi-robot system according to the distributed fixed-time estimator and based on the fixed-time controller, and substituting the control input into the multi-robot system to complete the fixed-time cooperative rotation consistency control.

[0073] In some embodiments of the present application, when the first mathematical model of the multi-robot system is established, it includes:

[0074] The first mathematical model of the multi-robot system is determined according to the following formula:

[0075] ;

[0076] ;

[0077] wherein, denotes the derivative with respect to time, denotes the position input of the i-th robot in a two-dimensional space, denotes the velocity input of the i-th robot in a two-dimensional space, denotes the derivative with respect to time, denotes the control input of the i-th robot in a two-dimensional space, i∈{1,2,···,n}, n represents the number of robots in the multi-robot system.

[0078] In some embodiments of the present application, when the second mathematical model of the moving target is established, it includes: the second mathematical model of the moving target is determined according to the following formula:

[0079] ;

[0080] ;

[0081] wherein, denotes the derivative with respect to time, denotes the state vector of the moving target, denotes the position information of the moving target, and the matrices A and E are constant matrices,

[0082] the velocity and acceleration of the moving target are determined based on the second mathematical model of the moving target as and The constant matrix pair (E, A) of the moving target satisfies an observability condition.

[0083] In some embodiments of the present application, when constructing a communication topology of a multi-robot system and a moving target, the communication topology of the multi-robot system is determined based on an undirected graph, and the undirected graph is determined according to the following formula:

[0084] G = {V, ε};

[0085] wherein G represents the undirected graph, V represents a point set, and each point represents a robot, the number of points is the same as the number of robots in the multi-robot system, ε represents an edge set, and the neighbor node set of the i th robot is N i , (j, i) ∈ ε represents that the i th robot is used to receive information of the j th robot.

[0086] In some embodiments of the present application, when constructing a communication topology of a multi-robot system and a moving target, the communication topology of the multi-robot system is determined based on an undirected graph, and the undirected graph is determined according to the following formula: ij ], a ij represents an element in the i th row and the j th column of the adjacency matrix Q, when (j, i) ∈ E, then a ij > 0, otherwise a ij = 0;

[0087] determine a Laplacian matrix based on the undirected graph, l ij represents an element in the i th row and the j th column of the Laplacian matrix , wherein when i ≠ j, l ij = -a ij ;

[0088] when a i0 = 1, it means that at least one robot obtains the position information of the moving target, then the diagonal matrix , .

[0089] In some embodiments of the present application, when a third mathematical model of the cooperative rotation of the multi-robot system is established based on the first mathematical model and the second mathematical model, the third mathematical model of the cooperative rotation of the multi-robot system is established, then the fixed-time position consistency convergence condition, the fixed-time velocity consistency convergence condition and the fixed-time rotation motion condition are satisfied.

[0090] In some embodiments of the present application, the fixed-time position consistency convergence condition, the fixed-time velocity consistency convergence condition and the fixed-time rotational motion condition are satisfied, including: the fixed-time position consistency convergence condition is satisfied, which means that the multi-robot system satisfies the requirement of fixed-time T position consistency convergence based on the control input;

[0091] ;

[0092] The fixed-time velocity consistency convergence condition is satisfied, which means that the multi-robot system satisfies the requirement of fixed-time T velocity consistency convergence based on the control input;

[0093] ;

[0094] The fixed-time rotational motion condition is satisfied, which means that the multi-robot system satisfies the requirement of fixed-time T rotational motion around the moving target based on the control input;

[0095] ;

[0096] wherein, , represents the acceleration of the i-th robot relative to the moving target, , represents the velocity of the i-th robot relative to the moving target, and S represents a skew-symmetric matrix, , and ω represents the angular velocity of the multi-robot system in rotational motion around the moving target.

[0097] In some embodiments of the present application, when constructing the distributed fixed-time estimator, the distributed fixed-time estimator determines according to the following formula:

[0098] ;

[0099] ;

[0100] ;

[0101] ;

[0102] wherein, represents the derivative with respect to time, represents the estimated value of the i-th robot to , represents the estimated value of the j-th robot to , 1、 2、 c3 and represents an estimator parameter, and​ > 0, c1 > 0, c2 > 0, , , , matrix , matrix denotes the maximum eigenvalue of matrix A, H -1 denotes the inverse matrix of matrix H, H -T denotes the transpose matrix of H -1 , A T denotes the transpose matrix of matrix A, denotes the error auxiliary variable of the ith robot, denotes the state auxiliary variable of the distributed fixed-time estimator, denotes the derivative of the state auxiliary variable with respect to time, , P(0) = P0= 0 m×m , m denotes the dimension of the moving target , denotes the auxiliary matrix, denotes the derivative of the auxiliary matrix with respect to time, the matrix L is selected such that -A + LE satisfies the Hurwitz condition.

[0103] In some embodiments of the present application, the fixed-time controller is determined according to the following formula:

[0104] ;

[0105] ;

[0106] ;

[0107] wherein k 1、 k 2、 γ, b1 and b2 are normal numbers, α1 and α2 are weight coefficients, and 0 < α1 < 1, α2 > 1, , and i ∈ {1, 2}, R represents the radius of rotation of the robot rotating around the moving target, denotes the fixed-time controller, denotes the derivative of the velocity auxiliary variable with respect to time, denotes the velocity auxiliary variable, for ensuring that the fixed-time controller does not require velocity information, denotes the time-varying rotation vector, , denotes the position consistency term parameter, for realizing the position consistency of the robot.

[0108] Specifically, the multi-robot system takes four robots as an example, and is verified according to simulation, and the initialization of all parameters and parameter matrices is shown in Table 1:

[0109]

[0110] 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 the cooperative rotational consistency control in a fixed time (set time). Figure 3 represents the error between the state information of the moving target estimated by each robot and the actual state, which has a large error at the initial time and gradually tends to 0, ensuring the accuracy and reliability of the construction of the distributed fixed-time estimator, Figure 4 represents the robot relative position signal, which also has a large error at the initial time and gradually tends to 0, Figure 5 represents the robot relative speed signal, which also has a large error and gradually tends to 0, Figure 6 represents the error between the position of the robot and the position of the moving target, which gradually tends to the rotational radius R = 2, Figure 7 represents the acceleration of each robot relative to the moving target and the speed of each robot relative to the moving target satisfies , indicating that the robot rotates around the moving target, and the existing technology can only achieve asymptotic stability (no explicit convergence time) or finite time stability (the convergence time is prolonged with the increase of the initial error). Through 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, the precision and reliability of cooperative control are improved. The communication topology between the multi-robot system and the moving target determines the positions, speeds, estimated values of the moving target, etc. that can be interacted between the robots through the edge set and the adjacency matrix, providing a basis for the state synchronization of the multi-robot. The internal state is a variable that completely describes the motion characteristics of the moving target, and the internal state is represented by a state vector.

[0111] In summary, the application has the beneficial effects that: by constructing the distributed fixed-time estimator and the fixed-time controller, the multi-robot system is ensured to complete the cooperative rotation consistency control within the preset time, and the multi-robot perception of the moving target is susceptible to measurement errors or information interaction delays, which leads to cooperative deviation, the internal state of the moving target is determined in real time based on the distributed fixed-time estimator, which provides reliable information support for the cooperative rotation of the multi-robot, the communication topology, the third mathematical model of the cooperative rotation, and the fixed-time controller are combined to ensure that the multi-robot realizes the consistency convergence of the position and the speed within the preset time, ensures the synchronization of the rotation track around the moving target, avoids the failure of the robot task caused by individual deviation, and thus ensures the reliability and stability of the multi-robot completing the cooperative control within the fixed time.

[0112] In another preferred mode based on the above embodiment, referring to Figure 8 The embodiment provides a cooperative control system for multi-robots for applying the above cooperative control method for multi-robots, which comprises:

[0113] The model establishing module is configured to establish a first mathematical model of the multi-robot system and a second mathematical model of the moving target, and to construct a communication topology of the multi-robot system and the moving target.

[0114] The model control module is configured to establish a third mathematical model of the cooperative rotation of the multi-robot system based on the first mathematical model and the second mathematical model.

[0115] The position determining module is configured to construct a distributed fixed-time estimator, to determine the internal state of the moving target based on the distributed fixed-time estimator, and to determine the real-time position of the moving target based on the internal state.

[0116] The cooperative control module is configured to determine the control input of the multi-robot system according to the distributed fixed-time estimator and based on the fixed-time controller, and to substitute the control input into the multi-robot system to complete the fixed-time cooperative rotation consistency control.

[0117] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system or a computer program product. Therefore, the present application can be in the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can be in the form of a computer program product implemented 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.

[0118] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart or flowsheet block or blocks. Figure 1 one or more flowcharts and / or blocks Figure 1 one or more flowcharts and / or blocks

[0119] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart or flowsheet block or blocks. Figure 1 one or more flowcharts and / or blocks Figure 1 one or more flowcharts and / or blocks

[0120] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart or flowsheet block or blocks. Figure 1 one or more flowcharts and / or blocks Figure 1 one or more flowcharts and / or blocks

[0121] Finally, it should be noted that the above-mentioned embodiments are merely intended for describing the technical solutions of the present application, but not for limiting it. Although the present application is described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions of the present application can be modified or equivalent replaced without departing from the spirit and scope of the present application, and any modification or equivalent replacement should be covered in the protection scope of the claims of the present application.

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. 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; 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, The state vector representing 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; 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, Indicates the i-th robot pair The estimated value, Indicates the j-th robot pair 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 represent the derivative of the auxiliary matrix with respect to time, and choose a matrix L such that -A+LE satisfies the Herwitz condition; 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 speed. This is to ensure that the fixed-time controller does not require speed information. Represents a time-varying rotation vector. , This indicates the position consistency parameter. Used to achieve positional consistency for robots.

2. The cooperative control method for multiple robots according to claim 1, 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.

3. The cooperative control method for multiple robots according to claim 2, 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 , .

4. The cooperative control method for multiple robots according to claim 3, 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.

5. The cooperative control method for multiple robots according to claim 4, 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.

6. A cooperative control system for multiple robots, used to apply the cooperative control method for multiple robots as described in any one of claims 1-5, 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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