Robot formation control method and system based on distributed observer and medium

Abstract

The application provides a robot formation control method and system based on a distributed observer, and a medium, relates to the field of artificial intelligence, and the method comprises the following steps: establishing a mobile robot mathematical model system; the robots in the mobile robot mathematical model system comprise a leader and a follower; obtaining three-dimensional state information of the leader; designing a time-varying distributed observer by introducing a time-varying gain; estimating the information of the leader within a specified finite time T through the time-varying distributed observer combined with the three-dimensional state information, and determining the observed state of the leader; designing a local controller; through the local controller, the observed state of the leader is combined to control the follower to monitor and track the state of the leader in real time, and the formation control target is completed. Through the introduction of the time-varying distributed observer and the flexible design of the local controller, the adaptability of the system in the dynamic and nonlinear environment is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of artificial intelligence, and particularly relates to a robot formation control method and system based on a distributed observer and a medium. BACKGROUND

[0002] The centralized time-varying distributed observer method relies on a central processing unit to collect and process information of all robots, providing overall state estimation and control decisions. Although the centralized method can provide higher accuracy, it has a huge communication load, which can easily cause a bandwidth bottleneck. In addition, single-point failure of the central processing unit can cause the entire system to fail, and as the number of robots increases, the computational complexity also increases significantly. Compared with the centralized method, the distributed time-varying distributed observer allows each robot to autonomously process partial information, thereby reducing communication load and improving system robustness. Each robot uses local information and limited communication to share data with other robots to cooperatively complete state estimation and control tasks. However, traditional distributed time-varying distributed observer design often assumes that the system state is static or linear, limiting its application effect in dynamic and nonlinear environments.

[0003] Unlike the centralized method, the distributed time-varying distributed observer allows each robot to autonomously process partial information, thereby reducing communication load and improving system robustness. Each robot uses local information and limited communication to share data with other robots to cooperatively complete state estimation and control tasks. However, traditional distributed time-varying distributed observer design often assumes that the system state is static or linear, limiting its application effect in dynamic and nonlinear environments.

[0004] However, in actual operation, the traditional distributed time-varying distributed observer usually assumes that the system state is static or linear, and cannot effectively deal with dynamic and nonlinear systems.

[0005] In practical applications, robots need to complete tasks within a limited time, which requires the time-varying distributed observer to provide accurate state estimation within a limited time. However, existing distributed time-varying distributed observer designs have many shortcomings in dealing with time-varying systems and limited-time state estimation. The defects of the prior art are as follows:

[0006] 1) Static or linear assumption: Most existing distributed time-varying distributed observer designs are based on the assumption of static or linear systems, while in actual applications, robot formation often needs to deal with dynamic and nonlinear environments. These assumptions limit the application effect of the time-varying distributed observer in complex environments and cannot meet actual needs.

[0007] 2) Communication load and computational complexity: Although the centralized time-varying distributed observer can provide higher-precision state estimation, it has very high communication load and computational complexity, especially in the case of a large number of robots, which can easily lead to system performance degradation and single-point failure risk.

[0008] 3) Finite-time state estimation: In practical applications, robot formation tasks often have time constraints, requiring time-varying distributed observers to provide accurate state estimation within a finite time. However, existing designs of time-varying distributed observers lack guarantees on the accuracy of state estimation within a finite time, failing to meet the time requirements of the task.

[0009] 4) Tracking of nonlinear reference signals: Existing methods often require linearization of the reference signal, which may lead to reduced accuracy and additional computational burden in practical operations. Furthermore, linearization limits the flexibility of the system in handling complex and nonlinear reference signals. SUMMARY

[0010] The present application aims to solve the problems of existing distributed time-varying distributed observer design methods, such as static or linear assumptions, high communication load and computational complexity, insufficient finite-time state estimation, and provide a robot formation control method, system and medium based on distributed observer.

[0011] The above objectives of the present application are achieved by the following technical solutions:

[0012] S1: Establish a mobile robot mathematical model system; the robots in the mobile robot mathematical model system include: a leader and a follower;

[0013] S2: Obtain the three-dimensional state information of the leader, including: position information, direction information;

[0014] S3: Design a time-varying distributed observer by introducing time-varying gain;

[0015] S4: Estimate the leader's information within a specified finite time T through the time-varying distributed observer combined with the three-dimensional state information, and determine the observed state of the leader;

[0016] S5: Design a local controller;

[0017] S6: Control the follower to monitor and track the state of the leader in real time through the local controller combined with the observed state of the leader, and complete the formation control goal.

[0018] Optionally, step S1 includes:

[0019] The mobile robot mathematical model system is as follows:

[0020]

[0021]

[0022] Let where and denote linear and angular velocities, respectively; ; and denote the position information; denote the orientation information; , and denote the rotational speeds of the left and right wheels, respectively; is the control torque; matrix , and are defined as follows: , , where , , , and are predefined constants, denotes the mass of the robot; denotes the Coriolis force; denotes the damping coefficient of the system; is a positive definite matrix;

[0023] Furthermore, , and satisfy:

[0024]

[0025]

[0026] where is the wheel radius of the th robot individual; is half the width of the th robot individual;

[0027] Use a directed graph to represent the communication in the multi-robot formation, let denote the followers;

[0028] Let the edge set represent the communication between each pair of robots; if , then denotes that the th follower receives data from the th follower;

[0029] Define the matrix if , then if , then ;

[0030] define the Laplacian matrix where , , denotes the neighbors of the i-th robot, i.e. ; ; for constructing a diagonal matrix;

[0031] define if the i-th robot is connected to the leader, then , otherwise , ;

[0032] define a topological graph consisting of the directed graph , the node 0 and the directed edges from the leader 0 to ;

[0033] assume that is contained in a leadered spanning tree.

[0034] Optionally, step S3 comprises:

[0035] S31: design the leader information as follows:

[0036]

[0037]

[0038] let be the desired trajectory of the i-th robot; denotes the desired velocity of the i-th robot; set to , or , and denotes the position information of the robot, denotes the direction information; denotes the input of the observer; S32: design a time-varying distributed observer for each robot to estimate the leader information in a specified finite time , the time-varying distributed observer is as follows:

[0039]

[0040]

[0041] ​​

[0042] wherein, and are states of the time-varying distributed observer; and are all pre-set parameters; is a time-varying gain for estimating the leader's information within a specified finite time represents the power of the time-varying gain for adjusting the strength of the control gain; and are the rate of change of the time-varying distributed observer states.

[0043] Optionally, based on the time-varying distributed observer, the following results are obtained:

[0044] Theorem 1: For the mobile robot mathematical model system, the time-varying distributed observer estimates the leader's information within a specified finite time , that is, for any , there are and , and and are bounded on represents the power of the time-varying gain; represents the leader position information, represents the leader speed information; represents the specified finite time;

[0045] Proof: For the time interval , the following analysis is performed, and the estimation error is defined as:

[0046]

[0047]

[0048] wherein, represents the th robot expected trajectory estimation error, represents the th robot expected speed estimation error;

[0049] wherein , it is obtained that:

[0050]

[0051]

[0052] wherein, the ​​The rate of change of the robot's expected trajectory estimation error Indicates the first The estimation error of the robot's expected trajectory. Indicates the first The rate of change of the robot's expected velocity Indicates the first The estimation error of the robot's expected speed;

[0053] Robot To write it in a compact form, namely:

[0054]

[0055]

[0056]

[0057] in, express The matrix formed by the estimation errors of the desired trajectory of each robot. Indicates the first The estimation error of the robot's expected trajectory. express The matrix formed by the estimation errors of the expected speed of each robot. Indicates the first The estimation error of the robot's expected speed. express The matrix formed by the inputs of the robot observers, Indicates the first The observer input of the robot;

[0058] Lemma 1: For a directed graph, there exists a positive definite matrix. , making ,in , , Indicates the first The information is connected between the robot and the leader; if connected, then... Otherwise ;

[0059] According to Lemma 1, we get

[0060]

[0061]

[0062] Prove in sequence and It converges to the origin within a specified finite time.

[0063] Introduce a Lyapunov function as follows:

[0064]

[0065] where is a positive definite matrix defined according to Lemma 1, which satisfies and satisfies

[0066] , denotes the minimum and maximum eigenvalues of an arbitrary square matrix; denotes the introduced Lyapunov function;

[0067] Lemma 2: For , given an arbitrary position number :

[0068]

[0069] where ; denotes the space composed of all dimensional real number vectors, and is a vector in , denotes a real number greater than 1, is the conjugate index of , defined as ;

[0070] According to Lemma 2, the derivative of is written as:

[0071]

[0072] According to Lemma 1, where is a positive definite matrix, , is a normal number;

[0073] Lemma 3: Assuming the time interval , then:

[0074]

[0075] where is a continuous function defined on , , is a constant, and the function is a positive function, i.e. ;

[0076] Lemma 4: Assume that in the time interval , then

[0077]

[0078] where , is a continuous non-negative function, is a positive constant;

[0079] According to Lemma 4, it is proved that will tend to zero in a specified time , set , , , it is proved that is non-negative and bounded;

[0080] In Lemma 4, set , that is is bounded, and is bounded, which shows that and will become zero in a specified finite time;

[0081] Take Lyapunov function:

[0082]

[0083] Derivate , as follows:

[0084]

[0085] where , are positive constants;

[0086] According to Lemma 4, it is proved that converges to the origin in a given finite time , set , , , since the boundedness of , is also bounded, thus , is bounded.

[0087] A robot formation control system based on a distributed observer includes a preset number of intelligent agents, a wireless communication module and a server;

[0088] Intelligent agents and servers, and intelligent agents and intelligent agents, communicate through the wireless communication module to achieve data transmission and remote control;

[0089] The server is used for centralized management and coordination of operations of multiple agents.

[0090] Optionally, the agent comprises a processor, a memory, a sensor module, a drive module and a power module; the memory, the sensor module, the drive module and the power module are connected to the processor.

[0091] Real-time data and control signals are transmitted through the internal bus special connection interface of the agent.

[0092] Optionally, the wireless communication module comprises a Wi-Fi sub-module and a 5G sub-module.

[0093] A computer-readable storage medium stores instructions that, when executed, perform a robot formation control method based on a distributed observer.

[0094] The technical solution provided by the present application has the following beneficial effects:

[0095] 1. A time-varying distributed observer is designed to accurately estimate the leader information within a given limited time. By introducing time-varying gains, it is proved that the estimation error is bounded, thereby ensuring the effectiveness of the time-varying distributed observer in dynamic environments.

[0096] A local controller is designed to track the state of each robot, achieve the group control goal, and does not rely on linearization processing of the reference signal, thereby improving the flexibility of the system in processing complex and nonlinear reference signals.

[0097] 2. In designing the control strategy, various system control requirements are considered to ensure that the system always meets the constraint conditions during the entire control process, and a suitable Lyapunov function is designed to ensure the stability and performance of the system. By introducing the time-varying distributed observer and flexible local controller design, the present application not only overcomes the defects of the prior art, such as static or linear assumptions, high communication load and computational complexity, insufficient limited time state estimation, etc., but also improves the adaptability of the system in dynamic and nonlinear environments, meets the complex demands in practical applications, and ensures the efficient execution of mobile robot formation in complex tasks. BRIEF DESCRIPTION OF DRAWINGS

[0098] The present application will be further described below in conjunction with the drawings and examples, wherein:

[0099] Figure 1 is a step diagram of the robot formation control method based on a distributed observer in the embodiments of the present application;

[0100] Figure 2is a communication topology diagram of a robot formation control method based on a distributed observer in embodiments of the present application;

[0101] Figure 3 is a trajectory tracking diagram at a specified time of a robot formation control method based on a distributed observer in embodiments of the present application;

[0102] Figure 4 is an angle tracking diagram at a specified time of a robot formation control method based on a distributed observer in embodiments of the present application;

[0103] Figure 5 is a module connection diagram of a robot formation control system based on a distributed observer in embodiments of the present application. DETAILED DESCRIPTION

[0104] In order to have a clearer understanding of the technical features, objectives and effects of the present application, the specific embodiments of the present application will be described in detail with reference to the accompanying drawings.

[0105] Embodiments of the present application provide a robot formation control method based on a distributed observer.

[0106] Please refer to Figure 1 , Figure 1 is a step diagram of a robot formation control method based on a distributed observer in embodiments of the present application, comprising:

[0107] S1: Establish a mobile robot mathematical model system; the robots in the mobile robot mathematical model system include: a leader and a follower;

[0108] Step S1 includes:

[0109] The mobile robot mathematical model system is as follows:

[0110]

[0111]

[0112] Let , wherein and represent linear velocity and angular velocity, respectively; ; and represent the position information; represent direction information; , and represent the rotational speeds of the left and right wheels, respectively; is a control torque; the matrix , and are defined as follows: , , where , , , and are predefined constants, denotes the mass of the robot; denotes the Coriolis force; denotes the damping coefficient of the system; is a positive definite matrix;

[0113] Furthermore, , and satisfy:

[0114]

[0115]

[0116] where is the wheel radius of the th robot individual; is half the width of the th robot individual;

[0117] The directed graph is used to represent the communication in the multi-robot formation, where denotes the followers;

[0118] The edge set represents the communication between each pair of robots; if , then denotes that the th follower receives data from the th follower;

[0119] The matrix is defined as if , and if ;

[0120] The Laplacian matrix is defined as , , denotes the th robot's neighbors, i.e. ; is used to construct a diagonal matrix;

[0121] The matrix is defined as if the th robot is connected to the leader, and , else , let ;

[0122] define a topological graph consisting of a directed graph , node 0 and directed edges from leader 0 to ;

[0123] assume is contained in a leadered spanning tree.

[0124] S2: obtaining three-dimensional state information of the leader, the three-dimensional state information comprising: position information, direction information;

[0125] S3: designing a time-varying distributed observer by introducing a time-varying gain;

[0126] Step S3 comprises:

[0127] S31: designing the leader information as follows:

[0128]

[0129]

[0130] Let be the desired trajectory of the th robot; denote the desired velocity of the th robot; is set to , or , and denote the position information of the robot, denote the direction information; denote the input of the observer;

[0131] S32: designing a time-varying distributed observer for each robot to estimate the information of the leader in the specified finite time , the time-varying distributed observer being as follows:

[0132]

[0133]

[0134] wherein, and are the states of the time-varying distributed observer; and are both preset parameters; is a time-varying gain used to estimate the leader's information within a specified finite time represents a time-varying gain power used to adjust the strength of the control gain and is the time-varying rate of change of the distributed observer state

[0135] Based on the time-varying distributed observer, the following results are obtained:

[0136] Theorem 1: For the mobile robot mathematical model system, the time-varying distributed observer estimates the leader's information within a specified finite time , i.e., for any , there exist and such that and are bounded on represents a time-varying gain power represents the leader's position information represents the leader's velocity information represents the specified finite time

[0137] Proof: For the time interval , the following analysis is performed, and the estimation error is defined as

[0138]

[0139]

[0140] where represents the desired trajectory estimation error of the th robot represents the desired velocity estimation error of the th robot

[0141] where , we obtain

[0142]

[0143]

[0144] where represents the rate of change of the desired trajectory estimation error of the th robot represents the desired trajectory estimation error of the th robot represents the rate of change of the desired velocity of the th robot​​ an estimate error of the desired trajectory of the i-th robot, an estimate error of the desired velocity of the i-th robot,

[0145] the robot , written in a compact form as

[0146]

[0147]

[0148]

[0149] wherein is a matrix composed of estimate errors of the desired trajectory of the i-th robot, is an estimate error of the desired trajectory of the i-th robot, is a matrix composed of estimate errors of the desired velocity of the i-th robot, is an estimate error of the desired velocity of the i-th robot, is a matrix composed of estimate errors of the desired trajectory of the i-th robot, is an estimate error of the desired trajectory of the i-th robot, is a matrix composed of estimate errors of the desired velocity of the i-th robot, is an estimate error of the desired velocity of the i-th robot, is a matrix composed of estimate errors of the desired trajectory of the i-th robot, is an estimate error of the desired trajectory of the i-th robot, is a matrix composed of estimate errors of the desired velocity of the i-th robot, is an estimate error of the desired velocity of the i-th robot,

[0150] Lemma 1: For a directed graph, there exists a positive definite matrix such that wherein , , is the information of the i-th robot connected to the leader, if connected, then , otherwise ;

[0151] According to Lemma 1, it is obtained that

[0152]

[0153]

[0154] and converge to the origin within a specified finite time; A Lyapunov function is introduced as follows:

[0155]

[0156]

[0157] wherein ​​is a positive definite matrix defined according to Lemma 1, which satisfies , and satisfies

[0158] , denotes the minimum and maximum eigenvalues of an arbitrary square matrix; denotes the introduced Lyapunov function;

[0159] Lemma 2: For , given an arbitrary position number :

[0160]

[0161] where ; denotes the space composed of all -dimensional real number vectors, and is a vector in , denotes a real number greater than 1, is the conjugate index of , defined as ;

[0162] According to Lemma 2, the derivative of is written as:

[0163]

[0164] According to Lemma 1, where is a positive definite matrix, , is a normal number;

[0165] Lemma 3: Assuming the time interval , then:

[0166]

[0167] where is a continuous function defined on , , is a constant, and the function is a positive function, i.e. ;

[0168] Lemma 4: Assuming in the time interval , then:

[0169]

[0170] where , It is a continuous nonnegative function. It is a positive number;

[0171] According to Lemma 4, prove At the specified time The interior tends to zero, let it be. , , ,prove Negatively bounded;

[0172] In Lemma 4, let... That is, It is bounded, it has... It is bounded, indicating and It will become zero within a specified limited time.

[0173] Take the Lyapunov function:

[0174]

[0175] right Differentiate as follows:

[0176]

[0177] in , All are positive numbers;

[0178] By using Lemma 4, we can prove... In a given finite time It converges inward to the origin; let , , ,because Boundedness, It is also bounded, therefore it has , It is bounded.

[0179] S4: By using a time-varying distributed observer and combining it with three-dimensional state information, estimate the leader's information within a specified finite time T and determine the leader's observation state.

[0180] S5: Design a local controller;

[0181] S6: Through the local controller, combined with the leader's observed state, the followers are controlled to monitor and track the leader's state in real time, thus achieving the formation control objective.

[0182] refer to Figure 5 , Figure 5It is a module connection diagram of a robot formation control system based on a distributed observer, comprising a preset number of intelligent agents, a wireless communication module and a server;

[0183] The intelligent agents and the server, and the intelligent agents and the intelligent agents, communicate through the wireless communication module to realize data transmission and remote control.

[0184] The server is used for centralized management and coordination of the operation of multiple intelligent agents.

[0185] The intelligent agents all comprise a processor, a memory, a sensor module, a drive module and a power module; the memory, the sensor module, the drive module and the power module are all connected to the processor.

[0186] The transmission of real-time data and control signals is realized through the internal bus special connection interface of the intelligent agent.

[0187] The wireless communication module comprises a Wi-Fi submodule and a 5G submodule.

[0188] In order to verify the effectiveness of the designed observer, four robots are selected for the simulation example, and the communication topology is as shown in Figure 2 .

[0189] The reference trajectory is as follows:

[0190]

[0191] Let , , , , , , the reference trajectory is written as:

[0192]

[0193] The parameters of the designed robot are cm, mm, the design s, and the results are as shown in Figure 2 and Figure 3 .

[0194] It can be found that the four robots all track to the target trajectory within the specified time, and track to the target angle within the specified time, and the simulation example verifies that the time-varying distributed observer of the design scheme has good position and angle tracking performance.

[0195] The research of the present application is based on three-dimensional system state, and the position information and direction information in the leader information are observed and tracked respectively. The leader information is estimated within a given limited time, and it is proved that the estimation error is bounded when multiplied by some time-varying gain. A local controller is designed to track the state of each robot to achieve the group control goal, and the requirement that the reference signal must be linearized can be eliminated.

[0196] The above merely is exemplary embodiments of the present disclosure, and cannot limit the scope of the present disclosure. That is, any equivalent changes and modifications made according to the teachings of the present disclosure are still within the scope of the present disclosure. Other embodiments of the present disclosure will be readily apparent to those skilled in the art upon considering the specification and practice of the present disclosure.

[0197] The present application is intended to cover any variations, uses, or adaptive changes of the present disclosure that follow the general principles of the present disclosure and include common knowledge or conventional technical means in the technical field not recorded in the present disclosure. The specification and examples are only considered as exemplary, and the scope and spirit of the present disclosure are defined by the claims.

Claims

1. A robot formation control method based on distributed observers, characterized in that, The method includes the following steps: S1: Establish a mathematical model system for mobile robots; the robots in the mathematical model system include: leaders and followers; S2: Obtain the leader's three-dimensional state information, which includes: position information and direction information; S3: Design a time-varying distributed observer by introducing a time-varying gain; Step S3 includes: S31: Design the following leader information: Let q i,1,* Let q be the desired trajectory of the i-th robot; i,2,* Represents the desired velocity of the i-th robot; * is set to x, y, or ψ, where x and y represent the robot's position information, and ψ represents its orientation information; u i,* (t) represents the input to the observer; S32: Design a time-varying distributed observer for each robot to estimate information about the leader over a specified finite time T. The time-varying distributed observer is shown below: in, and It represents the state of the time-varying distributed observer; r>0 and β1∈(1,+∞) are all pre-set parameters; It is a time-varying gain used to estimate leader information over a specified finite time T; β1 represents the time-varying gain raised to the power of β1, used to adjust the strength of the control gain; and It is the rate of change of the state of the time-varying distributed observer; S4: By using a time-varying distributed observer and combining it with three-dimensional state information, estimate the leader's information within a specified finite time T and determine the leader's observation state. S5: Design a local controller; S6: Through the local controller, combined with the leader's observed state, the followers are controlled to monitor and track the leader's state in real time, thus achieving the formation control objective.

2. The robot formation control method based on a distributed observer as described in claim 1, characterized in that, Step S1 includes: The mathematical model system for the mobile robot is as follows: Let i = 1, ..., N, where υ i and ω i These represent linear velocity and angular velocity, respectively. and This indicates the location information; Indicates direction information; Ω i =[Ω i,1 Ω i,2 ] T Ω i,1 and Ω i,2 These represent the rotational speeds of the left and right wheels, respectively; τ i It controls the torque; the matrices M, C, and D are defined as follows: Where m1, m2, c, d1, and d2 are predefined constants, m1 and m2 represent the mass of the robot; c represents the Coriolis force; d1 and d2 represent the damping coefficients of the system; and M is a positive definite matrix. In addition, υ i ω i and Ω i satisfy: Where r i b is the radius of the wheel of the i-th robot individual; i It is half the width of the i-th robot individual; Use a directed graph G to represent communication in a multi-robot formation, and let V = {1,2,…,N} represent N followers; Let edge set ε represent the communication between each robot pair; if (i,j)∈ε, it means that the j-th follower receives data from the i-th follower; Define matrix If (i,j)∈ε, then a ij =1, if ε then a ij =0; Define the Laplacian matrix L = D1 - A, where D1 = diag(υ1,υ2,...,υ) N ), N i N represents the neighbors of the i-th robot. i ={j|j∈V|(j,i)∈ε}; diag is used to construct a diagonal matrix; Define a i0 (i∈V), if the i-th robot is connected to the leader, then a i0 =1, otherwise a i0 =0, let a 0i =0; Define a topology graph It consists of a directed graph G, node 0, and directed edges from leader 0 to G; Assumption It is contained in a spanning tree with a leader.

3. The robot formation control method based on a distributed observer as described in claim 1, characterized in that, Based on the time-varying distributed observer, the following results are obtained: Theorem 1: For the mathematical model system of the mobile robot, the time-varying distributed observer estimates the leader's information within a specified finite time T, i.e., for any i∈{1,2,…,N}, we have and and and It is bounded in [0,T); x represents the 2β1 power of the time-varying gain; r Indicates the leader's location information. This indicates the leader's speed information; T indicates a specified finite time. Proof: Analyze the time interval [0, T] as follows, and define the estimation error: in, This represents the error in estimating the expected trajectory of the i-th robot. This indicates the estimation error of the expected speed of the i-th robot; Where i = 1, 2, ..., N, we get: in, The rate of change of the error in the expected trajectory estimation of the i-th robot This represents the estimation error of the j-th robot's desired trajectory. This represents the rate of change of the expected speed of the i-th robot. This represents the estimation error of the expected speed of the j-th robot; The robots i = 1, 2, ..., N can be written in a compact form, namely: Where χ1 represents the matrix formed by the estimation errors of the N robot expected trajectories. χ² represents the estimation error of the desired trajectory of the Nth robot, and χ² represents the matrix formed by the estimation errors of the desired velocities of the N robots. This represents the estimation error of the expected speed of the Nth robot. Let u represent the matrix formed by the inputs from N robot observers. N,* This represents the observer input for the Nth robot; Lemma 1: For a directed graph, there exists a positive definite matrix P such that PH + H T P<0, where H=L+B, B=diag(a) 10 ,a 20 ,...,a N0 ), a N0 This indicates the information that the Nth robot is connected to the leader; if they are connected, then a... N0 =1, otherwise a N0 =0; According to Lemma 1, we get Prove that χ2 and χ1 converge to the origin in a specified finite time interval; Introducing the Lyapunov function, as follows: Where P is a positive definite matrix defined according to Lemma 1, which satisfies PH+H T P>0, and simultaneously satisfying λ min (·),λ max (·) represents the minimum and maximum eigenvalues ​​of any square matrix; This indicates the introduced Lyapunov function; Lemma 2: For Given an arbitrary position number δ: in p>1; R n Let R represent the space consisting of all n-dimensional real vectors, where x and y are in the form of vectors. n In the vector, p represents a real number greater than 1, and q is the conjugate exponent of p, defined as... According to Lemma 2, The derivative is written as: According to Lemma 1, where It is a positive definite matrix. c1 is a positive constant; Lemma 3: Assume a time interval Then we have: Where V(t), η(t), a(t): It is a continuous function defined on [0,+∞). It is a constant, and the function a(t) is a positive function, that is, a(t)>0; Lemma 4: Assume that within the time interval Then we have: in η(t), b(t): It is a continuous non-negative function, and a,β∈(1,+∞) are positive constants; According to Lemma 4, it is proven that χ² will tend to zero within a specified time T. Let... a = a1, prove Negatively bounded; In Lemma 4, let α = β1, that is, It is bounded, it has... It is bounded, indicating that χ² and It will become zero within a specified limited time. Take the Lyapunov function: right Differentiate as follows: Where a1 and c2 are both positive numbers; By Lemma 4, we prove that χ1 converges to the origin in a given finite time T; let... a = a1, because Boundedness, It is also bounded, therefore it has It is bounded.

4. A robot formation control system based on a distributed observer, used to implement the robot formation control method based on a distributed observer as described in any one of claims 1-3, characterized in that, It includes a preset number of intelligent agents, a wireless communication module, and a server; The intelligent agent communicates with the server, as well as with other intelligent agents, through a wireless communication module to achieve data transmission and remote control. Servers are used for centralized management and coordination of the operations of multiple agents.

5. A robot formation control system based on a distributed observer as described in claim 4, characterized in that, Each intelligent agent includes: a processor, a memory, a sensor module, a driver module, and a power module; the memory, sensor module, driver module, and power module are all connected to the processor. Real-time data and control signals are transmitted through a dedicated connection interface on the intelligent agent's internal bus.

6. A robot formation control system based on a distributed observer as described in claim 4, characterized in that, The wireless communication module includes a Wi-Fi submodule and a 5G submodule.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores instructions that, when executed by a computer, perform the method as described in any one of claims 1-3.

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