Intermittent network communication synchronous control method for shoal robot

Abstract

The invention belongs to the technical field of automatic control, and discloses a shoal robot intermittent network communication synchronous control method, which comprises the following steps of: firstly, performing accurate modeling by regarding each robot in a shoal robot system as a node in a network through a positive complex network; and secondly, a state observer and an intermittent control protocol based on observation are designed, so that the system can be controlled when needed and is kept in a natural state when not needed, and the running state of the shoal robot is monitored in real time, so that the control efficiency is improved, and the control cost is reduced. And finally, proving the positivity and stability of the system by using a matrix decomposition technology, linear programming and a Lyapunov function theory, so that the shoal robots are synchronized. The invention provides a stable, efficient and resource-saving intermittent network communication synchronous control technology for the shoal robot.

Description

Technical Field

[0001] The invention belongs to the technical field of automatic control, and in particular relates to an intermittent network communication synchronization control method for a shallow robot. Background Art

[0002] With the increasing attention paid to marine resources, people have an increasing demand for marine exploration technology and equipment. As a transition zone between the ocean and the land, the shoal is characterized by violent wave disturbances and large differences in the mechanical properties of dry and wet particles on the ground. This complexity poses a great challenge to traditional robots. In particular, the density of the medium in the water and land environment is very different. Traditional robots often find it difficult to swim and run quickly in the shoal environment, which limits their application in this area. As a robot system that can switch freely between water and land environments, the shoal robot has broad application prospects. It plays an important role in tasks such as marine environment monitoring, underwater rescue, topographic mapping, and mine detection. However, these tasks are often complex, real-time, diverse, and incompletely synchronized, requiring robots to have multi-task execution capabilities, high flexibility, and environmental adaptability. Therefore, it is particularly important to ensure that the shoal robot can perform tasks normally.

[0003] In the fields of marine development, environmental protection and disaster relief, the growing demand for shoal operations has provided new development opportunities for shoal robots. In actual situations, the environment in which shoal robots are needed to perform tasks is often harsh, and once the system fails, it will have serious consequences for subsequent tasks. Summary of the invention

[0004] The purpose of the present invention is to provide a method for synchronous control of intermittent network communication of a shallow robot to solve the above-mentioned technical problems.

[0005] In order to solve the above technical problems, the specific technical solution of a method for synchronous control of intermittent network communication of a shallow robot of the present invention is as follows:

[0006] A method for synchronously controlling intermittent network communication of a shallow robot comprises the following steps:

[0007] Step 1: Establish a positive complex network state space model of the shallow robot system;

[0008] Step 2: Construct a state space model of isolated nodes in the shallow robot system;

[0009] Step 3: Design the control protocol for isolated nodes in the shallow robot system;

[0010] Step 4: Design the state observer of the positive complex network in the shallow robot system;

[0011] Step 5: Establish the observer-based control protocol of the positive complex network in the shallow robot system;

[0012] Step 6: Establish the complex network closed-loop system of the shallow robot;

[0013] Step 7: Design the conditions for the smooth operation of the complex network in the shallow robot system;

[0014] Step 8: Verify the positivity and stability of isolated nodes of the positive complex network in the Shoal robot system;

[0015] Step 9, verify the positivity of the positive complex network closed-loop system in the shallow robot system;

[0016] Step 10: Verify the consistency of the positive complex network closed-loop system in the Shoal robot system. Further, the positive complex network state space model of the Shoal robot system in step 1 includes:

[0017] A complex network with N identical nodes is described as:

[0018]

[0019] y i (k) = Cx i (k),

[0020] Where i = 1, 2, ..., N, represents the state vector of the i-th node, which contains the battery power, motor temperature, position, and speed information of the shallow robot; represents the input vector of the i-th node, which contains the signal received by the sensor of the i-th node of the shallow robot at time k; represents the output vector of the i-th node, specifically, the shoal robot of the i-th node at time k, which completes the corresponding behavior according to the coordinated movement, information sharing and task allocation among the shoal robots; is the coupling configuration matrix showing the network topology. If node i can receive information from node j, then otherwise is a positive semidefinite inner coupling matrix; the matrices A, B, C have appropriate dimensions, and it is assumed that and Furthermore, the state space model of isolated nodes in the shallow robot system in step 2 is described as follows:

[0021] s(k+1)=A0s(k)+B0u0(k),

[0022] y0(k)=C0s(k),

[0023] in Indicates the status of the isolated node, which contains the battery power, motor temperature, position, and speed information of the shallow robot representing the isolated node; Represents the output vector of the isolated node, specifically, the shallow robot of the isolated node at time k, which assigns tasks to other nodes according to task requirements; represents the input vector of the isolated node; the isolated node assigns the target task to different nodes and synchronizes them; A0, B0 and C0 have appropriate dimensions and assume and The control protocol of isolated nodes in the shallow robot system designed in step 3 is as follows:

[0024] u0(k)=Fs(k),

[0025] Where F is the controller gain matrix that needs to be designed.

[0026] Furthermore, the step 4 designs a state observer of the positive complex network in the shallow robot system, which is in the following form:

[0027]

[0028] in, is the state x of the complex network system i The estimate, is the output vector of the state observer, G is the gain matrix of the system, and is the gain matrix of the observer.

[0029] Furthermore, the step 5 establishes a control protocol based on an observer for a positive complex network in the shallow robot system, which is in the following form:

[0030]

[0031] in,

[0032]

[0033] For node i=1,…,N, the observed measurement error Defined as:

[0034]

[0035] Define local synchronization error i (t):

[0036] e i (k) = xi (k)-s(k).

[0037] Furthermore, the step 6 establishes a complex network closed-loop system of the shallow robot in the following form:

[0038]

[0039] in,

[0040]

[0041] Furthermore, the conditions for the smooth operation of the complex network in the shallow robot system designed in step 7 are as follows:

[0042] Design existence constant φ>0,0<μ1<1,μ2>1,λ>1, Vector v1>0,v2>0,v3>0,v1′>0,v2′>0,v3′>0, and vector Make

[0043]

[0044]

[0045]

[0046] The gain matrix of the positive complex network state observer and controller designed for the shallow robot system in steps 4 and 5 is:

[0047]

[0048] and

[0049] 2lnλ+μ1τ+μ2(T-τ)<0.(8w) Then, within the parameter range and conditions that define the stable operation of the Shoal robot system, the Shoal robot positive complex network closed-loop system achieves positivity and synchronization in step 6;

[0050] in, is a Kronecker product operator, 1 N is a column vector whose N rows are all 1. Represents an n-dimensional column vector whose nth element is 1 and the rest are 0.

[0051] Furthermore, the process of verifying the positivity and stability of isolated nodes of the positive complex network in the Shoal Robot System in step 8 is as follows:

[0052] From condition (8a), we can see that

[0053]

[0054] Choose a conormal Lyapunov function: Then find the variance,

[0055]

[0056] Scaling the gain matrix F given in (8v):

[0057]

[0058] Formula (9.1) can be re-expressed as:

[0059]

[0060] This shows that isolated nodes satisfy positivity and stability, that is, in the Shoal robot system, the battery power, task execution progress, etc. of the Shoal robot modeled by isolated nodes can remain positive during the execution of the task.

[0061] Furthermore, the process of verifying the positivity of the positive complex network closed-loop system in the shallow robot system in step 9 is as follows:

[0062] When k∈[mT,mT+τ), it means that there is a controller in the complex network of the shallow robot system. Then, from (8c), we can see that

[0063]

[0064] in,

[0065]

[0066] because Can get According to (8d), (8e) and (8f), we can get

[0067]

[0068] and

[0069]

[0070] in,

[0071]

[0072] Through (8g), (8h) and (8i), we know

[0073]

[0074] and

[0075]

[0076] in, When k∈[mT+τ,(m+1)T), it means that the positive complex network in the shallow robot system has no control input. Then, from (8j), (8k), (8l) and (8m), we can deduce

[0077]

[0078] and

[0079]

[0080] in,

[0081]

[0082] Finally, combine Can get So far, when

[0083] k∈[mT,mT+τ), closed-loop matrix All the elements inside are positive, satisfying the positivity condition; when k∈[mT+τ,(m+1)T), the closed-loop matrix All the elements inside are positive, satisfying the positivity.

[0084] Furthermore, the process of verifying the consistency of the positive complex network closed-loop system in the shallow robot system in step 10 is as follows:

[0085] The consistency proof process of the complex network closed-loop system is as follows:

[0086]

[0087] in When k∈[mT,mT+τ), it means that the complex network in the shallow robot system has control input.

[0088]

[0089] Formula (8v) can be scaled to:

[0090]

[0091] Through (11.1) and (11.2), we get

[0092] by condition and We get V1(k+1)≤μ1V1(k).

[0093] When k∈[mT+τ,(m+1)T), it means that the positive complex network in the shallow robot system has no control input, then

[0094]

[0095] The gain matrix of formula (8v) can be scaled to:

[0096]

[0097]

[0098] Combining conditions (11.3) and (11.4), we get

[0099]

[0100] Thus V2(k+1)≤μ2V2(k) is satisfied.

[0101] When k∈[mT,mT+τ), it means that the complex network in the shallow robot system has control input.

[0102]

[0103] When k∈[mT,mT+τ), it means that the positive complex network in the shallow robot system has no control input.

[0104]

[0105] Therefore, whether it is k∈[mT,mT+τ) or k∈[mT,mT+τ), no matter there is control input in the complex network of the Shoal robot system or not, the Shoal robot system is consistent. The Shoal robot modeled by isolated nodes makes the other Shoal robots reach consistency, thereby achieving synchronization. One Shoal robot leads the other Shoal robots to perform tasks together. When the current state needs to be changed, k∈[mT,mT+τ), the Shoal robot system increases control input to adjust its own actions; when the current state does not need to be changed, k∈[mT,mT+τ), the Shoal robot system executes the current state.

[0106] The intermittent network communication synchronization control method of a shallow robot of the present invention has the following advantages:

[0107] The present invention effectively alleviates this problem by designing a state observer. The observer can monitor the operating state of the shoal robot in real time, including information such as battery power, motor temperature, sensor working state, etc., and provide accurate data support for subsequent control decisions. At the same time, the state observer can estimate the state variables that are difficult to directly measure inside the system based on the measured values ​​of the system's external variables (such as input variables and output variables) through a certain algorithm or model. This is particularly important for complex systems such as shoal robots, because the underwater environment is complex and changeable, and it is often difficult or costly to directly measure all state variables. When a system fails, the state observer can quickly locate the source of the fault and evaluate the degree of the fault, providing maintenance personnel with accurate fault information, which helps to quickly troubleshoot and restore the normal operation of the system. In addition, the present invention can construct a positive complex network model by treating each robot in the shoal robot system as a node in the network, the communication and cooperation relationship between robots as the connection between nodes, and the number of robots is always non-negative. This model helps to understand and analyze the overall behavior of the shoal robot system. By utilizing the characteristics of information propagation and synchronization in complex networks, coordinated movement, information sharing and task allocation between shoal robots can be achieved, thereby improving the overall performance and efficiency of the system. To verify the effectiveness of the proposed state observer and distributed control protocol, the present invention uses two mathematical tools: linear programming and co-positive Lyapunov function.

[0108] In summary, the present invention provides an efficient, stable and resource-saving intermittent network communication synchronization control technology for the Shoal robot based on the state space model of the positive complex network system. By designing a state observer and a distributed intermittent control protocol, using matrix decomposition technology, linear programming and Yu Zheng Lyapunov function, each robot in the Shoal robot system maintains a relatively stable state, ensuring that the Shoal robot system can perform tasks normally and achieve the purpose of synchronization control. BRIEF DESCRIPTION OF THE DRAWINGS

[0109] Figure 1 This is a schematic diagram of the complex network of the Shoal robot system.

[0110] Figure 2 It is the complex network synchronization flow chart of the Shoal robot system. DETAILED DESCRIPTION

[0111] In order to better understand the purpose, structure and function of the present invention, a method for synchronous control of intermittent network communication of a shallow robot of the present invention is further described in detail below in conjunction with the accompanying drawings.

[0112] A method for synchronously controlling intermittent network communication of a shallow robot of the present invention comprises the following steps:

[0113] Step 1: Establish a positive complex network state space model of the shallow robot system, and describe a complex network with N identical nodes as:

[0114]

[0115] y i (k) = Cx i (k),

[0116] Where i = 1, 2, ..., N, represents the state vector of the i-th node, which contains information such as the battery power, motor temperature, position, and speed of the shallow robot; represents the input vector of the i-th node, which contains the signal received by the sensor of the i-th node of the shallow robot at time k; Represents the output vector of the i-th node, specifically the shoal robot of the i-th node at time k, which completes the corresponding behavior based on the coordinated movement, information sharing and task allocation between the shoal robots. is the coupling configuration matrix showing the network topology. If node i can receive information from node j, then otherwise is a positive semidefinite inner coupling matrix; the matrices A, B, C have appropriate dimensions, and it is assumed that and

[0117] Step 2: Construct the state space model of isolated nodes in the shallow robot system as follows:

[0118] s(k+1)=A0s(k)+B0u0(k),

[0119] y0(k)=C0s(k),

[0120] in Indicates the status of the isolated node, which contains information such as the battery level, motor temperature, position, speed, etc. of the Shoal robot representing the isolated node; Represents the output vector of the isolated node, specifically the shallow robot of the isolated node at time k, which assigns tasks to other nodes according to task requirements. represents the input vector of the isolated node; the isolated node will assign the target task to different nodes and synchronize them. A0, B0 and C0 have appropriate dimensions and assume and

[0121] Step 3: Design the control protocol for isolated nodes in the shallow robot system, which is as follows:

[0122] u0(k)=Fs(k),

[0123] Where F is the controller gain matrix that needs to be designed.

[0124] Step 4: Design the state observer of the positive complex network in the shallow robot system, which is in the following form:

[0125]

[0126] in, is the state x of the complex network system i The estimate, is the output vector of the state observer, G is the gain matrix of the system, and is the gain matrix of the observer.

[0127] Step 5: Establish the observer-based control protocol of the positive complex network in the shallow robot system, which is in the following form:

[0128]

[0129] in,

[0130]

[0131] For node i=1,…,N, the observed measurement error Defined as:

[0132]

[0133] Define local synchronization error i (t):

[0134] e i (k) = x i (k)-s(k).

[0135] Step 6: Establish the complex network closed-loop system of the shallow robot in the following form:

[0136]

[0137] in,

[0138]

[0139] Step 7: Design the following conditions for the smooth operation of the complex network in the shallow robot system:

[0140] Design existence constant φ>0,0<μ1<1,μ2>1,λ>1, Vector v1>0,v2>0,v3>0,v1′>0,v2′>0,v3′>0, and vector Make

[0141]

[0142]

[0143] The gain matrix of the positive complex network state observer and controller designed in steps 4 and 5 for the shallow robot system is:

[0144]

[0145] and

[0146] 2lnλ+μ1τ+μ2(T-τ)<0.(8w) Then, within the parameter range and conditions that define the stable operation of the Shoal robot system, the Shoal robot positive complex network closed-loop system achieves positivity and synchronization in step 6.

[0147] in, is a Kronecker product operator, 1 N is a column vector whose N rows are all 1. Represents an n-dimensional column vector whose nth element is 1 and the rest are 0.

[0148] Step 8: Verify the positivity and stability of isolated nodes in the positive complex network of the Shoal Robot System as follows:

[0149] From condition (8a), we can see that

[0150]

[0151] Choose a conormal Lyapunov function: Then we can find the variance,

[0152]

[0153] Scaling the gain matrix F given in (8v):

[0154]

[0155] Formula (9.1) can be re-expressed as:

[0156]

[0157] This shows that isolated nodes satisfy positivity and stability. That is, in the Shoal robot system, the battery power, task execution progress, etc. of the Shoal robot modeled by isolated nodes can maintain positivity during the task execution process.

[0158] Step 9: The verification process of the positivity of the positive complex network closed-loop system in the shallow robot system is as follows:

[0159] When k∈[mT,mT+τ), it means that there is a controller in the complex network of the shallow robot system. Then, from (8c), we can see that

[0160]

[0161] in,

[0162]

[0163] for Can get According to (8d), (8e) and (8f), we can get

[0164]

[0165] and

[0166]

[0167] in,

[0168]

[0169] Through (8g), (8h) and (8i), we know

[0170]

[0171] and

[0172]

[0173] in, When k∈[mT+τ,(m+1)T), it means that the positive complex network in the shallow robot system has no control input. Then, from (8j), (8k), (8l) and (8m), we can deduce

[0174]

[0175] and

[0176]

[0177] in,

[0178]

[0179] Finally, combine Can get So far, when

[0180] k∈[mT,mT+τ), closed-loop matrix All the elements inside are positive, satisfying the positivity condition; when k∈[mT+τ,(m+1)T), the closed-loop matrix All the elements inside are positive, satisfying the positivity.

[0181] Step 10: The verification process for the consistency of the positive complex network closed-loop system in the shallow robot system is as follows:

[0182] The following is the proof process of consistency of the complex network closed-loop system:

[0183]

[0184] in When k∈[mT,mT+τ), it means that the complex network in the shallow robot system has control input.

[0185]

[0186] Formula (8v) can be scaled to:

[0187]

[0188] Through (11.1) and (11.2), we can get

[0189]

[0190] by condition and We get V1(k+1)≤μ1V1(k).

[0191] When k∈[mT+τ,(m+1)T), it means that the positive complex network in the shallow robot system has no control input, then

[0192]

[0193] The gain matrix of formula (8v) can be scaled to:

[0194]

[0195]

[0196] Combining conditions (11.3) and (11.4), we get

[0197]

[0198] Thus V2(k+1)≤μ2V2(k) is satisfied.

[0199] When k∈[mT,mT+τ), it means that the complex network in the shallow robot system has control input.

[0200]

[0201] When k∈[mT,mT+τ), it means that the positive complex network in the shallow robot system has no control input.

[0202]

[0203] Therefore, whether k∈[mT,mT+τ) or k∈[mT,mT+τ), the Shoal robot system is consistent regardless of whether there is control input in the complex network. The Shoal robot modeled by isolated nodes can make the other Shoal robots reach consistency and thus achieve synchronization. In practical applications, it is reflected in a Shoal robot leading the other Shoal robots to perform tasks together. When the current state needs to be changed, k∈[mT,mT+τ), the Shoal robot system increases control input to adjust its own actions; when the current state does not need to be changed, k∈[mT,mT+τ), the Shoal robot system executes the current state.

[0204] It is to be understood that the present invention is described by some embodiments, and it is known to those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the scope of protection of the present invention.

Claims

1. A method for synchronous control of intermittent network communication of a shallow robot, characterized in that: The steps include: Step 1: Establish a positive complex network state space model of the shallow robot system; Step 2: Construct a state space model of isolated nodes in the shallow robot system; Step 3: Design the control protocol for isolated nodes in the shallow robot system; Step 4: Design the state observer of the positive complex network in the shallow robot system; Step 5: Establish the observer-based control protocol of the positive complex network in the shallow robot system; Step 6: Establish the complex network closed-loop system of the shallow robot; Step 7: Design the conditions for the smooth operation of the complex network in the shallow robot system; Step 8: Verify the positivity and stability of isolated nodes of the positive complex network in the Shoal robot system; Step 9, verify the positivity of the positive complex network closed-loop system in the shallow robot system; Step 10: Verify the consistency of the positive complex network closed-loop system in the Shoal robot system.

2. The intermittent network communication synchronization control method of the shallow robot according to claim 1 is characterized in that: The positive complex network state space model of the shallow robot system in step 1 includes: describing a complex network with N identical nodes as: y i (k)=Cx i (k), Where i = 1, 2, ..., N, represents the state vector of the i-th node, which contains the battery power, motor temperature, position, and speed information of the shallow robot; represents the input vector of the i-th node, which contains the signal received by the sensor of the shallow robot at the i-th node at time k; represents the output vector of the i-th node, specifically, the shoal robot of the i-th node at time k, which completes the corresponding behavior according to the coordinated movement, information sharing and task allocation among the shoal robots; is the coupling configuration matrix showing the network topology. If node i can receive information from node j, then otherwise is a positive semidefinite inner coupling matrix; the matrices A, B, C have appropriate dimensions, and it is assumed that and 3. The intermittent network communication synchronization control method of the shallow robot according to claim 1 is characterized in that: The state space model of isolated nodes in the shallow robot system constructed in step 2 is described as: s(k+1)=A0s(k)+B0u0(k), y0(k)=C0s(k), in Indicates the status of the isolated node, which contains the battery power, motor temperature, position, and speed information of the shallow robot representing the isolated node; Represents the output vector of the isolated node, specifically, the shallow robot of the isolated node at time k, which assigns tasks to other nodes according to task requirements; represents the input vector of the isolated node; the isolated node assigns the target task to different nodes and synchronizes them; A0, B0 and C0 have appropriate dimensions and assume and The control protocol of isolated nodes in the shallow robot system designed in step 3 is as follows: u0(k)=Fs(k), Where F is the controller gain matrix that needs to be designed.

4. The intermittent network communication synchronization control method of the shallow robot according to claim 1 is characterized in that: The step 4 designs the state observer of the positive complex network in the shallow robot system, which is in the following form: in, is the state x of the complex network system i The estimate, is the output vector of the state observer, G is the gain matrix of the system, and is the gain matrix of the observer.

5. The intermittent network communication synchronization control method of the shallow robot according to claim 1 is characterized in that: The step 5 establishes the observer-based control protocol of the positive complex network in the shallow robot system, which is in the following form: in, For node i=1,…,N, the observed measurement error Defined as: Define local synchronization error i (t): e i (k)=x i (k)-s(k)。 6. The intermittent network communication synchronization control method of the shallow robot according to claim 1 is characterized in that: The step 6 establishes the complex network closed-loop system of the shallow robot, which is as follows: in, 7. The intermittent network communication synchronization control method of the shallow robot according to claim 1 is characterized in that: The conditions for the stable operation of the complex network in the shallow robot system designed in step 7 are as follows: Design existence constant φ>0,0<μ1<1,μ2>1, Vector v1>0,v2>0,v3>0,v1′>0,v2′>0,v3′>0, and vector Make The gain matrix of the positive complex network state observer and controller designed for the shallow robot system in steps 4 and 5 is: and 2lnλ+μ1τ+μ2(T-τ)<0. (8w) Then, under the parameter range and conditions that define the stable operation of the Shoal Robot system, the Shoal Robot positive complex network closed-loop system achieves positivity and synchronization in step 6; in, is a Kronecker product operator, 1 N is a column vector whose N rows are all 1. Represents an n-dimensional column vector whose nth element is 1 and the rest are 0.

8. The intermittent network communication synchronization control method of the shallow robot according to claim 7 is characterized in that: The process of step 8 verifying the positivity and stability of isolated nodes in the positive complex network of the Shoal Robot System is as follows: From condition (8a), we can see that Choose a conormal Lyapunov function: Then find the variance, Scaling the gain matrix F given in (8v): Formula (9.1) can be re-expressed as: This shows that isolated nodes satisfy positivity and stability, that is, in the Shoal robot system, the battery power, task execution progress, etc. of the Shoal robot modeled by isolated nodes can remain positive during the execution of the task.

9. The intermittent network communication synchronization control method of the shallow robot according to claim 7 is characterized in that: The process of verifying the positivity of the positive complex network closed-loop system in the shallow robot system in step 9 is as follows: When k∈[mT,mT+τ), it means that there is a controller in the complex network of the shallow robot system. Then, from (8c), we can see that in, because Can get According to (8d), (8e) and (8f), we can get and in, Through (8g), (8h) and (8i), we know and in, When k∈[mT+τ,(m+1)T), it means that the positive complex network in the shallow robot system has no control input, then From (8j), (8k), (8l) and (8m), we can infer and in, Finally, combine Can get So far, when k∈[mT,mT+τ), closed-loop matrix All the elements inside are positive, satisfying the positivity condition; when k∈[mT+τ,(m+1)T), the closed-loop matrix All the elements inside are positive, satisfying the positivity property.

10. The intermittent network communication synchronization control method of the shallow robot according to claim 7, characterized in that: The process of verifying the consistency of the positive complex network closed-loop system in the shallow robot system in step 10 is as follows: The consistency proof process of the complex network closed-loop system is as follows: in When k∈[mT,mT+τ), it means that the complex network in the shallow robot system has control input. Formula (8v) can be scaled to: Through (11.1) and (11.2), we get by condition and We get V1(k+1)≤μ1V1(k). When k∈[mT+τ,(m+1)T), it means that the positive complex network in the shallow robot system has no control input, then The gain matrix of formula (8v) can be scaled to: Combining conditions (11.3) and (11.4), we get Thus V2(k+1)≤μ2V2(k) is satisfied. When k∈[mT,mT+τ), it means that the complex network in the shallow robot system has control input. When k∈[mT,mT+τ), it means that the positive complex network in the shallow robot system has no control input. Therefore, whether it is k∈[mT,mT+τ) or k∈[mT,mT+τ), no matter there is control input in the complex network of the Shoal robot system or not, the Shoal robot system is consistent. The Shoal robot modeled by isolated nodes makes the other Shoal robots reach consistency, thereby achieving synchronization. One Shoal robot leads the other Shoal robots to perform tasks together. When the current state needs to be changed, k∈[mT,mT+τ), the Shoal robot system increases control input to adjust its own actions; when the current state does not need to be changed, k∈[mT,mT+τ), the Shoal robot system executes the current state.

Images