Design method of cooperative controller for underwater vehicles based on Markov jump communication topology

Abstract

This invention discloses a method for designing a collaborative controller for underwater robots using a Markov jump communication topology. The method comprises the following steps: designing a multi-underwater robot system; designing a collaborative tracking controller based on communication time delay and a Markov jump communication topology; designing a Lyapunov function containing the underwater robot state information and stability constraints for the collaborative tracking controller; verifying the stability of the collaborative tracking controller using a weak infinitesimal operator of the Lyapunov function; and calculating the gain parameters of the collaborative tracking controller. The controller of the invention enables the communication topology to stably and collaboratively track a target point even in the presence of Markov jumps, achieving consistency in the state information of multiple underwater robots and simultaneously solving for the necessary parameters required by the controller.

Description

Technical Field

[0001] The present invention belongs to the field of underwater robot cooperative controllers, and in particular relates to a design method of an underwater robot cooperative controller based on Markov jump communication topology. Background Art

[0002] The ocean, covering 71% of the Earth's surface, is a rich yet underexploited treasure trove and a key battlefield for the future. Entering the 21st century, humanity faces three major challenges: population expansion and limited living space; ecological degradation and rapid human development; and depleted land resources and growing social production. Therefore, underwater robots (AUVs) play a vital role in marine ecological monitoring and resource exploration. With the advancement of marine science, research on AUVs has become increasingly widespread, playing an irreplaceable role in both military and civilian applications. Early applications were primarily for offshore oil and gas development and torpedo salvage. Later, advances in computer technology, artificial intelligence, electronics, small navigation equipment, command and control hardware, logic, and software have subtly influenced the development of AUVs. However, many underwater tasks require greater precision, such as target tracking, leading to the emergence of collaborative operations involving multiple AUVs. Considering the collaborative nature of multiple AUVs, communication delays and Markov jump communication topologies, caused by uncertainties in the marine environment, become crucial considerations. An underwater robot system is a six-degree-of-freedom model, essentially controlling its three-dimensional position (X, Y, Z, pitch, roll, and roll). Therefore, a design method for a collaborative underwater robot controller based on a Markov jump communication topology is urgently needed to enable multiple underwater robots to collaboratively track a target point. Summary of the Invention

[0003] In view of the transmission time delay in underwater acoustic communication in the prior art and the prone occurrence of communication topology jumps between multiple underwater robots, the present invention discloses a design method for an underwater robot collaborative controller based on Markov jump communication topology. The use of this controller effectively enhances the stability of collaborative tracking of multiple underwater robots under the communication time delay and the Markov jump state of the communication topology.

[0004] The present invention provides a method for designing a collaborative controller for underwater robots using a Markov jump communication topology. The method is based on a multi-underwater robot system, selects the three-axis coordinate positions and three-axis rotation angles of the underwater robots to form six-degree-of-freedom state information, and designs a controller that takes communication time delay and Markov jump communication topology into consideration. The method includes the following steps:

[0005] Step 1: Combine the dynamic equations and kinematic equations of multiple underwater robots to obtain the multi-underwater robot system:

[0006]

[0007] in,

[0008] is the control input; where x i 、y i 、z i Respectively represent the x-axis, y-axis and z-axis positions of each underwater robot in the geodetic coordinate system, φ i ,θ i ,ψ i Respectively represent the angles of rotation of each underwater robot on the three axes; M i is the inertia matrix; J i is the transformation matrix from the hull coordinate system to the earth coordinate system; C i is the Coriolis matrix; D i is the fluid damping matrix; g i is the descriptive term for gravity and buoyancy; T i is the external force applied to the underwater robot; i represents the i-th underwater robot, and N is the total number of underwater robots;

[0009] Step 2: Cooperative tracking controller based on communication delay and Markov jump communication topology:

[0010]

[0011] Where i, j = 1,…, N, i ≠ j; k i is the proportional gain coefficient, α i is the differential gain coefficient; define the adjacency matrix A(p)=[a ij (p)]∈R N*N , represents the matrix under the pth mode. If the i-th underwater robot can receive the status information of the j-th underwater robot, then a ij (p)>0, otherwise a ij (p) = 0; in the pth mode, if the i-th underwater robot can receive the state information of the target point, then b i (p)>0, otherwise b i (p) = 0; p represents the Markov jump mode of the communication topology; is the state information of the i-th underwater robot, X d is the target point information, is the real-time tracking error, is the state information of the i-th underwater robot considering time delay, d i (t) = 0.5sint + 0.5 is a two-way time-varying lag;

[0012] Step 3: Design the Lyapunov function containing the underwater robot state information and the stability constraints of the cooperative tracking controller;

[0013] Step 4: Verify the stability of the cooperative tracking controller based on the weak infinitesimal operator of the Lyapunov function, and calculate the gain parameters and correlation matrix of the cooperative tracking controller.

[0014] In the underwater robot cooperative controller design method of the Markov jump communication topology of the present invention, the Lyapunov function in step 3 is specifically:

[0015]

[0016]

[0017]

[0018]

[0019]

[0020]

[0021]

[0022]

[0023] Among them, E i ,F i ,G i ,H i ,L i ,M i ,N i ,O i , Is a positive definite symmetric matrix, the matrix X i ,Y i ,P i ,Q i ,

[0024] In the underwater robot cooperative controller design method of the Markov jump communication topology of the present invention, the stability constraint condition of the cooperative tracking controller in step 3 is specifically:

[0025] For a multi-underwater robot system, if there exists a positive symmetric matrix E i ,F i ,G i ,H i ,L i ,M i ,N i ,O i, Matrix X i ,Y i ,P i ,Q i , If the following inequality holds, the multi-underwater robot system can track the target point, that is, when t→∞ Then the error system of the underwater robot is asymptotically stable, and the errors of position and velocity with the target gradually converge to zero:

[0026]

[0027] Among them, e l =[0 n×(l-1)n ,I n×n ,0 n×(27-l)n ], n represents the robot's degree of freedom,

[0028]

[0029]

[0030] Π N+i =[e i -e N+i -2e 5N+i ],Π 2N+i =[e N+i -e 2N+i -2e 6N+i ], where i, j = 1,…, N, i ≠ j,

[0031] where Λ i Represents L i 、N i , represent

[0032] where Δ i Represents M i , O i , represent

[0033] is the maximum value of the two-way time-varying delay, is the bidirectional time-varying delayed derivative The minimum value of .

[0034] In the underwater robot cooperative controller design method of the Markov jump communication topology of the present invention, the weak infinitesimal operator of the Lyapunov function in step 4 is specifically:

[0035] Perform weak infinitesimal operator operation on V1:

[0036]

[0037] Perform weak infinitesimal operator operations on V2:

[0038]

[0039] Perform weak infinitesimal operator operations on V3:

[0040]

[0041] Perform weak infinitesimal operator operations on V4:

[0042]

[0043] Perform weak infinitesimal operator operations on V5:

[0044]

[0045] Perform weak infinitesimal operator operations on V6:

[0046]

[0047] Perform weak infinitesimal operator operations on V7:

[0048]

[0049] In the design method of underwater robot cooperative controller with Markov jump communication topology of the present invention, the following inequality is introduced to To perform scaling:

[0050] Introduce the following two inequalities:

[0051]

[0052] We can get:

[0053]

[0054] Similarly, we introduce the following two inequalities:

[0055]

[0056]

[0057] Similarly, we can get:

[0058]

[0059] Finally, we get:

[0060]

[0061] In the underwater robot cooperative controller design method of the Markov jump communication topology of the present invention, the stability of the cooperative tracking controller is verified and the gain parameters and correlation matrix parameter values ​​of the cooperative tracking controller are calculated in step 4 as follows:

[0062] Step 4.1: Introduce the free matrix P i ,Q i , and set:

[0063]

[0064]

[0065] Step 4.2: The following inequality is finally obtained through calculation. According to the constraints, the error system is stable:

[0066]

[0067] in

[0068] Step 4.3: According to the constraints, we can get Therefore, the multi-underwater robot system realizes tracking control and obtains the proportional gain coefficient k of the controller according to the constraint conditions. i , differential gain coefficient α i And the correlation matrix E i ,F i ,G i ,H i ,L i ,M i ,N i ,O i ,X i ,Y i ,P i ,Q i ,

[0069] In the underwater robot cooperative controller design method of the Markov jump communication topology of the present invention, the LMI toolbox of MATLAB is used in step 4.3 to solve the gain parameters and correlation matrix of the cooperative tracking controller.

[0070] The present invention proposes a method for designing a collaborative controller for underwater robots with a Markov jump communication topology. The collaborative controller designed by this method takes into account bidirectional time-varying time delay, introduces a Markov jump communication topology, and uses LMI to solve more accurate gain parameters in the controller. In this way, during the tracking process in an actual marine environment, multiple underwater robots can still stably and collaboratively track the target point even if communication failures occur between some underwater robots due to severe wind and waves or uncertain conditions, or even if some of the multiple underwater robots cannot detect the target point. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 Flowchart of a method for designing a cooperative controller for underwater vehicles with Markov jump communication topology;

[0072] Figure 2 Schematic diagram of Markov jump of the communication topology structure for cooperative tracking of multiple underwater vehicles;

[0073] Figure 3 The change diagram of the X-axis value of the target tracked by multiple underwater robots in a collaborative manner;

[0074] Figure 4 The change diagram of the Y-axis value of the target tracked by multiple underwater robots in a collaborative manner;

[0075] Figure 5 The change diagram of the Z-axis value of the target tracked by multiple underwater robots in a collaborative manner;

[0076] Figure 6 The change diagram of the rotation angle value on the X axis of the target tracked by multiple underwater robots in a collaborative manner;

[0077] Figure 7 The change diagram of the rotation angle value on the Y axis of the target tracked by multiple underwater robots in a collaborative manner;

[0078] Figure 8 The change diagram of the rotation angle value on the Z axis of the target tracked by multiple underwater robots in a collaborative manner;

[0079] Figure 9 Spatial simulation diagram of multiple underwater robots collaboratively tracking a target. DETAILED DESCRIPTION

[0080] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0081] like Figure 1As shown, the method for designing an underwater robot cooperative controller with a Markov jump communication topology of the present invention is based on a multi-underwater robot system, selects the three-axis coordinate positions and three-axis rotation angles of the underwater robots to form six-degree-of-freedom state information, and designs a controller considering communication time delay and Markov jump communication topology, including the following steps:

[0082] Step 1: Combine the dynamic equations and kinematic equations of multiple underwater robots to obtain the multi-underwater robot system:

[0083] The dynamic equation of multiple underwater robots can be expressed as:

[0084]

[0085] Among them, M i =diag{m ui ,m vi ,m wi ,m pi ,m qi ,I ri} is the inertia matrix, where diag{} means converting the elements into a diagonal matrix. is the linear velocity and angular velocity of the underwater robot in the hull coordinate system;

[0086]

[0087] is the Coriolis matrix;

[0088] D i =diag{k u +k u|u| ,k v +k v|v| ,k w +k w|w| ,k p +k p|p| ,k q +k q|q| ,k r +k r|r|} is the fluid damping matrix;

[0089] {k u ,k v ,k w ,k p ,k q ,k r} is the primary damping coefficient, {k u|u| ,k v|v| ,k w|w| ,k p|p| ,k q|q| ,k r|r|} is the secondary damping coefficient;

[0090] Descriptive terms for gravity and buoyancy.

[0091] The kinematic equation can be expressed as:

[0092]

[0093] in, is the transformation matrix from the hull coordinate system to the earth coordinate system, as follows:

[0094]

[0095]

[0096] The multi-underwater robot system is:

[0097]

[0098] in,

[0099] is the control input; is the six-degree-of-freedom state information, where x i 、y i 、z i Respectively represent the x-axis, y-axis and z-axis positions of each underwater robot in the geodetic coordinate system, φ i ,θ i ,ψ i Respectively represent the angles of rotation of each underwater robot on the three axes; g i is the descriptive term for gravity and buoyancy; T i is the external force applied to the underwater robot; i represents the i-th underwater robot, and N is the total number of underwater robots.

[0100] Step 2: Cooperative tracking controller based on communication delay and Markov jump communication topology:

[0101]

[0102] Where i, j = 1,…, N, i ≠ j; k i is the proportional gain coefficient, α i is the differential gain coefficient; define the adjacency matrix A(p)=[a ij (p)]∈R N*N , represents the matrix under the pth mode. If the i-th underwater robot can receive the status information of the j-th underwater robot, then a ij (p)>0, otherwise a ij (p) = 0; in the pth mode, if the i-th underwater robot can receive the state information of the target point, then bi (p)>0, otherwise b i (p) = 0; p represents the Markov jump mode of the communication topology; is the state information of the i-th underwater robot, X d is the target point information, is the real-time tracking error, is the state information of the i-th underwater robot considering time delay, d i (t) = 0.5sint + 0.5 is a two-way time-varying lag, is the minimum value of the two-way time-varying delay, represents the lower bound of the time delay of the i-th underwater robot, is the maximum value of the two-way time-varying delay, represents the upper bound of the time delay of the i-th underwater robot; is the bidirectional time-varying delayed derivative The minimum value of represents the lower bound of the time-delay derivative of the ith underwater robot, is the bidirectional time-varying delayed derivative The maximum value of represents the upper bound of the time-delay derivative of the i-th underwater vehicle.

[0103] Step 3: Design a Lyapunov function containing the underwater robot state information and the stability constraints of the cooperative tracking controller. The Lyapunov function is specifically:

[0104]

[0105]

[0106]

[0107]

[0108]

[0109]

[0110]

[0111]

[0112] Among them, E i ,F i ,G i ,H i ,L i ,M i ,N i ,O i , Is a positive definite symmetric matrix, the matrix X i ,Y i ,P i ,Q i ,

[0113] The stability constraints of the cooperative tracking controller in step 3 are specifically:

[0114] For a multi-underwater robot system, if there exists a positive symmetric matrix E i ,F i ,G i ,H i ,L i ,M i ,N i ,O i , Matrix X i ,Y i ,P i ,Q i , If the following inequality holds, the multi-underwater robot system can track the target point, that is, when t→∞ Then the error system of the underwater robot is asymptotically stable, and the errors of position and velocity with the target gradually converge to zero:

[0115]

[0116]

[0117]

[0118] Among them, e l =[0 n×(l-1)n ,I n×n ,0 n×(27-l)n ], n represents the robot's degree of freedom,

[0119]

[0120]

[0121] Π N+i =[e i -e N+i -2e 5N+i ],Π 2N+i =[e N+i -e 2N+i -2e 6N+i ], where i, j = 1,…, N, i ≠ j,

[0122] where Λ i Represents Li 、N i , represent

[0123] where Δ i Represents M i , O i , represent

[0124] is the maximum value of the two-way time-varying delay, is the bidirectional time-varying delayed derivative The minimum value of .

[0125] Step 4: Verify the stability of the cooperative tracking controller based on the weak infinitesimal operator of the Lyapunov function, and calculate the gain parameters and correlation matrix of the cooperative tracking controller.

[0126] First, the modally dependent Lyapunov function Perform weak infinitesimal operator operations, specifically:

[0127] (1) Perform weak infinitesimal operator operation on V1:

[0128]

[0129] (2) Perform weak infinitesimal operator operations on V2:

[0130]

[0131] (3) Perform weak infinitesimal operator operations on V3:

[0132]

[0133] (4) Perform weak infinitesimal operator operations on V4:

[0134]

[0135] According to the literature, Wirtinger-based integral inequality: Application to time-delay systems (Seuret A et al. Automatica, 2013, 49 (9): 2860-2866.) introduces the following inequality To perform scaling:

[0136] Specifically, we introduce the following two inequalities:

[0137]

[0138]

[0139] According to the theorem in “Reciprocally convex approach to stability of systems with time-varying delays” (PooGyeon Park et al. Automatica, 2011, 47(1): 235-238.), we can obtain:

[0140]

[0141] Similarly, we introduce the following two inequalities:

[0142]

[0143]

[0144] Similarly, we can get:

[0145]

[0146] Finally, we get:

[0147]

[0148] (5) Perform weak infinitesimal operator operations on V5:

[0149]

[0150]

[0151] (6) Perform weak infinitesimal operator operations on V6:

[0152]

[0153] (7) Perform weak infinitesimal operator operations on V7:

[0154]

[0155] In step 4, the stability of the cooperative tracking controller is verified and the gain parameters and correlation matrix parameter values ​​of the cooperative tracking controller are calculated as follows:

[0156] Step 4.1: Introduce the free matrix P i ,Q i , and set:

[0157]

[0158]

[0159] set up:

[0160]

[0161] Similarly, we can get:

[0162]

[0163]

[0164]

[0165] also, is the transition probability matrix.

[0166] Step 4.2: The following inequality is finally obtained through calculation. According to the constraints, the error system is stable:

[0167]

[0168] in

[0169] Step 4.3: According to the constraints, we can get Therefore, the multi-underwater robot system realizes tracking control and obtains the proportional gain coefficient k of the controller according to the constraint conditions. i , differential gain coefficient α i And the correlation matrix E i ,F i ,G i ,H i ,L i ,M i ,N i ,O i ,X i ,Y i ,P i ,Q i ,

[0170] In specific implementation, the LMI toolbox of MATLAB can be used to solve the gain parameters and correlation matrix of the cooperative tracking controller.

[0171] Simulation experiment through simulink:

[0172] Figure 2The figure shows the Markov jump transition of the multi-underwater robot cooperative tracking communication topology. In this embodiment, the number of robots N is 3, and the number of topology switching modes Q is 2, that is, the communication topology is 2. As shown in the figure, in the first mode, the three underwater robots can receive status information from each other, then a 12 (1)>0,a 13 (1)>0,a 21 (1)>0,a 23 (1)>0,a 31 (1)>0,a 32 (1)>0, b1(1)>0, b2(1)>0, b3(1)>0. In the second mode, underwater robot 2 and underwater robot 3 cannot receive status information from each other, and underwater robot 3 cannot receive target point information, then a 12 (1)>0,a 13 (1)>0,a 22 (1)>0,a 23 (1) = 0, a 31 (1)>0,a 32 (1)=0, b1(2)>0, b2(2)>0, b3(2)=0.

[0173] The designed Lyapunov function is used to perform weak infinitesimal operator operations to prove the stability of tracking control and use LMI to solve the necessary parameters:

[0174] k1=diag{0.2944,0.2944,0.2944,0.2943,0.2943,0.2943},

[0175] k2=diag{0.1887,0.1887,0.1887,0.1887,0.1887,0.1887},

[0176] k3=diag{0.1588,0.1588,0.1588,0.1588,0.1588,0.1588},

[0177] α1=diag{0.7944,0.7944,0.7944,0.7944,0.7944,0.7944},

[0178] α2=diag{0.8015,0.8015,0.8015,0.8015,0.8015,0.8015},

[0179] α3=diag{0.8071,0.8071,0.8071,0.8072,0.8072,0.8072}.

[0180] aij (1)=[0,1,1;1,0,1;1,1,0],b i (1) = [1,0,0; 0,1,0; 0,0,1],

[0181] a ij (2)=[0,1,1;1,0,0;1,0,0],b i (2) = [1,0,0; 0,1,0; 0,0,0],

[0182] The target point is designed to be when time t∈(0s,180s), X d =[40; 60; -100; 7; 8; 9], when time t≥180s, X d =[60; 40; -100; 7; 8; 9], the initial six-degree-of-freedom states of the three underwater robots are [100; 85; -10; 5; 5; 5], [90; 90; -10; 5; 5; 5], [95; 100; -10; 5; 5; 5] respectively.

[0183] Figure 3-5 This is an image showing the real-time position changes of each underwater robot on the X, Y, and Z axes in the geodetic coordinate system during the collaborative tracking of the target point by multiple underwater robots in the simulation experiment. It can be clearly seen that the values ​​of the three parts can stably track the corresponding values ​​of the target point.

[0184] Figure 6-8 This is an image of the real-time changes in the rotation angles of each underwater robot on the X, Y, and Z axes in the geodetic coordinate system during the collaborative tracking of the target point by multiple underwater robots in the simulation experiment. It can be clearly seen that the values ​​of the three parts can stably track the corresponding values ​​of the target point.

[0185] Figure 9 In the simulation experiment, when multiple underwater robots cooperate to track the target point, the image of each underwater robot changes in real time in the three-dimensional space in the geodetic coordinate system, and multiple underwater robots track the target point.

[0186] The above description is only a preferred embodiment of the present invention and is not intended to limit the concept of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A design method for underwater robot cooperative controller based on Markov jump communication topology, characterized by: Based on a multi-underwater robot system, the three-axis coordinate positions and three-axis rotation angles of the underwater robots are selected to form six-degree-of-freedom state information. A controller is designed that takes into account communication delay and Markov jump communication topology. The design includes the following steps: Step 1: Combine the dynamic equations and kinematic equations of multiple underwater robots to obtain the multi-underwater robot system: in, is the control input; where x i 、y i 、z i Respectively represent the x-axis, y-axis and z-axis positions of each underwater robot in the geodetic coordinate system, φ i ,θ i ,ψ i Respectively represent the angles of rotation of each underwater robot on the three axes; M i is the inertia matrix; J i is the transformation matrix from the hull coordinate system to the earth coordinate system; C i is the Coriolis matrix; D i is the fluid damping matrix; g i is the descriptive term for gravity and buoyancy; T i is the external force applied to the underwater robot; i represents the i-th underwater robot, and N is the total number of underwater robots; Step 2: Cooperative tracking controller based on communication delay and Markov jump communication topology: Where i, j = 1,…, N, i ≠ j; k i is the proportional gain coefficient, α i is the differential gain coefficient; define the adjacency matrix A(p)=[a ij (p)]∈R N*N , represents the matrix under the pth mode. If the i-th underwater robot can receive the status information of the j-th underwater robot, then a ij (p)>0, otherwise a ij (p) = 0; in the pth mode, if the i-th underwater robot can receive the state information of the target point, then b i (p)>0, otherwise b i (p) = 0; p represents the Markov jump mode of the communication topology; is the state information of the i-th underwater robot, X d is the target point information, is the real-time tracking error, is the state information of the i-th underwater robot considering time delay, d i (t) = 0.5sint + 0.5 is a two-way time-varying lag; Step 3: Design a Lyapunov function containing the underwater robot state information and a stability constraint condition for the cooperative tracking controller. The Lyapunov function containing the underwater robot state information is specifically: Among them, E i ,F i ,G i ,H i ,L i ,M i ,N i ,O i , is a positive definite symmetric matrix, the matrix Step 4: Verify the stability of the cooperative tracking controller based on the weak infinitesimal operator of the Lyapunov function, and calculate the gain parameters and correlation matrix of the cooperative tracking controller.

2. The method for designing a cooperative controller for an underwater robot with a Markov jump communication topology according to claim 1, characterized in that: The stability constraints of the cooperative tracking controller in step 3 are specifically: For a multi-underwater robot system, if there exists a positive symmetric matrix E i ,F i ,G i ,H i ,L i ,M i ,M i ,O i , matrix If the following inequality holds, the multi-underwater robot system can track the target point, that is, when t→∞ Then the error system of the underwater robot is asymptotically stable, and the errors of position and velocity with the target gradually converge to zero: Among them, e l =[0 n×(l-1)n ,I n×n ,0 n×(27-l)n ], n represents the robot's degree of freedom, Π N+i =[e i -e N+i -2e 5N+i ],Π 2N+i =[e N+i -e 2N+i -2e 6N+i ], where i, j = 1,…, N, i ≠ j, where Λ i Represents L i 、N i , represent where Δ i Represents M i , O i , represent is the maximum value of the two-way time-varying delay, is the bidirectional time-varying delayed derivative The minimum value of .

3. The method for designing a cooperative controller for an underwater robot with a Markov jump communication topology according to claim 2, wherein: The weak infinitesimal operator of the Lyapunov function in step 4 is specifically: Perform weak infinitesimal operator operation on V1: Perform weak infinitesimal operator operations on V2: Perform weak infinitesimal operator operations on V3: Perform weak infinitesimal operator operations on V4: Perform weak infinitesimal operator operations on V5: Perform weak infinitesimal operator operations on V6: Perform weak infinitesimal operator operations on V7:

4. The method for designing a cooperative controller for an underwater robot with a Markov jump communication topology according to claim 3, wherein: Introduce the following inequality To perform scaling: Introduce the following two inequalities: We can get: Similarly, we introduce the following two inequalities: Similarly, we can get: Finally, we get:

5. The method for designing a cooperative controller for an underwater robot with a Markov jump communication topology according to claim 4, characterized in that: In step 4, the stability of the cooperative tracking controller is verified and the gain parameters and correlation matrix parameter values ​​of the cooperative tracking controller are calculated as follows: Step 4.1: Introduce the free matrix P i ,Q i , and set: Step 4.2: The following inequality is finally obtained through calculation. According to the constraints, the error system is stable: in Step 4.3: According to the constraints, we can get Therefore, the multi-underwater robot system realizes tracking control and obtains the proportional gain coefficient k of the controller according to the constraint conditions. i , differential gain coefficient α i And the correlation matrix F i ,F i ,G i ,H i ,L i ,M i ,N i ,O i ,X i ,Y i ,P i ,Q i , 6. The method for designing a cooperative controller for an underwater robot with a Markov jump communication topology according to claim 5, characterized in that: In step 4.3, the LMI toolbox of MATLAB is used to solve the gain parameters and correlation matrix of the cooperative tracking controller.

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