Full-distributed underwater robot cluster attitude optimal consistency control method and system

Abstract

The invention discloses a fully-distributed underwater robot cluster attitude optimal consistency control method and system, relates to the technical field of underwater robot control, and aims to overcome the defects that an existing cooperative control protocol cannot perform optimal design on control input and global information needs to be used for solving control parameters. The method is technically characterized by comprising the following steps: modeling an underwater robot cluster attitude system into a high-order nonlinear multi-rigid-body attitude system, constructing a consistency adjustment variable, and designing a fully-distributed attitude consistency optimization control protocol; aiming at a fully-distributed attitude consistency optimization control protocol, solving an optimal control variable which enables the overall performance function of the system to be optimal based on an optimal control theory; and controlling the attitude of the underwater robot cluster based on the optimal control variable. According to the method, the attitude component of the underwater robot can be converged to a preset consistency final value, the solution of the control gain parameter does not depend on any global information, and the global performance function of the system can be optimal.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater robot control, and in particular to a method and system for optimal consistency control of a fully distributed underwater robot cluster posture. Background Art

[0002] Underwater robots have the advantages of flexible deployment and strong maneuverability, and have become one of the key equipment in the field of ocean exploration. An underwater robot cluster system is usually a network system composed of multiple underwater robots with autonomous capabilities. The robots can complete complex underwater collaborative exploration tasks through information exchange. Attitude consistency coordination is the prerequisite for underwater robot cluster systems to perform various tasks, and has important research value in the field of underwater robot control technology. The document "Event-triggered fixed-time attitude consensus with fixed and switching topologies, IEEE Transactions on Automatic Control, 2022, 67(8): 4138-4145" discloses an event-triggered cluster system attitude coordination control method. This method designs a coordination control protocol based on axis-angle attitude representation to achieve attitude consistency of the cluster system. The technical problem of the control algorithm described in the document is that it does not consider the optimization problem of the system's performance indicators, resulting in the control protocol being unable to achieve the desired control performance with the optimal control input. In addition, the control protocol designed in the document needs to use the eigenvalue information of the global communication topology when solving the parameters, which is not conducive to its application in large-scale underwater robot cluster systems. Summary of the invention

[0003] In view of the above problems, the present invention proposes a fully distributed underwater robot cluster posture optimal consistency control method and system to overcome the shortcomings of existing collaborative control protocols that are unable to optimize the control input and require the use of global information to solve control parameters.

[0004] According to one aspect of the present invention, a fully distributed underwater robot cluster attitude optimal consistency control method is proposed, the method comprising:

[0005] Step 1: Model the underwater robot cluster attitude system as a high-order nonlinear multi-rigid body attitude system, construct consistency adjustment variables, and design a fully distributed attitude consistency optimization control protocol;

[0006] Step 2: for the fully distributed attitude consistency optimization control protocol, based on the optimal control theory, solve the optimal control variables that make the global performance function of the system optimal;

[0007] Step three: Control the posture of the underwater robot cluster based on the optimal control variables.

[0008] Furthermore, the high-order nonlinear multi-rigid body posture system described in step 1 is established as follows:

[0009]

[0010] In the formula, J i represents the inertia matrix of the underwater robot; ω i represents the attitude angular velocity, The skew-symmetric matrix representing the attitude angular velocity; u i Indicates the control input quantity; Represents the underwater robot posture quaternion and satisfies N represents the total number of robots; I3 represents the third-order identity matrix.

[0011] Furthermore, the consistency adjustment variable in step 1 is constructed as follows:

[0012]

[0013] In the formula, γ is a constant greater than 0.

[0014] Furthermore, the fully distributed attitude consistency optimization control protocol described in step 1 is designed as follows:

[0015]

[0016] In the formula, τ i is the control variable to be solved;

[0017] Furthermore, the system global performance function in step 2 is:

[0018]

[0019] In the formula, ξ=[ξ i ] i∈{1,...,N} , is the error variable, α i To meet the conditions and A non-negative vector of The graph Laplacian matrix representing the topology of communication with the underwater robot cluster, where And l ij =-a ij ,i≠j,a ij It is used to represent the communication relationship between the i-th robot and the j-th robot, a ij =1 means that the i-th robot can directly obtain the status information of the j-th robot, otherwise aij =0; τ = [τ i ] i∈{1,...,N} , and is a pre-given positive parameter; I 3N Represents the identity matrix of dimension 3N.

[0020] Furthermore, the specific process of step 2 includes:

[0021] Select the following Hamiltonian function:

[0022]

[0023] Where V represents the value function associated with the global performance function, represents the partial derivative of the value function with respect to the error variable;

[0024] Control variable τ i The optimal value of is obtained by solving the equation get:

[0025]

[0026] Substituting the above formula into the Hamiltonian function and solving it, we get Then the optimal control variable is obtained:

[0027]

[0028] In the formula, the optimal control gain parameter is

[0029] According to another aspect of the present invention, a fully distributed underwater robot cluster attitude optimal consistency control system is proposed, the system comprising:

[0030] A control protocol design module, which is configured to model the underwater robot cluster attitude system as a high-order nonlinear multi-rigid body attitude system, construct consistency adjustment variables, and design a fully distributed attitude consistency optimization control protocol;

[0031] An optimal control variable solving module, configured to solve the optimal control variable that makes the system global performance function optimal based on the optimal control theory for the fully distributed attitude consistency optimization control protocol;

[0032] The attitude control module is configured to control the attitude of the underwater robot cluster based on the optimal control variables.

[0033] Furthermore, the high-order nonlinear multi-rigid body posture system in the control protocol design module is as follows:

[0034]

[0035] In the formula, J i represents the inertia matrix of the underwater robot; ω i represents the attitude angular velocity, The skew-symmetric matrix representing the attitude angular velocity; u i Indicates the control input quantity; Represents the underwater robot posture quaternion and satisfies N represents the total number of robots; I3 represents the third-order identity matrix.

[0036] Furthermore, the consistency adjustment variable in the control protocol design module is constructed as follows:

[0037]

[0038] In the formula, γ is a constant greater than 0;

[0039] The fully distributed attitude consistency optimization control protocol is designed as follows:

[0040]

[0041] In the formula, τ i is the control variable to be solved;

[0042] Furthermore, the system global performance function in the optimal control variable solving module is:

[0043]

[0044] In the formula, ξ=[ξ i ] i∈{1,...,N} , is the error variable, α i To meet the conditions and A non-negative vector of The graph Laplacian matrix representing the topology of communication with the underwater robot cluster, where And l ij =-a ij ,i≠j,a ij It is used to represent the communication relationship between the i-th robot and the j-th robot, a ij =1 means that the i-th robot can directly obtain the status information of the j-th robot, otherwise a ij =0; τ = [τ i ] i∈{1,...,N} , and is a pre-given positive parameter; I 3Nrepresents the identity matrix of dimension 3N;

[0045] The specific process of solving the optimal control variables includes:

[0046] Select the following Hamiltonian function:

[0047]

[0048] Where V represents the value function associated with the global performance function, represents the partial derivative of the value function with respect to the error variable;

[0049] Control variable τ i The optimal value of is obtained by solving the equation get:

[0050]

[0051] Substituting the above formula into the Hamiltonian function and solving it, we get Then the optimal control variable is obtained:

[0052]

[0053] In the formula, the optimal control gain parameter is

[0054] The beneficial technical effects of the present invention are:

[0055] The present invention proposes a fully distributed underwater robot cluster posture optimal consistency control method and system. First, the underwater robot cluster posture system is modeled as a high-order nonlinear multi-rigid body posture system, consistency adjustment variables are constructed, and a fully distributed posture consistency optimization control protocol is designed; then, for the fully distributed posture consistency optimization control protocol, the optimal control variables that make the system global performance function optimal are solved based on the optimal control theory; finally, the underwater robot cluster posture is controlled based on the optimal control variables. Using the fully distributed posture consistency optimization control protocol designed by the present invention, the posture components of each underwater robot can eventually converge to a predetermined consistency final value, and the solution of the control gain parameters does not need to rely on any global information. In addition, compared with the non-optimal control protocol, the fully distributed posture consistency optimization control protocol designed by the present invention can make the system global performance function reach the minimum (optimal) value. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] The present invention can be better understood by referring to the description given below in conjunction with the accompanying drawings, which together with the following detailed description are included in this specification and form a part of this specification, and are used to further illustrate the preferred embodiments of the present invention and explain the principles and advantages of the present invention.

[0057] Figure 1 is a flow chart of a method for optimal consistency control of a fully distributed underwater robot cluster posture according to an embodiment of the present invention;

[0058] Figure 2 is a schematic diagram of the communication topology between five underwater robots (respectively marked as 1 to 5) in an embodiment of the present invention;

[0059] Figure 3 is the attitude component q under the fully distributed attitude consistency optimization control protocol in the embodiment of the present invention i1 Graph of evolution over time;

[0060] Figure 4 is the attitude component q under the fully distributed attitude consistency optimization control protocol in the embodiment of the present invention i2 The time evolution curve of

[0061] Figure 5 is the attitude component q under the fully distributed attitude consistency optimization control protocol in the embodiment of the present invention i3 The time evolution curve of

[0062] Figure 6 It is a time evolution curve diagram of the global performance function F under the action of four groups of non-optimal control gain parameters and the optimal control gain parameters of the present invention in an embodiment of the present invention. DETAILED DESCRIPTION

[0063] In order to enable those skilled in the art to better understand the scheme of the present invention, exemplary implementations or embodiments of the present invention will be described below in conjunction with the accompanying drawings. Obviously, the described implementations or embodiments are only implementations or embodiments of a part of the present invention, not all of them. Based on the implementations or embodiments of the present invention, all other implementations or embodiments obtained by ordinary technicians in the field without creative work should fall within the scope of protection of the present invention.

[0064] The present invention provides a fully distributed underwater robot cluster posture optimal consistency control method and system. Considering that the underwater robot is a rigid body, the underwater robot cluster posture system is modeled as a high-order nonlinear multi-rigid body posture system, a consistency misadjustment variable is constructed, and a fully distributed posture consistency optimization control protocol is designed; based on the optimal control theory, the control gain parameters that can ensure the optimal global performance function of the system are solved; and the underwater robot cluster posture is controlled based on the optimal control variable. And the control protocol designed by differential equation theory analysis can ensure that the posture components of multiple underwater robots can reach a predetermined consistency final value. The present invention can achieve the desired control performance with the optimal control input, and the solution of the control gain parameters does not need to rely on any global information. The control protocol has the advantage of being fully distributed, which is more conducive to application in large-scale underwater robot cluster systems.

[0065] The embodiment of the present invention proposes a fully distributed underwater robot cluster posture optimal consistency control method, such as Figure 1 As shown, the method includes:

[0066] Step 1: Model the underwater robot cluster attitude system as a high-order nonlinear multi-rigid body attitude system, construct consistency adjustment variables, and design a fully distributed attitude consistency optimization control protocol;

[0067] Step 2: for the fully distributed attitude consistency optimization control protocol, based on the optimal control theory, solve the optimal control variables that make the global performance function of the system optimal;

[0068] Step three: Control the posture of the underwater robot cluster based on the optimal control variables.

[0069] The embodiments of the present invention are described in detail below.

[0070] First, in step one, the underwater robot is considered as a rigid body, the underwater robot cluster attitude system is modeled as a nonlinear multi-rigid body attitude system, the consistency adjustment variables are constructed, and a fully distributed attitude consistency optimization control protocol is designed.

[0071] The following underwater robot cluster posture model is given:

[0072]

[0073] Where N represents the total number of robots; is the inertia matrix of the underwater robot, is the attitude angular velocity, is the underwater robot attitude quaternion and satisfies u i To control the input quantity; The skew-symmetric matrix representing the attitude angular velocity, that is, the × in the upper right corner represents the skew-symmetric matrix of the matrix.

[0074] Construct the following consistency adjustment variable:

[0075]

[0076] In the formula, the parameter γ is a constant greater than 0.

[0077] For the underwater robot cluster posture model given in equation (1), the design goal of the consistency control protocol is to ensure the following conditions:

[0078]

[0079] In the formula, q c is the final consistency value that each underwater robot needs to achieve, and its specific value is s i (0) is the consistency adjustment variable s i The initial value of α i To meet the conditions and A non-negative vector of ; The graph Laplacian matrix representing the topology of communication with the underwater robot cluster, where And l ij =-a ij ,i≠j,a ij It is used to represent the communication relationship between the i-th robot and the j-th robot, a ij =1 means that the i-th robot can directly obtain the status information of the j-th robot, otherwise a ij =0.

[0080] The derivative of formula (2) with respect to time can be obtained:

[0081]

[0082] In the formula, I3 represents the third-order identity matrix.

[0083] Select variables The fully distributed attitude consistency optimization control protocol is designed as:

[0084]

[0085] In the formula, τ i is the control variable to be solved.

[0086] Then, in step 2, for the fully distributed attitude consistency optimization control protocol designed in step 1, the optimal control variables that can ensure the optimal global performance function of the system are solved based on the optimal control theory.

[0087] The following global performance functions are selected for the control protocol (5):

[0088]

[0089] In the formula, ξ=[ξ i ] i∈{1,...,N} , is the error variable; τ=[τ i ] i∈{1,...,N} , and is a pre-given positive parameter; I 3N Represents the identity matrix of dimension 3N.

[0090] Select the following Hamiltonian function:

[0091]

[0092] Where V represents the value function associated with the global performance function (6), represents the partial derivative of the value function with respect to the error variable. According to the optimal control theory, the control variable τ i The optimal value of can be obtained by solving the equation get:

[0093]

[0094] Substituting equation (8) into the Hamiltonian function (7) yields:

[0095]

[0096] By solving equation (9), we have:

[0097]

[0098] Substituting formula (10) into formula (8) yields:

[0099]

[0100] In the formula, the optimal control gain parameter is

[0101] Then, in step three, the posture of the underwater robot cluster is controlled based on the optimal control variables.

[0102] Furthermore, for the fully distributed attitude consistency optimization control protocol designed in step 1, the control protocol designed by differential equation theory analysis can ensure that the attitude components of multiple underwater robots can reach a predetermined consistency final value. as follows.

[0103] Substituting the fully distributed attitude consistency optimization control protocol (5) and equation (11) into equation (4), we have:

[0104]

[0105] According to cluster consistency theory, when the control gain parameter k is greater than zero, we have:

[0106]

[0107] Established. When , the following first-order nonhomogeneous linear differential equation holds:

[0108]

[0109] Let q i =[q i1 ,q i2 ,q i3 ] T and i =[s i1 ,s i2 ,s i3 ] T , then formula (14) can be further rewritten as:

[0110]

[0111] According to the differential equation theory, the solution of equation (15) is:

[0112]

[0113] In the formula, c l is an arbitrary constant. When the parameter γ>0 holds, it can be inferred from formula (16):

[0114]

[0115] Right now According to the above analysis, the posture components of multiple underwater robots can reach a predetermined consistency final value.

[0116] The following examples are used to verify the beneficial technical effects of the present invention.

[0117] Consider a cluster system consisting of five underwater robots (labeled 1 to 5), and the communication topology between the robots is as follows: Figure 2 As shown, the Laplace matrix corresponding to the communication topology is expressed as follows:

[0118]

[0119] The inertia matrix parameters of each robot are selected as:

[0120]

[0121] Let γ = 2, as well as Then the optimal control gain parameter can be calculated as The attitude consistency optimization control protocol proposed by the present invention controls the gain parameter k only with the pre-given parameter and The solution process does not need to use global information, so it has the advantage of being fully distributed. In addition, the initial values ​​of the states of the five underwater robots are given as follows:

[0122]

[0123] Select α = [1, 0, 0, 0, 0] T Satisfy the conditions and The predetermined consistency final value can be calculated as q c =[-0.09,-0.19,-0.29] T By adopting the fully distributed attitude consistency optimization control protocol designed by the present invention, the attitude component curves of each underwater robot can be obtained as follows: Figure 3-Figure 5 As shown in the figure, the simulation curve shows that the posture components of the five underwater robots can eventually converge to the pre-given consistency final value, and the consistency convergence time is 6 seconds.

[0124] In addition, in order to further verify the superiority of the protocol proposed in this invention, the time evolution curves of the global performance function under the action of multiple groups of different control gain parameters k are given, such as Figure 6 As shown in the figure, by comparing the curves, it can be seen that the final values ​​of the global performance function under the four groups of non-optimal control gain parameters are 42.17, 25.63, 23.78 and 35.44 respectively, while the final value of the global performance function under the optimal control gain parameters designed by the present invention is 22.33. Therefore, the fully distributed attitude consistency optimization control protocol designed by the present invention can make the global performance function of the system reach the minimum (optimal) value.

[0125] It should be noted that the contents not introduced in detail in the present invention (such as graph theory, optimal control theory, differential equation theory, matrix theory) are common knowledge in the field.

[0126] Another embodiment of the present invention provides a fully distributed underwater robot cluster posture optimal consistency control system, the system comprising:

[0127] A control protocol design module, which is configured to model the underwater robot cluster attitude system as a high-order nonlinear multi-rigid body attitude system, construct consistency adjustment variables, and design a fully distributed attitude consistency optimization control protocol;

[0128] An optimal control variable solving module, configured to solve the optimal control variable that makes the system global performance function optimal based on the optimal control theory for the fully distributed attitude consistency optimization control protocol;

[0129] The attitude control module is configured to control the attitude of the underwater robot cluster based on the optimal control variables.

[0130] In this embodiment, preferably, the high-order nonlinear multi-rigid body posture system in the control protocol design module is as follows:

[0131]

[0132] In the formula, J i represents the inertia matrix of the underwater robot; ω i represents the attitude angular velocity, The skew-symmetric matrix representing the attitude angular velocity; u i Indicates the control input quantity; Represents the underwater robot posture quaternion and satisfies N represents the total number of robots; I3 represents the third-order identity matrix.

[0133] In this embodiment, preferably, the consistency adjustment variable in the control protocol design module is constructed as follows:

[0134]

[0135] In the formula, γ is a constant greater than 0;

[0136] The fully distributed attitude consistency optimization control protocol is designed as follows:

[0137]

[0138] In the formula, τ i is the control variable to be solved;

[0139] In this embodiment, preferably, the system global performance function in the optimal control variable solving module is:

[0140]

[0141] In the formula, ξ=[ξ i ] i∈{1,...,N} , is the error variable, αi To meet the conditions and A non-negative vector of The graph Laplacian matrix representing the topology of communication with the underwater robot cluster, where And l ij =-a ij ,i≠j,a ij It is used to represent the communication relationship between the i-th robot and the j-th robot, a ij =1 means that the i-th robot can directly obtain the status information of the j-th robot, otherwise a ij =0; τ = [τ i ] i∈{1,...,N} , and is a pre-given positive parameter; I 3N represents the identity matrix of dimension 3N;

[0142] The specific process of solving the optimal control variables includes:

[0143] Select the following Hamiltonian function:

[0144]

[0145] Where V represents the value function associated with the global performance function, represents the partial derivative of the value function with respect to the error variable;

[0146] Control variable τ i The optimal value of is obtained by solving the equation get:

[0147]

[0148] Substituting the above formula into the Hamiltonian function and solving it, we get Then the optimal control variable is obtained:

[0149]

[0150] In the formula, the optimal control gain parameter is

[0151] The function of a fully distributed underwater robot cluster posture optimal consistency control system described in an embodiment of the present invention can be explained by the aforementioned fully distributed underwater robot cluster posture optimal consistency control method. Therefore, for the parts not described in detail in the system embodiment, please refer to the above method embodiment and will not be repeated here.

[0152] Although the present invention has been described according to a limited number of embodiments, it will be apparent to those skilled in the art, with the benefit of the above description, that other embodiments are contemplated within the scope of the invention thus described. The disclosure of the present invention is intended to be illustrative rather than restrictive of the scope of the invention, which is defined by the appended claims.

Claims

1. A fully distributed underwater robot cluster attitude optimal consistency control method, characterized in that: include: Step 1: Model the underwater robot cluster attitude system as a high-order nonlinear multi-rigid body attitude system, construct consistency adjustment variables, and design a fully distributed attitude consistency optimization control protocol; Step 2: for the fully distributed attitude consistency optimization control protocol, based on the optimal control theory, solve the optimal control variables that make the global performance function of the system optimal; Step three: Control the posture of the underwater robot cluster based on the optimal control variables.

2. The method for optimal consistency control of the attitude of a fully distributed underwater robot cluster according to claim 1 is characterized in that: The high-order nonlinear multi-rigid body posture system described in step 1 is established as follows: In the formula, J i represents the inertia matrix of the underwater robot; ω i represents the attitude angular velocity, The skew-symmetric matrix representing the attitude angular velocity; u i represents the control input; [q i Τ ,q i0 ] Τ Represents the underwater robot posture quaternion and satisfies N represents the total number of robots; I3 represents the third-order identity matrix.

3. The method for optimal consistency control of the attitude of a fully distributed underwater robot cluster according to claim 2 is characterized in that: The consistency adjustment variable described in step 1 is constructed as follows: In the formula, γ is a constant greater than 0.

4. The method for optimal consistency control of the attitude of a fully distributed underwater robot cluster according to claim 3 is characterized in that: The fully distributed attitude consistency optimization control protocol described in step 1 is designed as follows: <h2 style=";text-align:left;direction:ltr">u<h2 style=";text-align:left;direction:ltr"> i <h2 style=";text-align:left;direction:ltr"> 2-2J<h2 style=";text-align:left;direction:ltr"> i <h2 style=";text-align:left;direction:ltr"> Q<h2 style=";text-align:left;direction:ltr"> i <h2 style=";text-align:left;direction:ltr"> -1 <h2 style=";text-align:left;direction:ltr"> f<h2 style=";text-align:left;direction:ltr"> i <h2 style=";text-align:left;direction:ltr"> +2J<h2 style=";text-align:left;direction:ltr"> i <h2 style=";text-align:left;direction:ltr"> Q<h2 style=";text-align:left;direction:ltr"> i <h2 style=";text-align:left;direction:ltr"> -1 <h2 style=";text-align:left;direction:ltr"> τ<h2 style=";text-align:left;direction:ltr"> i In the formula, τ i is the control variable to be solved; 5. A fully distributed underwater robot cluster attitude optimal consistency control method according to claim 4, characterized in that: The system global performance function described in step 2 is: In the formula, ξ=[ξ i ] i∈{1,...,N} , is the error variable, α i To meet the conditions and A non-negative vector of The graph Laplacian matrix representing the topology of communication with the underwater robot cluster, where And l ij =-a ij ,i≠j,a ij It is used to represent the communication relationship between the i-th robot and the j-th robot, a ij =1 means that the i-th robot can directly obtain the status information of the j-th robot, otherwise a ij =0; τ = [τ i ] i∈{1,...,N} , and is a pre-given positive parameter, I 3N Represents the identity matrix of dimension 3N.

6. The method for optimal consistency control of the attitude of a fully distributed underwater robot cluster according to claim 5 is characterized in that: The specific process of step 2 includes: Select the following Hamiltonian function: Where V represents the value function associated with the global performance function, represents the partial derivative of the value function with respect to the error variable; Control variable τ i The optimal value of is obtained by solving the equation get: Substituting the above equation into the Hamiltonian function and solving it, we get Then the optimal control variable is obtained: In the formula, the optimal control gain parameter is 7. A fully distributed underwater robot cluster attitude optimal consistency control system, characterized in that: include: A control protocol design module, which is configured to model the underwater robot cluster attitude system as a high-order nonlinear multi-rigid body attitude system, construct consistency adjustment variables, and design a fully distributed attitude consistency optimization control protocol; An optimal control variable solving module, configured to solve the optimal control variable that makes the system global performance function optimal based on the optimal control theory for the fully distributed attitude consistency optimization control protocol; The attitude control module is configured to control the attitude of the underwater robot cluster based on the optimal control variables.

8. The fully distributed underwater robot cluster attitude optimal consistency control system according to claim 7, characterized in that: The high-order nonlinear multi-rigid body attitude system in the control protocol design module is as follows: In the formula, J i represents the inertia matrix of the underwater robot; ω i represents the attitude angular velocity, The skew-symmetric matrix representing the attitude angular velocity; u i represents the control input; [q i Τ ,q i0 ] Τ Represents the underwater robot posture quaternion and satisfies N represents the total number of robots; I3 represents the third-order identity matrix.

9. A fully distributed underwater robot cluster attitude optimal consistency control system according to claim 8, characterized in that: The consistency adjustment variable in the control protocol design module is constructed as follows: In the formula, γ is a constant greater than 0; The fully distributed attitude consistency optimization control protocol is designed as follows: <h2 style=";text-align:left;direction:ltr">u<h2 style=";text-align:left;direction:ltr"> i <h2 style=";text-align:left;direction:ltr"> 2-2J<h2 style=";text-align:left;direction:ltr"> i <h2 style=";text-align:left;direction:ltr"> Q<h2 style=";text-align:left;direction:ltr"> i <h2 style=";text-align:left;direction:ltr"> -1 <h2 style=";text-align:left;direction:ltr"> f<h2 style=";text-align:left;direction:ltr"> i <h2 style=";text-align:left;direction:ltr"> +2J<h2 style=";text-align:left;direction:ltr"> i <h2 style=";text-align:left;direction:ltr"> Q<h2 style=";text-align:left;direction:ltr"> i <h2 style=";text-align:left;direction:ltr"> -1 <h2 style=";text-align:left;direction:ltr"> t<h2 style=";text-align:left;direction:ltr"> i In the formula, τ i is the control variable to be solved; 10. A fully distributed underwater robot cluster attitude optimal consistency control system according to claim 9, characterized in that: The system global performance function in the optimal control variable solving module is: In the formula, ξ=[ξ i ] i∈{1,...,N} , is the error variable, α i To meet the conditions and A non-negative vector of The graph Laplacian matrix representing the topology of communication with the underwater robot cluster, where And l ij =-a ij ,i≠j,a ij It is used to represent the communication relationship between the i-th robot and the j-th robot, a ij =1 means that the i-th robot can directly obtain the status information of the j-th robot, otherwise a ij =0; τ = [τ i ] i∈{1,...,N} , and is a pre-given positive parameter; I 3N represents the identity matrix of dimension 3N; The specific process of solving the optimal control variables includes: Select the following Hamiltonian function: Where V represents the value function associated with the global performance function, represents the partial derivative of the value function with respect to the error variable; Control variable τ i The optimal value of is obtained by solving the equation get: Substituting the above equation into the Hamiltonian function and solving it, we get Then the optimal control variable is obtained: In the formula, the optimal control gain parameter is

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