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

Abstract

The application discloses a kind of full-distributed underwater robot cluster posture optimal consistency control method and system, it is related to underwater robot control technical field, to overcome the insufficient that existing cooperative control protocol cannot optimize design to control input and control parameter solution needs to use global information.This application technical points include: underwater robot cluster posture system is modeled as high-order nonlinear multi-rigid-body posture system, constructs consistency regulating variable, designs full-distributed posture consistency optimization control protocol;For full-distributed posture consistency optimization control protocol, based on optimal control theory, the optimal control variable that makes the system global performance function optimal is solved;Based on optimal control variable, the posture of underwater robot cluster is controlled.The application can make underwater robot posture component converge to the consistency terminal value given in advance, and the solution of control gain parameter is not dependent on any global information, and the system global performance function can be optimized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of underwater robot control, and particularly relates to a full-distributed underwater robot cluster attitude optimal consistency control method and system. BACKGROUND

[0002] Underwater robots have the advantages of flexible deployment and strong maneuverability, and have become one of the key equipments in the field of ocean exploration. An underwater robot cluster system is usually a network system composed of multiple underwater robots with autonomous ability, and complex underwater cooperative detection tasks can be completed through information exchange between the robots. Attitude consistency cooperation is the premise 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 a cluster system attitude cooperation control method based on event triggering. The method designs a cooperative control protocol based on the axis angle attitude representation, and realizes the attitude consistency of the cluster system. The technical problem existing in the control algorithm described in the document is that the performance index optimization problem of the system is not considered, which leads to the fact that the control protocol cannot achieve the desired control performance with optimal control input, and 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 application in large-scale underwater robot cluster systems. SUMMARY

[0003] In view of the above problems, the present application proposes a full-distributed underwater robot cluster attitude optimal consistency control method and system to overcome the shortcomings that the existing cooperative control protocol cannot optimize the control input and the control parameter solving needs to use global information.

[0004] According to an aspect of the present application, a full-distributed underwater robot cluster attitude optimal consistency control method is proposed, which comprises:

[0005] Step one, model the underwater robot cluster attitude system as a high-order nonlinear multi-rigid-body attitude system, construct a consistency regulating variable, and design a full-distributed attitude consistency optimal control protocol;

[0006] Step two, for the full-distributed attitude consistency optimal control protocol, solve the optimal control variable that makes the global performance function of the system optimal based on the optimal control theory;

[0007] Step three, control the underwater robot cluster posture based on the optimal control variable.

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

[0009]

[0010] wherein, J i represents the inertia matrix of the underwater robot; ω i represents the attitude angular velocity, represents the skew-symmetric matrix of the attitude angular velocity; u i represents the control input; represents the underwater robot posture quaternion and satisfies N represents the total number of robots; I3 represents a three-order unit matrix.

[0011] Further, the consistency adjustment variable in step one is constructed as follows:

[0012]

[0013] wherein, γ is a constant greater than 0.

[0014] Further, the full-distributed posture consistency optimization control protocol in step one is designed as follows:

[0015]

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

[0017] Further, the system global performance function in step two is:

[0018]

[0019] wherein, ξ = [ξ i ] i∈{1,...,N} , is the error variable, α i is a non-negative vector satisfying the condition and , represents the graph Laplacian matrix of the underwater robot cluster communication topology, wherein and l ij =-a ij , i≠j, a ij is used to represent the communication relationship between the ith robot and the jth robot, a ij =1 indicates that the ith robot can directly obtain the state information of the jth robot, otherwise aij = 0; τ = [τ i ] i∈{1,...,N} , and is a pre-defined positive parameter; I 3N denotes a 3N-dimensional identity matrix.

[0020] Further, the specific process of step two includes:

[0021] The following Hamiltonian function is selected:

[0022]

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

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

[0025]

[0026] Substituting the above equation into the Hamiltonian function and solving it yields and further obtaining the optimal control variable as:

[0027]

[0028] wherein the optimal control gain parameter is

[0029] According to another aspect of the present application, a full-distributed underwater robot cluster posture optimal consistency control system is provided, which comprises:

[0030] a control protocol design module configured to model the underwater robot cluster posture system as a high-order nonlinear multi-rigid-body posture system, construct a consistency regulating variable, and design a full-distributed posture consistency optimal control protocol;

[0031] an optimal control variable solving module configured to solve, based on optimal control theory, an optimal control variable that makes the system global performance function optimal for the full-distributed posture consistency optimal control protocol;

[0032] a posture control module configured to control the underwater robot cluster posture based on the optimal control variable.

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

[0034]

[0035] where J i represents the inertia matrix of the underwater robot; ω i represents the attitude angular velocity, represents the skew-symmetric matrix of the attitude angular velocity; u i represents the control input; represents the underwater robot attitude quaternion and satisfies N represents the total number of robots; I3 represents a three-order unit matrix.

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

[0037]

[0038] where γ is a constant greater than 0;

[0039] The full-distributed attitude consistency optimal control protocol is designed as follows:

[0040]

[0041] where τ i is the control variable to be solved;

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

[0043]

[0044] where ξ = [ξ i ] i∈{1,...,N} , is an error variable, α i is a non-negative vector satisfying the condition and is a non-negative vector satisfying the condition represents the graph Laplacian matrix of the underwater robot cluster communication topology, where and l ij =-a ij , i≠j, a ij is used to represent the communication relationship between the ith robot and the jth robot, a ij =1 indicates that the ith robot can directly obtain the state information of the jth robot, otherwise a ij =0; τ = [τ i ] i∈{1,...,N} , and are pre-defined positive parameters; I 3Ndenotes a 3N-dimensional identity matrix;

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

[0046] The following Hamilton function is selected:

[0047]

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

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

[0050]

[0051] Substituting the above formula into the Hamilton function and solving it obtains and further obtains the optimal control variable as

[0052]

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

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

[0055] The present application provides a full-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, a consistency regulating variable is constructed, and a full-distributed posture consistency optimization control protocol is designed; then, for the full-distributed posture consistency optimization control protocol, the optimal control theory is used to solve the optimal control variable that makes the system global performance function optimal; finally, the underwater robot cluster posture is controlled based on the optimal control variable. The full-distributed posture consistency optimization control protocol designed by the present application can make the posture components of each underwater robot ultimately converge to a pre-defined consistency terminal value, and the solution of the control gain parameter does not need to depend on any global information. In addition, compared with the non-optimal control protocol, the full-distributed posture consistency optimization control protocol designed by the present application can make the system global performance function reach the minimum (optimal) value. BRIEF DESCRIPTION OF DRAWINGS

[0056] The present application can be better understood by reference to the following description taken in conjunction with the accompanying drawings, which together with the detailed description, illustrate the preferred embodiments of the application, and, wherein: ​

[0057] Figure 1 is a flow chart of the full-distributed underwater robot cluster attitude optimal consistency control method described in the embodiments of the present application;

[0058] Figure 2 is a communication topology schematic diagram between 5 underwater robots (labeled 1 to 5 respectively) in the embodiments of the present application;

[0059] Figure 3 is a time evolution curve diagram of the attitude component q i1 under the action of the full-distributed attitude consistency optimal control protocol in the embodiments of the present application;

[0060] Figure 4 is a time evolution curve diagram of the attitude component q i2 under the action of the full-distributed attitude consistency optimal control protocol in the embodiments of the present application;

[0061] Figure 5 is a time evolution curve diagram of the attitude component q i3 under the action of the full-distributed attitude consistency optimal control protocol in the embodiments of the present application;

[0062] Figure 6 is a time evolution curve diagram of the global performance function F under the action of 4 groups of non-optimal control gain parameters and the optimal control gain parameter of the present application. DETAILED DESCRIPTION

[0063] In order for those skilled in the art to better understand the present application, the exemplary embodiments or examples of the present application will be described in the following with reference to the accompanying drawings. Obviously, the described embodiments or examples are only part of the embodiments or examples of the present application, not all. Based on the embodiments or examples in the present application, all other embodiments or examples obtained by those skilled in the art without creative labor should belong to the scope of protection of the present application.

[0064] The application provides a full-distributed underwater robot cluster attitude optimal consistency control method and system. Considering that the underwater robot is a rigid body, the underwater robot cluster attitude system is modeled as a high-order nonlinear multi-rigid-body attitude system, a consistency adjustment variable is constructed, and a full-distributed attitude consistency optimal control protocol is designed; based on optimal control theory, a control gain parameter capable of ensuring that the global performance function of the system is optimal is solved; and based on the optimal control variable, the underwater robot cluster attitude is controlled. And the differential equation theory is used to analyze that the designed control protocol can ensure that the attitude components of the multiple underwater robots can reach a pre-set consistency terminal value. The application can realize the expected control performance with optimal control input, and the solution of the control gain parameter does not need to depend on any global information, and the control protocol has the advantage of full distribution, which is more conducive to application in a large-scale underwater robot cluster system.

[0065] An embodiment of the application provides a full-distributed underwater robot cluster attitude optimal consistency control method, as shown in Figure 1 The method comprises the following steps.

[0066] Step 1: modeling the underwater robot cluster attitude system as a high-order nonlinear multi-rigid-body attitude system, constructing a consistency adjustment variable, and designing a full-distributed attitude consistency optimal control protocol.

[0067] Step 2: based on the full-distributed attitude consistency optimal control protocol, solving an optimal control variable that makes the global performance function of the system optimal based on optimal control theory.

[0068] Step 3: based on the optimal control variable, controlling the underwater robot cluster attitude.

[0069] The following will describe the embodiment of the application in detail.

[0070] Firstly, in step 1, considering that the underwater robot is a rigid body, the underwater robot cluster attitude system is modeled as a nonlinear multi-rigid-body attitude system, a consistency adjustment variable is constructed, and a full-distributed attitude consistency optimal control protocol is designed.

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

[0072]

[0073] In the formula, 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 is the control input; Skew-symmetric matrix representing the attitude angular velocity, i.e., the × in the upper right corner represents the skew-symmetric matrix of the matrix.

[0074] The consistent regulating variable is constructed as follows:

[0075]

[0076] where the parameter γ is a constant greater than 0.

[0077] For the underwater robot swarm attitude model given in equation (1), the design goal of the consistent control protocol is to ensure that the following condition is met:

[0078]

[0079] where q c is the consistent final value to be reached by each underwater robot, and the specific value is s i (0) is the initial value of the consistent regulating variable s i , α i is a non-negative vector that satisfies the conditions and ; represents the graph Laplacian matrix of the communication topology of the underwater robot swarm, where and l ij = -a ij , i≠j, a ij is used to represent the communication relationship between the i th robot and the j th robot, a ij = 1 indicates that the i th robot can directly obtain the state information of the j th robot, otherwise a ij = 0.

[0080] Taking the derivative of equation (2) with respect to time gives:

[0081]

[0082] where I3 represents a three-order unit matrix.

[0083] The variable is selected to design the full-distributed attitude consistency optimization control protocol as:

[0084]

[0085] where τ i is the control variable to be solved.

[0086] Then, in step two, for the full-distributed attitude consistency optimization control protocol designed in step one, based on optimal control theory, the optimal control variable that can ensure the global performance function of the system to be optimal is solved.

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

[0088]

[0089] where ξ = [ξ i ] i∈{1,...,N} , is the error variable; τ = [τ i ] i∈{1,...,N} , and is a pre-specified positive parameter; I 3N denotes the 3N-dimensional identity matrix.

[0090] The following Hamiltonian function is selected:

[0091]

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

[0093]

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

[0095]

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

[0097]

[0098] Substituting equation (10) into equation (8) gives:

[0099]

[0100] where the optimal control gain parameter is

[0101] Then, in step three, the underwater robot swarm pose is controlled based on the optimal control variable.

[0102] Further, for the globally distributed pose consensus optimization control protocol designed in step one, the differential equation theory is used to analyze that the designed control protocol can ensure that the pose components of the multiple underwater robots can reach the pre-specified consensus final value As follows.

[0103] Substitute the full-distributed attitude consensus optimal control protocol (5) and formula (11) into formula (4), and there is:

[0104]

[0105] According to the cluster consensus theory, when the control gain parameter k is greater than zero, there is:

[0106]

[0107] When , there is the following first-order non-homogeneous linear differential equation:

[0108]

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

[0110]

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

[0112]

[0113] In the formula, c l is an arbitrary constant. When the parameter γ>0 is established, according to formula (16), it can be deduced that:

[0114]

[0115] That is, is established. According to the above analysis, the attitude components of multiple underwater robots can reach the pre-given consensus terminal value

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

[0117] Consider a cluster system composed of 5 underwater robots (labeled 1 to 5 respectively), the communication topology between each robot is as shown in Figure 2 , then the Laplace matrix corresponding to the communication topology is represented as follows:

[0118]

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

[0120]

[0121] Let γ=2, And The optimal control gain parameter can be calculated as The attitude consistency optimal control protocol proposed in the application has a control gain parameter k only related to the pre-given parameters And The solving process does not need to use global information, thus having the advantage of complete distribution. In addition, given the initial values of the states of the five underwater robots as follows:

[0122]

[0123] Select α=[1, 0, 0, 0, 0] T Satisfy the conditions And The pre-given consistency terminal value q c =[-0.09, -0.19, -0.29] T can be calculated. The attitude component curve of each underwater robot can be obtained by using the complete distributed attitude consistency optimal control protocol designed in the application, as shown in Figures 3-5 The simulation curve shows that the attitude components of the five underwater robots can finally converge to the pre-given consistency terminal value, and the consistency convergence time is 6 seconds.

[0124] In addition, in order to further verify the superiority of the protocol proposed in the application, a plurality of groups of global performance function time evolution curves under the action of different control gain parameters k are given, as shown in Figure 6 The comparison of the curves shows that the final values of the global performance function under the action of four groups of non-optimal control gain parameters are 42.17, 25.63, 23.78 and 35.44, and the final value of the global performance function under the action of the optimal control gain parameter designed in the application is 22.33, thus the complete distributed attitude consistency optimal control protocol designed in the application can make the system global performance function reach the minimum (optimal) value.

[0125] It should be noted that the contents not described in detail in the application (such as graph theory, optimal control theory, differential equation theory and matrix theory) belong to the common knowledge in the field.

[0126] Another embodiment of the application provides a complete distributed underwater robot cluster attitude optimal consistency control system, which comprises:

[0127] a control protocol design module, configured to model the underwater robot cluster attitude system as a high-order nonlinear multi-rigid-body attitude system, and construct a consensus regulating variable, design a full-distributed attitude consensus optimal control protocol;

[0128] an optimal control variable solving module, configured to solve, based on optimal control theory, optimal control variables that make a system global performance function optimal, for the full-distributed attitude consensus optimal control protocol;

[0129] an attitude control module, configured to control the underwater robot cluster attitude based on the optimal control variables.

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

[0131]

[0132] wherein J i represents an inertia matrix of the underwater robot; ω i represents an attitude angular velocity, represents a skew-symmetric matrix of the attitude angular velocity; u i represents a control input quantity; represents an underwater robot attitude quaternion and satisfies N represents the total number of robots; I3 represents a three-order unit matrix.

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

[0134]

[0135] wherein γ is a constant greater than 0;

[0136] The full-distributed attitude consensus optimal control protocol is designed as follows:

[0137]

[0138] wherein τ i is a control variable to be solved;

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

[0140]

[0141] wherein ξ=[ξ i ] i∈{1,...,N} , is an error variable, and αi To meet the condition and non-negative vector, denotes the graph Laplacian matrix of the communication topology of the underwater robot cluster, wherein and l ij =-a ij , i≠j, a ij is used to represent the communication relationship between the ith robot and the jth robot, a ij =1 indicates that the ith robot can directly obtain the state information of the jth robot, otherwise a ij =0; τ=[τ i ] i∈{1,...,N} , and are pre-defined positive parameters; I 3N denotes a unit matrix with a dimension of 3N;

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

[0143] The following Hamilton function is selected:

[0144]

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

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

[0147]

[0148] Substitute the above formula into the Hamilton function and solve to obtain and further obtain the optimal control variable as:

[0149]

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

[0151] The function of the full-distributed underwater robot cluster posture optimal consistency control system described in the embodiment of the application can be explained by the foregoing full-distributed underwater robot cluster posture optimal consistency control method, therefore, the part of the system embodiment that is not described in detail can be referred to the method embodiment above, and will not be described here.

[0152] While the application has been described in accordance with a limited number of embodiments, these are merely illustrative of the many possible embodiments of the application. Other embodiments can be devised without departing from the scope of the application as defined by the appended claims. The disclosure of the application is illustrative only and not restrictive of the scope of the application, which is defined by the appended claims.

Claims

1. A method for optimal attitude consistency control of a fully distributed underwater robot swarm, characterized in that, include: Step 1: Model the underwater robot swarm 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; the high-order nonlinear multi-rigid-body attitude system is established as follows: ； In the formula, The inertia matrix represents the underwater robot; Indicates attitude angular velocity, A skew-symmetric matrix representing attitude angular velocity; Indicates the control input quantity; Describe the quaternion of the underwater robot's attitude and satisfy the following conditions: ; Indicates the total number of robots; Represents a third-order identity matrix; The consistency adjustment variables are constructed as follows: ； In the formula, A constant greater than 0; The fully distributed attitude consistency optimization control protocol is designed as follows: ； In the formula, Let these be the control variables to be solved; ; ; Step 2: For the fully distributed attitude consistency optimization control protocol, solve for the optimal control variables that make the global performance function of the system optimal based on optimal control theory; Step 3: Control the attitude of the underwater robot cluster based on the optimal control variables.

2. The method for optimal attitude consistency control of a fully distributed underwater robot swarm according to claim 1, characterized in that, The system global performance function mentioned in step two is: ； In the formula, , For error variables, Consistency moderating variable initial value, To meet the conditions and non-negative vectors, The graph Laplacian matrix represents the communication topology with the underwater robot swarm, where ,and , Used to indicate the first The robot and the first Communication relationships between robots Indicates the first The robot can directly obtain the first... The robot's status information, otherwise ; , , , and For a pre-given positive parameter, The dimension is The identity matrix.

3. The method for optimal attitude consistency control of a fully distributed underwater robot swarm according to claim 2, characterized in that, Step two includes the following specific steps: Choose the following Hamiltonian function: ； In the formula, This represents the value function associated with the global performance function. It represents the partial derivative of the value function with respect to the error variable; control variables The optimal value is obtained by solving the equation. get: ； Substituting the above equation into the Hamiltonian function and solving it yields the following result. Therefore, the optimal control variable is obtained as follows: ； In the formula, the optimal control gain parameter is: .

4. A fully distributed underwater robot swarm attitude optimal consistency control system, characterized in that, include: The control protocol design module is configured to model the underwater robot swarm 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; the high-order nonlinear multi-rigid-body attitude system is as follows: ； In the formula, The inertia matrix represents the underwater robot; Indicates attitude angular velocity, A skew-symmetric matrix representing attitude angular velocity; Indicates the control input quantity; Describe the quaternion of the underwater robot's attitude and satisfy the following conditions: ; Indicates the total number of robots; Represents a third-order identity matrix; The consistency adjustment variables are constructed as follows: ； In the formula, A constant greater than 0; The fully distributed attitude consistency optimization control protocol is designed as follows: ； In the formula, Let these be the control variables to be solved; ; ; The optimal control variable solving module is configured to solve for the optimal control variables that make the global performance function of the system optimal based on optimal control theory for the fully distributed attitude consistency optimization control protocol. An attitude control module is configured to control the attitude of the underwater robot cluster based on the optimal control variables.

5. The fully distributed underwater robot swarm attitude optimal consistency control system according to claim 4, characterized in that, The system global performance function in the optimal control variable solution module is: ； In the formula, , For error variables, To meet the conditions and non-negative vectors The graph Laplacian matrix represents the communication topology with the underwater robot swarm, where ,and , Used to indicate the first The robot and the first Communication relationships between robots Indicates the first The robot can directly obtain the first... The robot's status information, otherwise ; , , , and A pre-defined positive parameter; The dimension is The identity matrix; The specific process of solving for the optimal control variables includes: Choose the following Hamiltonian function: ； In the formula, This represents the value function associated with the global performance function. It represents the partial derivative of the value function with respect to the error variable; control variables The optimal value is obtained by solving the equation. get: ； Substituting the above equation into the Hamiltonian function and solving it yields the following result. Therefore, the optimal control variable is obtained as follows: ； In the formula, the optimal control gain parameter is: .

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