A multi-auv system formation coordination control method with non-convex control input constraints

Abstract

The application provides a multi-AUV system formation coordination control method with non-convex control input constraints, converts the coordination control of the multi-AUV system formation without a leader into a formation consistency problem, and defines the consistency state of the multi-AUV system formation without a leader. In the case that the water acoustic communication bandwidth is limited, the application selects a double-layer communication channel mainly composed of position and speed information. Considering the existence of communication delay and non-convex control input constraints, a discrete-time leaderless formation consistency constraint controller algorithm with communication delay is designed by introducing a constraint operator. By using the properties of graph theory, random matrix and SIA matrix, and selecting appropriate controller parameters, the multi-AUV system formation can reach the defined consistency state and maintain the stability of the formation shape.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of multi-autonomous underwater unmanned vehicle system formation coordination control method with non-convex control constraint, belong to multi-underwater unmanned vehicle system formation coordination control field. BACKGROUND

[0002] With the deepening of ocean exploration, autonomous underwater vehicle (AUV) has become an important tool for ocean exploration and development. Although AUV has the advantages of low cost, convenient maintenance and low cost, but single AUV has certain limitations in task execution process, therefore, in order to overcome the shortcomings of single AUV, in recent multi-vehicle system becomes the focus, especially the formation coordination control problem of multi-AUV system. The deployment point of each member in multi-AUV formation system is random and irregular, and it is usually necessary to form a team according to the task demand of multi-AUV system, and this process is described and verified by the formation consistency problem of multi-AUV system. The formation consistency of multi-AUV system refers to the consensus of information state value reached by mutual negotiation among members under certain network topology. However, due to various objective conditions constraints, such as the constraint of different direction driving force, the control input of single AUV cannot be arbitrarily large, and is often limited in a certain constraint set, which may be a non-convex set. Therefore, it is necessary to ensure that under the constraint of non-convex control input, the formation of multi-AUV system can keep fixed formation and complete underwater task.

[0003] For the coordination control problem of the formation of the multi-AUV system, most of the research results are based on the system under ideal environment, and the non-convex control input constraint is not considered. For example, the document Formation Control of Multiple Autonomous Underwater Vehicles under Communication Delay, Packet Discreteness and Dropout proposes a formation control scheme for the multi-AUV system under the conditions of communication delay, packet discreteness and packet loss, adopts a curve fitting method to predict the state of the AUV, and solves the coordination control problem of the formation under the conditions of packet discreteness and packet loss. The document Formation Control of a Multi-Autonomous Underwater Vehicle Event-Triggered Mechanism Based on the Hungarian Algorithm aims at the leader failure problem in the leader-follower formation of the multi-AUV system, adopts the Hungarian algorithm to reconstruct the failed formation at the minimum cost, and solves the problem of increased communication task of the leader after the formation reconstruction. The present application introduces a constraint operator and proposes a constraint controller algorithm for the non-convex control input constraint, so as to realize the coordination control of the formation of the multi-AUV system with non-convex control input. SUMMARY

[0004] The purpose of the present application is to propose a formation coordination control method for the multi-AUV system under the non-convex control input constraint, so that the multi-AUV system with non-convex control input constraint can quickly form a formation shape and keep the stability of the formation shape, and realize underwater surveying.

[0005] The purpose of the present application is achieved by the following steps:

[0006] Step 1: Based on a single AUV, a linear second-order integral model of the AUV is obtained by the feedback linearization method. An AUV formation coordination control system based on feedback linearization is designed;

[0007] Step 2: The multi-AUV formation mainly relies on underwater acoustic communication. The underwater communication system of the formation generally exists communication delay in the surveying task. In order to reduce the influence of the communication delay on the system, a formation communication system composed of a double-layer communication channel mainly of position information and speed information, i.e. a double-layer independent position-speed communication topology, is designed;

[0008] Step 3: The formation shape of the multi-AUV system is selected to be a leaderless formation shape, and the average state of each AUV in the formation is taken as a reference point, and the formation shape of the leaderless multi-AUV system is designed;

[0009] Step 4, the formation coordination control problem of the leaderless multi-AUV system in step 3 is converted into the formation consensus problem of the multi-AUV system, and a leaderless formation consensus state is designed;

[0010] Step 5, based on the linear second-order integral model of the AUV monomer in step 1, a mathematical model of the discrete-time multi-AUV system formation is given;

[0011] Step 6, for the case of non-convex control input constraints, a constraint operator is introduced;

[0012] Step 7, by introducing the constraint operator in step 6, considering the influence of the limited bandwidth of underwater acoustic communication, a formation consensus constrained controller algorithm of the discrete-time leaderless multi-AUV system with communication delay is designed;

[0013] Step 8, by using the correlation properties of graph theory, random matrix and SIA matrix, it is determined that the multi-AUV system formation with non-convex control input constraints in step 5 can realize the formation consensus state designed in step 4 under the conditions of selecting appropriate communication topology, controller parameters and controller period;

[0014] Step 9, the initial state of the monomer AUV in the formation, the communication topology, the control period, the controller parameters and the non-convex set corresponding to the control input are selected, the related parameters, the linear second-order integral model of the monomer AUV in step 1 and the constraint controller algorithm in step 7 are substituted into the AUV formation coordination control system in step 1, and the leaderless multi-AUV system formation with non-convex control input constraints can realize the formation shape set in step 3 and maintain the formation shape for underwater exploration.

[0015] Compared with the prior art, the beneficial effects of the present application are that the present application can effectively solve the formation coordination control problem of the multi-AUV system under the condition of non-convex control constraints, and can ensure that the discrete-time leaderless multi-AUV system formation with double-layer independent communication topology can coordinate the motion state of each member and quickly and stably form a formation shape during underwater exploration by using the underwater communication system under the condition of existing bounded communication delay and non-convex control input constraints. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 is an AUV formation coordination control system based on a feedback linearization model;

[0017] Figure 2 is a schematic diagram of a leaderless multi-AUV system formation;

[0018] Figure 3 is a two-dimensional space schematic diagram of a constraint operator;

[0019] Figure 4 is a non-convex control input implementation flowchart;

[0020] Figure 5 is a position communication topology graph and a velocity communication topology graph;

[0021] Figure 6 is a multi-AUV system formation eastward position convergence graph;

[0022] Figure 7 is a multi-AUV system formation northward position convergence graph;

[0023] Figure 8 is a multi-AUV system formation depth position convergence graph;

[0024] Figure 9 is a multi-AUV system formation pitch angle convergence graph;

[0025] Figure 10 is a multi-AUV system formation heading angle convergence graph;

[0026] Figure 11 is a multi-AUV system formation surge velocity convergence graph;

[0027] Figure 12 is a multi-AUV system formation sway velocity convergence graph;

[0028] Figure 13 is a multi-AUV system formation heave velocity convergence graph;

[0029] Figure 14 is a multi-AUV system formation pitch angle velocity convergence graph;

[0030] Figure 15 is a multi-AUV system formation heading angle velocity convergence graph;

[0031] Figure 16 is a multi-AUV system formation three-dimensional trajectory graph;

[0032] Figure 17 is a non-convex control input convergence graph;

[0033] Figure 18 is a raw control input convergence graph. DETAILED DESCRIPTION

[0034] The application will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0035] The present invention provides a coordinated control method for a multi-AUV system formation with non-convex control constraints. The coordinated control of a multi-AUV system formation without a navigator is converted into a formation consistency problem, and the consistency state of the multi-AUV system formation without a navigator is defined. In view of the limited bandwidth of underwater acoustic communication, the present invention selects a double-layer communication channel mainly composed of position and velocity information. Considering the existence of communication delay and non-convex control input constraints, a consistency constraint controller algorithm for a discrete-time leaderless formation with communication delay is designed by introducing a constraint operator. By utilizing the properties of graph theory, random matrices and SIA matrices, and selecting appropriate controller parameters, the multi-AUV system formation can achieve a defined consistency state and maintain the stability of the formation. The specific implementation process is:

[0036] Step 1: Take the i-th individual AUV in the formation i Based on the feedback linearization method, the linear second-order integral model of AUV is obtained as follows:

[0037]

[0038] in Indicates AUV i The posture state, Indicates AUV i The speed state, Indicates AUV i Control input, i∈{1,2,…,n}. Based on the feedback linearization model of a single AUV, a multi-AUV formation coordination control system is designed, such as Figure 1 shown.

[0039] Step 2: Design G for the case where the underwater acoustic communication bandwidth is limited. p ,G v It is a two-layer independent position-speed communication topology.

[0040] Step 3: Single AUV i The state at time t is The relative fixed reference point of the fixed formation without a leader is O(t), and the design vector Δl i For AUV i The expected position in 3D space relative to the reference point O(t).

[0041] Step 4: Figure 2 As shown, by setting the formation relative to a fixed reference point O(t) to coincide with the average state of the formation The formation coordination control problem of the multi-AUV system without a navigator in step 3 is transformed into the formation consistency problem of the multi-AUV system. The consistency state of the formation without a navigator is designed as:

[0042]

[0043]

[0044] Step 5: Design According to the linear second-order integral model of the single AUV in step 1, the mathematical model of the discrete-time multi-AUV system formation is selected as follows:

[0045]

[0046]

[0047] in Represents AUV i The position state, velocity state, and control input at time kT, where T is the control period and k is the discrete time coefficient, k = 0, 1, 2, .... And u i (k) Satisfy the non-convex constraint, that is, for any u i (k),i=1,2,…,n,u i (k) are all constrained to be non-empty non-convex sets inside.

[0048] Step 6: Design for non-empty bounded closed sets i=1,2,...,n,0∈U i , there exists a positive constant σ i ,satisfy By introducing the constraint operator Transform vector x into a vector in set U i The largest vector with the same direction like Figure 3 As shown, The details are as follows

[0049]

[0050] Step 7: By introducing the constraint operator in step 6 Design a consensus constraint controller algorithm for discrete-time multi-AUV system formation:

[0051]

[0052] in are the position communication delay and speed communication delay, respectively, ij (k) and b ij (k) are the position adjacency matrix A p and the velocity adjacency matrix A v The ijth element of and is the controller gain at time kT, and the specific implementation process of non-convex control input is as follows Figure 4 shown.

[0053] For any i,j=1,2,...,n,k=0,1,2,..., select a non-negative constant integer N A , design when When is the bounded communication delay of the formation, when When The design is the unbounded communication delay of the formation. According to probability If communication is successful, communication delay is bounded, and communication delay is unbounded, then there exists a positive integer So that for any μ∈(0,1), it satisfies and Taking μ as a value very close to 1, for the above-mentioned situation where the communication delay is unbounded, the formation At least one of the communications is successful. At this point, the formation consistency problem with unbounded communication delay is transformed into the formation consistency problem with bounded communication delay. Therefore, the designed consistency controller algorithm is also applicable to the case of unbounded communication delay.

[0054] Step 8. Definition

[0055]

[0056] in

[0057]

[0058] Design location communication topology G p (k),G p (k+1),…,G p (k+N A -1) and the speed communication topology G p (k),G p (k+1),…,G p (k+N A -1) respectively have directed trees; the controller parameters satisfy Control cycle satisfied By utilizing the related properties of graph theory, random matrices and SIA matrices, the multi-AUV system formation can achieve the consistency state set in step 4 and maintain the stability of the formation.

[0059] Step 9: Design a simulation experiment of a multi-AUV system formation consisting of 5 AUVs. Figure 5The location communication topology G shown p and speed communication topology G v As a communication structure. For the communication topology graph G p , G v The corresponding adjacency matrix A p and A v , when a ij ≠0,b ij ≠0, select a ij =0.1, b ij =0.1. Select the non-convex control input constraint set U i for:

[0060] U i ={x|||x||≤1}∪{x|||x-[-1,1,0,0,0] T ||≤1}∪{x|||x-[-1,-1,0,0,0] T ||≤1},i=1,2,...,n,

[0061] at this time σ i = 1. Randomly select the initial state and select the relative expected position as Δl1 = [2, 0, 0, 0] T , Δl2=[0,2,0,0,0] T , Δl3=[0,0,2,0,0] T , Δl4=[-2, 0, 0, 0, 0] T ,Δl5=[0,-2,0,0,0] T , the control period and controller parameters are selected as T=0.04, and Select N A =3,μ=0.99, when k=0, When k=1, When k = 2, When k=3, When k>3, in Respectively probability. express The probability that m c =3. Substitute the above-mentioned relevant parameter values, the linear second-order integral model in step 1, and the consistency constraint algorithm in step 7 into the AUV formation coordination control system in step 1. The simulation results are as follows: Figures 6 to 18 shown.

[0062] From the simulation results Figures 6 to 16It can be seen that the leaderless multi-AUV system formation with double-layer independent communication topology can reach the expected position, form the set formation and maintain the formation to carry out underwater survey in the presence of communication delay. Figure 17 and Figure 18 It can be seen that the control input can meet the set non-convex set restriction during the formation and maintenance of the formation.

[0063] In conclusion, the application discloses a coordination control method for a discrete-time leaderless multi-AUV system formation with non-convex control input restriction. When the single body in the multi-AUV system formation carries out the underwater survey task, the control input is not possible to be arbitrary large due to the multi-directional force and the restriction of objective conditions, and is often restricted in a certain constraint set, which may be a non-convex set. The design is based on the single AUV, a linear second-order integral model of the AUV is obtained through the feedback linearization method, and a multi-AUV formation coordination control system is designed. A double-layer independent position-velocity communication topology is selected to reduce the influence of the limited underwater acoustic communication bandwidth. The average state of the multi-AUV system formation is taken as the expected state, the formation shape is designed, and the coordination control problem of the multi-AUV system formation is converted into the consistency problem of the multi-AUV system formation. The linear second-order integral model of the single AUV is used to design the mathematical model of the discrete-time multi-AUV system formation. Considering the non-convex control input restriction and the presence of communication delay, a constraint operator is introduced, and a consistency constraint algorithm for the discrete-time leaderless multi-AUV system formation with double-layer independent communication topology is designed. The graph theory, the correlation of random matrix and the related properties of SIA matrix are used to determine that the multi-AUV system formation with non-convex control input restriction can achieve the designed formation consistency target under the condition of selecting the appropriate communication topology graph, the controller parameters and the controller period. The initial state is randomly selected, the related parameters, the linear second-order integral model of the single AUV and the consistency algorithm are substituted into the coordination control system of the multi-AUV system formation, and after a period of adjustment, the single AUV in the formation reaches the expected position and keeps the relative position unchanged, that is, the formation forms the formation shape and keeps the shape unchanged during the operation. The application can effectively realize the coordination control of the leaderless multi-AUV system formation with double-layer independent communication topology in the presence of non-convex control input restriction and communication delay, so that the multi-AUV system formation forms the set formation shape and maintains the stable formation to carry out underwater survey.

Claims

1. A method for formation coordination control of multi-AUV system with non-convex control input constraints, characterized in that: The steps are as follows: Step 1: Obtain the linear second-order integral model of AUV monomer by the method of feedback linearization, and design the AUV formation coordination control system based on feedback linearization; Step 2: The multi-AUV formation relies on underwater acoustic communication, and the underwater communication system of the formation in the survey task has communication delay. A formation communication system composed of two layers of communication channels based on position information and speed information, namely a double-layer independent position-speed communication topology, is designed; Step 3: The formation structure of the multi-AUV system selects a leaderless formation, and the average state of each AUV in the formation is taken as the reference point to design the formation of the leaderless multi-AUV system; Step 4: The formation coordination control problem of the leaderless multi-AUV system in step 3 is converted into the formation consistency problem of the multi-AUV system, and the leaderless formation consistency state is designed; Step 5: Based on the linear second-order integral model of the AUV monomer in step 1, the mathematical model of the discrete-time multi-AUV system formation is given; Step 6: For the case of non-convex control input constraints, a constraint operator is introduced; Step 7: By introducing the constraint operator in step 6, the influence of limited underwater acoustic communication bandwidth is considered, and a formation consistency constraint controller algorithm for the discrete-time leaderless multi-AUV system with communication delay is designed; wherein, respectively represent the position state and velocity state of the AUV i at time kT, T is the control period, and k is the discrete time coefficient; respectively represent the position state and velocity state of the AUV i and the position communication delay and velocity communication delay of the AUV j ; ij (k) is the element of the i-th row and j-th column of the position adjacency matrix A p (k) is the element of the i-th row and j-th column of the velocity adjacency matrix A ij (k) is the element of the i-th row and j-th column of the velocity adjacency matrix A v ; and represent the controller gain of the AUV i at time kT. Step 8: Using graph theory, the related properties of random matrices and SIA matrices are used to determine that under the selection of appropriate communication topology, controller parameters and controller period, the multi-AUV system formation with non-convex control input constraints in step 5 can realize the formation consistency state designed in step 4; Step 9: The initial state of the monomer AUV in the formation, the communication topology, the control period, the controller parameters and the non-convex set corresponding to the control input are selected, the related parameters, the linear second-order integral model of the monomer AUV in step 1 and the constraint controller algorithm in step 7 are substituted into the AUV formation coordination control system in step 1, and the leaderless multi-AUV system formation with non-convex control input constraints can realize the formation shape set in step 3 and maintain the formation shape for underwater survey.

2. The method of claim 1, wherein: The i-th monomer AUV in step 1 i Based on the feedback linearization method, the linear second-order integral model of the AUV is obtained as follows: wherein represents a pose state of the AUV i , represents a velocity state of the AUV i , represents a control input quantity of the AUV i , i e {1,2,..., n}.

3. The method of claim 1, wherein: The mathematical model of the discrete-time multi-AUV system formation selected in step 5 is as follows: wherein respectively represent the position state, velocity state, control input of AUV i at time kT, T is control period, k is discrete time coefficient, k = 0, 1, 2,..., u i (k) satisfies non-convex constraint limit, that is, for any u i (k), i = 1, 2,..., n, u i (k) are all constrained in non-empty non-convex set .

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