Command filtering-based distributed inclusion control method for multiple AUV (Autonomous Underwater Vehicle) systems in consideration of dead zone of actuator

Abstract

The invention discloses a command filtering-based multi-AUV (Autonomous Underwater Vehicle) system distributed inclusion control method considering an actuator dead zone, relates to the technical field of ship underwater control, and aims to solve the problem that the distributed inclusion control of an AUV system in the prior art is difficult to realize near the actuator dead zone. According to the design of the controller, all follower AUVs can converge to a convex hull formed by a navigator AUV under the condition that ocean current disturbance, model uncertainty and actuator dead zones exist in the multi-AUV system, cooperative operation with the navigator AUV is achieved, and distributed inclusion control over the multi-AUV system is completed. According to the method and the device, the problem that in the prior art, distributed control of the AUV system in the vicinity of a dead zone of an actuator is difficult to realize is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater ship control, and in particular to a distributed inclusion control method for a multi-AUV system based on command filtering taking into account an actuator dead zone. Background Art

[0002] In recent years, China has actively accelerated the construction of a strong maritime nation. Autonomous underwater vehicles (AUVs), as robots that can operate autonomously underwater, have certain intelligence, and have many advantages such as a large range of activities, strong mobility and safety. They play an increasingly important role in resource exploration and seabed measurement. Faced with increasingly difficult operational requirements, the operational capacity of a single AUV is limited, while the multi-AUV system has the advantages of good redundancy, high efficiency and robustness, and has a broader application prospect in large-scale and high-efficiency ocean exploration activities. For distributed multi-AUV systems, inclusive control can liberate the demand for communication equipment in the formation system and reduce the communication pressure of the system. In inclusive control, only multiple navigators need to communicate with the surface mothership, receive instructions and plan the mission trajectory, while followers only communicate with some navigators and neighbor followers. In this process, all followers will act together with the convex hull formed by multiple navigators to reach the mission area and start operations.

[0003] In view of the complex and changeable characteristics of the actual ocean environment, AUVs are more susceptible to unknown current disturbances due to their relatively small mass. At the same time, since the dynamic model of AUVs itself has significant nonlinear and uncertain characteristics, this increases the complexity and challenge of designing the trajectory tracking control algorithm of the AUV system.

[0004] As a type of robot, AUV, like other types of robots, usually needs to use the power generated by actuators to perform various movements, so the actuator is an indispensable part of the AUV control loop. Actuator dead zone is a common non-smooth and nonlinear physical phenomenon, which usually appears in robot systems due to limitations in mechanical structure manufacturing processes. Actuator dead zone refers to the phenomenon that the actuator does not produce any action or response to a certain small range of input signals. The actuator only starts to operate when the input signal exceeds a specific threshold. Therefore, it is difficult to implement distributed control of the AUV system near the actuator dead zone. Summary of the invention

[0005] The purpose of the present invention is to propose a distributed inclusive control method for multiple AUV systems based on command filtering taking into account the dead zone of the actuator, in view of the problem that the distributed inclusive control of the AUV system in the prior art is difficult to achieve near the dead zone of the actuator.

[0006] The technical solution adopted by the present invention to solve the above technical problems is:

[0007] A distributed inclusion control method for a multi-AUV system based on command filtering considering actuator dead zone comprises the following steps:

[0008] Step 1: Construct the dynamic models of the leader AUV and the follower AUV respectively;

[0009] Step 2: Design a disturbance observer using the dynamic models of the leader AUV and the follower AUV;

[0010] Step 3: Construct the actuator dead zone model and design the second-order command filter and virtual control law;

[0011] Step 4: Design an inclusive controller using the actuator dead zone model, second-order command filter and virtual control law, and use the inclusive controller to ensure that all follower AUVs are contained in the convex hull formed by the leader AUV in space;

[0012] The included controller is represented as:

[0013]

[0014]

[0015]

[0016]

[0017] Among them, m i represents the output gain of the ith follower, Ω i represents the piecewise function of the dead zone produced by the ith follower at the output, represents the output signal of the second-order command filter of the i-th follower AUV, ξ i represents the error of the i-th follower AUV, represents the output of the distributed inclusive controller based on command filtering of the ith follower AUV, which is used as the actual control input of the ith follower AUV when considering the dead zone. represents the intermediate reference value of the i-th follower AUV, represents the desired control law of the i-th follower AUV, K 2i represents the constant matrix of the i-th follower AUV, K 1i represents the intermediate matrix of the i-th follower AUV, L i represents the intermediate matrix of the i-th follower AUV, represents a positive constant, η i represents the position and angle vector of the i-th follower AUV, Represents ηi The first derivative of 0i represents the thrust distribution matrix of the i-th follower AUV, express The first derivative of i Indicates that the i-th follower AUV contains an error, g i represents the intermediate variable of the i-th follower AUV, represents the observed value, t represents the time, M ηi represents the mass and moment of inertia matrix of the ith AUV, C ηi represents the Coriolis force matrix of the ith AUV, D ηi represents the i-th AUV fluid damping force matrix, i∈F, and F represents the follower set.

[0018] Furthermore, the dynamic model of the pilot AUV is expressed as:

[0019]

[0020] Among them, η l represents the six-degree-of-freedom position and attitude vector of the lth leader AUV in the inertial coordinate system, Represents η l The first derivative of Represents η l The second derivative of M ηl represents the mass and inertia matrix of the lth AUV, C ηl represents the Coriolis force (moment) matrix of the lth AUV, D ηl represents the l-th AUV fluid damping force matrix, B 0l represents the thrust distribution matrix of the lth leader AUV, u l represents the control amount of the thruster of the lth leader AUV, g ηl Represents the force and torque vectors generated by the gravity and buoyancy of the lth leader AUV.

[0021] Furthermore, the dynamic model of the follower AUV is expressed as:

[0022]

[0023]

[0024] Among them, η l represents the position and angle vector of the leader AUV, W i represents the total uncertainty, u i represents the control amount of the thruster of the i-th follower AUV, J l represents the transformation matrix between the inertial coordinate system and the motion coordinate system of the lth leader AUV, vl represents the longitudinal velocity of the lth leader AUV.

[0025] Furthermore, the total uncertainty W i It is expressed as:

[0026]

[0027] Among them, d i represents the impact of ocean current disturbance, and Δ represents the uncertainty value.

[0028] Furthermore, the interference observer is expressed as:

[0029]

[0030] in, represents the observed value, σ i and δ i represents the intermediate variable of the uncertainty of the i-th follower AUV, L i The constant matrix representing the uncertainty of the i-th follower AUV, Represents η i The second-order derivative of Denotes δ i The first derivative of .

[0031] Furthermore, the It is expressed as:

[0032]

[0033] Furthermore, the actuator dead zone model is expressed as:

[0034]

[0035] m i =diag(m i1 ,m i2 ,…,m ij ), j∈Q,

[0036]

[0037] Ω i =[Ω i1 ,Ω i2 ,…,Ω ij ] T , j∈Q,

[0038]

[0039] Where Q represents a non-empty set {1,2,3,4,5,6}, Indicates the design intermediate reference quantity, mij represents the gain of the j-th degree of freedom of the ith follower AUV, m il and m ir They represent the left gain and right gain of the dead zone of the i-th follower AUV actuator, Ω l Represents the piecewise function matrix of the dead zone generated by the l-th follower AUV, Ω lj represents the piecewise function that produces the dead zone on the j-th degree of freedom of the l-th follower AUV, diag represents the diagonal matrix; p il and p ir They represent the left and right breakpoints of the dead zone of the actuator of the i-th follower AUV, respectively.

[0040] Further, the second-order command filter is expressed as:

[0041]

[0042] in, represents the second-order command filter input signal, α i and represents the intermediate variable, express The first-order derivative of , p represents the damping ratio of the command filter, and q represents the bandwidth of the command filter;

[0043] For any t ≥ 0, if the following conditions are met, for any positive constant Γ > 0, there exists 0 < p ≤ 1 and q > 0 such that holds, and |α i (t)| and All are bounded;

[0044]

[0045] Define command filter output signal for:

[0046]

[0047] in, express The first derivative of express The second-order derivative of , w1, w2 represent positive constants, express The first derivative of .

[0048] Furthermore, the virtual control law is expressed as:

[0049]

[0050] Among them, η rirepresents the reference information of the neighbors of the i-th follower AUV, Represents η ri The first derivative of .

[0051] Furthermore, the specific steps of designing a controller using the actuator dead zone model, the second-order command filter and the virtual control law are as follows:

[0052] First, for the general uncertainty W in the system i (t), the following disturbance observer is designed to accurately estimate it:

[0053]

[0054] Define the follower AUV inclusion error as follows:

[0055] ε i (t) = η i (t)-η ri (t)

[0056]

[0057] Among them, a ij and b il represents the communication weight;

[0058] Design of virtual control law:

[0059]

[0060] Using a second-order command filter, the filtering error is defined as:

[0061]

[0062] Define the error:

[0063]

[0064] Design the following distributed controller:

[0065]

[0066]

[0067]

[0068] The beneficial effects of the present invention are:

[0069] The controller designed in this application enables all follower AUVs to converge to the convex hull formed by the leader AUV in the presence of current disturbances, model uncertainty and actuator dead zone, and work in collaboration with the leader AUV to complete the distributed inclusive control of the multi-AUV system. This application solves the problem that the distributed inclusive control of the AUV system in the prior art is difficult to achieve near the actuator dead zone. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 is a schematic diagram of the body coordinate system;

[0071] Figure 2 This is a schematic diagram of the actuator dead zone;

[0072] Figure 3 It is the structure diagram of the second-order command filter;

[0073] Figure 4 This is a schematic diagram of the submarine flight node;

[0074] Figure 5 This is a schematic diagram of the directed communication topology network of the pilot-follower multi-AUV system;

[0075] Figure 6 This is a schematic diagram of the three-dimensional spatial position change of each AUV in the pilot-follow multi-AUV system;

[0076] Figure 7 This is a schematic diagram of the position change of each AUV in the pilot-follow multi-AUV system;

[0077] Figure 8 This is a schematic diagram of the angle change of each AUV in the pilot-follow multi-AUV system;

[0078] Fig. 9 is the follower AUV filtering error of the leader-follower multi-AUV system || χ i (t)|| 2 Schematic diagram of changes;

[0079] Fig.10 Observation error of follower AUV in pilot-follower multi-AUV system Schematic diagram of changes;

[0080] Fig.11 The follower AUV in the leader-follower multi-AUV system contains the error ||ε i (t)|| 2 Schematic diagram of changes;

[0081] Fig.12 Design error ||ξ for the follower AUV in the leader-follower multi-AUV system i (t)|| 2 Schematic diagram of changes. DETAILED DESCRIPTION

[0082] It should be particularly noted that, in the absence of conflict, the various embodiments disclosed in this application can be combined with each other.

[0083] Specific implementation method 1: refer to Figure 1 Specifically describing this embodiment, the embodiment described in 1. A distributed inclusive control method for a multi-AUV system based on command filtering considering the actuator dead zone comprises the following steps:

[0084] Step 1: Construct the dynamic models of the leader AUV and the follower AUV respectively;

[0085] Step 2: Design a disturbance observer using the dynamic models of the leader AUV and the follower AUV;

[0086] Step 3: Construct the actuator dead zone model and design the second-order command filter and virtual control law;

[0087] Step 4: Design an inclusive controller using the actuator dead zone model, second-order command filter and virtual control law, and use the inclusive controller to ensure that all follower AUVs are contained in the convex hull formed by the leader AUV in space;

[0088] The included controller is represented as:

[0089]

[0090]

[0091]

[0092]

[0093] Among them, m i represents the output gain of the ith follower, Ω i represents the piecewise function of the dead zone produced by the ith follower at the output, represents the output signal of the second-order command filter of the i-th follower AUV, ξ i represents the error of the i-th follower AUV, represents the output of the distributed inclusive controller based on command filtering of the ith follower AUV, which is used as the actual control input of the ith follower AUV when considering the dead zone. represents the intermediate reference value of the i-th follower AUV, represents the desired control law of the i-th follower AUV, K 2i represents the constant matrix of the i-th follower AUV, K 1irepresents the intermediate matrix of the i-th follower AUV, L i represents the intermediate matrix of the i-th follower AUV, represents a positive constant, η i represents the position and angle vector of the i-th follower AUV, Represents η i The first derivative of 0i represents the thrust distribution matrix of the i-th follower AUV, express The first derivative of i Indicates that the i-th follower AUV contains an error, g i represents the intermediate variable of the i-th follower AUV, represents the observed value, t represents the time, M ηi represents the mass and moment of inertia matrix of the ith AUV, C ηi represents the Coriolis force matrix of the ith AUV, D ηi represents the i-th AUV fluid damping force matrix, i∈F, and F represents the follower set.

[0094] Parameter definition:

[0095] M——mass inertia matrix;

[0096] η=[x,y,z,φ,θ,ψ] T ——The position and angle vector of AUV in the inertial coordinate system;

[0097] v=[u,v,w,p,q,r] T ——Linear velocity and angular velocity vector of AUV in the motion coordinate system;

[0098] J——Transformation matrix between inertial coordinate system and motion coordinate system;

[0099] C RB ——Coriolis force and centripetal force matrix of rigid body;

[0100] C A ——Coriolis force and centripetal force matrix of the added mass;

[0101] D – hydrodynamic damping matrix;

[0102] g η - force and torque vectors due to gravity and buoyancy;

[0103] τ — control forces and torques generated by the propulsion system;

[0104] B0——thrust distribution matrix;

[0105] u——thruster control quantity.

[0106] This application first establishes an inertial coordinate system and a motion coordinate system, then establishes a multi-AUV kinematic and dynamic model and a mathematical model of the actuator dead zone, and finally gives the design of a second-order command filter and a distributed inclusion controller for the AUV dynamic model.

[0107] Coordinate system establishment

[0108] (1) Geodetic coordinate system E-xyz

[0109] The reference ellipsoid is selected as the reference to establish the geodetic coordinate system. The tangent plane of the earth surface in the operation area of ​​the marine robot formation is selected as the reference plane, E is the origin, the Ex axis is parallel to the horizontal plane, the positive direction of the Ey axis is consistent with the right side when the AUV formation is moving forward, and the Ez axis points to the center of the earth.

[0110] (2) Body coordinate system O-ξσζ

[0111] like Figure 1 As shown in the figure, O is the origin of the AUV body coordinate system, and the positive direction of the Oξ axis is selected to point from O to the front of the AUV; the Oζ axis is located on the mid-longitudinal section of the robot, and the positive direction is vertically downward; the Oσ axis is located on the mid-transverse section of the AUV, perpendicular to the Oξζ plane, and points to the starboard side.

[0112] Multi-AUV kinematics, dynamic equations and actuator dead zones

[0113] This application takes AUV as an example, assuming that there are M leader AUVs and N follower AUVs in a leader-follower multi-AUV system, and sets L = (1, 2, ..., M) and F = (M+1, M+2, ..., M+N).

[0114] In view of the situation where there are model uncertainties and unknown ocean current disturbances in the multi-AUV system, a feasible mathematical expression is considered. The dynamic equation of the follower AUV can be written as:

[0115]

[0116] Where i∈F,C ηi =C RBηi +C Aηi , W i (t) represents the total uncertainty of the system, which is expressed as follows:

[0117]

[0118] Among them, d i (t) represents the impact of ocean current disturbance; Δ represents the uncertainty value.

[0119] Considering the dead zone of the AUV system, the actuator dead zone can be used Figure 2 express.

[0120] The dead zone study model is of the following form:

[0121]

[0122] Among them, p il and p ir Indicates the left and right breakpoints of the dead zone, m il and m ir represents the gain, i∈F.

[0123] Because AUV is a multi-dimensional nonlinear system, model (3) is expanded to the multi-dimensional level:

[0124]

[0125] Among them, there exists a non-empty set Q = {1,2,3,4,5,6}, then u i =[u i1 ,u i2 ,...,u ij ] T , j∈Q, j∈Q,m i =diag(m i1 ,m i2 ,...,m ij ), j∈Q,

[0126]

[0127] Ω i =[Ω i1 ,Ω i2 ,...,Ω ij ] T , j∈Q,

[0128]

[0129] Second-order command filtering and distributed inclusion controller design

[0130] In order to avoid the "computational explosion" problem that may occur in the backstepping control method, this application designs a second-order command filter in the following form:

[0131]

[0132] in, is the second-order command filter input signal, α i (t) and is an intermediate variable, p and q are positive constants. 0<p≤1 represents the damping ratio of the command filter, and q>0 represents the bandwidth of the command filter. If the following conditions are met, for any positive constant Γ>0, there exists 0<p≤1 and q>0 such that holds, and |α i (t)| and All are bounded.

[0133]

[0134] The structure diagram of the second-order command filter is as follows Figure 3 As shown:

[0135] Define command filter output signal for:

[0136]

[0137] According to the design analysis of the command filter, the output signal It is obtained by the integral method rather than the differential method, which greatly reduces the complexity of differential calculation and effectively avoids the problem of "computational explosion". In addition, from the principle analysis, increasing the parameter q can make the error of the command filter converge to arbitrary precision.

[0138] The leader-follower multi-AUV system adopts a directed communication topology network. Considering the model uncertainty, external interference and dead zone of the system, this patent designs a distributed inclusive controller based on command filtering, and finally completes the distributed inclusive control of the multi-AUV system.

[0139] First, for the general uncertainty W in the system i (t), the following disturbance observer is designed to accurately estimate it:

[0140]

[0141] Among them, i∈F, represents the observed value, σ i (t) and δ i (t) is the intermediate variable, L i is a positive constant matrix.

[0142] Define the follower AUV inclusion error as follows:

[0143] ε i (t) = η i (t)-η ri (t) (11)

[0144]

[0145] Among them, i∈F, ε i (t) is the error, ηri (t) represents the reference information of the follower AUV’s neighbors, a ij and b ij is the communication weight.

[0146] Design of virtual control law:

[0147]

[0148] Among them, K 1i is a positive constant matrix.

[0149] Defining Error

[0150]

[0151] Design the following distributed controller:

[0152]

[0153]

[0154]

[0155] in, To consider the actual control input when the dead zone is taken into account, represents the design intermediate reference quantity, represents the expected control law, K 2i is a positive constant matrix.

[0156] Design matrix K 1i , K 2i and L i When the following conditions are met:

[0157]

[0158] The leader-follower multi-AUV system is capable of achieving distributed inclusive control.

[0159] In this application, we choose to use directed communication between multiple AUV systems instead of undirected communication, which can save certain communication resources. We use algebraic graph theory to describe the communication network of multiple AUV systems. is a directed graph. Assume that there are M leaders and N followers in the multi-AUV system, let L = {1, 2, ..., M} represent the leader AUV set, and F = {M + 1, M + 2, ..., M + N} represent the follower AUV set. Consider each AUV as a communication node, let is the set of all communication nodes. represents the AUV numbered i. The communication connection relationship between each communication node is regarded as an edge. As the set of all edges, It means that the AUV with number j can obtain the information of the AUV with number i, which is called yes The child nodes of yes The parent node of . Represents the adjacency matrix.

[0160] definition is a subgraph about the follower AUV, where

[0161] For the adjacency matrix when When i≠j, a ij =1>0; otherwise a ij = 0 (for undirected graphs, When When ij =a ji =1; otherwise a ij =0). In the directed graph If follower i has a directed path from leader l, it means that follower i can obtain information from leader l, denoted by b il =1>0; otherwise b il =0.

[0162] node To Node The path in the directed graph can be represented as an ordered sequence of edges Satisfaction relationship All The node is The neighbors of a node are represented by If in the directed graph In the , all follower AUVs have at least one leader AUV as the root node, then the leader set L is said to be globally reachable.

[0163] AUV dynamics model

[0164] This application assumes that there are M leader AUVs and N follower AUVs in a leader-follower multi-AUV system, and sets L = (1, 2, ..., M) and F = (M+1, M+2, ..., M+N).

[0165] The dynamic model of the navigator AUV can be expressed as:

[0166]

[0167] in, represents the position and angle vector of the leader AUV, l∈L.

[0168] According to (1), the dynamic model of the follower AUV can be expressed as:

[0169]

[0170] in, represents the position and angle vector of the follower AUV, W i (t) represents the total uncertainty, i∈F.

[0171]

[0172] Among them, d i (t) represents the impact of ocean current disturbance; Δ represents the uncertainty value.

[0173] The control objective of this application can be expressed as: design a controller u so that in the presence of ocean current disturbances, model uncertainty and actuator dead zone, all follower AUVs of the multi-AUV system can converge to the convex hull formed by the leader AUV, work in collaboration with the leader AUV, and effectively avoid the occurrence of the "computational explosion" problem.

[0174] Combined with the actual engineering background, we put forward the following assumptions:

[0175] Assumption 1: Position and angle vector η and its first-order derivative Measurable.

[0176] Assumption 2 The leader AUV is not disturbed and can move according to the pre-set navigation trajectory.

[0177] Assume that the communication between 3AUVs is directed communication, and each follower OBFN has at least one leader AUV as the root node.

[0178] Assumption 4 For Ω i ,exist is a positive constant, i∈F, j∈Q.

[0179] Assumption 5 The total uncertainty of the system W i (t) itself is unknown, satisfying is a positive constant.

[0180] Actuator Deadband Model

[0181] The AUV system in this application adopts the following dead zone research model:

[0182]

[0183] Among them, p il and p ir Indicates the left and right breakpoints of the dead zone, m il and m ir represents the gain, i∈F.

[0184] Since AUV is a multi-dimensional nonlinear system, model (22) is expanded to the multi-dimensional level:

[0185]

[0186] Among them, there exists a non-empty set Q = {1,2,3,4,5,6}, then u i =[u i1 ,u i2 ,...,u ij ] T , j∈Q, j∈Q,m i =diag(m i1 ,m i2 ,...,m ij ), j∈Q,

[0187]

[0188] Ω i =[Ω i1 ,Ω i2 ,...,Ω ij ] T , j∈Q,

[0189]

[0190] If the desired controller is designed Build and The conversion relationship can be further used to obtain the actual control input when the dead zone is considered.

[0191] Second-order command filter design

[0192] In order to avoid the "computational explosion" problem that may occur in the backstepping control method, the present invention designs a second-order command filter in the following form:

[0193]

[0194] in, is the second-order command filter input signal, α i (t) and is an intermediate variable, p and q are positive constants. 0<p≤1 represents the damping ratio of the command filter, and q>0 represents the bandwidth of the command filter. If the following conditions are met, for any positive constant Γ>0, there exists 0<p≤1 and q>0 such that holds, and |α i (t)| and All are bounded.

[0195]

[0196] Define command filter output signal for:

[0197]

[0198] According to the design analysis of the command filter, the output signal It is obtained by the integral method rather than the differential method, which greatly reduces the complexity of differential calculation and effectively avoids the problem of "computational explosion". In addition, from the principle analysis, increasing the parameter q can make the error of the command filter converge to arbitrary precision.

[0199] Design of adaptive attitude tracking controller

[0200] The leader-follower multi-AUV system adopts a directed communication topology network. Considering the model uncertainty, external interference and dead zone of the system, this application designs a distributed inclusive controller based on command filtering, and finally completes the distributed inclusive control of the multi-AUV system.

[0201] First, for the general uncertainty W in the system i (t), the following disturbance observer is designed to accurately estimate it

[0202]

[0203] Among them, i∈F, represents the observed value, σ i (t) and δ i (t) is the intermediate variable, L i is a positive constant matrix.

[0204] Define the follower AUV inclusion error as follows:

[0205] ε i (t) = η i (t)-η ri (t) (30)

[0206]

[0207] Where i∈F, ε i (t) is the error, η ri(t) represents the reference information of the follower AUV’s neighbors, a ij and b il is the communication weight.

[0208] Design of virtual control law:

[0209]

[0210] Among them, K 1i is a positive constant matrix.

[0211] Using the second-order command filter shown in (26), the filtering error is defined as:

[0212]

[0213] in, Represents the output signal of the command filter.

[0214] Define the error:

[0215]

[0216] Design the following distributed controller:

[0217]

[0218]

[0219]

[0220] in, To consider the actual control input when the dead zone is taken into account, represents the design intermediate reference quantity, represents the expected control law, K 2i is a positive constant matrix.

[0221] For the pilot-follower multi-AUV system (19) and (20), a directed communication topology is adopted. Considering the model uncertainty, external interference and actuator dead zone of the system, the matrix K is designed. 1i , K 2i and L i When the following conditions are met:

[0222]

[0223] Under the action of the second-order command filter (26), the disturbance observer (29) and the distributed inclusive controller (35), all follower AUVs can converge to a certain point in the encirclement formed by the leader AUV, and the follower AUV and the leader AUV can move in coordination, so that the inclusive control of the multi-AUV system can be realized.

[0224] Proof: Define the Lyapunov function

[0225]

[0226] in, represents the observation error.

[0227] Combining (32)-(37), find V i (t) The first-order derivative with respect to time t:

[0228]

[0229] Continue to calculate:

[0230]

[0231] for According to hypothesis 4,

[0232]

[0233] According to Young's inequality, the following equation holds:

[0234]

[0235]

[0236]

[0237] Combining (42)-(45), It can be expressed as:

[0238]

[0239] in,

[0240]

[0241]

[0242] According to the command filter definition and (38), both κ and θ are positive constants.

[0243] According to (46), find Integration over time t:

[0244]

[0245] According to (49), when t→∞, V i (t) will eventually converge to the following set:

[0246]

[0247] Indicates ε i (t), ξ i (t) and Eventually uniformly bounded.

[0248] According to the literature (Chen Hui. Distributed Inclusion Control of Multi-Benthic AUV System[D]. Harbin Engineering University, 2021.), the inclusion error ε i (t) When the system is finally uniformly bounded, all follower AUVs can converge to a point in the convex hull formed by the leader AUV, and the follower AUVs move in coordination with the leader AUV, and the control problem of the multi-AUV system is solved. The proof is complete.

[0249] Comparison with existing technologies

[0250] If the control requirements of AUV trajectory tracking under the influence of ocean current disturbance, model uncertainty and thruster failure are to be achieved, in addition to the algorithm of the present invention, there are also solutions based on fault detection, adaptive neural network and the like. The following briefly introduces these two solutions and compares them with the algorithm of the present invention.

[0251] Based on dead zone compensation scheme

[0252] Reference (Ji Xing, Su Yumin, Zhang Guocheng. Depth control of underactuated AUV with dead zone compensation [J]. Ship Mechanics, 2016, 20 (11): 1420-1426.) Depth control of underactuated AUV with dead zone compensation, for the depth control problem of underwater robots, considering the dead zone of the body transmission system, combined with the underactuated characteristics of the robot itself, a depth controller with adaptive compensation function is designed using PID control technology. Reference (Guo Y, Yu C, Xiang X, et al. PELOS-based path following control for autonomous underwater vehicle withinput saturation and dead-zone [J]. Ocean Engineering, 2024, 296: 116956.) proposes a strategy based on nonlinear model predictive control to solve the underwater robot tracking control problem considering the nonlinearity of the dead zone, and designs a model predictive controller with an inverse dead zone model to compensate for the adverse effects of the actuator dead zone. Although some research has been done on the dead zone problem of underwater robots, the above solutions have not fully considered the complex interference to the underwater robots.

[0253] Therefore, this application has made improvements on this basis. Aiming at the inclusion control problem of multi-AUV systems, while considering the actuator dead zone, the unknown ocean current disturbances and model uncertainties are regarded as the overall uncertainty of the system, and the disturbance observer is used to estimate the overall uncertainty, so as to design a distributed inclusion controller for multi-OBFN systems that is closer to actual engineering needs.

[0254] Disturbance Observer Based Scheme

[0255] In view of the complex and changeable characteristics of the actual marine environment, underwater robots are more susceptible to the disturbance of unknown ocean currents due to their relatively small mass, and the disturbance observer is a means to effectively estimate the system disturbance. Wu Jianguo (Wu Jianguo, Chen Kai, Chen Wujin, et al. Quantized feedback sliding mode control of AUV based on nonlinear disturbance observer [J]. Journal of Underwater Unmanned Systems, 2021, 29(05): 556-564.) et al. Considering that underwater robots need to quantize state variables in actual engineering applications, they designed a method based on nonlinear disturbance observer to solve the underwater robot trajectory tracking problem, which suppressed the chattering phenomenon in traditional quantized feedback sliding mode control. The literature (Qin H, Wu Z, Y Sun, et al. Fault-Tolerant Prescribed Performance Control Algorithm for Underwater Acoustic Sensor Network Nodes with Thruster Saturation [J]. IEEE Access, 2019, PP (99): 1-1.) proposed a method to deal with lumped uncertainty in order to solve the model parameter uncertainty and external interference problems of benthic underwater robots. The interference observer was designed to achieve effective estimation of the total uncertainty.

[0256] However, compared with this application, the research objects of the above schemes are all single underwater robots, not multi-underwater robot systems, and none of them consider the "computational explosion" problem that may occur during algorithm design. This application is aimed at a multi-AUV system. Based on the above scheme, it combines interference observers and command filters to improve the control algorithm and designs a distributed inclusion controller based on command filtering. It not only eliminates the influence of the actuator dead zone, but also realizes the effective estimation of the overall uncertainty. At the same time, it also effectively avoids the "computational explosion" problem, so that the follower AUV can complete collaborative operations with the leader AUV.

[0257] Simulation Example

[0258] Simulation Preparation

[0259] In order to verify the effectiveness of the distributed inclusive control method proposed in the present invention, a pilot-follow multi-AUV system composed of individuals as ocean bottom flying nodes (OBFN) was selected as the verification object, in the form of multiple pilots and multiple followers. In the simulation experiment, the pilot-follow multi-AUV system was designed to have 5 pilot AUVs (numbered 1, 2, 3, 4, 5) and 7 follower AUVs (numbered 6, 7, ..., 12). Among them, OBFN is a type of AUV that can be equipped with a seismic detector and is an expanded type of AUV that can be deployed on the seabed surface on a large scale, such as Figure 4 shown.

[0260] In the leader-follower multi-AUV system, the kinematic and dynamic models of the leader AUV can be expressed as follows:

[0261]

[0262] In the leader-follower multi-AUV system, the kinematic and dynamic models of the follower AUV can be expressed as follows:

[0263]

[0264] Among them, i=6,7,...,12.

[0265] The pilot-follower multi-AUV system adopts a directed communication topology network. Each follower AUV has at least one pilot AUV as the root node. Figure 4 Representing topological structure

[0266] Referring to the relevant projects and hydrodynamic test results of the National Key Laboratory of Underwater Robot Technology, the following AUV actual model data will be used as a reference for this chapter (Ding Z, Wang H, Sun Y, Qin H. Adaptive prescribed performance second-order sliding mode tracking control of autonomous underwater vehicle using neural network-based disturbance observer. Ocean Engineering 2022; 260: 111939.), Table 1 and Table 2 show the inertia coefficient and hydrodynamic parameters of AUV, respectively.

[0267] Table 1 Various inertia coefficients of AUV

[0268]

[0269] Table 2 Hydrodynamic parameters of AUV

[0270]

[0271] The designed motion trajectory of the Navigator AUV is:

[0272] Table 3 Preset trajectory of the leader AUV

[0273]

[0274]

[0275] Set the initial position and angle of the follower AUV:

[0276] Table 4 Initial position and angle of follower AUV

[0277]

[0278] Set the initial linear velocity and angular velocity of the follower AUV:

[0279] Table 5 Initial linear velocity and angular velocity of the follower AUV

[0280]

[0281] The initial positions and velocities of the leader and followers in the leader-follower multi-AUV system are randomly selected to ensure that no two AUVs have the same position at the initial time. The leader trajectory in the leader-follower multi-AUV system is pre-designed, and the five leader AUVs move according to the designed trajectory.

[0282] The uncertainty coefficient of the system model is Δ=0.2, and the external ocean current disturbance is selected as follows:

[0283]

[0284] For Deadband, select the parameters:

[0285] m il =0.95-0.05sin(0.02πt) (55)

[0286] m il =1.05+0.05cos(0.02πt) (56)

[0287] Left breakpoint p il =-0.3, right breakpoint p ir =0.5, i∈F. Selection of the second-order command filter parameters, p=0.5, q=500. Selection of the disturbance observer parameters, L i =4I6. Selection of controller parameters, K1i =I6,K 2i =I6, i∈F.

[0288] Simulation Analysis

[0289] According to the simulation preparation conditions in the early stage, simulation experiments were carried out to obtain the following Figure 6 Results shown.

[0290] analyze Figure 6 It can be seen that at 0s, the followers are randomly distributed outside the convex hull formed by the leader. Under the distributed inclusion control algorithm designed in this application, as time goes on, at t=10s, the follower AUVs have all entered the convex hull, and from the images at t=20s and t=30s, it can be seen that the follower AUV has been moving in coordination with the leader AUV, moving with the convex hull formed by the leader, indicating that the distributed inclusion control consistency of the leader-follower multi-AUV system can be achieved.

[0291] analyze Figure 7 and Figure 8 It can be seen that the state quantities of the follower AUV in each dimension can converge to a position near the inclusion range formed by the leader state quantity at t = 7.2s. Although due to the existence of the dead zone, the state quantity curve of the follower AUV has extremely small fluctuations, which is of a negligible order, indicating that the distributed inclusion controller considering the actuator dead zone is effective.

[0292] analyze Fig. 9 , the second-order command filter used in this application can well estimate the virtual control law, and the filtering error ||χ i (t)|| 2 It always remains in a very small range and finally converges to near 0 at t=1s, showing an excellent filtering effect and effectively avoiding the "computational explosion" problem that may occur due to differential operations.

[0293] analyze Fig.10 Considering the model uncertainty and external ocean current disturbance of the system, the disturbance observer is used to effectively estimate it, and the estimation error Although the initial value is large, it converges to near 0 at t=6.7s as time goes on, which reflects the reliability of the observer.

[0294] analyze Fig.11 and Fig.12 , from the information in the figure, we can see that it contains the error ||ε i (t)|| 2 and design error ||ξ i (t)|| 2They converge to near 0 at t=3s and t=2.4s respectively. The above simulation results show that for the leader-follower multi-AUV systems (51) and (52), when considering the existence of model uncertainty, external interference and actuator dead zone in the system, the communication network adopts a directed communication topology. Under the action of the second-order command filter (26), the disturbance observer (29) and the distributed inclusion controller (35), the inclusion error of the follower AUV is ultimately uniformly bounded, and the inclusion control consistency of the multi-AUV system is achieved.

[0295] It should be noted that the specific implementation is only an explanation and description of the technical solution of the present invention, and cannot be used to limit the scope of protection of the rights. Any partial changes made according to the claims and description of the present invention should still fall within the scope of protection of the present invention.

Claims

1. A distributed inclusive control method for multi-AUV systems based on command filtering considering actuator dead zone, characterized in that The following steps are involved: Step 1: Construct the dynamic models of the leader AUV and the follower AUV respectively; Step 2: Design a disturbance observer using the dynamic models of the leader AUV and the follower AUV; Step 3: Construct the actuator dead zone model and design the second-order command filter and virtual control law; Step 4: Design an inclusive controller using the actuator dead zone model, second-order command filter and virtual control law, and use the inclusive controller to ensure that all follower AUVs are contained in the convex hull formed by the leader AUV in space; The included controller is represented as: Among them, m i represents the output gain of the ith follower, Ω i represents the piecewise function of the dead zone produced by the ith follower at the output, represents the output signal of the second-order command filter of the i-th follower AUV, ξ i represents the error of the i-th follower AUV, represents the output of the distributed inclusive controller based on command filtering of the ith follower AUV, which is used as the actual control input of the ith follower AUV when considering the dead zone. represents the intermediate reference value of the i-th follower AUV, represents the desired control law of the i-th follower AUV, K 2i represents the constant matrix of the i-th follower AUV, K 1i represents the intermediate matrix of the i-th follower AUV, L i represents the intermediate matrix of the i-th follower AUV, represents a positive constant, η i represents the position and angle vector of the i-th follower AUV, Represents η i The first derivative of 0i represents the thrust distribution matrix of the i-th follower AUV, express The first derivative of i Indicates that the i-th follower AUV contains an error, g i represents the intermediate variable of the i-th follower AUV, represents the observed value, t represents the time, M ηi represents the mass and moment of inertia matrix of the ith AUV, C ηi represents the Coriolis force matrix of the ith AUV, D ηi represents the i-th AUV fluid damping force matrix, i∈F, and F represents the follower set.

2. According to claim 1, a distributed inclusive control method for a multi-AUV system based on command filtering considering actuator dead zone is characterized in that The dynamic model of the pilot AUV is expressed as: Among them, η l represents the six-degree-of-freedom position and attitude vector of the lth leader AUV in the inertial coordinate system, Represents η l The first derivative of Represents η l The second derivative of M ηl represents the mass and inertia matrix of the lth AUV, C ηl represents the Coriolis force (moment) matrix of the lth AUV, D ηl represents the lth AUV fluid damping force matrix, B 0l represents the thrust distribution matrix of the lth leader AUV, u l represents the control amount of the thruster of the lth leader AUV, g ηl Represents the force and torque vectors generated by the gravity and buoyancy of the lth leader AUV.

3. A distributed inclusive control method for a multi-AUV system based on command filtering considering actuator dead zone according to claim 2, characterized in that The dynamic model of the follower AUV is expressed as: Among them, η l represents the position and angle vector of the leader AUV, W i represents the total uncertainty, u i represents the control amount of the thruster of the i-th follower AUV, J l represents the transformation matrix between the inertial coordinate system and the motion coordinate system of the lth leader AUV, v l represents the longitudinal velocity of the lth leader AUV.

4. A distributed inclusive control method for a multi-AUV system based on command filtering considering actuator dead zone according to claim 3, characterized in that The total uncertainty W i It is expressed as: Among them, d i represents the impact of ocean current disturbance, and Δ represents the uncertainty value.

5. A distributed inclusive control method for a multi-AUV system based on command filtering considering actuator dead zone according to claim 4, characterized in that The disturbance observer is expressed as: in, represents the observed value, σ i and δ i represents the intermediate variable of the uncertainty of the i-th follower AUV, L i The constant matrix representing the uncertainty of the ith follower AUV, Represents η i The second-order derivative of Denotes δ i The first derivative of .

6. A distributed inclusive control method for a multi-AUV system based on command filtering considering actuator dead zone according to claim 5, characterized in that Said It is expressed as:

7. A distributed inclusive control method for a multi-AUV system based on command filtering considering actuator dead zone according to claim 6, characterized in that The actuator dead zone model is expressed as: m i =diag(m i1 ,m i2 ,…,m ij ),j∈Q, Oh i =[Ω i1 ,Oh i2 ,…,Oh ij ] T ,j∈Q, Where Q represents a non-empty set {1,2,3,4,5,6}, Indicates the design intermediate reference quantity, m ij represents the gain of the j-th degree of freedom of the ith follower AUV, m il and m ir They represent the left gain and right gain of the dead zone of the i-th follower AUV actuator, Ω l Represents the piecewise function matrix of the dead zone generated by the l-th follower AUV, Ω lj represents the piecewise function that produces the dead zone on the j-th degree of freedom of the l-th follower AUV, diag represents the diagonal matrix; p il and p ir They represent the left and right breakpoints of the dead zone of the actuator of the i-th follower AUV, respectively.

8. The distributed inclusive control method for a multi-AUV system based on command filtering considering actuator dead zone according to claim 7 is characterized in that The second-order command filter is expressed as: in, represents the second-order command filter input signal, α i and represents the intermediate variable, express The first-order derivative of , p represents the damping ratio of the command filter, and q represents the bandwidth of the command filter; For any t ≥ 0, if the following conditions are met, for any positive constant Γ > 0, there exists 0 < p ≤ 1 and q > 0 such that holds, and |α i (t)| and All are bounded; Define command filter output signal for: in, express The first derivative of express The second-order derivative of , w1, w2 represent positive constants, express The first derivative of .

9. A distributed inclusive control method for a multi-AUV system based on command filtering considering actuator dead zone according to claim 8, characterized in that The virtual control law is expressed as: Among them, η ri represents the reference information of the neighbors of the i-th follower AUV, Represents η ri The first derivative of .

10. A distributed inclusive control method for a multi-AUV system based on command filtering considering actuator dead zone according to claim 9, characterized in that The specific steps of designing a controller using an actuator dead zone model, a second-order command filter and a virtual control law are as follows: First, for the general uncertainty W in the system i (t), the following disturbance observer is designed to accurately estimate it: Define the follower AUV inclusion error as follows: e i (t)=η i (t)-η ri (t) Among them, a ij and b il represents the communication weight; Design of virtual control law: Using a second-order command filter, the filtering error is defined as: Define the error: Design the following distributed controller:

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