A command-filtering-based multi-aUV system distributed containment control method considering actuator dead-zone

Abstract

A distributed inclusion control method for multiple AUV systems based on command filtering, considering actuator dead zones, is disclosed. This method relates to the field of underwater ship control technology. Addressing the problem in existing technologies where distributed inclusion control of AUV systems near actuator dead zones is difficult to achieve, this application designs a controller that enables all follower AUVs to converge into the convex hull of the leader AUV, cooperating with it in the presence of ocean current disturbances, model uncertainties, and actuator dead zones, thus completing the distributed inclusion control of the multiple AUV system. This application solves the problem in existing technologies where distributed inclusion control of AUV systems near actuator dead zones is difficult to achieve.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of underwater control of ships, in particular to a multi-AUV system distributed containment control method based on command filtering considering actuator dead zone. BACKGROUND

[0002] In recent years, China actively speeds up the construction of a maritime power, and the autonomous underwater vehicle (AUV) as a kind of robot that can operate autonomously underwater has certain intelligence, has many advantages such as large activity range, strong maneuverability and safety, and plays an increasingly important role in resource exploration and seabed measurement. In the face of increasing operation requirements, the operation capacity of a single AUV is limited, while a multi-AUV system has the advantages of good redundancy, high efficiency and robustness, and has a broader application prospect in large-scale and high-time-efficiency marine exploration activities. For a distributed multi-AUV system, containment control can liberate the demand of the formation system for communication equipment and reduce the communication pressure of the system. In the containment control, only multiple leaders need to communicate with the surface mother ship, accept instructions and plan the task trajectory, while the followers only communicate with part of the leaders and the neighbor followers. In this process, all followers will move together with the convex hull formed by multiple leaders, so as to reach the task area and start operation.

[0003] Due to the complex and variable characteristics of the actual marine environment, the AUV is more easily disturbed by unknown ocean current disturbance due to its relatively small mass. At the same time, the dynamic model of the AUV itself has significant nonlinearity and uncertainty characteristics, which increases the complexity and challenge of designing an AUV system trajectory tracking control algorithm.

[0004] As a kind of robot, the AUV usually needs to use the power generated by the actuator to make various movements like other kinds of robots, so the actuator is an indispensable part of the control loop of the AUV. The actuator dead zone is a common non-smooth and nonlinear physical phenomenon, which usually occurs in a robot system due to the limitations of the manufacturing process of the mechanical structure. The actuator dead zone refers to the phenomenon that the actuator does not produce any action or response to a small range of input signals, and only when the input signal exceeds a certain threshold, the actuator starts to work. Therefore, it is difficult to control the AUV system distributed containment control near the actuator dead zone. SUMMARY

[0005] The purpose of the present application is to solve the problem that the distributed containment control of the AUV system in the prior art is difficult to implement near the actuator dead zone, and to propose a multi-AUV system distributed containment control method based on command filtering considering actuator dead zone.

[0006] The present application adopts the technical scheme to solve the above technical problems:

[0007] A command filter-based multi-AUV system distributed containment control method considering actuator dead zone, comprising the following steps:

[0008] Step one: respectively construct the dynamic model of the leader AUV and the follower AUV;

[0009] Step two: design a disturbance observer by using the dynamic model of the leader AUV and the follower AUV;

[0010] Step three: construct an actuator dead zone model, and design a second-order command filter and a virtual control law;

[0011] Step four: design a containment controller by using the actuator dead zone model, the second-order command filter and the virtual control law, and realize that all follower AUVs are contained in the convex hull formed by the leader AUV in space by using the containment controller;

[0012] The containment controller is represented as:

[0013]

[0014]

[0015]

[0016]

[0017] Wherein, m i represents the output gain of the i-th follower, Ω i represents the segment function of the i-th follower in the output dead zone, 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 command filter-based distributed containment controller of the i-th follower AUV, as the actual control input of the i-th follower AUV considering the dead zone, represents the intermediate reference quantity 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, x represents ηi The first derivative, B 0i This represents the thrust allocation matrix for the i-th follower AUV. express The first derivative, ε i This indicates that the AUV of the i-th follower includes error, g i Let represent the intermediate variable of the i-th follower AUV. Let M represent the observed value, t represent time, and M represent the time. ηi Let C represent the mass and moment of inertia matrix of the i-th AUV. ηi Let D represent the Coriolis force matrix of the i-th AUV. ηi Let F represent the fluid damping force matrix of the i-th AUV, where i ∈ F and F represents the set of followers.

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

[0019]

[0020] Where, η l This represents the six-degree-of-freedom position and attitude vector of the l-th navigator AUV in the inertial coordinate system. Indicates η l The first derivative, Indicates η l The second derivative, M ηl Let C represent the mass and moment of inertia matrix of the l-th AUV. ηl D represents the Coriolis force (moment) matrix of the l-th AUV. ηl B represents the fluid damping force matrix of the l-th AUV. 0l Let u represent the thrust distribution matrix of the l-th navigator AUV. l g represents the control quantity of the thrusters of the l-th navigator AUV. ηl This represents the force and torque vector generated by gravity and buoyancy of the l-th navigator AUV.

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

[0022]

[0023]

[0024] Where, η l W represents the position and angle vector of the navigator AUV. i Indicating total uncertainty, u i J represents the control quantity of the thruster of the i-th follower AUV. l This represents the transformation matrix between the inertial coordinate system and the motion coordinate system of the l-th navigator AUV.l This represents the longitudinal velocity of the l-th navigator AUV.

[0025] Furthermore, the total uncertainty W i Represented as:

[0026]

[0027] Where, d i This represents the impact of ocean current disturbances, with Δ representing the uncertainty value.

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

[0029]

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

[0031] Furthermore, the aforementioned Represented as:

[0032]

[0033] Furthermore, the actuator dead-time 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 the non-empty set {1,2,3,4,5,6}, Indicates intermediate reference value in the design, mij represents the gain on the jth degree of freedom of the ith follower AUV, m il and m ir represent the left and right gain of the ith follower AUV actuator dead zone, respectively, Ω l represents the piecewise function matrix of the ith follower AUV that generates dead zone, Ω lj represents the piecewise function of the jth degree of freedom of the ith follower AUV that generates dead zone, diag represents a diagonal matrix; p il and p ir represent the left and right breakpoints of the ith follower AUV actuator dead zone, respectively.

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

[0041]

[0042] wherein, represents the second-order command filter input signal, a i and represents an intermediate variable, represents the first 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 exist 0 is established, and |a i (t)|, and are bounded;

[0044]

[0045] The command filter output signal y is defined as:

[0046]

[0047] wherein, represents the first derivative of , represents the second derivative of , w1, w2 represent normal numbers, represents the first derivative of .

[0048] Further, the virtual control law is represented as:

[0049]

[0050] wherein, η ri ​​Reference information representing the i-th follower AUV related neighbor, The first derivative of η ri .

[0051] Further, the specific steps for designing the 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 i (t) existing in the system, the following disturbance observer is designed to accurately estimate it:

[0053]

[0054] The follower AUV is defined as the following form of containing error:

[0055] ε i (t) = η i (t) - η ri (t)

[0056]

[0057] Wherein, a ij and b il represent the communication weights;

[0058] The virtual control law is designed as follows:

[0059]

[0060] The second-order command filter is adopted, and the filter error is defined as:

[0061]

[0062] The error is defined as:

[0063]

[0064] The following distributed containing controller is designed:

[0065]

[0066]

[0067]

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

[0069] This application designs a controller that enables all follower AUVs in a multi-AUV system to converge into the convex hull of the leader AUV, working collaboratively with it under conditions of ocean current disturbances, model uncertainties, and actuator dead zones. This achieves distributed inclusion control of the multi-AUV system. This application solves the problem in existing technologies where distributed inclusion control of AUV systems is difficult to implement near actuator dead zones. Attached Figure Description

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

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

[0072] Figure 3 This is a diagram of a second-order command filter structure;

[0073] Figure 4 A schematic diagram of the seabed flight node;

[0074] Figure 5 A schematic diagram of the directed communication topology network for a multi-AUV navigation-following system;

[0075] Figure 6 A schematic diagram illustrating the three-dimensional spatial position changes of each AUV in a multi-AUV navigation-following system.

[0076] Figure 7 A schematic diagram illustrating the positional changes of each AUV in a multi-AUV navigation-following system;

[0077] Figure 8 Schematic diagram of the angle changes of each AUV in the navigation-following multi-AUV system;

[0078] Figure 9 For navigation-following multi-AUV systems, follower AUV filtering error ||χ i (t)|| 2 Schematic diagram of the changes;

[0079] Figure 10 For navigation-following multi-AUV system follower AUV observation error Schematic diagram of the changes;

[0080] Figure 11 For navigation-following multi-AUV systems, the follower AUV includes error ||ε i (t)|| 2 Schematic diagram of the changes;

[0081] Figure 12 For leading-following multi-AUV systems, follower AUV design error ||ξ i (t)|| 2 Schematic diagram of the changes. DETAILED DESCRIPTION

[0082] It should be noted that the various embodiments disclosed in the present application can be combined with each other as long as there is no conflict.

[0083] Embodiment I: Reference Figure 1 To specifically describe the present embodiment, the present embodiment is a kind of command filtering multi-AUV system distributed containment control method considering actuator dead zone, comprising the following steps:

[0084] Step one: respectively construct the dynamics model of leader AUV and follower AUV;

[0085] Step two: design disturbance observer using the dynamics model of leader AUV and follower AUV;

[0086] Step three: build actuator dead zone model, and design second order command filter and virtual control law;

[0087] Step four: design containment controller using actuator dead zone model, second order command filter and virtual control law, and realize that all follower AUVs are contained in the convex hull formed by leader AUV in space using containment controller;

[0088] The containment controller is represented as:

[0089]

[0090]

[0091]

[0092]

[0093] Wherein, m i represents the output gain of the i-th follower follower, Ω i represents the segment function of the i-th follower follower in the output dead zone, 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 i-th follower AUV based on command filtering distributed containment controller, as the actual control input when the i-th follower AUV considers dead zone, represents the intermediate reference quantity 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 1iL i L η i η η i B 0i B B ε i g i x y ηi M ηi C ηi D

[0094] Parameter definitions:

[0095] M - mass and inertia matrix

[0096] η = [x, y, z, φ, θ, ψ] T - position and orientation vector of the AUV in the inertial frame

[0097] v = [u, v, w, p, q, r] T - linear and angular velocity vector of the AUV in the body frame

[0098] J - transformation matrix between the inertial and body frames

[0099] C RB - Coriolis and centripetal force matrix for rigid bodies

[0100] C A - Coriolis and centripetal force matrix for added mass

[0101] D - hydrodynamic damping matrix

[0102] g η - force and moment vector due to gravity and buoyancy

[0103] τ - control force and moment generated by the propulsion system

[0104] B0 - thrust allocation matrix

[0105] u - control variable for the thrusters

[0106] Firstly, the inertial coordinate system and the moving coordinate system are established, and then the multi-AUV kinematics and dynamics model and the mathematical model of actuator dead zone are established. Finally, the design of the second-order command filter and the distributed inclusion controller is given for the AUV dynamics model.

[0107] Coordinate system establishment

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

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

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

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

[0112] Multi-AUV kinematics, dynamics equation and actuator dead zone

[0113] Taking AUV as an example, it is assumed that there are M leader AUVs and N follower AUVs in the leader-following multi-AUV system, and sets L=(1,2,...,M) and F=(M+1,M+2,...,M+N) are set.

[0114] In view of the model uncertainty and unknown sea current disturbance of the multi-AUV system, the feasible mathematical expression form is considered. The dynamics 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, and its expression is as follows:

[0117]

[0118] Where, d i (t) represents the influence caused by the sea current disturbance; Δ represents the uncertainty value.

[0119] Considering the existence of dead zone in the AUV system, the actuator dead zone can be expressed asFigure 2 represents.

[0120] The dead-zone investigation model is in the following form:

[0121]

[0122] where p il and p ir represent the left and right breakpoints of the dead-zone, m il and m ir represent the gains, i∈F.

[0123] Since the AUV is a multi-dimensional nonlinear system in the form of

[0124]

[0125] where 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 filter and distributed containment controller design

[0130] To avoid the problem of "computation explosion" that may occur in backstepping control method, the second-order command filter in the following form is designed:

[0131]

[0132] where x i (t) is the second-order command filter input signal, α (t) and β are intermediate variables, and p and q are positive constants. 0 < p ≤ 1 represents the damping ratio of the command filter, and q > 0 is the bandwidth of the command filter. For If the following condition is satisfied, for any positive constant Γ > 0, there exist 0 < p ≤ 1 and q > 0 such that holds, and |α i (t)|, and are bounded.

[0133]

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

[0135] The command filter output signal is defined as:

[0136]

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

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

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

[0140]

[0141] Wherein, i ∈ F, represents the observation value, σ i (t) and δ i (t) are intermediate variables, and L i is a positive constant matrix.

[0142] The follower AUV is defined as the containment error in the following form:

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

[0144]

[0145] Wherein, i ∈ F, ε i (t) is the containment error, and η​ri (t) represents the reference information of the follower's AUV related neighbors, a ij and b ij It is the communication weight.

[0146] Designing virtual control laws:

[0147]

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

[0149] Define error

[0150]

[0151] Design a distributed containment controller as follows:

[0152]

[0153]

[0154]

[0155] in, To account for the actual control input when dead time is considered, Indicates intermediate reference values ​​in the design. K represents the expected control law. 2i It is a positive constant matrix.

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

[0157]

[0158] The pilot-follower multi-AUV system enables distributed containment control.

[0159] This application chooses directed communication between multiple AUV systems instead of undirected communication, which saves certain communication resources. The communication network of the multiple AUV system is described using algebraic graph theory, denoted as... This is a directed graph. Assume a multi-AUV system has M navigators and N followers. Let L = {1, 2, ..., M} represent the set of navigator AUVs, and F = {M+1, M+2, ..., M+N} represent the set of follower AUVs. Consider each AUV as a communication node, let... The set of all communication nodes, in the text Let i represent the AUV with the number i. Treat the communication connections between the various communication nodes as edges, and let... As a set of all edges, edges An AUV with index j can obtain information from an AUV with index i, denoted as is a child node of is a parent node of denotes an adjacency matrix.

[0160] Define as a subgraph of follower AUVs, where

[0161] For the adjacency matrix When and i≠j, a ij =1>0; otherwise a ij =0 (for undirected graph, i.e., when , a ij =a ji =1; otherwise a ij =0). In a directed graph , if a follower i exists a directed path from a leader l, indicating that the follower i can obtain information from the leader l, denoted as b il =1>0; otherwise b il =0.

[0162] A node is a neighbor of a node in a directed graph , denoted as satisfying the relationship All nodes that satisfy the relationship are neighbors of the node . If in a directed graph all follower AUVs exist at least one leader AUV as a root node, the leader set L is called globally reachable.

[0163] Dynamics model of AUV

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

[0165] The dynamics model of the leader AUV can be expressed as:

[0166]

[0167] wherein, denotes the position and orientation vector of the leader AUV, l e L.

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

[0169]

[0170] where, denotes the position and orientation vector of the follower AUV, W i (t) denotes the total uncertainty, i e F.

[0171]

[0172] where, d i (t) denotes the influence caused by the sea current disturbance; Δ denotes the uncertainty value.

[0173] The control objective of the present application can be expressed as: design the controller u to make the multi-AUV system converge to the convex hull composed of the leader AUVs in the presence of sea current disturbance, model uncertainty and actuator dead zone, all the follower AUVs can work cooperatively with the leader AUVs, and effectively avoid the problem of "computational explosion".

[0174] In combination with the actual engineering background, the following assumptions are proposed:

[0175] Assumption 1 The position and orientation vector η and its first derivative are measurable.

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

[0177] Assumption 3 The communication between AUVs is directional communication, and each follower AUV has at least one leader AUV as a root node.

[0178] Assumption 4 For Ω i , there exists is a positive constant, i e F, j e Q.

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

[0180] Actuator dead zone model

[0181] In the present application, the AUV system adopts the following form of dead zone research model:

[0182]

[0183] where p il and p ir denote the left and right breakpoints of the dead zone, m il and m ir denote the gain, i∈F.

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

[0185]

[0186] where 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, the conversion relationship between and is constructed, and the actual control input considering the dead zone

[0191] Second-order command filter design

[0192] In order to avoid the "calculation explosion" problem that may occur in the backstepping control method, a second-order command filter of the following form is designed:

[0193]

[0194] where, is the input signal of the second-order command filter, α i (t) and are intermediate variables, and p and q are positive constants. 0 < p ≤ 1 represents the damping ratio of the command filter, and q > 0 is the bandwidth of the command filter. For If the following condition is satisfied, for any positive constant Γ > 0, there exist 0 < p ≤ 1 and q > 0 such that holds, and |α i (t)|, and are bounded.

[0195]

[0196] Define the command filter output signal as:

[0197]

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

[0199] Adaptive attitude tracking controller design

[0200] The leader-follower multi-AUV system adopts a directed communication topology network, and considers the cases where the system has model uncertainty, external disturbance and dead zone. The present application designs a distributed containment controller based on command filtering, and finally completes the distributed containment control of the multi-AUV system.

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

[0202]

[0203] Wherein, i ∈ F, represents the observation value, σ i (t) and δ i (t) are intermediate variables, and L i is a positive constant matrix.

[0204] Define the containment error of the follower AUV as follows:

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

[0206]

[0207] Wherein, i ∈ F, ε i (t) is the containment error, and η ri(t) denotes the reference information of the follower AUV related neighbors, a ij and b il are the communication weights.

[0208] The virtual control law is designed as:

[0209]

[0210] where K 1i is a positive constant matrix.

[0211] The filter error is defined as:

[0212]

[0213] where, denotes the output signal of the command filter.

[0214] The error is defined as:

[0215]

[0216] The distributed containment controller is designed as:

[0217]

[0218]

[0219]

[0220] where, is the actual control input considering the dead zone, denotes the designed intermediate reference, denotes the desired control law, K 2i is a positive constant matrix.

[0221] For the leader-follower multi-AUV system (19) and (20), the directed communication topology is adopted, and the model uncertainty, external disturbance and actuator dead zone are considered. The matrices K 1i , K 2i and L i satisfy the following conditions:

[0222]

[0223] Under the action of the second-order command filter (26), the disturbance observer (29) and the distributed containment controller (35), all the follower AUVs can converge to the vicinity of a certain point position in the enclosure formed by the leader AUV, and the follower AUVs and the leader AUV do cooperative motion, and the multi-AUV system containment control is achieved.

[0224] Proof: Define Lyapunov function

[0225]

[0226] where, represents the observation error.

[0227] Combining (32)-(37), we have i (t) the first derivative of V

[0228]

[0229] Continue to calculate:

[0230]

[0231] For According to assumption 4,

[0232]

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

[0234]

[0235]

[0236]

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

[0238]

[0239] where,

[0240]

[0241]

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

[0243] According to (46), we have The integral with respect to time t:

[0244]

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

[0246]

[0247] indicates that epsilon i (t), xi i (t) and Finally, the consensus is bounded.

[0248] According to the literature (Chen H. Multi-habitat AUV system distributed containment control [D]. Harbin Engineering University, 2021.), the containment error epsilon i When the final consensus of (t) is bounded, all follower AUVs can converge to a point near the convex hull formed by the leader AUV, and the follower AUVs and the leader AUVs cooperate to move, and the multi-AUV system containment control problem is solved. The proof is complete.

[0249] Comparison with prior art

[0250] If you want to achieve the control requirements of AUV trajectory tracking under the influence of sea current disturbance, model uncertainty and thruster failure, in addition to the algorithm of the present application, there are also schemes based on fault detection and adaptive neural network, the following will briefly introduce these two schemes, and compare them with the algorithm of the present application.

[0251] Dead zone compensation scheme

[0252] The literature (Ji X, Su Y, Zhang G. 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 robot, considering the existence of dead zone in the transmission system of the body, combining with the underactuated characteristics of the robot itself, a depth controller with adaptive compensation function is designed by using PID control technology. The literature (Guo Y, Yu C, Xiang X, et al. PELOS-based path following control for autonomous underwater vehicle with input saturation and dead-zone [J]. Ocean Engineering, 2024, 296: 116956.) proposed a strategy based on nonlinear model predictive control, to solve the tracking control problem of underwater robot considering dead zone nonlinearity, a model predictive controller with inverse dead zone model was designed to compensate for the adverse effects of actuator dead zone. For the dead zone problem of underwater robot, although the above schemes have done some research, however, the complex disturbances suffered by the underwater robot have not been fully considered.

[0253] Therefore, the present application improves on the basis thereof, and in view of the containment problem of the multi-AUV system, considers the unknown sea current disturbance and model uncertainty as the overall uncertainty of the system while considering the actuator dead zone, and estimates the overall uncertainty using a disturbance observer, thereby designing a more practical multi-OBFN system distributed containment controller.

[0254] Disturbance observer scheme

[0255] In view of the complex and variable characteristics of the actual marine environment, underwater robots are more susceptible to unknown sea current disturbances due to their relatively small mass, and the disturbance observer is a means that can effectively estimate system disturbances. Wu Jianguo (Wu Jianguo, Chen Kai, Chen Wuqin, et al. Quantized feedback sliding mode control of AUV based on nonlinear disturbance observer [J]. Journal of Underwater Unmanned System, 2021, 29(05): 556-564.) and others considered that underwater robots need to quantize state variables and the like in actual engineering applications, and designed a method based on a nonlinear disturbance observer for underwater robot trajectory tracking to suppress the chattering phenomenon in traditional quantized feedback sliding mode control. The document (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.) addresses the model parameter uncertainty and external disturbance problems of the benthic underwater robot, and proposes a lumped uncertainty processing method to effectively estimate the total uncertainty through the design of a disturbance observer.

[0256] However, compared with the present application, the research objects of the above schemes are single underwater robots, not multi-underwater robot systems, and none of them considers the "computational explosion" problem that may occur when designing the algorithm. The present application is directed to a multi-AUV system, and improves the control algorithm based on the above scheme, combined with the disturbance observer and command filter, to design a distributed containment controller based on command filtering, which not only eliminates the influence of the actuator dead zone, but also effectively estimates the overall uncertainty, while effectively avoiding the "computational explosion" problem, so that the follower AUV can complete the cooperative work with the leader AUV.

[0257] Simulation example

[0258] Simulation preparation

[0259] In order to verify the effectiveness of the distributed containment control method proposed in the patent, a leader-follower multi-AUV system composed of individual ocean bottom flying nodes (OBFNs) is selected as the verification object, and the form of multiple leaders and multiple followers is adopted. In the simulation experiment, five leader AUVs (numbered 1, 2, 3, 4, and 5) and seven follower AUVs (numbered 6, 7, …, and 12) are designed in the leader-follower multi-AUV system. The OBFN is a type of AUV that can carry a geophone and is a type of extended AUV that can be deployed on a large scale to the seabed surface, as shown in FIG. 1. Figure 4

[0260] In the leader-follower multi-AUV system, the kinematic and dynamic models of the leader AUVs can be represented by the following formulas:

[0261]

[0262] In the leader-follower multi-AUV system, the kinematic and dynamic models of the follower AUVs can be represented by the following formulas:

[0263]

[0264] where i = 6, 7, …, and 12.

[0265] The leader-follower multi-AUV system adopts a directed communication topology network, and each follower AUV has at least one leader AUV as a root node, Figure 4 representing the topological structure

[0266] Referring to the related projects of the National Key Laboratory of Underwater Robot Technology and the hydrodynamic test results, the following AUV actual model data will be used as the reference basis 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 represent the inertia coefficients and hydrodynamic parameters of the AUV, respectively.

[0267] Table 1 Inertia coefficients of AUV

[0268]

[0269] ​Table 2AUV hydrodynamic parameters

[0270]

[0271] The designed trajectory of the leader AUV is:

[0272] Table 3Designed trajectory of the leader AUV

[0273]

[0274]

[0275] The initial position and angle of the follower AUV are set as:

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

[0277]

[0278] The initial linear and angular velocities of the follower AUV are set as:

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

[0280]

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

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

[0283]

[0284] For the dead zone, the parameters are selected as:

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

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

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

[0288] Simulation analysis

[0289] According to the simulation preparation conditions in the early stage, the simulation experiment is carried out, and the results shown in FIG. Figure 6

[0290] Analysis Figure 6 It can be seen that at 0s, the followers are randomly distributed outside the convex hull formed by the leader, and under the action of the distributed containment control algorithm designed in the 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 AUVs always move in coordination with the leader AUV, moving with the convex hull formed by the leader, indicating that the distributed containment control consistency of the leader-follower multi-AUV system can be realized.

[0291] Analysis Figure 7 and Figure 8 It can be seen that the state quantities of the follower AUVs in each dimension can converge to a position near the containment range formed by the leader state quantities at t=7.2s, although there is a small fluctuation in the state quantity curve of the follower AUV due to the existence of the dead zone, which is of a negligible magnitude, indicating that the distributed containment controller considering the actuator dead zone is effective.

[0292] Analysis Figure 9 The second-order command filter used in the application can well estimate the virtual control law, and the filtering error ||χ i (t)|| 2 is always kept in a very small range, and finally converges to the vicinity of 0 at t=1s, showing excellent filtering effect and effectively avoiding the "calculation explosion" problem that may occur due to differentiation operation.

[0293] Analysis Figure 10 Considering the model uncertainty and external sea current disturbance existing in the system, a disturbance observer is used to effectively estimate it, and the estimation error Although the initial value is large, it converges to the vicinity of 0 at t=6.7s as time goes on, reflecting the reliability of the observer.

[0294] Analysis Figure 11 and Figure 12 From the information in the figure, it can be seen that the containment error ||ε i (t)|| 2 and the design error ||ξ i (t)|| 2 ​Converge to the vicinity of 0 at t=3s and t=2.4s, respectively. The above simulation results show that for the leader-follower multi-AUV system (51) and (52), considering the model uncertainty, external disturbance and actuator dead zone of the system, under the action of the second-order command filter (26), the disturbance observer (29) and the distributed containment controller (35), the containment error of the follower AUV is ultimately uniformly bounded, and the containment control consistency of the multi-AUV system is achieved.

[0295] It should be noted that the specific embodiments are only an explanation and illustration of the technical solutions of the present application, and cannot limit the protection scope. Any partial change made according to the claims and description of the present application shall still fall within the protection scope of the present application.

Claims

1. A command-filtered multi-AUV system distributed containment control method considering actuator dead zone, characterized in that The method comprises the following steps: Step 1: constructing a dynamic model of a leader AUV and a follower AUV respectively; Step 2: designing a disturbance observer by using the dynamic model of the leader AUV and the follower AUV; Step 3: constructing an actuator dead-zone model, designing a second-order command filter and a virtual control law; Step 4: designing an inclusion controller by using the actuator dead-zone model, the second-order command filter and the virtual control law, and realizing that all follower AUVs are included in a convex hull formed by the leader AUV in space by using the inclusion controller; The inclusion controller is represented as: where m i represents the output gain of the i-th follower follower, Ω i represents the piecewise function of the i-th follower follower in the output producing dead zone, 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 containment controller based on the command filter of the i-th follower AUV, as the actual control input when the i-th follower AUV considers the dead zone, represents the intermediate reference quantity in 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, represents a positive constant, η i represents the position and angle vector of the i-th follower AUV, represents the first derivative of η i , B 0i represents the thrust allocation matrix of the i-th follower AUV, represents the first derivative of , ε i represents the containment error of the i-th follower AUV, g i represents the intermediate variable of the i-th follower AUV, represents the observation value, t represents the time, M ηi represents the mass and inertia matrix of the i-th AUV, C ηi represents the Coriolis force matrix of the i-th AUV, D ηi represents the fluid damping force matrix of the i-th AUV, i ∈ F, F represents the follower set.

2. The command-filtering multi-AUV system distributed containment control method considering the dead zone of actuators according to claim 1, characterized in that The dynamic model of the leader AUV is represented as: where η l represents the six-degree-of-freedom position and attitude vector of the lth follower AUV in the inertial coordinate system, represents the first-order derivative of η l , represents the second-order derivative of η l , M ηl represents the mass and inertia matrix of the lth AUV, C ηl represents the Coriolis force matrix of the lth AUV, D ηl represents the fluid damping force matrix of the lth AUV, B 0l represents the thrust allocation matrix of the lth follower AUV, u l represents the control amount of the thrusters of the lth follower AUV, g ηl represents the force and moment vector generated by the gravity and buoyancy of the lth follower AUV.

3. The command-filtering multi-AUV system distributed containment control method considering the dead zone of actuators according to claim 2, characterized in that The dynamic model of the follower AUV is represented as: where 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 moving coordinate system of the l-th leader AUV, v l represents the longitudinal velocity of the l-th leader AUV.

4. The command-filtering multi-AUV system distributed containment control method considering the dead zone of actuators according to claim 3, characterized in that The total uncertainty W i is represented as: where d i represents the influence of the ocean current disturbance, and Δ represents the uncertainty.

5. The command-filtered multi-AUV system distributed containment control method considering the dead zone of actuators according to claim 4, wherein The disturbance observer is represented as: where, represents the observation, σ i and δ i represents the intermediate variable of the uncertainty of the i-th follower AUV, L i represents the constant matrix of the uncertainty of the i-th follower AUV, represents the second derivative of η i , represents the first derivative of δ i .

6. The command-filtering multi-AUV system distributed containment control method considering the dead zone of actuators according to claim 5, characterized in that The is represented as:

7. The command-filtering multi-AUV system distributed containment control method considering the dead zone of actuators according to claim 6, characterized in that The actuator dead-zone model is represented as: m i = diag(m i1 ,m i2 ,…,m ij ), j e Q, Ω i = [Ω i1 , Ω i2 ,..., Ω ij ] T , j e Q, where Q represents a non-empty set {1, 2, 3, 4, 5, 6}, represents a design intermediate reference quantity, m ij represents a gain of the jth degree of freedom of the ith follower AUV, m il and m ir respectively represent the left gain and the right gain of the ith follower AUV actuator dead zone, Ω l represents a piecewise function matrix of the lth follower AUV generating a dead zone, Ω lj represents a piecewise function of the jth degree of freedom of the lth follower AUV generating a dead zone, diag represents a diagonal matrix; p il and p ir respectively represent the left breakpoint and the right breakpoint of the ith follower AUV actuator dead zone.

8. The command-filtering multi-AUV system distributed containment control method considering the dead zone of actuators according to claim 7, characterized in that The second-order command filter is represented as: wherein represents a second order command filter input signal, a i and represents an intermediate variable, represents a first derivative of the command filter input signal, p represents a damping ratio of the command filter, and q represents a bandwidth of the command filter; For any t > 0, if the following condition is satisfied, for any positive constant Γ > 0, there exist 0 < p < 1 and q > 0 such that holds, and |a i (t)|, and are bounded; Defining a command filter output signal f = 1 - a wherein denotes the first derivative of denotes the second derivative of denotes the first derivative of 9. The command-filtering multi-AUV system distributed containment control method considering the dead zone of actuators according to claim 8, characterized in that The virtual control law is represented as: where η ri represents the reference information of the i-th follower AUV related neighbor, represents the first derivative of η ri , K 1i represents the intermediate matrix of the i-th follower AUV.

10. The method of claim 9, wherein the method is a command filtered multi-AUV system distributed containment control method considering actuator dead zone. The specific steps of designing the inclusion controller by using the actuator dead-zone model, the second-order command filter and the virtual control law are as follows: First, for the general uncertainty W i (t) of the system, the following disturbance observer is designed to accurately estimate it: Defining an inclusion error of the follower AUV in the following form: ε i (t) = η i (t) - η ri (t) wherein a ij and b il represent the communication weight; Designing a virtual control law: Defining a filter error by using a second-order command filter:

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