Unmanned surface vessel formation fixed time path tracking control method

Abstract

The invention provides an unmanned surface vessel formation fixed time path tracking control method. The method specifically comprises the following steps of performing kinematics and dynamics modeling on USV and establishing a formation coupling error of the USV; designing a fixed time preset performance function and a position error conversion function, reconstructing a formation coupling error, and limiting the formation coupling error within a specified range; designing a fixed time extended state observer, and simultaneously observing the unmeasurable speed and the system lumped disturbance of the USV by using the fixed time extended state observer; and designing an anti-saturation fixed time output feedback formation controller, and tracking a USV formation path. The technical scheme of the invention overcomes the problem of low precision of USV formation path tracking under multiple constraints in the prior art.

Description

Technical Field

[0001] The present invention relates to the field of unmanned surface ship path tracking control, and in particular to a fixed-time path tracking control method for an unmanned surface ship formation. Background Art

[0002] As a miniaturized, intelligent, and multi-purpose unmanned navigation marine carrier platform, unmanned surface vehicles (USVs) can perform various complex marine tasks in harsh environments and effectively replace human operations. In recent years, the increasingly complex and dynamic marine environment, coupled with the limitations of the capabilities of individual ships, has promoted the development of USV collaborative formation operations, which has become an important trend in the maritime application of unmanned ships. USV formation collaborative operations can perform complex tasks beyond the capabilities of a single ship and have many advantages, such as enhanced adaptability, improved fault tolerance, enhanced stability, and improved work efficiency. USV formation path tracking is one of the key technologies of USVs, which enables the USV formation to maintain the desired formation and track the desired path. The Prescribed Performance Control (PPC) method has attracted widespread attention because it can improve the transient performance of the system and limit the system error to a pre-set error range. However, in the actual navigation process, USVs are inevitably affected by the unknown speed information of adjacent ships, the unmodeled dynamics of the system, unknown external interference, and actuator input saturation.

[0003] Therefore, there is a need for a fixed-time path tracking control method for an unmanned surface vessel formation with high USV formation path tracking accuracy under multiple constraints. Summary of the invention

[0004] The main purpose of the present invention is to provide a fixed-time path tracking control method for an unmanned surface vessel formation to solve the problem of low path tracking accuracy of a USV formation under multiple constraints in the prior art.

[0005] To achieve the above object, the present invention provides a fixed-time path tracking control method for an unmanned surface vessel formation, which specifically comprises the following steps:

[0006] S1, kinematic and dynamic modeling of USV and establishment of USV formation coupling error.

[0007] S2, design the fixed time preset performance function and position error conversion function, reconstruct the formation coupling error, and limit the formation coupling error to the specified range.

[0008] S3, design a fixed-time dilated state observer, and use the fixed-time dilated state observer to simultaneously observe the unmeasurable speed of the USV and the system lumped disturbance.

[0009] S4, design an anti-saturation fixed-time output feedback formation controller to track the path of the USV formation.

[0010] Furthermore, step S1 specifically includes the following steps:

[0011] S1.1, consider a formation consisting of n USVs, only some of which obtain the desired path information, and construct the kinematic and dynamic models of the USVs:

[0012]

[0013] Where η i is the position vector of the i-th USV, is η i The derivative of i is the velocity vector of the i-th USV, μ i The derivative of i is the rotation matrix, M i is the inertia matrix, τ i To control force and torque, W i is the total disturbance of the system.

[0014] S1.2, based on step S1.1, establish the formation coupling error e for the i-th USV ηi :

[0015]

[0016] In the formula, e ηi =[e xi ,e yi ,e ψi ] T , e xi ,e yi ,e ψi are the coupling errors of USV along the longitudinal, transverse and vertical directions, N i is the total number of USVs in the formation, a ij is the weight of the connection between the i-th USV and the j-th USV. If the i-th USV can receive the data information of the j-th USV, then a ij =1, otherwise a ij =0, b i is the weight of the connection between the virtual leader and the i-th USV. If the i-th USV can receive the data information of the virtual leader, then b i =1, otherwise b i =0,η ijd is the expected relative position of the i-th USV and the j-th USV in the formation, η ris the position vector of the virtual leader, η ird is the expected relative position of the i-th USV and the virtual leader.

[0017] Furthermore, step S2 specifically includes the following steps:

[0018] S2.1, design fixed time preset performance function

[0019]

[0020] In the formula, ρ χi is the preset performance function variable, b1 and b2 are positive gain coefficients, and the constant ρ χ∞ is the artificially set convergence value, β1(t) is the designed piecewise function;

[0021]

[0022] Where T1 is the defined convergence value, q is a set positive parameter and q>1, t is the current time, and t0 is the set initial time;

[0023] S2.2, designed position error conversion function ε χi for:

[0024]

[0025] In the formula, z χi =e χi / ρ χi is the function variable of the new error conversion function, e χi is the position error before transformation, and e χi (t) are respectively χi (t) upper and lower bounds;

[0026] S2.3, based on step S2.2, the position error conversion function is derived to obtain:

[0027]

[0028] In the formula, For z χi The derivative of is χi The derivative of

[0029] Calculate ε respectively xi , ε yi and ε ψi The derivatives of are and

[0030]

[0031] Defining ε ηi =[ε xi ,ε yi ,ε ψi ] T is the new position coupling error vector, where ε xi ,ε yi ,ε ψi are the components of the transformed position coupling error vector along the USV surge, sway and heave directions, respectively, xi 、z yi and z ψi are the components of the new error conversion function's independent variable along the USV's longitudinal, transverse and heave directions, e xi 、e yi and e ψi are the components of the position coupling error vector before transformation along the USV surge, sway and heave directions, ρ xi , yi and ρ ψi They are the components of the preset performance function vector along the USV surge, sway and heave directions respectively.

[0032] Reconstruct the formation coupling error:

[0033]

[0034] in, is ηi The derivative of for e ηi The derivative of i is the gain matrix, B i is the offset matrix;

[0035] In formula (10),

[0036]

[0037] in, and e xi e xi The upper and lower bounds of and e yi e yi The upper and lower bounds of and e ψi e ψi The upper and lower bounds of .

[0038] Furthermore, the fixed-time dilated state observer designed in step S3 is:

[0039]

[0040] In the formula, is η i The estimated value of is μ i The estimated value of It is W i The estimated value of k mi (m=1,2,3) and κ mi is the positive parameter of FXESO, m=1,2,3, is the position observation error, sig() is the sign function;

[0041] Among them, α m =mα-m+1,m=1,2,3, α is a positive parameter set; β m =β+(m-1)(α-1), β is a positive parameter set;

[0042] In formula (11):

[0043] is a symbolic power vector; where x ei ,y ei , ei are the position estimation errors of the FXESO of the i-th USV in the surge, sway and heave directions respectively;

[0044] is a symbolic power vector;

[0045] k mi and κ mi is the positive parameter of FXESO, where m=1,2,3.

[0046] Furthermore, step S4 specifically includes the following steps:

[0047] S4.1, according to the formation coupling error in step S1.2, we get:

[0048]

[0049] In the formula, d i is the aggregate weight of the i-th USV;

[0050] S4.2, design the virtual control variable μ for the i-th USV id :

[0051]

[0052] In formula (13), λ1 and λ2 are positive parameters, -1<α4<1,α5>1.

[0053] S4.3, define the speed coupling error ε μi :

[0054] ε μi =μ i -μ id (14); In the formula, ε μi =[ε ui ,ε vi ,ε ri ] T ε ui , ε vi , ε ri They are respectively the USV's sway velocity coupling error, sway velocity coupling error and bow angular velocity coupling error.

[0055] S4.4, use formula (15) to estimate the velocity coupling error

[0056]

[0057] S4.5, define the sliding surface s as shown in formula (16): i :

[0058]

[0059] In formula (16), λ3 is a positive parameter;

[0060] S4.6, the designed piecewise hyperbolic tangent saturation function h(x) is:

[0061]

[0062] In formula (17), x max and x min are the upper and lower bounds of the actuator input saturation x, respectively. If 0≤x <x max ,but is a new variable containing the piecewise hyperbolic tangent saturation function argument. If x min ,but c is a positive parameter set to be greater than 1.

[0063] S4.6, design the auxiliary system based on the piecewise hyperbolic tangent saturation function:

[0064]

[0065] In the formula, ξ i is the status of the auxiliary system, λ4, λ5 and λ6 are positive parameters, Δτ i is the saturation deviation, are the control quantities of the i-th USV in the longitudinal, transverse and heave directions respectively; is the control vector of the i-th USV.

[0066] S4.7, Design of anti-saturation fixed-time distributed formation controller

[0067]

[0068] In formula (19), λ7, λ8 and λ9 are positive parameters, s i The sliding surface.

[0069] The present invention has the following beneficial effects:

[0070] The present invention designs a distributed output feedback formation controller with anti-saturation and fixed-time preset performance to solve the USV formation path tracking problem under multiple constraints, so that the USV formation can reach the desired formation within a fixed time. A preset performance function and error conversion function with fixed-time performance are proposed to reconstruct the formation coupling error, which improves the transient performance of the USV formation path tracking system and reduces the formation tracking error so that it is strictly limited to the specified convergence range. A fixed-time dilated state observer is designed to simultaneously observe the unmeasurable speed and the system lumped disturbance, which improves the overall control performance and system robustness. A piecewise hyperbolic tangent saturation function is designed, and then an auxiliary system is proposed to deal with the actuator input saturation problem. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] In order to more clearly illustrate the specific implementation of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the specific implementation or the prior art description. Obviously, the drawings described below are some implementations of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work. In the drawings:

[0072] Figure 1 A communication topology diagram of a USV formation according to an embodiment of the present invention is shown.

[0073] Figure 2 A graph showing the path tracking of a USV formation on a U-curve.

[0074] Figure 3 The error diagrams of FXESO estimation of surge velocity for five USVs are shown.

[0075] Figure 4 Shows Figure 3 A magnified detail of a certain place.

[0076] Figure 5 The error diagrams of FXESO estimation of sway velocity of five USVs are shown.

[0077] Figure 6 Shows Figure 5 A magnified detail of a certain place.

[0078] Figure 7 The error diagrams of FXESO estimation of the bow angular velocity of five USVs are shown.

[0079] Figure 8 Shows Figure 7 A magnified detail of a certain place.

[0080] Fig. 9 A graph of the absolute value of the lumped perturbation observation error is shown.

[0081] Fig.10 Shows Fig. 9 A magnified detail of a certain place.

[0082] Fig.11 The longitudinal forces of the five USVs in the USV formation are shown.

[0083] Fig.12 Shows Fig.11 A magnified detail of a certain place.

[0084] Fig.13 The rolling forces of the five USVs in the USV formation are shown.

[0085] Fig.14 Shows Fig.13 A magnified detail of a certain place.

[0086] Fig.15 The yaw moments of the five USVs in the USV formation are shown.

[0087] Fig.16 Shows Fig.15 A magnified detail of a certain place.

[0088] Fig.17 A schematic diagram of formation position coupling error is shown. DETAILED DESCRIPTION

[0089] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0090] like Figure 1 The fixed time path tracking control method of an unmanned surface vessel formation shown in the figure specifically comprises the following steps:

[0091] S1, kinematic and dynamic modeling of USV and establishment of USV formation coupling error.

[0092] S2, design the fixed-time preset performance function and position error conversion function, reconstruct the formation coupling error, limit the formation coupling error within the specified range, and improve the transient performance of the system.

[0093] S3, design a fixed-time dilated state observer, and use the fixed-time dilated state observer to simultaneously observe the unmeasurable speed of the USV and the system lumped disturbance.

[0094] S4, design an anti-saturation fixed-time output feedback formation controller to track the path of the USV formation.

[0095] Specifically, step S1 includes the following steps:

[0096] S1.1, consider a formation consisting of n USVs, only some of which obtain the desired path information, and construct the kinematic and dynamic models of the USVs:

[0097]

[0098] Where η i is the position vector of the i-th USV, is η i The derivative of i is the velocity vector of the i-th USV, μ i The derivative of i is the rotation matrix, M i is the inertia matrix, τ i To control force and torque, W i is the total disturbance of the system.

[0099] S1.2, based on step S1.1, establish the formation coupling error e for the i-th USV ηi :

[0100]

[0101] In the formula, e ηi =[e xi ,e yi ,e ψi ] T , e xi ,e yi ,eψi are the coupling errors of USV along the longitudinal, transverse and vertical directions, N i is the total number of USVs in the formation, a ij is the weight of the connection between the i-th USV and the j-th USV. If the i-th USV can receive the data information of the h-th USV, then the j-th USV ij =1, otherwise a ij =0, b i is the weight of the connection between the virtual leader and the i-th USV. If the i-th USV can receive the data information of the virtual leader, then b i =1, otherwise b i =0,η ijd is the expected relative position of the i-th USV and the j-th USV in the formation, η r is the position vector of the virtual leader, η ird is the expected relative position of the i-th USV and the virtual leader.

[0102] Specifically, step S2 includes the following steps:

[0103] S2.1, in order to improve the steady-state and transient performance of the USV formation path tracking system, the formation coupling error must satisfy the following inequality constraints:

[0104]

[0105] In the formula, and e χi (t) are respectively χi The upper and lower bounds of (t) are defined as follows:

[0106]

[0107] In the formula, δ i ∈(0,1] is the overshoot constraint.

[0108] In order to improve the transient performance of the system, a fixed time preset performance function is designed

[0109]

[0110] In the formula, ρ χi is the preset performance function variable, b1 and b2 are positive gain coefficients, and the constant ρ χ∞ is the artificially set convergence value, β1(t) is the designed piecewise function;

[0111]

[0112] Where T1 is the defined convergence value, q is a set positive parameter and q>1, t is the current time, and t0 is the set initial time;

[0113] S2.2, designed position error conversion function ε xi for:

[0114]

[0115] In the formula, z xi =e xi / ρ χi is the function variable of the new error conversion function, e χi is the position error before transformation, and e χi (t) are respectively χi (t) upper and lower bounds;

[0116] S2.3, based on step S2.2, the position error conversion function is derived to obtain:

[0117]

[0118] In the formula, For z χi The derivative of is χi The derivative of

[0119] Calculate ε respectively xi , ε yi and ε ψi The derivatives of are and

[0120]

[0121] Defining ε ηi =[ε xi ,ε yi ,ε ψi ] T is the new position coupling error vector, where ε xi ,ε yi ,ε ψi are the components of the transformed position coupling error vector along the USV surge, sway and heave directions, respectively, xi 、z yi and z ψi are the components of the new error conversion function's independent variable along the USV's longitudinal, transverse and heave directions, e xi 、e yi and e ψiare the components of the position coupling error vector before transformation along the USV surge, sway and heave directions, ρ xi , yi and ρ ψi are the components of the preset performance function vector along the USV surge, sway and heave directions,

[0122] Reconstruct the formation coupling error:

[0123]

[0124] in, is ηi The derivative of for e ηi The derivative of i is the gain matrix, B i is the offset matrix;

[0125] In formula (10),

[0126]

[0127] in, and e xi e xi The upper and lower bounds of and e yi e yi The upper and lower bounds of and e ψi e ψi The upper and lower bounds of .

[0128] Specifically, the fixed-time dilated state observer designed in step S3 is:

[0129]

[0130] In the formula, is η i The estimated value of is μ i The estimated value of It is W i The estimated value of k mi (m=1,2,3) and κ mi is the positive parameter of FXESO, m=1,2,3, is the position observation error, sig() is the sign function;

[0131] Among them, α m =mα-m+1,m=1,2,3, α is a positive parameter set; β m =β+(m-1)(α-1), β is a positive parameter set;

[0132] In formula (11):

[0133]

[0134] A signed power vector; where x ei ,y ei , ei are the position estimation errors of the FXESO of the i-th USV in the surge, sway and heave directions, respectively.

[0135] is a symbolic power vector;

[0136] k mi and κ mi is the positive parameter of FXESO, where m=1,2,3.

[0137] Then the estimation error of FXESO is as follows:

[0138]

[0139] It can be shown that the estimation error of FXESO can converge to a bounded region near the origin in a fixed time.

[0140] Specifically, step S4 includes the following steps:

[0141] S4.1, according to the formation coupling error in step S1.2, we get:

[0142]

[0143] In the formula, d i is the aggregate weight of the i-th USV;

[0144] S4.2, design the virtual control variable μ for the i-th USV id :

[0145]

[0146] In formula (13), λ1 and λ2 are positive parameters, -1<α4<1,α5>1.

[0147] S4.3, define the speed coupling error ε μi :

[0148] ε μi =μ i -μ id (14); where ε μi =[ε ui ,εvi ,ε ri ] T ε ui , ε vi , ε ri They are respectively the USV's sway velocity coupling error, sway velocity coupling error and bow angular velocity coupling error.

[0149] S4.4, however, because the ship speed information is unknown, the speed coupling error is estimated using formula (15)

[0150]

[0151] S4.5, define the sliding surface s as shown in formula (16): i :

[0152]

[0153] In formula (16), λ3 is a positive parameter;

[0154] S4.6, design a piecewise hyperbolic tangent saturation function, and based on it design an auxiliary system to deal with the actuator input saturation problem, and finally design an anti-saturation output feedback formation controller to achieve path tracking of the USV formation. The designed piecewise hyperbolic tangent saturation function h(x) is:

[0155]

[0156] In formula (17), x max and x min are the upper and lower bounds of the actuator input saturation x, respectively. If 0≤x <x max ,but is a new variable containing the piecewise hyperbolic tangent saturation function argument. If x min ,but c is a positive parameter set to be greater than 1. By setting the parameter c>1, the actuator input saturation phenomenon can be processed in advance before the actuator input reaches the saturation upper and lower bounds.

[0157] S4.6, design the auxiliary system based on the piecewise hyperbolic tangent saturation function:

[0158]

[0159] In the formula, ξ i is the status of the auxiliary system, λ4, λ5 and λ6 are positive parameters, Δτ i is the saturation deviation between the control input processed by the piecewise hyperbolic tangent saturation function and the actual control input, are the control quantities of the i-th USV in the longitudinal, transverse and heave directions respectively; is the control vector of the i-th USV.

[0160] S4.7, Design of anti-saturation fixed-time distributed formation controller

[0161]

[0162] In formula (19), λ7, λ8 and λ9 are positive parameters, s i The sliding surface.

[0163] In order to prove the feasibility and superiority of the present invention, a simulation verification of U-shaped path tracking of a USV formation consisting of 5 USVs was carried out. The verification process is as follows:

[0164] Based on the distributed anti-saturation output feedback formation controller in step 4, and assuming that only the first USV can obtain the desired path information, a simulation experiment is carried out when the initial positions of the five USVs are different.

[0165] The communication topology of the USV formation is shown in the figure below. Figure 1 shown. Figure 2 Figure 2 is the path tracking curve of the USV formation on the U-shaped curve. It can be seen that when the speed information of adjacent USVs is unavailable, there is model uncertainty, there is external interference, and the actuator input is saturated, the five USVs achieve the desired formation from different initial positions. Figure 3-Figure 8 The FXESO estimates the sway velocity estimation error, sway velocity estimation error and bow angular velocity estimation error of the five USVs respectively. It can be seen that the estimation errors can eventually converge to 0. Fig. 9 This is a curve diagram of the absolute value of the lumped disturbance observation error. It can be seen that the error finally converged. Figure 11-Figure 16 The control forces and torques of the five USVs under the controller designed by the present invention are shown. It can be seen that under the action of the anti-saturation auxiliary system, the forces and torques of the USVs are within the saturation limit value range of the actuator input and eventually converge to a smaller value. Fig.17 Schematic diagram of formation position coupling error. It can be seen that under the effect of the preset performance function designed in the present invention, the error is strictly limited within the set upper and lower boundaries.

[0166] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A fixed-time path tracking control method for an unmanned surface vessel formation, characterized in that: The specific steps include: S1, kinematic and dynamic modeling of USV and establishment of USV formation coupling error; S2, design a fixed time preset performance function and a position error conversion function, reconstruct the formation coupling error, and limit the formation coupling error to a specified range; S3, design a fixed-time dilated state observer, and use the fixed-time dilated state observer to simultaneously observe the unmeasurable speed of the USV and the system lumped disturbance; S4, design an anti-saturation fixed-time output feedback formation controller to track the path of the USV formation.

2. The method for tracking and controlling a fixed time path of an unmanned surface vessel formation according to claim 1, characterized in that: Step S1 specifically includes the following steps: S1.1, consider a formation consisting of n USVs, only some of which obtain the desired path information, and construct the kinematic and dynamic models of the USVs: Where η i is the position vector of the i-th USV, is η i The derivative of i is the velocity vector of the i-th USV, μ i The derivative of i is the rotation matrix, M i is the inertia matrix, τ i To control force and torque, W i is the total disturbance of the system; S1.2, based on step S1.1, establish the formation coupling error e for the i-th USV ηi : In the formula, e ηi =[e xi ,e yi ,e ψi ] T , e xi ,e yi ,e ψi are the coupling errors of USV along the longitudinal, transverse and vertical directions, N i is the total number of USVs in the formation, a ij is the weight of the connection between the i-th USV and the j-th USV. If the i-th USV can receive the data information of the j-th USV, then a ij =1, otherwise a ij =0, b i is the weight of the connection between the virtual leader and the i-th USV. If the i-th USV can receive the data information of the virtual leader, then b i =1, otherwise b i =0,η ijd is the expected relative position of the i-th USV and the j-th USV in the formation, η r is the position vector of the virtual leader, η ird is the expected relative position of the i-th USV and the virtual leader.

3. The method for tracking and controlling a fixed time path of an unmanned surface vessel formation according to claim 1, characterized in that: Step S2 specifically includes the following steps: S2.1, design fixed time preset performance function In the formula, ρ χi is the preset performance function variable, b1 and b2 are positive gain coefficients, and the constant ρ χ∞ is the artificially set convergence value, β1(t) is the designed piecewise function; Where T1 is the defined convergence value, q is a set positive parameter and q>1, t is the current time, and t0 is the set initial time; S2.2, the designed position error conversion function εχi is: In the formula, z χi =e χi / ρ χi is the function variable of the new error conversion function, e χi is the position error before transformation, and e χi (t) are respectively χi (t) upper and lower bounds; S2.3, based on step S2.2, the position error conversion function is derived to obtain: In the formula, For z χi The derivative of is χi The derivative of Calculate ε respectively xi , ε yi and ε ψi The derivatives of are and Defining ε ηi =[ε xi , ε yi , ε ψi ] T is the new position coupling error vector, where ε xi , ε yi , ε ψi are the components of the transformed position coupling error vector along the USV surge, sway and heave directions, respectively, xi 、z yi and z ψi are the components of the new error conversion function's independent variable along the USV's longitudinal, lateral and heave directions, e xi、 e yi and e ψi are the components of the position coupling error vector before transformation along the USV surge, sway and heave directions, ρ xi , yi and ρ ψi are the components of the preset performance function vector along the USV surge, sway and heave directions respectively; Reconstruct the formation coupling error: in, is ηi The derivative of for e ηi The derivative of i is the gain matrix, B i is the offset matrix; In formula (10), in, and e xi e xi The upper and lower bounds of and e yi e yi The upper and lower bounds of and e ψi e ψi The upper and lower bounds of .

4. The method for tracking and controlling a fixed time path of an unmanned surface vessel formation according to claim 1, characterized in that: The fixed-time dilated state observer designed in step S3 is: In the formula, is η i The estimated value of is μ i The estimated value of It is W i The estimated value of k mi (m=1,2,3) and κ mi is the positive parameter of FXESO, m=1,2,3, is the position observation error, sig() is the sign function; Among them, α m =mα-m+1, m=1,2,3, α is a positive parameter set; β m =β+(m-1)(α-1), β is a positive parameter set; In formula (11): is a symbolic power vector; where x ei ,y ei , ei are the position estimation errors of the FXESO of the i-th USV in the surge, sway and heave directions respectively; is a symbolic power vector; k mi and κ mi is the positive parameter of FXESO, where m=1,2,3.

5. The method for tracking and controlling a fixed time path of an unmanned surface vessel formation according to claim 1, characterized in that: Step S4 specifically includes the following steps: S4.1, according to the formation coupling error in step S1.2, we get: In the formula, d i is the aggregate weight of the i-th USV; S4.2, design the virtual control variable μ for the i-th USV id : In formula (13), λ1 and λ2 are positive parameters, -1<α4<1, α5>1; S4.3, define the speed coupling error ε μi : e μi =μ i -m id (14); where ε μi = [ε ui , ε vi , ε r i] T ; ε ui , ε vi , ε ri They are the USV's swell velocity coupling error, sway velocity coupling error and bow angular velocity coupling error respectively; S4.4, use formula (15) to estimate the velocity coupling error S4.5, define the sliding surface s as shown in formula (16): i : In formula (16), λ3 is a positive parameter; S4.6, the designed piecewise hyperbolic tangent saturation function h(x) is: In formula (17), x max and x min are the upper and lower bounds of the actuator input saturation x, respectively. If 0≤x <x max ,but is a new variable containing the piecewise hyperbolic tangent saturation function argument. If x min ,but c is a positive parameter set to be greater than 1; S4.6, design the auxiliary system based on the piecewise hyperbolic tangent saturation function: In the formula, ξ i is the status of the auxiliary system, λ4, λ5 and λ6 are positive parameters, Δτ i is the saturation deviation, are the control quantities of the i-th USV in the longitudinal, transverse and heave directions respectively; is the control vector of the i-th USV; S4.7, Design of anti-saturation fixed-time distributed formation controller In formula (19), λ7, λ8 and λ9 are positive parameters, s i The sliding surface.

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