An unmanned surface vehicle formation preset time control method based on a non-singular sliding surface

Abstract

The present application discloses a kind of unmanned ship formation preset time control method based on non-singular sliding surface, the present application relates to unmanned ship formation technical field, especially based on non-singular sliding surface unmanned ship formation preset time control, application contains the following steps: step (1): establish the mathematical model of the motion of the i unmanned ship three degrees of freedom;Step (2): determine the formation geometry movement model of n unmanned ship;Step (3): obtain the tracking error dynamics of the i unmanned ship underactuated ship heading and position: step (4): design the preset time non-singular sliding surface of the i unmanned ship underactuated ship;Step (5): design the preset time heading controller of the i unmanned ship underactuated ship;Step (6): design the preset time surge controller of the i unmanned ship underactuated ship;Step (7): simulation verification.The present application is based on non-singular sliding mode control theory, proposes a kind of unmanned ship formation preset time control method based on non-singular sliding surface.This method can realize the stability and robustness of unmanned ship formation in complex marine environment, and ensure that system converges to desired state within preset time, can effectively solve the control singularity problem existing in terminal sliding mode method, and ensure that controller has strong adaptability to external interference in execution process.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of unmanned ship formation, and particularly relates to an unmanned ship formation preset time control method based on a non-singular sliding surface. BACKGROUND

[0002] In recent years, unmanned ship technology has been widely applied in the fields of ocean resource exploration, environmental monitoring, rescue tasks, etc. Unmanned ship formation control is one of the key applications of unmanned ship technology, which can improve the efficiency and accuracy of operations through the cooperation of multiple unmanned ships. In complex marine environments, unmanned ship formation can effectively cope with disturbances such as wind, waves, tides, etc., and complete resource exploration, environmental monitoring, etc. through multi-ship cooperation. The core of unmanned ship formation control is how to ensure that each unmanned ship can accurately track the formation formation, while maintaining stability under external disturbances. However, the application of underactuated unmanned ships in formation control faces many difficulties, mainly in the following aspects:

[0003] Firstly, underactuated unmanned ships are more susceptible to wind, wave, current, etc. disturbances in complex marine environments due to the lack of direct control of lateral motion. Traditional control methods are difficult to maintain efficient control while ensuring system stability. The heading error and position error of the unmanned ship will increase with the increase of external disturbances, which will further affect the overall stability of the formation. How to design an effective control strategy to enable underactuated unmanned ships to stably perform formation tasks under complex conditions has become an important direction of technical research. Secondly, traditional control methods mostly rely on linear control theory or optimal control methods, which are difficult to adapt to the uncertainty and nonlinear characteristics existing in the unmanned ship system. In the underactuated unmanned ship system, the nonlinear dynamics and uncertainty of model parameters further increase the control difficulty. Especially when multiple unmanned ships are working together, the nonlinear coupling effect of the formation system is more obvious, and in this case, the conventional control method often cannot guarantee the global stability and convergence of the system. Therefore, designing a control method that can cope with system uncertainty and improve system robustness is particularly important for underactuated unmanned ship formation control. In addition, in the multi-degree-of-freedom system of underactuated unmanned ships, the non-directness between control input and expected output increases the control complexity of the system. The limited degree of freedom of the underactuated system makes it difficult for traditional formation control methods to meet actual needs. In this case, how to optimize the relationship between control input and output to ensure the rationality of the controller design is one of the key problems to be solved in the current unmanned ship formation control field.

[0004] Therefore, based on nonsingular sliding mode control theory, this invention proposes a preset-time formation control method suitable for underactuated unmanned surface vessels (USVs). This method can achieve stability and robustness of USV formations in complex marine environments and ensure that the system converges to the desired state within a preset time. By rationally designing the Lyapunov function and sliding mode surface, this invention can effectively solve the control singularity problem existing in traditional methods and ensure that the controller has strong adaptability to external disturbances during execution. Summary of the Invention:

[0005] The present invention discloses a method for pre-setting time control of unmanned surface vessel formation based on non-singular sliding surface.

[0006] The objective of this invention is achieved as follows:

[0007] A pre-set time control method for unmanned surface vessel (USV) formations based on non-singular sliding mode surfaces includes the following steps:

[0008] Step (1): Establish a three-degree-of-freedom mathematical model of the motion of the i-th unmanned surface vessel:

[0009] To study the motion of unmanned surface vessels (USVs) on the water surface, mathematical motion models of their surface motion (three degrees of freedom: pitch, sway, and yaw) are established in both fixed and hull coordinate systems. These models include a three-degree-of-freedom kinematic model and a three-degree-of-freedom dynamic model, with the specific expressions as follows:

[0010] Three-degree-of-freedom kinematic model of an unmanned surface vessel in a fixed coordinate system:

[0011]

[0012] In the above formula: x i y i , ψ i Let u represent the northward, eastward, and bow angles of the i-th unmanned surface vessel in a fixed coordinate system, respectively; i v i r i These represent the pitch speed, sway speed, and bow roll speed of the i-th unmanned surface vessel, respectively.

[0013] Three-degree-of-freedom dynamic model of the unmanned surface vessel in the hull coordinate system:

[0014]

[0015] In the above formula: m 11 m 22 m 33 and D u D v D r τ represents the mass and damping coefficient of the unmanned surface vessel. wui , τwvi , τ wri represents the unknown ocean disturbance received by the unmanned surface vehicle during sailing; τ ri , τ ui represent the bow yaw control force and surge control force acting on the i-th unmanned surface vehicle, respectively;

[0016] Step (2): Determine the formation geometric movement model of n unmanned surface vehicles:

[0017] Based on the mathematical model established in step (1), through the regular polygon formation design, the center of the regular polygon is the virtual leader, and each unmanned surface vehicle is located at the vertex of the regular polygon; the expected position of the vertex of the regular polygon is calculated through geometric formula, and the formation shape is determined according to the number of unmanned surface vehicles; this step ensures the uniform spacing between unmanned surface vehicles, and meets the structural requirements of the formation task;

[0018] Step (3): Obtain the tracking error dynamics of the heading and position of the i-th underactuated unmanned surface vehicle:

[0019] Based on the formation established in step (2), the actual heading information and yaw rate information of the unmanned surface vehicle are obtained through the ship body navigation system of the unmanned surface vehicle, and compared with the reference heading and position information to obtain the heading error and position error thereof, and the position tracking error of the i-th unmanned surface vehicle is:

[0020] x ei = x di - x i

[0021] y ei = y di - y i

[0022] In the above formula: (x di , y di ) is the expected position of the unmanned surface vehicle, (x i , y i ) is the actual position of the unmanned surface vehicle, x ei is the position error about x direction in the fixed coordinate system, and y ei is the position error about y direction in the fixed coordinate system;

[0023] In order to solve the underactuated problem of the system model, the position error ρ ei of the i-th unmanned surface vehicle and the heading error ψ ei are defined as:

[0024]

[0025] ψ ei = ψ ri - ψ i

[0026] In the above formula: ψ ri is the desired heading angle of the ith unmanned surface vehicle, ψ i is the actual heading angle of the ith unmanned surface vehicle;

[0027] Step (4): Design the preset time nonsingular sliding mode surface of the ith underactuated unmanned surface vehicle:

[0028] Based on the error defined in step (3), using the sliding mode control theory, in order to avoid the singularity problem in traditional terminal sliding mode control, the nonsingular sliding mode surface is designed, the nonsingular preset time heading error sliding mode surface of the ith underactuated unmanned surface vehicle:

[0029]

[0030] In the above formula: δ 1i is a very small normal number, 0 < a 1i < 1, T 1i is a positive number greater than zero representing the upper limit of the preset convergence time, p 1i , q 1i represent the design parameters greater than zero, sign(·) represents the sign function;

[0031] Nonsingular preset time position error sliding mode surface of the ith underactuated unmanned surface vehicle:

[0032]

[0033] In the above formula: δ 2i is a very small normal number, 0 < a 2i < 1, T 1i is a positive number greater than zero representing the upper limit of the preset convergence time, p 1i , q 1i represent the design parameters greater than zero, sign(·) represents the sign function;

[0034] Step (5): Design the preset time heading controller of the ith underactuated unmanned surface vehicle:

[0035] Based on the sliding mode surface designed in step (4), the heading controller is designed, which is responsible for ensuring that the heading error of the unmanned surface vehicle converges to zero within the preset time;

[0036] The preset time heading and surge controllers described in step (5) are:

[0037] Nonsingular sliding mode preset time heading controller τ ri of the ith underactuated unmanned surface vehicle:

[0038]

[0039] In the formula: 0 < alpha 1i <1, 0 < alpha 3i <1, p 1i , q 1i , p 2i , q 2i , mu 1i , mu 2i Indicate that the designed parameter is greater than zero, T 1i , T 2i Is a positive number greater than zero, indicating the upper limit of the preset convergence time, Is a greater than zero interference compensation term, and sign(·) represents a sign function;

[0040] Step (6): design the preset time surge controller of the ith underactuated unmanned ship:

[0041] Based on the preset time non-singular sliding mode surface designed in step (4), the preset time surge controller of the ith underactuated unmanned ship is designed, which can ensure that the unmanned ship accurately tracks the expected position within the preset time, so that the whole unmanned ship formation moves in the correct direction and maintains the formation;

[0042] The non-singular sliding mode preset time surge controller tau of the ith underactuated unmanned ship ui :

[0043]

[0044] In the formula: 0 < alpha 2i <1, 0 < alpha 4i <1, p 1i , q 1i , p 2i , q 2i , mu 1i , mu 2i Indicate that the designed parameter is greater than zero, T 1i , T 2i Is a positive number greater than zero, indicating the upper limit of the preset convergence time, Is a greater than zero interference compensation term, and sign(·) represents a sign function;

[0045] Step (7): simulation verification:

[0046] The preset time heading controller and the preset time surge controller designed in steps (1)-(6) are simulated on a certain type of unmanned ship.

[0047] The present application includes the following beneficial effects:

[0048] 1. The preset time control strategy based on the preset time ensures that the system converges within a fixed time, has strong anti-interference ability and global stability, and is suitable for unmanned ship formation tasks in complex environments, such as high-precision applications of ocean monitoring and rescue.

[0049] 2. The non-singular sliding mode control strategy is adopted, the singularity in the terminal sliding mode control is improved by designing a segmented sliding mode surface and a control law, and the stability and response speed of the control system are improved. BRIEF DESCRIPTION OF DRAWINGS

[0050] Figure 1 The step flowchart described in the application;

[0051] Figure 2 The formation principle diagram described in the application;

[0052] Figure 3 The straight path formation control chart of a certain type of unmanned ship formation under the application;

[0053] Figure 4 The heading error dynamic variable curve chart of a certain type of unmanned ship formation under the application;

[0054] Figure 5 The position error tracking curve chart of a certain type of unmanned ship formation under the application;

[0055] Figure 6 The control force curve chart of each unmanned ship of a certain type of unmanned ship formation under the application;

[0056] Figure 7 The sliding mode surface output curve chart of each unmanned ship of a certain type of unmanned ship formation under the application. DETAILED DESCRIPTION

[0057] In order to make the above-mentioned purposes, features and advantages of the application more obvious and easy to understand, the application will be further described below with reference to the drawings:

[0058] Example 1

[0059] As Figure 1 A preset time control method for unmanned ship formation based on a non-singular sliding mode surface, comprising the following steps:

[0060] Step (1): Establish a three-degree-of-freedom mathematical model of the i-th unmanned ship motion;

[0061] To study the motion of the unmanned surface vehicle (USV) on the water surface, the kinematic model and the dynamic model of the USV in three degrees of freedom (DOF) are established in the fixed coordinate system and the body coordinate system. The specific process of establishing the mathematical model of the USV in three DOF is as follows: the fixed coordinate system and the body coordinate system of the space motion of the marine carrier are established, and the mathematical model of the USV in three DOF is established in the corresponding coordinate system as follows:

[0062] The kinematic model of the USV in three DOF in the fixed coordinate system:

[0063]

[0064] In the above formulae, x i , y i , and ψ i represent the northward position, the eastward position, and the bow angle of the i-th USV in the fixed coordinate system, respectively; u i , v i , and r i represent the surge speed, the sway speed, and the yaw angular speed of the i-th USV, respectively.

[0065] The dynamic model of the USV in three DOF in the body coordinate system:

[0066]

[0067] In the above formulae, m 11 , m 22 , and m 33 represent the mass of the USV, and D u , D v , and D r represent the damping coefficient of the USV; τ wui , τ wvi , and τ wri represent the unknown ocean disturbance during the navigation of the USV; τ ri and τ ui represent the yaw control force and the surge control force acting on the i-th USV, respectively.

[0068] Step (2): determining the formation geometric movement model of the n USVs:

[0069] Based on the mathematical model established in step (1), the formation configuration of a regular polygon is designed, the center of the regular polygon is a virtual leader, and each USV is located at the vertex of the regular polygon. The expected positions of the vertices of the regular polygon are calculated through geometric formula, and the shape of the formation is determined according to the number of USVs. This step ensures that the distances between the USVs are uniform, and meets the structural requirements of the formation task. For example, Figure 2The center of the regular polygon is the virtual leader and each vertex is the desired position of each unmanned vehicle in the formation. The geometric center (x L ,y L ) of the regular polygon is the position of the virtual leader and L is the side length of the regular polygon. To calculate the desired position of each unmanned vehicle in the formation, first calculate the circumscribed circle radius of the regular polygon:

[0070] R = L / 2sin(π / n)

[0071] In the above formula, n = 2,...,n is the number of sides of the regular polygon, and then calculate the position of the polygon vertex:

[0072] x i = x L + Rcos(2π(i-1) / n)

[0073] y i = y L + Rsin(2π(i-1) / n)

[0074] In the above formula, i = 1,...n represents the position of the ith vertex, and according to the position of the polygon vertex, the desired position of each unmanned vehicle in the formation can be calculated:

[0075] x di (t) = x L (t) + Lcos(2π(i-1) / n) / 2sin(π / n)

[0076] y di (t) = y L (t) + Lsin(2π(i-1) / n) / 2sin(π / n)

[0077] Step (3): Obtain the tracking error dynamics of the heading and position of the ith underactuated unmanned vehicle:

[0078] Based on the formation configuration established in step (2), the actual heading information and yaw rate information of the unmanned vehicle are obtained through the unmanned vehicle hull navigation system, and compared with the reference heading and position information to obtain the actual error of the heading tracking and the actual error of the yaw rate tracking. The position tracking error of the ith unmanned vehicle is:

[0079] x ei = x di -x i

[0080] y ei = y di -y i

[0081] In the above formula, (x di ,ydi ) is the desired position of the USV, (x i ,y i ) is the actual position of the USV, x ei is the position error about x direction in the fixed coordinate system, y ei is the position error about y direction in the fixed coordinate system;

[0082] To solve the under-actuated problem of the system model, define the position error of the ith USV as ρ ei and the heading error as ψ ei :

[0083]

[0084] ψ ei = ψ ri - ψ i

[0085] In the above formula: Δ ρ is the threshold value of the error, which is a very small normal number. According to the kinematic model of the USV, the error model of the converted USV can be obtained as follows:

[0086]

[0087] In the above formula:

[0088] d ui = -cos(ψ ei ) τ wu,i / m 11 -sin(ψ ei ) τ wvi / m 22 , g i = -cos(ψ e ) / m 11 ,

[0089] h i = -1 / m 33 , d ri = - τ wri / m 33 ,

[0090] g i = -cos(ψ e ) / m 11 ,

[0091]

[0092] Step (4): Design a non-singular sliding mode surface considering the preset time:

[0093] Based on the error defined in step (3), the non-singular sliding surface is designed by using the sliding mode control theory to avoid the singularity problem in terminal sliding mode control.

[0094] The non-singular preset time heading error sliding surface of the ith underactuated USV:

[0095]

[0096] In the above formula: δ 1i is a very small normal number, 0 < α 1i < 1, T 1i is a positive number greater than zero representing the upper limit of the preset convergence time, p 1i , q 1i represent the designed parameters greater than zero, and sign(·) represents the sign function.

[0097] The non-singular preset time position error sliding surface of the ith underactuated USV:

[0098]

[0099] In the above formula: δ 2i is a very small normal number, 0 < α 2i < 1, T 1i is a positive number greater than zero representing the upper limit of the preset convergence time, p 1i , q 1i represent the designed parameters greater than zero, and sign(·) represents the sign function.

[0100] Next, the non-singular preset time heading and surge controller of the ith underactuated USV is designed based on the sliding surface, and the system preset time stability proof is as follows:

[0101] Step 1: Prove the convergence of the heading tracking error of the ith underactuated USV.

[0102] Take the Lyapunov function:

[0103]

[0104] If s ψi = 0, the derivative is:

[0105]

[0106] When |ψ ei | > δ 1i , we have:

[0107]

[0108] When |ψ ei ≤ δ 1i , we have:

[0109]

[0110] Stability analysis of the sliding mode surface for the ith underactuated USV:

[0111]

[0112] Taking the derivative of V 2i , we have:

[0113]

[0114] According to the theorem of convergence in a predetermined time, the system state will converge to the sliding mode surface in a fixed time, i.e. Therefore, the heading error will converge to the neighborhood of zero in a predetermined time T = T 1i + T 2i , i.e.

[0115] Step 2: Proof of the convergence of the position error of the ith underactuated USV;

[0116] Taking the Lyapunov function:

[0117]

[0118] If s ρi = 0, taking the derivative, we have:

[0119]

[0120] When |ρ ei | > δ 2i , we have:

[0121]

[0122] When |ρ ei | ≤ δ 2i , we have:

[0123]

[0124] Stability analysis of the sliding mode surface for the ith underactuated USV:

[0125]

[0126] Taking the derivative of V 4i , we have:

[0127]

[0128] According to the theorem of the preset time convergence, the system state will converge to the sliding mode surface in a fixed time, that is Therefore, the heading error will converge to the neighborhood of zero in the preset time T=T 1i +T 2i , that is

[0129] The convergence analysis of the preset time control method of the USV formation based on the nonsingular sliding mode surface is completed, and then the preset time heading controller and the preset time surge controller are designed according to the basic principle of the sliding mode control;

[0130] Step (5): design the preset time heading controller of the ith underactuated USV:

[0131] The heading controller is responsible for ensuring that the heading error of the USV converges to zero in the preset time based on the sliding mode surface designed in step (4);

[0132] The preset time heading and surge controllers in step (5) are:

[0133] The preset time heading controller τ ri of the ith underactuated USV based on the nonsingular sliding mode is:

[0134]

[0135] In the above formula: 0 1i <1, 0 3i <1, p 1i , q 1i , p 2i , q 2i , μ 1i , μ 2i represent the designed parameters greater than zero, T 1i , T 2i is a positive number greater than zero representing the upper limit of the preset convergence time, is a positive interference compensation term, and sign(·) represents the sign function;

[0136] Step (6): design the preset time surge controller of the ith underactuated USV:

[0137] The surge controller is responsible for ensuring that the USV can accurately track the desired position in the preset time based on the sliding mode surface designed in step (4), so that the overall USV formation moves in the correct direction and maintains the formation;

[0138] The preset time surge controller τ ui of the ith underactuated USV based on the nonsingular sliding mode is:

[0139]

[0140]

[0141] In the above formula: 0 < a 2i <1, 0 < a 4i <1, p 1i , q 1i , p 2i , q 2i , mu 1i , mu 2i represents a parameter to be designed greater than zero, T 1i , T 2i is a positive number greater than zero representing a preset upper limit of convergence time, is a greater than zero interference compensation term, sign(·) represents a sign function;

[0142] Step (7): simulation verification:

[0143] The preset time underactuated unmanned surface vehicle (USV) heading and surge controller designed based on steps (1) to (6) is simulated in the following simulation environment: the number of sides of the regular polygon formation of the USV is n = 3, the preset upper limit of convergence time is T 1i = 10 s, T 2i = 10 s, the time-varying disturbance is set as tau wui = 0.01 sin(0.1t), tau wvi = 0.01 cos(0.1t), tau wri = 0.01 sin(0.2t), the mass and damping coefficient of the USV are set as m 11 = 0.1, m 22 = 0.2, m 33 = 0.4 and D u = D v = D r = 0.1, the initial heading angle of each USV is 0°, the initial yaw angle velocity is 0 rad / s, the initial surge velocity is 0 m / s, and the interference compensation is set as The parameter to be designed in the controller is set as mu 1i = mu 2i = 3, alpha 1i = alpha 2i = 0.8, p 1i = q 1i = p 2i = q 2i = 1, alpha 3i = alpha 4i = 0.8, and the error threshold is set as delta 1i=0.02, the simulation path is set as y=1.2x, and the initial positions of the unmanned ship are (x1, y1)=(1m, -1m), (x2, y2)=(-3m, 1m) and (x3, y3)=(-2m, -2m).

[0144] The preset time based on the singular sliding mode surface is used to design the preset time based on the singular sliding mode surface, and the preset time based on the singular sliding mode surface is used to design the preset time based on the singular sliding mode surface. Figure 3 The linear path formation control diagram of the unmanned ship formation under the application is shown, and the curve result shows that the method can quickly form and maintain the formation in the disturbed environment; Figure 4 The heading error dynamic variable curve diagram of the unmanned ship formation under the application is shown, and the curve result shows that the heading error of each unmanned ship converges rapidly within the upper limit of the preset time and converges to zero, wherein the 3rd follower has a large difference from the expected heading, and thus the shaking is severe. Figure 5 The position error tracking curve diagram of the unmanned ship formation under the application is shown, and the curve shows that the position error of each unmanned ship can dynamically converge to zero within the upper limit of the preset convergence time to ensure the stability of the underactuated unmanned ship formation; Figure 6 The control force curve diagram of the unmanned ship formation under the application is shown, because the designed singular sliding mode surface switching function causes a small shaking of the surge control force in the convergence process, it can be seen from the figure that the system has good transient performance and steady-state performance, and can gradually stabilize after reaching a certain value, and the control force is relatively smooth and meets the actual engineering needs. Figure 7 The sliding mode surface output curve diagram of each unmanned ship of the unmanned ship formation under the application is shown, and it can be seen from the figure that the output is a continuous curve, and a slight shaking occurs at 4s due to the switching of the sliding mode surface.

[0145] The singular sliding mode preset time control is adopted, the singular sliding mode surface is designed, and the preset time based on the singular sliding mode surface is designed, the preset time based on the singular sliding mode surface is designed, the singular sliding mode surface is solved in the derivation process, and the designed control method can greatly improve the steady-state performance and anti-interference ability of the underactuated unmanned ship formation system.

[0146] The above only describes the preferred embodiments of the application, and is not used to limit the application, and the application can have various changes and variations for those skilled in the art. Any modification, equivalent replacement, improvement made within the spirit and principle of the application shall be included in the protection scope of the application.

Claims

1. A non-singular sliding mode surface-based unmanned surface vehicle formation pre-set time control method, characterized in that It comprises the following steps: Step (1): Establish the third freedom mathematical model of the i-th unmanned surface vehicle (USV) motion: Research on the motion of the USV on the water surface, in the fixed coordinate system and the ship coordinate system, the three degrees of freedom of the USV are established, including the three degrees of freedom kinematics model and the three degrees of freedom dynamics model; Step (2): Determine the formation geometry moving model of n USVs: Based on the mathematical model established in step (1), through the regular polygon formation configuration design, the center of the regular polygon is the virtual leader, and each USV is located at the vertex of the regular polygon; The expected position of the vertex of the regular polygon is calculated through the geometric formula, and the shape of the formation is determined according to the number of USVs; This step ensures that the distance between the USVs is uniform, and meets the structural requirements of the formation task; Step (3): Obtain the tracking error dynamics of the i-th underactuated USV heading and position: Based on the formation configuration established in step (2), the actual heading information and yaw angular velocity information of the USV are obtained through the ship body navigation system of the USV, and compared with the reference heading and position information to obtain the heading error and position error of the USV. The position tracking error of the i-th USV is: x ei = x di - x i y ei = y di - y i In the above formula: (x di ,y di ) is the desired position of the unmanned ship, (x i ,y i ) is the actual position of the unmanned ship, x ei is the position error about the x direction in the fixed coordinate system, and y ei is the position error about the y direction in the fixed coordinate system; To solve the underactuated problem of the system model, the position error of the ith USV is defined as ei and the heading error is defined as ei : ψ ei = ψ ri - ψ i In the above formula: ψ ri is the desired heading angle of the i-th unmanned surface vehicle, ψ i is the actual heading angle of the i-th unmanned surface vehicle; Step (4): Design the preset time non-singular sliding mode surface considering the i-th underactuated USV: Based on the error defined in step (3), a non-singular sliding mode surface is designed using sliding mode control theory to avoid the singularity problem in terminal sliding mode control; Step (5): Design the preset time heading controller of the i-th underactuated USV: Based on the sliding mode surface designed in step (4), a heading controller is designed, which is responsible for ensuring that the heading error of the USV converges to zero within a preset time; Step (6): Design the preset time surge controller of the i-th underactuated USV: Based on the preset time non-singular sliding mode surface designed in step (4), a preset time surge controller is designed for the i-th underactuated USV, which can ensure that the USV accurately tracks the expected position within a preset time, so that the overall USV formation moves in the correct direction and maintains the formation; Step (7): Simulation verification: The preset time heading controller and the preset time surge controller designed in steps (1) to (6) are simulated on a certain type of USV.

2. The non-singular sliding mode surface based unmanned surface vehicle formation pre-set time control method according to claim 1, characterized in that: The third freedom mathematical model of the i-th USV motion established in step (1): The third freedom kinematics model of the USV in the fixed coordinate system: In the above formula: x i , y i , ψ i respectively represent the north position, east position and heading angle of the i unmanned ship in the fixed coordinate system; u i , v i , r i respectively represent the surge speed, sway speed and yaw angular velocity of the i unmanned ship; The third freedom dynamics model of the USV in the ship coordinate system: In the above formula: m 11 , m 22 , m 33 and D u , D v , D r represent the mass and damping coefficient of the unmanned ship; τ wui , τ wvi , τ wri represent the unknown ocean disturbance received by the unmanned ship during navigation; τ ri , τ ui represent the bow yaw control force and longitudinal control force acting on the i unmanned ship, respectively.

3. The non-singular sliding mode surface based unmanned surface vehicle formation pre-set time control method according to claim 1, characterized in that: The preset time non-singular sliding mode surface in step (4) is: The non-singular preset time heading error sliding mode surface of the i-th underactuated USV: In the above formulae: δ 1i is a very small normal number, 0 < α 1i < 1, T 1i is a positive number greater than zero representing a preset upper limit of convergence time, p 1i , q 1i represent a parameter to be designed greater than zero, and sign(·) represents a sign function. The non-singular preset time position error sliding mode surface of the i-th underactuated USV: a small positive number, 0 < a 2i < 1, T 1i is a positive number greater than zero representing a preset upper limit of convergence time, p 1i , q 1i represents a parameter to be designed greater than zero, and sign( ) represents a sign function.

4. The non-singular sliding mode surface based unmanned surface vehicle formation pre-specified time control method of claim 1, wherein: The preset time heading controller in step (5) is: Non-singular sliding mode preset time heading controller τ for the ith underactuated unmanned surface vehicle ri : In the above formula: 0 < a 1i <1, 0 < a 3i <1, p 1i , q 1i , p 2i , q 2i , m 1i , m 2i denotes a design parameter to be greater than zero, T 1i , T 2i is a positive number greater than zero representing a preset upper limit of convergence time, is an interference compensation term greater than zero, and sign(·) represents a sign function.

5. The non-singular sliding mode surface based unmanned surface vehicle formation pre-specified time control method of claim 1, wherein: The preset time surge heading controller in step (5) is: Non-singular sliding mode pre-set time longitudinal control of the ith underactuated unmanned surface vehicle τ ui : In the above formula: 0 < a 2i <1, 0 < a 4i <1, p 1i , q 1i , p 2i , q 2i , m 1i , m 2i denotes a design parameter to be greater than zero, T 1i , T 2i is a positive number greater than zero representing a preset upper limit of convergence time, is an interference compensation term greater than zero, and sign(·) represents a sign function.

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