Unmanned ship formation preset time control method based on non-singular sliding mode surface

Abstract

The invention discloses an unmanned ship formation preset time control method based on a non-singular sliding mode surface, and relates to the technical field of unmanned ship formation, in particular to unmanned ship formation preset time control based on the non-singular sliding mode surface, comprising the following steps: step (1), establishing a motion three-degree-of-freedom mathematical model of the ith unmanned ship; (2) determining a formation geometric movement model of n unmanned ships; (3) obtaining tracking error dynamic states of the heading and the position of the ith under-actuated unmanned ship; (4) designing a preset time nonsingular sliding mode surface of the ith under-actuated unmanned ship; (5) designing a preset time heading controller of the ith under-actuated unmanned ship; step (6), designing a preset time surging controller of the ith under-actuated unmanned ship; and (7) performing simulation verification. The invention provides an unmanned ship formation preset time control method based on a non-singular sliding mode surface based on a non-singular sliding mode control theory. The method can realize the stability and robustness of the unmanned ship formation in a complex marine environment, ensures that the system converges to an expected state within a preset time, can effectively solve the problem of control singularity existing in a terminal sliding mode method, and ensures that a controller has relatively strong adaptability to external interference in an execution process.

Description

Technical field:

[0001] The invention relates to the technical field of unmanned boat formations, and in particular to a method for controlling preset time of an unmanned boat formation based on a non-singular sliding surface. Background technology:

[0002] In recent years, unmanned boat technology has been widely used in the fields of marine resource exploration, environmental monitoring, and rescue missions. Unmanned boat formation control is one of the key applications of unmanned boat technology, which can improve operating efficiency and accuracy through the collaborative operation of multiple unmanned boats. In complex marine environments, unmanned boat formations can effectively cope with interference from factors such as wind, waves, and tides, and complete tasks such as resource exploration and environmental monitoring through the collaboration of multiple ships. The core of unmanned boat formation control lies in how to ensure that each unmanned boat can accurately track the formation while maintaining stability under external interference. However, the application of underactuated unmanned boats in formation control faces many difficulties, which are mainly manifested in the following aspects:

[0003] First, due to the lack of direct control of lateral motion, underactuated unmanned boats are more susceptible to disturbances such as wind, waves, and currents in complex marine environments. Traditional control methods make it difficult to ensure the stability of the system while maintaining efficient control. The heading error and position error of the unmanned boat will increase with the increase of external disturbances, thereby affecting the overall stability of the formation. How to design an effective control strategy so that the underactuated unmanned boat can stably perform formation tasks under complex conditions has become an important direction of technical research. Secondly, most traditional control methods rely on linear control theory or optimal control methods, which are difficult to adapt to the uncertainty and nonlinear characteristics of the unmanned boat system. In the underactuated unmanned boat system, the uncertainty of nonlinear dynamics and model parameters further increases the control difficulty. Especially when multiple unmanned boats work together, the nonlinear coupling effect of the formation system is more obvious. In this case, conventional control methods often cannot guarantee the global stability and convergence of the system. Therefore, it is particularly important to design a control method that can cope with system uncertainty and improve system robustness for the formation control of underactuated unmanned boats. In addition, in the multi-degree-of-freedom system of underactuated unmanned boats, the indirectness between control input and expected output increases the control complexity of the system. The limited 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 controller design is one of the key issues that need to be solved in the current field of unmanned boat formation control.

[0004] Therefore, based on the non-singular sliding mode control theory, the present invention proposes a preset time formation control method suitable for underactuated unmanned boats. The method can achieve the stability and robustness of the unmanned boat formation in a complex marine environment and ensure that the system converges to the desired state within a preset time. By reasonably designing the Lyapunov function and the sliding surface, the present invention can effectively solve the control singularity problem existing in the traditional method and ensure that the controller has strong adaptability to external interference during the execution process. Summary of the invention:

[0005] The invention discloses a method for controlling the preset time of an unmanned boat formation based on a non-singular sliding surface.

[0006] The object of the present invention is achieved in that:

[0007] A method for controlling the preset time of an unmanned boat formation based on a non-singular sliding surface comprises the following steps:

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

[0009] The motion of the unmanned boat on the water surface is studied. In the fixed coordinate system and the hull coordinate system, the mathematical motion model of its surface motion with three degrees of freedom, namely, sway, swing and pitch, is established. The mathematical model includes a three-degree-of-freedom kinematic model and a three-degree-of-freedom dynamic model. The specific expression is:

[0010] The three-degree-of-freedom kinematic model of the unmanned boat in a fixed coordinate system:

[0011]

[0012] In the above formula: x i ,y i , ψ i They represent the north position, east position and heading angle of the i-th unmanned boat in the fixed coordinate system; u i , v i , r i Respectively represent the longitudinal speed, lateral speed and bow angular velocity of the i-th unmanned boat;

[0013] The three-degree-of-freedom dynamic model of the unmanned boat in the hull coordinate system:

[0014]

[0015] In the above formula: m 11 , m 22 , m 33 and D u , D v , D r represents the mass and damping coefficient of the unmanned boat; τ wui , τwvi , τ wri Represents the unknown ocean disturbance encountered by the unmanned boat during its navigation; τ ri , τ ui They represent the bow roll control force and surge control force acting on the i-th unmanned boat respectively;

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

[0017] Based on the mathematical model established in step (1), a regular polygon formation configuration is designed, with the center of the regular polygon being the virtual leader and each unmanned boat located at the vertex of the regular polygon. The expected position of the vertex of the regular polygon is calculated by a geometric formula, and the formation shape is determined according to the number of unmanned boats. This step ensures that the spacing between the unmanned boats is uniform, meeting the structural requirements of the formation mission;

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

[0019] Based on the formation configuration established in step (2), the actual heading information and bow angular velocity information of the unmanned boat are obtained through the unmanned boat hull navigation system, and compared with the reference heading and position information to obtain its heading error and position error. The position tracking error of the i-th unmanned boat 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 desired position of the unmanned boat, (x i ,y i ) is the actual position of the unmanned boat, x ei is the position error about the x direction in the fixed coordinate system, y ei is the position error about the y direction in the fixed coordinate system;

[0023] In order to solve the under-actuated problem of the system model, the position error ρ of the i-th unmanned boat is defined as ei and the heading error is ψ ei :

[0024]

[0025] ψ ei =ψ ri -ψ i

[0026] In the above formula: ψ ri is the expected heading angle of the i-th unmanned boat, ψ i is the actual heading angle of the i-th unmanned boat;

[0027] Step (4): Design a non-singular sliding mode surface considering the preset time of the i-th underactuated unmanned vehicle:

[0028] Based on the error defined in step (3), the sliding mode control theory is adopted to design a non-singular sliding mode surface in order to avoid the singularity problem in the traditional terminal sliding mode control. The non-singular preset time heading error sliding mode surface of the i-th underactuated unmanned boat is:

[0029]

[0030] In the above formula: δ 1i is a very small positive constant, 0<α 1i <1, T 1i is a positive number greater than zero, indicating the preset upper limit of convergence time, p 1i ,q 1i represents the parameter to be designed that is greater than zero, sign(·) represents the sign function;

[0031] The sliding mode surface of the non-singular preset time position error of the i-th underactuated unmanned boat is:

[0032]

[0033] In the above formula: δ 2i is a very small positive constant, 0<α 2i <1, T 1i is a positive number greater than zero, indicating the preset upper limit of convergence time, p 1i ,q 1i represents the parameter to be designed that is greater than zero, sign(·) represents the sign function;

[0034] Step (5): Design the preset time heading controller of the i-th underactuated unmanned boat:

[0035] A heading controller is designed based on the sliding surface designed in step (4), and the heading controller is responsible for ensuring that the heading error of the unmanned boat converges to zero within a preset time;

[0036] The heading and sway controllers at the preset time in step (5) are:

[0037] Non-singular sliding mode preset time heading controller τ for the i-th underactuated unmanned vehicle ri :

[0038]

[0039] In the above formula: 0<α 1i <1,0<α 3i <1, p 1i ,q 1i , p 2i ,q 2i , μ 1i , μ 2i represents the design parameter greater than zero, T 1i , T 2i Is a positive number greater than zero, indicating the preset upper limit of convergence time. is an interference compensation term greater than zero, sign(·) represents the sign function;

[0040] Step (6): Design the preset time surge controller of the i-th underactuated unmanned boat:

[0041] Based on the sliding surface surge controller designed in step (4), the surge controller ensures that the unmanned boats can accurately track the desired position within a preset time, so that the unmanned boat formation as a whole moves in the correct direction and maintains the formation;

[0042] Non-singular sliding mode preset time surge controller τ for the i-th underactuated unmanned vehicle ui :

[0043]

[0044] In the above formula: 0<α 2i <1,0<α 4i <1, p 1i ,q 1i , p 2i ,q 2i , μ 1i , μ 2i represents the design parameter greater than zero, T 1i , T 2i Is a positive number greater than zero, indicating the preset upper limit of convergence time. is an interference compensation term greater than zero, sign(·) represents the sign function;

[0045] Step (7): Simulation verification:

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

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

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

[0049] 2. A non-singular sliding mode control strategy is adopted. By designing the segmented sliding surface and control law, the singularity in the terminal sliding mode control is improved, and the stability and response speed of the control system are improved. Description of the drawings:

[0050] Figure 1 A flowchart of the steps of the present invention;

[0051] Figure 2 This is a formation principle diagram of the present invention;

[0052] Figure 3 It is a straight path formation control diagram of a certain type of unmanned boat formation under the present invention;

[0053] Figure 4 It is a dynamic variable curve diagram of the heading error of a certain type of unmanned boat formation under the present invention;

[0054] Figure 5 It is a position error tracking curve diagram of a certain type of unmanned boat formation under the present invention;

[0055] Figure 6 A control force curve diagram of each unmanned boat in a certain type of unmanned boat formation under the present invention;

[0056] Figure 7 The sliding surface output curve diagram of each unmanned boat in a certain type of unmanned boat formation under the present invention. Specific implementation method:

[0057] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and understandable, the present invention is further described below with reference to the accompanying drawings:

[0058] Example 1

[0059] like Figure 1 , a method for controlling the preset time of an unmanned boat formation based on a non-singular sliding surface, comprising the following steps:

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

[0061] In order to study the motion of unmanned boats on the water surface, the kinematic model and dynamic model of its surface motion are established for the three degrees of freedom of its sway, sway and pitch in the fixed coordinate system and the hull coordinate system. The specific process of establishing the three-degree-of-freedom mathematical model of the unmanned boat motion is to establish a fixed coordinate system and a hull coordinate system for the spatial motion of the marine vehicle, and to establish the three-degree-of-freedom mathematical model of the unmanned boat surface motion in the corresponding coordinate system as follows:

[0062] The three-degree-of-freedom kinematic model of the unmanned boat in a fixed coordinate system:

[0063]

[0064] In the above formula: x i ,y i , ψ i They represent the north position, east position and heading angle of the i-th unmanned boat in the fixed coordinate system; u i , v i , r i Respectively represent the longitudinal speed, lateral speed and bow angular velocity of the i-th unmanned boat;

[0065] The three-degree-of-freedom dynamic model of the unmanned boat in the hull coordinate system:

[0066]

[0067] In the above formula: m 11 , m 22 , m 33 and D u , D v , D r represents the mass and damping coefficient of the unmanned boat; τ wui , τ wvi , τ wri Represents the unknown ocean disturbance encountered by the unmanned boat during its navigation; τ ri , τ ui They represent the bow roll control force and surge control force acting on the i-th unmanned boat respectively;

[0068] Step (2): Determine the geometric movement model of the formation of n unmanned boats:

[0069] Based on the mathematical model established in step (1), a regular polygon formation configuration is designed, with the center of the regular polygon as the virtual leader and each unmanned boat located at the vertex of the regular polygon. The expected position of the vertices of the regular polygon is calculated by a geometric formula, and the formation shape is determined according to the number of unmanned boats. This step ensures that the spacing between the unmanned boats is uniform and meets the structural requirements of the formation mission. Figure 2As shown in the figure, the center of the regular polygon is the virtual leader, and each vertex is the expected position of each unmanned boat in the formation. L ,y L ) is the position of the virtual navigator, and L is the side length of the regular polygon. To calculate the expected position of each unmanned boat in the formation, first calculate the radius of the circumscribed circle 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 vertices:

[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 i-th vertex. According to the position of the polygon vertex, the expected position of each unmanned boat 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 i-th underactuated unmanned vehicle:

[0078] Based on the formation configuration established in step (2), the actual heading information and bow angular velocity information of the unmanned boat are obtained through the unmanned boat hull navigation system, and compared with the reference heading and position information to obtain the actual heading tracking error and bow angular velocity tracking error. The position tracking error of the i-th unmanned boat 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 unmanned boat, (x i ,y i ) is the actual position of the unmanned boat, x ei is the position error about the x direction in the fixed coordinate system, y ei is the position error about the y direction in the fixed coordinate system;

[0082] In order to solve the under-actuated problem of the system model, the position error ρ of the i-th unmanned boat is defined as ei and the heading error is ψ ei :

[0083]

[0084] ψ ei =ψ ri -ψ i

[0085] In the above formula: Δ ρ The error threshold is a very small positive constant. According to the kinematic model of the unmanned boat, the error model of the converted unmanned boat can be further obtained:

[0086]

[0087]

[0088]

[0089] In the above formula:

[0090] d ui = -cos(ψ ei )τ wu，i / m 11 -sin(ψ ei )τ wvi m 22 , g i = -cos(ψ e ) / m 11 ,

[0091] h i =-1 / m 33 d ri =-τ wri / m 33 ,

[0092] g i = -cos(ψ e ) / m 11 ,

[0093]

[0094] Step (4): Design a non-singular sliding surface considering the preset time:

[0095] Based on the error defined in step (3), the sliding mode control theory is used to design a non-singular sliding surface in order to avoid the singularity problem in the terminal sliding mode control;

[0096] The sliding mode surface of the non-singular preset time heading error of the i-th underactuated unmanned boat is:

[0097]

[0098] In the above formula: δ 1i is a very small positive constant, 0<α 1i <1, T 1i is a positive number greater than zero, indicating the preset upper limit of convergence time, p 1i ,q 1i represents the parameter to be designed that is greater than zero, sign(·) represents the sign function;

[0099] The sliding mode surface of the non-singular preset time position error of the i-th underactuated unmanned boat is:

[0100]

[0101] In the above formula: δ 2i is a very small positive constant, 0<α 2i <1, T 1i is a positive number greater than zero, indicating the preset upper limit of convergence time, p 1i ,q 1i represents the parameter to be designed that is greater than zero, sign(·) represents the sign function;

[0102] Next, the i-th underactuated unmanned boat is designed with a preset time heading and surge controller based on a non-singular sliding mode. The system predefined time stability proof is as shown in steps 1 to 2:

[0103] Step 1: Prove the convergence of the bow tracking error of the i-th underactuated unmanned vehicle;

[0104] Take the Lyapunov function:

[0105]

[0106] If ψi = 0, and taking its derivative we get:

[0107]

[0108] When |ψ ei |>δ1i hour:

[0109]

[0110] When |ψ ei |≤δ 1i hour:

[0111]

[0112] Stability analysis of sliding surface of the i-th underactuated unmanned boat:

[0113]

[0114] V 2i The derivative is:

[0115]

[0116] According to the theorem of preset time convergence, the system state will converge to the sliding surface within a fixed time, that is, Therefore, the heading error will be at the preset time T = T 1i +T 2i Converges to the neighborhood of zero, that is

[0117] Step 2: Prove the convergence of the position error of the i-th underactuated unmanned vehicle;

[0118] Take the Lyapunov function:

[0119]

[0120] If ρi = 0, and taking its derivative we get:

[0121]

[0122] When |ρ ei |>δ 2i hour:

[0123]

[0124] When |ρ ei |≤δ 2i hour:

[0125]

[0126] Stability analysis of sliding surface of the i-th underactuated unmanned boat:

[0127]

[0128] V 4i The derivative is:

[0129]

[0130] According to the theorem of preset time convergence, the system state will converge to the sliding surface within a fixed time, that is, Therefore, the heading error will be at the preset time T = T 1i +T 2i Converges to the neighborhood of zero, that is

[0131] At this point, the convergence analysis of the preset time control method of the unmanned boat formation based on the non-singular sliding surface is completed. Then, according to the basic principle of sliding mode control, the preset time heading controller and the preset time surge controller are designed.

[0132] Step (5): Design the preset time heading controller of the i-th underactuated unmanned boat:

[0133] A heading controller is designed based on the sliding surface designed in step (4), and the heading controller is responsible for ensuring that the heading error of the unmanned boat converges to zero within a preset time;

[0134] The heading and sway controllers at the preset time in step (5) are:

[0135] Preset time heading controller τ of the i-th underactuated unmanned boat based on non-singular sliding mode ri :

[0136]

[0137] In the above formula: 0<α 1i <1,0<α 3i <1, p 1i ,q 1i , p 2i ,q 2i , μ 1i , μ 2i represents the design parameter greater than zero, T 1i , T 2i Is a positive number greater than zero, indicating the preset upper limit of convergence time. is an interference compensation term greater than zero, sign(·) represents the sign function;

[0138] Step (6): Design the preset time surge controller of the i-th underactuated unmanned boat:

[0139] Based on the sliding surface surge controller designed in step (4), the surge controller ensures that the unmanned boats can accurately track the desired position within a preset time, so that the unmanned boat formation as a whole moves in the correct direction and maintains the formation;

[0140] Non-singular sliding mode preset time surge controller τ for the i-th underactuated unmanned vehicle ui :

[0141]

[0142]

[0143] In the above formula: 0<α 2i <1,0<α 4i <1, p 1i ,q 1i , p 2i ,q 2i , μ 1i , μ 2i represents the design parameter greater than zero, T 1i , T 2i Is a positive number greater than zero, indicating the preset upper limit of convergence time. is an interference compensation term greater than zero, sign(·) represents the sign function;

[0144] Step (7): Simulation verification:

[0145] Based on the preset time underactuated unmanned boat regular polygon formation heading and sway controller designed in steps (1) to (6), the simulation environment is set as follows: the number of sides of the unmanned boat regular polygon formation is n=3, and the preset convergence time upper limit is T 1i =10s, T 2i = 10s, the time-varying interference is set to τ wui =0.01sin(0.1t),τ wvi =0.01cos(0.1t),τ wri =0.01sin(0.2t), the mass and damping coefficient of the unmanned boat are set to 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 unmanned boat is 0°, the initial bow angular velocity is 0 rad / s, the initial sway velocity is 0 m / s, and the interference compensation is set to The parameters to be designed in the controller are set as μ 1i =μ 2i =3,α 1i =α 2i =0.8, p 1i =q 1i =p 2i =q 2i =1,α 3i =α 4i=0.8, the error threshold is set to δ 1i =0.02, the simulation path is set to y=1.2x, and the initial position of the unmanned boat is (x1, y1)=(1m, -1m), (x2, y2)=(-3m, 1m), (x3, y3)=(-2m, -2m).

[0146] The sliding mode control method is adopted to design a non-singular sliding surface. A certain type of unmanned boat is taken as the simulation object, and the bow and surge controller of the polygonal formation of under-actuated unmanned boats based on preset time is simulated and verified. Figure 3 The straight path formation control diagram of a certain type of unmanned boat formation under the present invention is shown. The curve results show that in an environment with interference, the present method can quickly form and maintain the formation; Figure 4 The dynamic variable curve of the heading error of a certain type of unmanned boat formation under the present invention is shown. The curve results show that the heading error of each unmanned boat converges quickly within the preset time limit and converges to zero. Among them, the No. 3 follower has a large difference from the expected heading and thus vibrates violently; Figure 5 The position error tracking curve of a certain type of unmanned boat formation under the present invention is shown, and the curve shows that the position error of each unmanned boat can dynamically converge to zero within the preset convergence time limit to ensure the stability of the underactuated unmanned boat formation; Figure 6 The control force curve of a certain type of unmanned boat formation under the present invention is shown. Because of the designed non-singular sliding surface switching function, the surging control force has a small jitter 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. The control force is relatively smooth and meets the actual engineering needs. Figure 7 The sliding surface output curve diagram of each unmanned boat in a certain type of unmanned boat formation under the present invention is shown. It can be seen from the figure that the output is a continuous curve, in which a slight jitter occurs at 4s due to the switching of the sliding surface.

[0147] The present invention adopts non-singular sliding mode preset time control, designs a non-singular sliding mode surface, and designs a preset time heading and surge controller based on the non-singular sliding mode surface, which solves the singularity problem of the sliding mode surface in the derivation process. The designed control method can greatly improve the steady-state performance and anti-interference ability of the under-actuated unmanned boat formation system.

[0148] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent substitution, and improvement made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for controlling the preset time of an unmanned boat formation based on a non-singular sliding surface, characterized in that It includes the following steps: Step (1): Establish a three-degree-of-freedom mathematical model for the motion of the i-th unmanned boat: Study the motion of the unmanned boat on the water surface. In the fixed coordinate system and the hull coordinate system, establish the mathematical motion model of its motion on the water surface with three degrees of freedom, namely, sway, swing and pitch, including: three-degree-of-freedom kinematic model and three-degree-of-freedom dynamic model. Step (2): Determine the geometric movement model of the formation of n unmanned boats: Based on the mathematical model established in step (1), a regular polygon formation configuration is designed, with the center of the regular polygon being the virtual leader and each unmanned boat located at the vertex of the regular polygon. The expected position of the vertex of the regular polygon is calculated by a geometric formula, and the formation shape is determined according to the number of unmanned boats. This step ensures that the spacing between the unmanned boats is uniform, meeting the structural requirements of the formation mission; Step (3): Obtain the tracking error dynamics of the heading and position of the i-th underactuated unmanned vehicle: Based on the formation configuration established in step (2), the actual heading information and bow angular velocity information of the unmanned boat are obtained through the unmanned boat hull navigation system, and compared with the reference heading and position information to obtain its heading error and position error. The position tracking error of the i-th unmanned boat is: x ei =x di -x i and ei =and di -and i In the above formula: (x di ,y di ) is the desired position of the unmanned boat, (x i ,y i ) is the actual position of the unmanned boat, x ei is the position error about the x direction in the fixed coordinate system, y ei is the position error about the y direction in the fixed coordinate system; In order to solve the under-actuated problem of the system model, the position error ρ of the i-th unmanned boat is defined as ei and the heading error is ψ ei : ψ ei =ψ ri -ψ i In the above formula: ψ ri is the expected heading angle of the i-th unmanned boat, ψ i is the actual heading angle of the i-th unmanned boat; Step (4): Design the non-singular sliding mode surface considering the preset time of the i-th underactuated unmanned vehicle: Based on the error defined in step (3), the sliding mode control theory is used to design a non-singular sliding surface in order to avoid the singularity problem in the terminal sliding mode control; Step (5): Design the preset time heading controller of the i-th underactuated unmanned boat: A heading controller is designed based on the sliding surface designed in step (4), and the heading controller is responsible for ensuring that the heading error of the unmanned boat converges to zero within a preset time; Step (6): Design the preset time surge controller of the i-th underactuated unmanned boat: Based on the sliding surface surge controller designed in step (4), the surge controller ensures that the unmanned boats can accurately track the desired position within a preset time, so that the unmanned boat formation as a whole 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 unmanned boat.

2. The method for controlling the preset time of an unmanned boat formation based on a non-singular sliding surface according to claim 1 is characterized in that: The mathematical model of the three-degree-of-freedom motion of the unmanned boat described in step (1) is as follows: The three-degree-of-freedom kinematic model of the unmanned boat in a fixed coordinate system: In the above formula: x i ,y i , ψ i They represent the north position, east position and heading angle of the i-th unmanned boat in the fixed coordinate system; u i , v i , r i Respectively represent the longitudinal speed, lateral speed and bow angular velocity of the i-th unmanned boat; The three-degree-of-freedom dynamic model of the unmanned boat in the hull coordinate system: In the above formula: m 11 , m 22 , m 33 and D u , D v , D r represents the mass and damping coefficient of the unmanned boat; τ wui , τ wvi , τ wri Represents the unknown ocean disturbance encountered by the unmanned boat during its navigation; τ ri , τ ui They represent the bow roll control force and surge control force acting on the i-th unmanned boat respectively.

3. The method for controlling the preset time of an unmanned boat formation based on a non-singular sliding surface according to claim 1, characterized in that: The non-singular sliding surface at the preset time described in step (4) is: The sliding mode surface of the non-singular preset time heading error of the i-th underactuated unmanned boat is: In the above formula: δ 1i is a very small positive constant, 0<α 1i <1, T 1i is a positive number greater than zero, indicating the preset upper limit of convergence time, p 1i ,q 1i represents the parameter to be designed that is greater than zero, sign(·) represents the sign function; The sliding mode surface of the non-singular preset time position error of the i-th underactuated unmanned boat is: In the above formula: δ 2i is a very small positive constant, 0<α 2i <1, T 1i is a positive number greater than zero, indicating the preset upper limit of convergence time, p 1i ,q 1i represents a parameter to be designed that is greater than zero, and sign(·) represents a sign function.

4. The method for controlling the preset time of an unmanned boat formation based on a non-singular sliding surface according to claim 1, characterized in that: The preset time heading controller in step (5) is: Non-singular sliding mode preset time heading controller τ for the i-th underactuated unmanned vehicle ri : In the above formula: 0<α 1i <1,0<α 3i <1, p 1i ,q 1i , p 2i ,q 2i , μ 1i , μ 2i represents the design parameter greater than zero, T 1i , T 2i Is a positive number greater than zero, indicating the preset upper limit of convergence time. is an interference compensation term greater than zero, and sign(·) represents the sign function.

5. The method for controlling the preset time of an unmanned boat formation based on a non-singular sliding surface according to claim 1, characterized in that: The preset time of the sway heading controller in step (5) is: Non-singular sliding mode preset time surge controller τ for the i-th underactuated unmanned vehicle ui : In the above formula: 0<α 2i <1,0<α 4i <1, p 1i ,q 1i , p 2i ,q 2i , μ 1i , μ 2i represents the design parameter greater than zero, T 1i , T 2i Is a positive number greater than zero, indicating the preset upper limit of convergence time. is an interference compensation term greater than zero, and sign(·) represents the sign function.

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