Water surface and underwater heterogeneous cooperative control method and system based on predefined time terminal sliding mode

Abstract

The invention provides a water surface and underwater heterogeneous cooperative control method and system based on a predefined time terminal sliding mode. The method specifically comprises the following steps: establishing a water surface unmanned ship mathematical model and an underwater unmanned vehicle mathematical model; a vertical projection guidance method is adopted, so that the underwater unmanned vehicle obtains the actual navigation track of the water surface unmanned ship; constructing a nonlinear interference estimator according to the external environment disturbance, estimating the disturbance and compensating the controller; designing a control law based on a predefined time stability theory and a Lyapunov stability theory, and obtaining a predefined time terminal sliding mode controller to perform water surface and underwater heterogeneous cooperative control; and designing an underwater acoustic environment adaptive hierarchical compensation mechanism, and switching the unmanned surface ship tracking method according to the communication quality. Explicit time parameters are introduced, a user is allowed to directly set the upper limit of system convergence time, flexibility and low conservative property are both achieved, and theoretical guarantee is provided for quick response and safe operation.

Description

Technical Field

[0001] The present invention relates to the technical field of trajectory tracking control of unmanned systems, and particularly to a method and system for heterogeneous cooperative control of surface and underwater based on predefined-time terminal sliding mode. Background Technique

[0002] In recent years, with the continuous deepening of ocean resource development, marine unmanned systems play an important role in complex tasks such as anti-submarine warfare and ocean monitoring. However, a single unmanned system is limited by endurance, payload, and communication constraints, and it is difficult to cope with the dynamically changing ocean environment. Therefore, a heterogeneous cooperative system of surface and underwater (surface unmanned boat and underwater unmanned vehicle) has become a research hotspot, and the task execution efficiency and safety can be significantly improved through cooperative operations. In this context, the sliding mode control method, with its advantages of fast convergence and strong robustness, has been widely applied in the field of cooperative control. Traditional sliding mode control effectively improves the steady-state performance and anti-interference ability of the system by introducing improved strategies such as terminal sliding mode and integral sliding mode.

[0003] However, in terms of the convergence time problem of heterogeneous cooperative control of surface and underwater, traditional finite-time control and fixed-time control methods have obvious limitations. The convergence time of these methods often depends on the initial conditions of the system or requires complex parameter adjustment, which is difficult to meet the requirements of practical engineering applications. In addition, existing research has not fully considered the data packet loss problem caused by weak signals in the underwater acoustic communication environment when designing a heterogeneous cooperative control system of surface and underwater, which will significantly reduce the cooperative control performance of the system. Therefore, developing a new control method that is easier to use in practical engineering and can effectively cope with the impact of weak communication is of great practical significance for ensuring the reliable operation of the surface and underwater cooperative control system in a complex ocean environment. Summary of the Invention

[0004] The purpose of the present invention is to propose a method and system for heterogeneous cooperative control of surface and underwater based on predefined-time terminal sliding mode; this method is based on the predefined-time terminal sliding mode control strategy, by designing a non-singular terminal sliding surface and implementing a dynamic switching mechanism, avoiding the singularity problem in the control process and improving the system control performance; at the same time, an explicit time parameter is introduced, allowing users to directly set the upper limit of the system convergence time, with both flexibility and low conservativeness, providing a theoretical guarantee for fast response and safe operation; further, in a weak underwater acoustic communication environment, through an underwater acoustic environment adaptive hierarchical compensation mechanism, the impact of communication quality degradation on the system control performance is effectively alleviated, enabling the surface unmanned boat and the underwater unmanned vehicle to safely, accurately and stably perform cooperative tracking tasks in a complex ocean environment.

[0005] To achieve the above purpose, the technical solution of the present invention is: a method for heterogeneous cooperative control of surface and underwater based on predefined-time terminal sliding mode, specifically including the following steps:

[0006] Establish a mathematical model of the unmanned surface vessel and a mathematical model of the unmanned underwater vehicle;

[0007] Adopt the vertical projection guidance method to enable the unmanned underwater vehicle to obtain the actual navigation trajectory of the unmanned surface vessel;

[0008] Construct a nonlinear disturbance estimator according to the external environmental disturbance, estimate the disturbance and compensate the controller;

[0009] Design a control law based on the predefined-time stability theory and the Lyapunov stability theory to obtain a predefined-time terminal sliding mode controller for heterogeneous cooperative control of the surface and underwater;

[0010] Design an underwater acoustic environment adaptive hierarchical compensation mechanism to switch the tracking method of the unmanned surface vessel according to the communication quality; when the communication quality is high, adopt the dynamic window data compensation method; when the communication quality is low, adopt the sound source orientation tracking method.

[0011] Preferably, the mathematical model of the unmanned surface vessel is as follows:

[0012]

[0013]

[0014] Where: Represents the position vector of the unmanned surface vessel in the inertial coordinate system, Respectively represent the x coordinate, y coordinate and heading angle of the unmanned surface vessel in the inertial coordinate system, and the superscript T represents the transpose; the velocity vector Is represented in the body-fixed coordinate system, including the longitudinal velocity , the transverse drift velocity And the yaw angular velocity ; Represents the control vector of the control input of the unmanned surface vessel, where , And Respectively represent the forward force, lateral force and yaw moment of the unmanned surface vessel; Represents the external environmental disturbance acting on the unmanned surface vessel in the body-fixed coordinate system, Respectively represent the longitudinal disturbance force, lateral disturbance force and heading disturbance moment of the unmanned surface vessel; Represents the coordinate transformation matrix of the unmanned surface vessel, Represents the inertia matrix of the unmanned surface vessel, Is the Coriolis and centripetal force matrix of the unmanned surface vessel, Is the damping matrix of the unmanned surface vessel.

[0015] Preferably, the mathematical model of the underwater unmanned vehicle is as follows:

[0016]

[0017]

[0018] Where: represents the position vector of the underwater unmanned vehicle in the inertial coordinate system, respectively represent the x - coordinate, y - coordinate, z - coordinate and heading angle of the underwater unmanned vehicle in the inertial coordinate system; the velocity vector is represented in the body - attached coordinate system and consists of the longitudinal velocity of the underwater unmanned vehicle, the side - slip velocity the heave velocity and the yaw angular velocity ; represents the control vector of the underwater unmanned vehicle's control input, which consists of the forward force the side - force the heave force and the yaw moment ; represents the external environmental disturbance acting on the underwater unmanned vehicle in the body - attached coordinate system, respectively represent the longitudinal disturbance force, lateral disturbance force, vertical disturbance force and yaw disturbance moment of the underwater unmanned vehicle; represents the coordinate transformation matrix of the underwater unmanned vehicle, represents the inertia matrix of the underwater unmanned vehicle, is the Coriolis and centripetal matrix of the underwater unmanned vehicle, is the damping matrix of the underwater unmanned vehicle, represents the restoring force and moment generated by gravity and buoyancy.

[0019] Preferably, the design of the nonlinear disturbance estimator for the surface unmanned ship is as follows:

[0020]

[0021] Where: represents the estimated disturbance value obtained from the nonlinear disturbance estimator of the surface unmanned ship, respectively represent the longitudinal disturbance estimated value, lateral disturbance estimated value and yaw disturbance estimated value of the surface unmanned ship; represents the intermediate auxiliary state vector of the surface unmanned ship; is the parameter matrix of the nonlinear disturbance estimator of the surface unmanned ship.

[0022] Preferably, the design of the nonlinear disturbance estimator for the underwater unmanned vehicle is as follows:

[0023]

[0024] Wherein: represents the estimated disturbance value obtained from the non - linear disturbance estimator of the underwater unmanned vehicle, respectively represent the longitudinal disturbance estimation value, lateral disturbance estimation value, vertical disturbance estimation value and heading disturbance estimation value of the underwater unmanned vehicle; represents the intermediate auxiliary state vector of the underwater unmanned vehicle; is the parameter matrix of the non - linear disturbance estimator of the underwater unmanned vehicle.

[0025] Preferably, the design of the predefined - time terminal sliding - mode control law for the surface unmanned ship is as follows:

[0026] First, define the position error of the surface unmanned ship :

[0027]

[0028] In the formula, represents the desired position and desired heading for the trajectory tracking of the surface unmanned ship, respectively represent the desired longitudinal position, desired lateral position and desired heading angle for the trajectory tracking of the surface unmanned ship, respectively represent the longitudinal position tracking error, lateral position tracking error and heading - angle tracking error of the surface unmanned ship;

[0029] Secondly, design the predefined - time terminal sliding - mode surface , respectively represent the longitudinal - motion sliding - mode surface, lateral - motion sliding - mode surface and yaw - motion sliding - mode surface of the surface unmanned ship. Let the parameter , and use the parameter and to respectively represent and , specifically as follows:

[0030]

[0031] Wherein, represents the design parameter of the surface unmanned ship, is a predefined time constant, is a small positive number; the transient sliding - mode surface of the surface unmanned ship is expressed as:

[0032]

[0033] Design the equivalent control law as follows:

[0034]

[0035] Among them, represents the equivalent control law of the unmanned surface vessel, is a design parameter related to the predefined time of the unmanned surface vessel, is a parameter related to the model of the unmanned surface vessel;

[0036] Design the switching control law as follows:

[0037]

[0038] Among them, represents the switching control law of the unmanned surface vessel, is a design parameter related to the predefined time of the unmanned surface vessel, and are the gain parameters of the unmanned surface vessel.

[0039] Finally, the predefined-time terminal sliding mode control law is as follows:

[0040] .

[0041] Preferably, the design of the predefined-time terminal sliding mode control law for the underwater unmanned vehicle is specifically as follows:

[0042] Define the position error of the underwater unmanned vehicle :

[0043]

[0044] In the formula, represents the desired position and desired heading of the underwater unmanned vehicle for trajectory tracking, respectively represent the desired longitudinal position, desired lateral position, desired vertical position and desired heading angle of the underwater unmanned vehicle for trajectory tracking, respectively represent the longitudinal position tracking error, lateral position tracking error, vertical position tracking error and heading angle tracking error of the underwater unmanned vehicle;

[0045] Secondly, design the predefined-time terminal sliding mode surface , respectively represent the longitudinal motion sliding mode surface, lateral motion sliding mode surface, vertical motion sliding mode surface and yaw motion sliding mode surface of the underwater unmanned vehicle. Let the parameter , and use the parameter and to respectively refer to and specifically as follows:

[0046]

[0047] Among them, represents the design parameters of the underwater unmanned vehicle, is a predefined time constant, is a small positive number; the transient sliding mode surface of the underwater unmanned vehicle The expression of is:

[0048]

[0049] Design the equivalent control law as follows:

[0050]

[0051] Among them, represents the equivalent control law of the underwater unmanned vehicle, is a design parameter related to the predefined time of the underwater unmanned vehicle, is a parameter related to the underwater unmanned vehicle model;

[0052] Design the switching control law as follows:

[0053]

[0054] Among them, represents the switching control law of the underwater unmanned vehicle, is a design parameter related to the predefined time of the underwater unmanned vehicle, and are the gain parameters of the underwater unmanned vehicle;

[0055] Finally, the predefined time terminal sliding mode control law is as follows:

[0056] .

[0057] Preferably, the dynamic window data compensation method is specifically as follows:

[0058] Define the data packet of the surface unmanned ship received by the underwater unmanned vehicle as , , , , among which, respectively represent the x, y coordinates and heading angle of the surface unmanned ship received at time t n , represents the number of data packets received, represents the time when the nth data packet is received;

[0059] Suppose represents the minimum number of data packets required for curve fitting; if is greater than Then, a quadratic polynomial is used to predict the state information of the unmanned surface vehicle.

[0060] The quadratic polynomial of the x-axis position information of the unmanned surface vehicle , the quadratic polynomial of the y-axis position information and the heading angle of the quadratic polynomial are respectively expressed as:

[0061]

[0062]

[0063]

[0064] m represents a variable; , , are the parameters of the fitting polynomial ; , , are the parameters of the fitting polynomial ; , and are respectively the parameters of the fitting polynomial ;

[0065] Use T to represent the time matrix, and use , , to represent the parameter vectors of the x and y coordinates and the heading angle respectively. Use , , to represent the observation data vectors of the x and y coordinates and the heading angle respectively. Use to represent the moment of the kth data packet received. As the data packets are continuously received and updated, dynamically points to the moment of the latest data packet that meets the conditions to ensure that the data used for curve fitting is continuously updated and the prediction error is reduced. Specifically as follows:

[0066] ;

[0067] , ;

[0068] , ;

[0069] , ;

[0070] By using the pseudo-inverse method to solve the equation, the following results are obtained:

[0071]

[0072]

[0073]

[0074] Let represent the currently predicted target time interval. Then, the estimated x-axis position, y-axis position, and heading angle information of the surface unmanned ship are:

[0075]

[0076]

[0077]

[0078] Among them, represents the time vector used to calculate the estimated state within the predicted time interval:

[0079] .

[0080] Preferably, the sound source orientation tracking method is specifically as follows:

[0081] The surface unmanned ship is equipped with a sound signal transmitting array;

[0082] The underwater unmanned vehicle is equipped with an acoustic receiving array, an acoustic signal preprocessing module, and an acoustic signal positioning and processing module;

[0083] The acoustic receiving array captures the encoded sound signal transmitted by the surface unmanned ship; the acoustic signal preprocessing is completed through the acoustic signal preprocessing module, including noise suppression and signal enhancement; the acoustic signal positioning and processing module calculates the time delay difference of the sound wave arriving at different acoustic receivers of the acoustic receiving array, and combines the array geometric relationship to calculate the sound source azimuth.

[0084] The present invention also proposes a heterogeneous cooperative control system for surface and underwater based on a predefined time terminal sliding mode, including a processor, a memory, and a computer program stored on the memory. When the processor executes the computer program, it specifically executes the steps in any of the above-mentioned heterogeneous cooperative control methods for surface and underwater based on a predefined time terminal sliding mode.

[0085] Compared with the prior art, the present invention has the following beneficial effects:

[0086] The present invention provides a method and system for heterogeneous cooperative control of surface and underwater vehicles based on predefined-time terminal sliding mode. Based on the predefined-time terminal sliding mode control strategy, by designing a nonsingular terminal sliding surface and implementing a dynamic switching mechanism, the singularity problem in the control process is avoided, and the control performance of the system is improved. At the same time, an explicit time parameter is introduced, allowing users to directly set the upper limit of the system convergence time, which has both flexibility and low conservatism, providing a theoretical guarantee for rapid response and safe operation.

[0087] In the weak underwater acoustic communication environment, through the underwater acoustic environment adaptive hierarchical compensation mechanism, the present invention effectively alleviates the influence of the communication quality degradation on the system control performance, enabling the surface unmanned ship and the underwater unmanned vehicle to safely, accurately and stably execute the cooperative tracking task in the complex marine environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 Flowchart of the method for heterogeneous cooperative control of surface and underwater vehicles based on predefined-time terminal sliding mode;

[0089] Figure 2 Schematic diagram of vertical projection guidance for heterogeneous cooperative control of surface and underwater vehicles;

[0090] Figure 3 Block diagram of heterogeneous cooperative control of surface and underwater vehicles based on predefined-time terminal sliding mode;

[0091] Figure 4 Heterogeneous cooperative trajectory tracking diagram of surface and underwater vehicles in this embodiment;

[0092] Figure 5 Trajectory tracking error diagram of the surface unmanned ship in this embodiment;

[0093] Figure 6 Trajectory tracking error diagram of the underwater unmanned vehicle in this embodiment;

[0094] Figure 7 Trajectory tracking error diagram of the underwater unmanned vehicle under different communication conditions in this embodiment. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0095] The following will specifically describe the technical solutions of the present invention in conjunction with the appended Figure 1-7 , drawings.

[0096] The present invention proposes a method for heterogeneous cooperative control of surface and underwater vehicles based on predefined-time terminal sliding mode, including the following steps:

[0097] Step S1: Establish a mathematical model of the surface unmanned ship and a mathematical model of the underwater unmanned vehicle.

[0098] The mathematical model of the surface unmanned ship is as follows:

[0099] (1)

[0100] (2)

[0101] Wherein: represents the position vector of the unmanned surface vessel in the inertial coordinate system, respectively represent the x coordinate, y coordinate and heading angle of the unmanned surface vessel in the inertial coordinate system. The superscript T represents the transpose, and the dot above the parameter represents the first-order derivative of the parameter with respect to time, represents a real number. The velocity vector is represented in the body-fixed coordinate system and includes the longitudinal velocity of the unmanned surface vessel, the transverse drift velocity and the yaw angular velocity represents the control vector of the unmanned surface vessel control input, where , and respectively represent the forward force, lateral force and yaw moment of the unmanned surface vessel. represents the external environmental disturbance acting on the unmanned surface vessel in the body-fixed coordinate system, respectively represent the longitudinal disturbance force, lateral disturbance force and yaw disturbance moment of the unmanned surface vessel. At the same time, represents the coordinate transformation matrix of the unmanned surface vessel, represents the inertia matrix of the unmanned surface vessel, is the Coriolis and centripetal force matrix of the unmanned surface vessel, is the damping matrix of the unmanned surface vessel.

[0102] The mathematical model of the underwater unmanned vehicle is as follows:

[0103] (3)

[0104] (4)

[0105] Wherein: represents the position vector of the underwater unmanned vehicle in the inertial coordinate system, respectively represent the x coordinate, y coordinate, z coordinate and heading angle of the underwater unmanned vehicle in the inertial coordinate system. The velocity vector is represented in the body-fixed coordinate system and consists of the longitudinal velocity of the underwater unmanned vehicle, the transverse drift velocity the heave velocity and the yaw angular velocity represents the control vector of the underwater unmanned vehicle control input and consists of the forward force of the underwater unmanned vehicle, the lateral force, heaving force and yaw moment constitute. represents the external environmental disturbance acting on the underwater unmanned vehicle in the body coordinate system, respectively represent the longitudinal disturbance force, lateral disturbance force, vertical disturbance force and bow disturbance moment of the underwater unmanned vehicle. At the same time, represents the coordinate transformation matrix of the underwater unmanned vehicle, represents the inertia matrix of the underwater unmanned vehicle, is the Coriolis and centripetal matrix of the underwater unmanned vehicle, is the damping matrix of the underwater unmanned vehicle, represents the restoring force and moment generated by gravity and buoyancy.

[0106] Step S2: Adopt the vertical projection guidance method to enable the underwater unmanned vehicle to obtain the actual navigation trajectory of the surface unmanned ship. The actual navigation trajectory of the surface unmanned ship is projected underwater by vertical projection, and the state information of the surface unmanned ship is transmitted to the underwater unmanned vehicle through the underwater acoustic communication machine, and we can get:

[0107] (5)

[0108] In the formula, , , respectively represent the desired longitudinal position, desired lateral position and desired bow angle of the underwater unmanned vehicle;

[0109] Step S3: In the face of disturbances in the ocean, construct a nonlinear disturbance estimator to quickly and accurately estimate the disturbances.

[0110] The nonlinear disturbance estimator of the surface unmanned ship is designed as follows:

[0111] (6)

[0112] Among them: represents the estimated disturbance value obtained from the nonlinear disturbance estimator of the surface unmanned ship, respectively represent the longitudinal disturbance estimation value, lateral disturbance estimation value and bow disturbance estimation value of the surface unmanned ship; represents the intermediate auxiliary state vector of the surface unmanned ship; is the parameter matrix of the designed nonlinear disturbance estimator of the surface unmanned ship.

[0113] The nonlinear disturbance estimator of the underwater unmanned vehicle is designed as follows:

[0114] (7)

[0115] Among them: denotes the estimated disturbance value obtained from the non - linear disturbance estimator of the underwater unmanned vehicle, which respectively denote the longitudinal disturbance estimation value, lateral disturbance estimation value, vertical disturbance estimation value, and yaw disturbance estimation value of the underwater unmanned vehicle; denotes the intermediate auxiliary state vector of the underwater unmanned vehicle; is the parameter matrix of the designed non - linear disturbance estimator of the underwater unmanned vehicle.

[0116] Step S4: Design a control law based on the predefined - time stability theory and Lyapunov stability theory to obtain a predefined - time sliding - mode controller. For the sake of clear and concise expression, the present invention adopts the following abbreviations: ,

[0117] First, define the position error of the surface unmanned ship :

[0118] (8)

[0119] wherein, denotes the desired position and desired yaw of the surface unmanned ship's trajectory tracking, respectively denote the desired longitudinal position, desired lateral position, and desired yaw angle of the surface unmanned ship's trajectory tracking, respectively denote the longitudinal position tracking error, lateral position tracking error, and yaw - angle tracking error of the surface unmanned ship;

[0120] Secondly, design the predefined - time terminal sliding - mode surface of the surface unmanned ship , respectively denote the longitudinal - motion sliding - mode surface, lateral - motion sliding - mode surface, and yaw - motion sliding - mode surface of the surface unmanned ship. Let the parameter , which is used to respectively represent and through the parameters and , specifically as follows:

[0121] (9)

[0122] where the design parameter of the surface unmanned ship satisfies . is a predefined time constant that satisfies , and is a small positive number. The expression of the transient sliding - mode surface of the surface unmanned ship is:

[0123] (10)

[0124] The equivalent control law is designed as follows:

[0125] (11)

[0126] Wherein, represents the equivalent control law of the unmanned surface vehicle, is a design parameter related to the predefined time of the unmanned surface vehicle, is a parameter related to the unmanned surface vehicle model. The dot above the parameter represents the second derivative of the parameter with respect to time.

[0127] The switching control law is designed as follows:

[0128] (12)

[0129] Wherein, represents the switching control law of the unmanned surface vehicle, is a design parameter related to the predefined time of the unmanned surface vehicle, and are the gain parameters of the unmanned surface vehicle.

[0130] Finally, the predefined time terminal sliding mode control law is as follows:

[0131] (13)

[0132] Similarly, define the position error of the underwater unmanned vehicle :

[0133] (14)

[0134] In the formula, represents the desired position and desired heading of the underwater unmanned vehicle for trajectory tracking, respectively represent the desired longitudinal position, desired lateral position, desired vertical position and desired heading angle of the underwater unmanned vehicle for trajectory tracking, respectively represent the longitudinal position tracking error, lateral position tracking error, vertical position tracking error and heading angle tracking error of the underwater unmanned vehicle;

[0135] The equivalent control law is designed as follows:

[0136] (15)

[0137] Wherein, represents the equivalent control law of the underwater unmanned vehicle, is a design parameter related to the predefined time of the underwater unmanned vehicle, is a parameter related to the underwater unmanned vehicle model.

[0138] The design switching control law is as follows:

[0139] (16)

[0140] Wherein, represents the switching control law of the underwater unmanned vehicle, is a design parameter related to the predefined time of the underwater unmanned vehicle, and are the gain parameters of the underwater unmanned vehicle, is the predefined-time terminal sliding mode surface of the underwater unmanned vehicle designed in the same way.

[0141] Finally, the predefined-time terminal sliding mode control law is as follows:

[0142] (17)

[0143] Furthermore, in the above technical solution, the stability analysis of the predefined-time sliding mode controller is carried out, and the predefined-time stability of the reaching phase and the sliding mode phase is verified respectively. In view of the similarity between the surface unmanned ship and the underwater unmanned vehicle in terms of control input and system composition, only the surface unmanned ship will be proved below, and the relevant proof of the underwater unmanned vehicle will be omitted.

[0144] The verification process of the predefined-time stability of the reaching phase includes:

[0145] Define the Lyapunov function of the sliding mode surface as . Substitute the formula of the sliding mode control law of the predefined-time sliding mode controller into its derivative to obtain:

[0146] (18)

[0147] In the formula, represents the disturbance estimation error, represents the design parameter, represents the predefined time of the reaching phase;

[0148] Furthermore, there is

[0149] (19)

[0150] Then the sliding mode surface can converge to 0 within the predefined time .

[0151] The verification process of the predefined-time stability of the sliding phase includes:

[0152] (i) and , then we can obtain . According to Lemma 2, will converge to 0 at the predefined time during the sliding phase .

[0153] (ii) and but , then define the error Lyapunov function as . Its derivative is:

[0154] (20)

[0155] Solving gives that the error will reach 0 within the predefined time .

[0156] According to the verification process of the predefined time stability of the reaching phase and the sliding phase, the system reaches the equilibrium state within the time of .

[0157] Step S5: Design an underwater acoustic environment adaptive hierarchical compensation mechanism

[0158] The underwater unmanned vehicle is equipped with a communication quality assessment module. According to the size of the packet loss rate, the adaptive hierarchical compensation mechanism will perform corresponding switching. When the packet loss rate is small, the dynamic window data compensation method is adopted; when the packet loss rate is large, the sound source orientation tracking method is adopted.

[0159] Design the dynamic window data compensation method: The data packets of the surface unmanned ship received by the underwater unmanned vehicle are defined as , , , , where respectively represent the x, y coordinates and heading angle of the surface unmanned ship received at time t n , represents the number of data packets received, represents the time when the nth data packet is received. Let represent the minimum number of data packets required for curve fitting.

[0160] If is greater than , then the quadratic polynomial is used to predict the state information of the surface unmanned ship; the quadratic polynomial of the x-axis position information of the surface unmanned ship is expressed as:

[0161] (21)

[0162] m represents a variable; in order to obtain the parameters of the fitting polynomial equation , and , use the following equation:

[0163] (22)

[0164] where T, P, and X represent the time matrix, parameter vector, and observation data vector respectively. Use to represent the time when the k-th received data packet arrives. As data packets are continuously received and updated, dynamically points to the time of the latest data packet that meets the conditions to ensure that the data used for curve fitting is continuously updated and the prediction error is reduced. Specifically as follows:

[0165] (23)

[0166] (24)

[0167] (25)

[0168] By using the pseudoinverse method to solve the equation, the following result can be obtained:

[0169] (26)

[0170] Let represent the currently predicted target time interval. Then, the estimated x-axis position information of the unmanned surface vessel is:

[0171] (27)

[0172] where represents the time vector used to calculate the estimated state within the prediction time interval:

[0173] (28)

[0174] Similarly, the y-axis position information and heading angle of the unmanned surface vessel can be predicted through the quadratic polynomials and . Here, , , , , and are the parameters of the fitting polynomials and respectively.

[0175] Furthermore, when the predicted data differs significantly from the valid data at the previous moment, can be dynamically increased, and more data is used for fitting to reduce the error.

[0176] Design sound source orientation tracking method: The surface unmanned ship is installed with a sound signal transmitting array, and the underwater unmanned vehicle is installed with an acoustic receiving array, a sound signal preprocessing module and a sound signal positioning and processing module. The acoustic receiving array captures the sound signals with specific codes transmitted by the surface unmanned ship, and completes functions such as noise suppression and signal enhancement through the sound signal preprocessing module. The sound signal positioning and processing module can estimate the sound source azimuth by calculating the time delay difference of the sound wave arriving at different acoustic receivers and combining the array geometric relationship. According to the relationship between the received signal strength and the distance attenuation, the sound source distance can be estimated.

[0177] The present invention also provides a heterogeneous cooperative control system for surface and underwater based on predefined time terminal sliding mode, including a processor, a memory, and a computer program stored on the memory. When the processor executes the computer program, it specifically executes the steps in any one of the above-mentioned heterogeneous cooperative control methods for surface and underwater based on predefined time terminal sliding mode.

[0178] The above are the preferred embodiments of the present invention. All changes made according to the technical solutions of the present invention, when the functions and effects generated do not exceed the scope of the technical solutions of the present invention, fall within the protection scope of the present invention.

Claims

1. A heterogeneous cooperative control method for surface and underwater based on predefined time terminal sliding mode, characterized in that Specifically, it includes the following steps: Establish a mathematical model of the surface unmanned ship and a mathematical model of the underwater unmanned vehicle; Adopt the vertical projection guidance method to enable the underwater unmanned vehicle to obtain the actual navigation trajectory of the surface unmanned ship; Construct a nonlinear disturbance estimator according to the external environmental disturbance, estimate the disturbance and compensate the controller; Design a control law based on the predefined-time stability theory and the Lyapunov stability theory to obtain a predefined-time terminal sliding mode controller for surface-underwater heterogeneous cooperative control; Design an underwater acoustic environment adaptive hierarchical compensation mechanism to switch the tracking method of the surface unmanned ship according to the communication quality; when the communication quality is high, adopt the dynamic window data compensation method; When the communication quality is low, adopt the sound source orientation tracking method.

2. The underwater and surface heterogeneous cooperative control method based on predefined time terminal sliding mode according to claim 1, wherein The mathematical model of the surface unmanned ship is as follows: In the formula: represents the position vector of the unmanned surface vehicle in the inertial coordinate system, respectively represent the x coordinate, y coordinate and heading angle of the unmanned surface vehicle in the inertial coordinate system, and the superscript T represents transpose; the velocity vector is represented in the body-fixed coordinate system, including the longitudinal velocity of the unmanned surface vehicle, the transverse drift velocity and the yaw angular velocity ; represents the control vector of the unmanned surface vehicle control input, where , and respectively represent the forward force, lateral force and yaw moment of the unmanned surface vehicle; represents the external environmental disturbance acting on the unmanned surface vehicle in the body-fixed coordinate system, respectively represent the longitudinal disturbance force, lateral disturbance force and yaw disturbance moment of the unmanned surface vehicle; represents the coordinate transformation matrix of the unmanned surface vehicle, represents the inertia matrix of the unmanned surface vehicle, is the Coriolis and centripetal force matrix of the unmanned surface vehicle, is the damping matrix of the unmanned surface vehicle.

3. A method for heterogeneous cooperative control of surface and underwater based on predefined time terminal sliding mode according to claim 1, characterized in that, The mathematical model of the underwater unmanned vehicle is as follows: In the formula: represents the position vector of the underwater unmanned vehicle in the inertial coordinate system, respectively represent the x - coordinate, y - coordinate, z - coordinate and heading angle of the underwater unmanned vehicle in the inertial coordinate system; the velocity vector is represented in the body - fixed coordinate system and consists of the longitudinal velocity of the underwater unmanned vehicle, the sway velocity the heave velocity and the yaw angular velocity ; represents the control vector of the underwater unmanned vehicle control input, which consists of the forward force of the underwater unmanned vehicle, the side - force the heave force and the yaw moment ; represents the external environmental disturbance acting on the underwater unmanned vehicle in the body - fixed coordinate system, respectively represent the longitudinal disturbance force, lateral disturbance force, vertical disturbance force and yaw - direction disturbance moment of the underwater unmanned vehicle; represents the coordinate transformation matrix of the underwater unmanned vehicle, represents the inertia matrix of the underwater unmanned vehicle, is the Coriolis and centripetal matrix of the underwater unmanned vehicle, is the damping matrix of the underwater unmanned vehicle, represents the restoring force and moment generated by gravity and buoyancy.

4. A method for heterogeneous cooperative control of surface and underwater based on predefined time terminal sliding mode according to claim 2, characterized in that The design of the nonlinear disturbance estimator for the surface unmanned ship is as follows: Wherein: represents the estimated disturbance value obtained from the non-linear disturbance estimator of the unmanned surface vehicle, respectively represents the longitudinal disturbance estimation value, the lateral disturbance estimation value, and the heading disturbance estimation value of the unmanned surface vehicle; represents the intermediate auxiliary state vector of the unmanned surface vehicle; is the parameter matrix of the non-linear disturbance estimator of the unmanned surface vehicle.

5. A method for heterogeneous collaborative control of surface and underwater based on predefined time terminal sliding mode according to claim 3, characterized in that The design of the nonlinear disturbance estimator for the underwater unmanned vehicle is as follows: Wherein: denotes the estimated disturbance value obtained from the non-linear disturbance estimator of the underwater unmanned vehicle, respectively denoting the longitudinal disturbance estimation value, lateral disturbance estimation value, vertical disturbance estimation value and heading disturbance estimation value of the underwater unmanned vehicle; denotes the intermediate auxiliary state vector of the underwater unmanned vehicle; is the parameter matrix of the non-linear disturbance estimator of the underwater unmanned vehicle.

6. A method for heterogeneous cooperative control of water surface and underwater based on predefined time terminal sliding mode according to claim 4, characterized in that The design of the predefined-time terminal sliding mode control law for the surface unmanned ship is as follows: specifically First, define the position error of the unmanned surface vehicle : In the formula, represents the desired position and desired heading of the surface unmanned ship trajectory tracking, respectively represent the desired longitudinal position, desired lateral position and desired heading angle of the surface unmanned ship trajectory tracking, respectively represent the longitudinal position tracking error, lateral position tracking error and heading angle tracking error of the surface unmanned ship; Secondly, design the predefined-time terminal sliding mode surface of the unmanned surface vehicle , respectively represent the longitudinal motion sliding mode surface, the lateral motion sliding mode surface and the yaw motion sliding mode surface of the unmanned surface vehicle. Let the parameter be used to respectively refer to and through the parameters and as follows: Among them, represents the design parameters of the unmanned surface vessel, is a predefined time constant, is a small positive number; the transient sliding mode surface of the unmanned surface vessel The expression of is: Design the equivalent control law as follows: Among them, represents the equivalent control law of the unmanned surface vehicle, is a design parameter related to the predefined time of the unmanned surface vehicle, is a parameter related to the model of the unmanned surface vehicle; Design the switching control law as follows: Among them, represents the switching control law of the unmanned surface vessel, is a design parameter related to the predefined time of the unmanned surface vessel, and are the gain parameters of the unmanned surface vessel; Finally, the predefined-time terminal sliding mode control law is as follows: 。 7. A method for heterogeneous cooperative control of water surface and underwater based on predefined time terminal sliding mode according to claim 5, characterized in that The design of the predefined-time terminal sliding mode control law for the underwater unmanned vehicle is as follows: specifically Define the position error of the underwater unmanned vehicle : In the formula, represents the desired position and desired heading of the underwater vehicle's trajectory tracking, respectively represent the desired longitudinal position, desired lateral position, desired vertical position, and desired heading angle of the underwater vehicle's trajectory tracking, respectively represent the longitudinal position tracking error, lateral position tracking error, vertical position tracking error, and heading angle tracking error of the underwater vehicle; Secondly, design the predefined-time terminal sliding mode surface of the underwater vehicle , respectively represent the longitudinal motion sliding mode surface, lateral motion sliding mode surface, vertical motion sliding mode surface and yaw motion sliding mode surface of the underwater vehicle. Let the parameter , and use it to and to respectively represent and as follows: Among them, represents the design parameters of the underwater unmanned vehicle, is a predefined time constant, is a small positive number; the transient sliding mode surface of the underwater unmanned vehicle has the following expression: Design the equivalent control law as follows: wherein, represents the equivalent control law of the underwater unmanned vehicle, is a design parameter related to the predefined time of the underwater unmanned vehicle, is a parameter related to the underwater unmanned vehicle model; Design the switching control law as follows: Among them, represents the switching control law of the underwater unmanned vehicle, is a design parameter related to the predefined time of the underwater unmanned vehicle, and are the gain parameters of the underwater unmanned vehicle; Finally, the predefined-time terminal sliding mode control law is as follows: 。 8. A method for underwater and surface heterogeneous cooperative control based on predefined time terminal sliding mode according to claim 1, characterized in that The specific dynamic window data compensation method is as follows: Define the data packet of the surface unmanned ship received by the underwater unmanned vehicle as , , , , where respectively represent the x, y coordinates and heading angle of the surface unmanned ship received at time t n , represents the number of data packets received represents the time when the nth data packet is received; Let represent the minimum number of data packets required for curve fitting; if is greater than , then the state information of the unmanned surface vehicle is predicted using a quadratic polynomial. Quadratic polynomial of the x-axis position information of the unmanned surface vessel , quadratic polynomial of the y-axis position information and the course angle of the quadratic polynomial are respectively expressed as: m represents a variable; , , are the parameters of the fitting polynomial ; , , are the parameters of the fitting polynomial ; , and are respectively the parameters of the fitting polynomial ; Use \(T\) to represent the time matrix. Use and and to represent the parameter vectors of the \(x\), \(y\) coordinates, and the heading angle respectively. Use and and to represent the observation data vectors of the \(x\), \(y\) coordinates, and the heading angle respectively. Use to represent the time of the \(k\)th received data packet. As data packets are continuously received and updated, dynamically points to the time of the latest data packet that meets the conditions to ensure that the data used for curve fitting is continuously updated; specifically as follows: ； ， ； ， ； ， ； By using the pseudoinverse method to solve the equation, the following results are obtained: Let represent the currently predicted target time interval. Then, the estimated x-axis position, y-axis position, and heading angle information of the unmanned surface vessel are as follows: wherein, represents a time vector for calculating an estimated state within a prediction time interval: 。 9. A method for heterogeneous cooperative control of surface and underwater based on predefined time terminal sliding mode according to claim 1, characterized in that, The specific sound source orientation tracking method is as follows: The surface unmanned ship is equipped with an acoustic signal transmitting array; The underwater unmanned vehicle is equipped with an acoustic receiving array, an acoustic signal preprocessing module and an acoustic signal positioning processing module; The acoustic receiving array captures the encoded acoustic signal transmitted by the surface unmanned ship; Complete the preprocessing of the acoustic signal including noise suppression and signal enhancement through the acoustic signal preprocessing module; the acoustic signal positioning processing module calculates the time delay difference of the sound wave arriving at different acoustic receivers of the acoustic receiving array, and combines the array geometric relationship to calculate the sound source azimuth.

10. A heterogeneous cooperative control system for surface and underwater based on predefined time terminal sliding mode, characterized in that, It includes a processor, a memory, and a computer program stored on the memory. When the processor executes the computer program, it specifically executes the steps in the surface-underwater heterogeneous cooperative control method based on the predefined-time terminal sliding mode as described in any one of claims 1-9.

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