A Method for Unmanned Boat Formation Shape-keeping Control under Communication Delay

Abstract

The present invention discloses a method for maintaining the formation of unmanned surface vehicles under communication delay, belonging to the technical field of intelligent ship navigation control, including: constructing an unmanned surface vehicle motion model based on the established three-degree-of-freedom motion model of the unmanned surface vehicle, its state space equation, and the environmental disturbance mathematical model; aiming at the problems of wind, wave, and current disturbances and communication delay suffered by the unmanned surface vehicle formation, constructing a super-twisting integral sliding mode observer and an adaptive delay estimator; combining the fixed-time theory, the formation controller of non-singular terminal sliding mode, and the super-twisting integral sliding mode observer to build a formation control system to achieve the formation maintenance of the unmanned surface vehicle formation; finally, verifying through simulation experiments. The present invention constructs a formation control system for the unmanned surface vehicle formation based on the fixed-time theory and the non-singular terminal sliding mode control method, effectively improving the control accuracy of the unmanned surface vehicle formation, realizing the formation maintenance control of the unmanned surface vehicle formation under compound disturbances, and having important significance for promoting the precise development of unmanned surface vehicle formation operations.

Description

Technical Field

[0001] The present invention belongs to the technical field of intelligent ship navigation control, and particularly relates to a method for maintaining the formation of unmanned boat formation under communication delay. Background Art

[0002] An unmanned boat formation refers to two or more unmanned boats that exchange information, cooperate with each other or independently execute complex tasks, and form an orderly formation to jointly complete the formation navigation task. Compared with a single unmanned boat, an unmanned boat formation has stronger payload detection capabilities, a wider task execution range, and higher fault tolerance control capabilities, which can effectively improve the task completion rate and efficiency, making surface operations more large-scale, intelligent, and efficient, and significantly improving the operation range and efficiency on the basis of the original single-boat operation tasks including marine environment monitoring, resource exploration, maritime search and rescue, etc.

[0003] When navigating in the actual environment, the unmanned boat formation is affected by the hydrological environment. It is necessary to consider not only the challenges of the uncertainty of the single-boat model parameters and external environmental disturbances, but also the communication delay problem between formations. Due to the strong nonlinear characteristics of the unmanned boat motion mathematical model, its system parameters have uncertainties and strong coupling. The dynamic changes of the environment and sensor noise further introduce uncertainties, making it difficult to accurately model the control system. At the same time, when navigating in the actual environment, factors such as sea waves, electromagnetic interference, shore-based buildings, and moving ships may cause communication signal delays or interruptions, directly affecting the navigation safety of the unmanned boat formation and resulting in task execution failures. Especially with the increase in the number of unmanned boats and the increase in navigation time, multiple unmanned boats communicate simultaneously, causing communication channel congestion, and complex protocols and algorithms will increase the communication processing time, thus causing communication delays. Therefore, it is extremely urgent to carry out effective research on control methods around the impact of composite disturbances on the formation maintenance of unmanned boat formations, which is of great significance.

[0004] During the mission execution of the unmanned boat formation, with the increase in mission complexity and the expansion of formation scale, the propagation time of signals in space increases, resulting in communication delay; the complex marine environment will interfere with the propagation path and speed of acoustic signals, further exacerbating the communication delay; the limited computing resources at the device end cause network queuing delay. The existence of the communication delay problem has various negative impacts on the overall performance of the unmanned boat formation. In terms of formation control performance, the communication delay causes the lag of information update between boats, reduces the formation keeping accuracy, makes each boat unable to adjust its state in real time, and finally destroys the formation consistency; at the level of system stability, due to the communication delay, the feedback control information is delayed, greatly increasing the risk of control algorithm failure, making the control instructions unable to accurately match the actual operating state of the unmanned boat, and then may trigger unstable responses of the system, and even lead to unstable phenomena such as oscillation in the entire formation system, seriously affecting the effective execution of the unmanned boat formation mission. Summary of the Invention

[0005] Aiming at the deficiencies in the background technology, the purpose of the present invention is to propose a formation keeping control method for unmanned boat formation under communication delay. Based on the established three-degree-of-freedom motion model of the unmanned boat, its state space equation and the mathematical model of environmental disturbance, an unmanned boat motion model is constructed. Then, aiming at the wind, wave and current disturbances and communication delay problems suffered by the unmanned boat formation during actual navigation, a super-twisting integral sliding mode observer is designed to estimate the disturbance and an adaptive time delay estimator is designed to estimate the time delay; based on this, combined with the fixed-time theory and the non-singular terminal sliding mode control method, a fixed-time non-singular terminal sliding mode formation controller is designed. And through simulation experiments, the stability of the designed method is verified, and finally the formation keeping control of the unmanned boat formation under communication delay is realized.

[0006] The specific technical solutions adopted by the present invention are as follows:

[0007] S1, based on the horizontal motion of the unmanned boat, construct the kinematics and dynamics of the three degrees of freedom of the unmanned boat to establish a three-degree-of-freedom motion model of the unmanned boat, and convert it into a state space equation;

[0008] S2, according to the Fossen manual, construct a wind, wave and current disturbance model of the unmanned boat, and combine it with the three-degree-of-freedom motion model of the unmanned boat to establish an unmanned boat motion model including environmental disturbance;

[0009] S3, adopt the leader-follower method to design the desired position of the unmanned boat according to the relative position and azimuth with the leading unmanned boat, build an unmanned boat tracking control subsystem and an unmanned boat formation control subsystem, and use the unmanned boat tracking control subsystem and the unmanned boat formation control subsystem to build a formation control system to realize the formation keeping of the unmanned boat formation;

[0010] 1) Based on the unmanned boat motion model, construct a super-twisting integral sliding mode observer to observe the disturbance and compensate it;

[0011] 2) Based on the deviation between the actual position and the desired position of the leading unmanned boat, a non-singular terminal sliding mode controller is designed based on a fixed-time convergence mechanism. The hyper-twisting integral sliding mode observer is used for disturbance estimation, and the tracking control subsystem of the unmanned boat is built to achieve the tracking of the desired trajectory by the leading unmanned boat within a preset time;

[0012] 3) The hyper-twisting integral sliding mode observer is used to estimate the wind, wave and current disturbances and model uncertainties in real time. Based on the lagging state information of the leading unmanned boat, the communication delay is estimated online, and the time-delay information of the leading unmanned boat is compensated. The formation control subsystem of the unmanned boat is built to solve the communication delay problem;

[0013] 4) Combining the fixed-time convergence mechanism, the non-singular terminal sliding mode controller and the hyper-twisting integral sliding mode observer under the communication delay, a formation control system composed of the tracking control subsystem of the unmanned boat and the formation control subsystem of the unmanned boat is built to achieve the formation shape maintenance of the unmanned boat formation;

[0014] S4. Verify the stability of the unmanned boat formation through simulation experiments.

[0015] Preferably, in the step S1, the process of constructing the three-degree-of-freedom motion model of the unmanned boat and converting it into a state space equation is as follows:

[0016] Based on the premise that the unmanned boat only has horizontal motion, a three-degree-of-freedom motion model of the unmanned boat is constructed according to the kinematics and dynamics of surge, sway and yaw. According to the conversion relationship between speed and position, the three-degree-of-freedom motion model of the unmanned boat is converted into a state space equation, and the calculation formula is as follows:

[0017]

[0018] In the formula is the position-related variable in the state variables of the unmanned boat, is the speed-related variable, is related to the converted speed-related variable; When, it is the leading unmanned boat; When, it is the following unmanned boat; is the position in the inertial coordinate system; is the control input of the unmanned boat; is the speed of the unmanned boat;

[0019] Among them,

[0020]

[0021]

[0022]

[0023] ;

[0024] wherein is the rotation matrix related to the heading angle of the unmanned boat, is the mass matrix, is the inverse matrix; is the external environmental disturbance; is the skew-symmetric matrix, is the Coriolis force and centripetal force matrix, is the damping matrix, including the forward thrust and the yawing moment.

[0025] Preferably, in the step S2, the motion model of the unmanned boat is constructed as follows:

[0026] S21, construct the wind-wave-current disturbance model

[0027] According to the Fossen manual, the wind-wave-current disturbance model is constructed for the wind force, wave force and current force, including the wind force disturbance model, the wave force disturbance model and the current force disturbance model. The specific process is as follows:

[0028] ① Wind force disturbance model: The six-component wind force coefficient method is adopted to calculate the lateral and longitudinal wind force components according to the windward area of the unmanned boat, the air density and the real-time wind speed, and the wind force distribution is equivalent to the center of gravity position of the unmanned boat through the moment conversion formula. The specific formula is as follows:

[0029]

[0030] wherein respectively represent the sum of the wind force and moment generated in the surge, sway and yaw directions; represents the wind density, with the unit of ; represents the angle between the wind direction and the heading of the unmanned boat; represents the wind force and moment coefficient; , and respectively represent the projected area of the front part of the unmanned boat hull, the projected area of the side above the waterline and the total length;

[0031] ② Wave force disturbance model: Based on the linear model of the force and moment caused by the first-order and second-order waves, the wave frequency and amplitude parameters under the fourth sea state are adopted, and the wave-induced force and moment are generated in combination with the geometric parameters of the unmanned boat hull. The specific formula is as follows:

[0032]

[0033] wherein They are the sums of the surge, sway, and yaw wave forces and moments respectively. is the wave-related coefficient, through adjusts the wave forces and moments. , is the Laplacian operator. is the damping coefficient. is the encounter frequency. is the drift force;

[0034] Among them, the drift force is calculated through the Wiener process:

[0035]

[0036] In the formula is the Gaussian white noise;

[0037] ③ Water flow force perturbation model: Construct the forces and moments applicable to constant water flow speed, decomposed into surge and sway direction components. Calculate the lateral and longitudinal water flow force components according to the contact area of the unmanned boat with the water flow, water flow density, and flow velocity, and equivalent the water flow force distribution to the center of gravity position of the unmanned boat through the moment conversion formula;

[0038]

[0039] In the formula are the sums of the forces and moments generated by the water flow in the surge, sway, and yaw directions respectively;

[0040] is the water flow density, with the unit of ; is the water flow force and moment coefficient; , and are the projected area of the front part of the unmanned boat hull, the projected area of the side above the waterline, and the total length respectively; is the angle between the forward direction of the unmanned boat and the water flow, represents the absolute flow velocity;

[0041] S22, construct the motion model of the unmanned boat

[0042] Perturbation coupling mechanism: Linearly superpose the wind, wave, and water flow forces generated during the processes of the wind force perturbation model, wave force perturbation model, and water flow force perturbation model onto the three-degree-of-freedom motion model of the unmanned boat to construct a motion model of the unmanned boat including environmental perturbations. The specific formula is as follows:

[0043]

[0044] In the formula represents the environmental perturbation caused by wind, wave, and water flow; among them, Represents the sum of the wind disturbance forces and moments designed by the wind disturbance model, , and respectively represent the sum of the wind disturbance forces and moments generated by the wind in the surge, sway, and yaw directions; Represents the sum of the wave disturbance forces and moments designed by the wave disturbance model, , and respectively represent the sum of the wind disturbance forces and moments generated by the wave in the surge, sway, and yaw directions; Represents the sum of the current disturbance forces and moments designed by the current disturbance model, respectively represent the sum of the wind disturbance forces and moments generated by the current in the surge, sway, and yaw directions.

[0045] Preferably, in the step S3, the specific steps of designing the desired position of the unmanned boat by using the leader-follower method are as follows:

[0046] Select a distance-angle following method, and design the desired position of the unmanned boat according to the relative position and azimuth with the leading unmanned boat. The specific design process is as follows:

[0047]

[0048] In the formula, the vector , respectively represent the desired position / attitude of the i-th unmanned boat relative to the reference point in the three degrees of freedom directions of surge, sway, and heading, represents the distance-related parameter between the i-th unmanned boat and the leading unmanned boat, represents the angle related to the i-th unmanned boat and the leading unmanned boat, represents the heading angle of the i-th unmanned boat itself.

[0049] Preferably, in the step 1) of the step S3, the specific steps of constructing the super-twisting integral sliding mode observer are as follows:

[0050] By defining the sliding mode surface as a linear combination of the state error and the integral error, use the super-twisting algorithm to construct the super-twisting integral sliding mode observer, and dynamically adjust the observer gain. The specific formula is as follows:

[0051]

[0052] In the formula , is the sliding mode surface, which is composed of the state error and the integral error Composed of linear combinations, auxiliary variables Is the observer pair The estimated value of Is related to the position of the unmanned boat And speed Related matrix Is the integral gain for smoothing the observation error; Is the super-twisting gain; Is the disturbance estimated value; Is the sign function.

[0053] Preferably, in step 2) of step S3, the specific steps for building the unmanned boat tracking control subsystem are as follows:

[0054] Design of the fixed-time convergence mechanism: Based on the Lyapunov function, set the upper bound of the convergence time to ensure that the tracking error approaches zero within the preset time, independent of the initial state. The specific design is as follows:

[0055]

[0056] Among them, the gain parameter , Is a positive odd number and satisfies , , And Is the fractional power extension of the sign function;

[0057] Design of the non-singular terminal sliding mode controller: Use the fractional power parameter to construct the non-singular terminal sliding mode surface, and achieve the dynamic convergence of the tracking error through the linear combination of the integral error and the state estimation error. The specific design of the sliding mode surface is as follows:

[0058]

[0059] In the formula Represents the tracking error between the actual position and speed of the leader unmanned boat and the desired position and speed after the state space transformation, Represents the integral sliding mode surface parameter, Represents the power parameter, Represents the non-linear function about ;

[0060] Design of the super-twisting integral sliding mode observer: Use the estimated wind-wave-current disturbance estimated value of the super-twisting integral sliding mode observer as the feed-forward input to cancel the influence of environmental disturbances on the trajectory tracking of the leader unmanned boat;

[0061] Based on the non-singular terminal sliding mode controller and the super-twisting integral sliding mode observer with fixed-time convergence, the specific process of building the unmanned boat tracking control subsystem is as follows:

[0062]

[0063] where is the mass matrix of the unmanned boat, is the rotation matrix, is the estimated value of the disturbance estimated by the super-twisting observer, is the desired acceleration.

[0064] Preferably, the parameter selection method of the non-singular terminal sliding mode controller is as follows:

[0065] Fractional power constraint: Set the numerator and denominator parameters of a specific odd number to avoid the singular point where the denominator of the derivative of the sliding surface is zero;

[0066] Disturbance boundary estimation: Use the output of the super-twisting integral sliding mode observer to dynamically update the disturbance boundary value as the robustness gain parameter of the super-twisting integral sliding mode observer. The specific design is as follows:

[0067]

[0068] where , which is the sign power function, is the tracking error, is the variable of the sliding surface function, is a very small positive odd number, the smooth transition parameter , ;

[0069] Integral sliding surface coefficient , the power parameter ; When the system state is far from the equilibrium point, plays a major approaching role to ensure the rapid convergence of the system; when the system state is close to the equilibrium point, plays a major role, and the system reaches the steady state within a fixed time; the system maintains a relatively fast convergence speed during the entire dynamic process, and at the same time when tends to zero, the derivative of the sliding surface does not contain negative exponent terms.

[0070] Preferably, in step 3) of step S3, the specific steps for building the unmanned boat formation control subsystem are as follows:

[0071] Use the super-twisting integral sliding mode observer to estimate the wind, wave and current disturbances and model uncertainties in real time, receive the lag state signal of the leading unmanned boat and extract the lag state information of the leading unmanned boat, and design an adaptive time-delay estimation method based on the lag state information of the leading unmanned boat through the Lyapunov stability theory to estimate the communication time-delay online. The specific design is as follows:

[0072]

[0073] In the formula is the estimated time delay value, is the adaptive gain coefficient, is the formation control error, is the lag state information of the leader unmanned boat;

[0074] Compensate the time delay information of the leader unmanned boat: Dynamically adjust the information of the leader unmanned boat according to the estimated time delay value to ensure stability when the follower unmanned boat performs formation control.

[0075] Preferably, in step 4) of step S3, the specific steps for building the formation control system are as follows:

[0076] Construct a non-singular terminal sliding mode surface using fractional power parameters, and achieve the dynamic convergence of the tracking error through the linear combination of the integral error and the state estimation error. The specific design of the sliding mode surface is:

[0077]

[0078]

[0079]

[0080]

[0081] In the formula, the integral sliding mode surface coefficient , the fractional power parameter , and are the tracking error components; is a very small positive odd number, is a piecewise function;

[0082] Time convergence: Set the upper bound of the convergence time based on the Lyapunov function to ensure that the tracking error approaches zero within the preset time, regardless of the initial state;

[0083] Disturbance feedforward compensation: Use the estimated value of the wind-wave-current disturbance estimated by the super-twisting integral sliding mode observer as the feedforward input to cancel the influence of the environmental disturbance on the trajectory tracking of the leader unmanned boat;

[0084] Time delay compensation: Compensate the time delay of the leader unmanned boat with the time delay estimated by the adaptive time delay estimator to resist the influence of the time delay.

[0085] The design calculation formula for building the formation control system is:

[0086]

[0087] In the formula, the gain parameter , is a positive odd number and satisfies , is the disturbance estimation value, is the lag state information.

[0088] Compared with the prior art, the present invention proposes a method for maintaining the formation of unmanned surface vehicles under communication delay. The advantages of this method are as follows:

[0089] In the present invention, a sliding mode formation control, time delay estimation, and disturbance estimation scheme are combined. Based on a fixed-time nonsingular fast terminal sliding mode leader-following unmanned surface vehicle formation control strategy with an adaptive time delay compensator and a disturbance observer, the unmanned surface vehicle formation can overcome external disturbances and communication delay problems and achieve cooperative tasks for multiple unmanned surface vehicles. Considering both the formation stability of the unmanned surface vehicle formation and the communication delay existing between unmanned surface vehicles, an adaptive time delay estimator is designed to compensate for the time delay information of the unmanned surface vehicles. At the same time, a nonlinear singular sliding mode surface is set, and the combination of fixed-time theory and sliding mode control can effectively cope with external disturbances received by the unmanned surface vehicles. An effective compensation for the disturbances is achieved by designing a super-twisting sliding mode observer, which enables the unmanned surface vehicle formation to maintain stability during cooperative navigation and also ensures the stability of the unmanned surface vehicle formation system.

[0090] The advantages of the present invention and the advantages of additional aspects will be described in detail in the following specific embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] Figure 1 is a flowchart of a method for maintaining the formation of unmanned surface vehicles under communication delay according to an embodiment of the present invention;

[0092] Figure 2 is a reference coordinate system of the unmanned surface vehicle motion model according to an embodiment of the present invention;

[0093] Figure 3 is a horizontal structure diagram of a leader-following unmanned surface vehicle according to an embodiment of the present invention;

[0094] Figure 4 is a curve trajectory diagram of an unmanned surface vehicle formation according to a simulation example of an embodiment of the present invention;

[0095] Figure 5 is a position and attitude change diagram of an unmanned surface vehicle formation trajectory tracking according to a simulation example of an embodiment of the present invention;

[0096] Figure 6 is a speed change diagram of an unmanned surface vehicle formation trajectory tracking according to a simulation example of an embodiment of the present invention;

[0097] Figure 7 is a control input change diagram of an unmanned surface vehicle formation trajectory tracking according to a simulation example of an embodiment of the present invention;

[0098] Figure 8This is the graph of the change in the position and attitude errors of the unmanned boat formation trajectory tracking in the embodiment of the present invention;

[0099] Figure 9 This is the graph of the change in the position and attitude errors of the unmanned boat formation trajectory tracking in the simulation example of the embodiment of the present invention. Detailed implementation manners

[0100] Next, the technical solutions in the embodiments of the present application will be further clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. It should be noted that the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative efforts belong to the scope of protection of the present application.

[0101] In order to make the invention purpose, technical solutions and advantages of the present application clearer, the embodiments of the present application will be further described in detail below with reference to the accompanying drawings of the specification: In order to better understand the above objects, features and advantages of the present invention, the advantages of the present invention will be further illustrated by comparing with embodiments in conjunction with the drawings and specific implementation manners.

[0102] The present invention proposes a method for maintaining the formation of an unmanned boat fleet under communication delay, as Figure 1 and Figure 2 shown. Based on the established three-degree-of-freedom motion model of the unmanned boat, its state-space equation and the mathematical model of environmental disturbances, an unmanned boat motion model is constructed. Then, aiming at the problems of wind, wave and current disturbances and communication delay in the actual navigation of the unmanned boat fleet, a super-twisting integral sliding mode observer is designed to estimate the disturbances and an adaptive time-delay estimator is designed to estimate the time delay. Based on this, combined with the fixed-time theory and the nonsingular terminal sliding mode control method, a fixed-time nonsingular terminal sliding mode formation controller is designed. And through simulation experiments, the stability of the designed method is verified, and finally the formation control of the unmanned boat fleet under communication delay is realized. The steps of this method are described in detail as follows:

[0103] S1. Based on the horizontal motion of the unmanned boat, construct a three-degree-of-freedom (surge, sway and yaw) motion model of the unmanned boat and convert it into a state-space equation;

[0104] Specifically, in the step S1, as Figure 3 shown, the process of constructing a three-degree-of-freedom motion model of the unmanned boat and converting it into a state-space equation is as follows:

[0105] In the movement of an unmanned boat, the original unmanned boat movement model has six degrees of freedom (surge, sway, yaw, heave, roll, and pitch). Based on the premise of only considering the horizontal movement of the unmanned boat, the vertical movements of heave, roll, and pitch are ignored, and only the horizontal movement analysis is retained. Only the kinematics and dynamics of the three degrees of freedom of surge, sway, and yaw are studied and modeled. According to the conversion relationship between speed and position, the three-degree-of-freedom movement model of the unmanned boat is then converted into a state-space equation. The calculation formula for the state-space equation of the unmanned boat modeling is as follows:

[0106]

[0107] In the formula is the position-related variable in the state variables of the unmanned boat (such as the position coordinate-related quantities corresponding to surge, sway, and yaw), is the speed-related variable, is related to converted speed-related variables (such as surge speed, sway speed, yaw angular velocity, etc.); When, it is the leading unmanned boat, providing a reference trajectory; When, it is the following unmanned boat; is the position in the inertial coordinate system; is the control input of the unmanned boat; is the speed of the unmanned boat;

[0108] Among them,

[0109]

[0110]

[0111]

[0112] ;

[0113] In the formula is the rotation matrix related to the heading angle of the unmanned boat, used to describe geometric relationships such as coordinate conversion when the unmanned boat is in different directions, is the mass matrix, is the inverse matrix of; is the external environmental disturbance (such as the disturbing forces or torques on the unmanned boat caused by wind, waves, water flow, etc.); is the skew-symmetric matrix, is the Coriolis force and centripetal force matrix, is the damping matrix.

[0114] S2. According to the Fossen manual, construct the disturbance model of wind, wave and current for the unmanned boat, and combine it with the three-degree-of-freedom motion model of the unmanned boat to construct the motion model of the unmanned boat including environmental disturbance;

[0115] Specifically, in the step S2, to construct the disturbance model of wind, wave and current and combine it with the three-degree-of-freedom motion model of the unmanned boat to construct the motion model of the unmanned boat including environmental disturbance, the specific steps are as follows:

[0116] S21. Construct the disturbance model of wind, wave and current

[0117] According to the Fossen manual, the disturbance model of wind, wave and current for the unmanned boat models the wind force, wave force and current force respectively, including the wind force disturbance model, the wave force disturbance model and the current force disturbance model. The specific process is as follows:

[0118] ① Wind force disturbance model: Adopt the six-component wind force coefficient method. Calculate the lateral and longitudinal wind force components according to the windward area of the unmanned boat, air density and real-time wind speed, and equivalent the wind force distribution to the center of gravity position of the unmanned boat through the moment conversion formula. The specific formula is as follows:

[0119]

[0120] In the formula respectively represent the total wind force and moment generated in the surge, sway and yaw directions; represents the air density, with the unit of ; represents the angle between the wind direction and the bow direction of the unmanned boat; represents the wind force and moment coefficient; 、 and respectively represent the projected area of the front part of the unmanned boat hull, the projected area of the side above the waterline and the total length;

[0121] ② Wave force disturbance model: Consider the linear model of the force and moment caused by the first-order and second-order waves; Adopt the wave frequency and amplitude parameters under the sea state of level 4, and generate the wave-induced force and moment in combination with the geometric parameters of the unmanned boat hull. The specific formula is as follows:

[0122]

[0123] In the formula 、 and are respectively the total wave force and moment in the surge, sway and yaw directions, is the coefficient related to the wave, and adjusts the wave force and moment through , , is the Laplace operator, is the damping coefficient, is the encounter frequency, is the drift force;

[0124] Among them, the drift force is calculated through the Wiener process:

[0125]

[0126] In the formula is Gaussian white noise;

[0127] ③ Hydrodynamic force perturbation model: Construct the forces and moments applicable to constant water flow velocity, decomposed into surge, sway direction components, calculate the lateral and longitudinal hydrodynamic force components according to the contact area of the unmanned boat with the water flow, water flow density and flow velocity, and equivalent the hydrodynamic force distribution to the center of gravity position of the unmanned boat through the moment conversion formula;

[0128]

[0129] In the formula are the total sums of the forces and moments generated by the water flow in the surge, sway and yaw directions respectively; is the water flow density, with the unit of ; are the hydrodynamic force and moment coefficients; , and are the projected area of the front part of the unmanned boat hull, the lateral projected area above the waterline and the total length respectively; is the angle between the forward direction of the unmanned boat and the water flow, represents the absolute flow velocity;

[0130] S22, construct the motion model of the unmanned boat

[0131] Perturbation coupling mechanism: Linearly superimpose the wind, wave and flow forces generated during the processes of the wind force perturbation model, wave force perturbation model and hydrodynamic force perturbation model onto the three-degree-of-freedom motion model of the unmanned boat to construct a motion model of the unmanned boat including environmental perturbations. The specific formula is as follows:

[0132]

[0133] In the formula represents the environmental perturbation caused by wind, wave and flow; among them, represents the total sum of the wind disturbance forces and moments designed by the wind perturbation model, , and represent the total sums of the wind disturbance forces and moments generated by the wind in the surge, sway and yaw directions respectively; represents the total sum of the wave disturbance forces and moments designed by the wave perturbation model, 、 and respectively represent the total wind disturbance forces and moments generated by waves in the surge, sway, and yaw directions; represents the total water flow disturbance forces and moments designed by the water flow disturbance model, 、 and respectively represent the total wind disturbance forces and moments generated by water flow in the surge, sway, and yaw directions.

[0134] S3. Using the leader-follower method, design the desired positions of the unmanned boats according to the relative positions and azimuths with the leading unmanned boat, build the unmanned boat tracking control subsystem and the unmanned boat formation control subsystem, and use the unmanned boat tracking control subsystem and the unmanned boat formation control subsystem to build the formation control system to achieve the maintenance of the unmanned boat formation;

[0135] 1) Based on the unmanned boat motion model, construct a super-twisting integral sliding mode observer to observe and compensate for disturbances;

[0136] 2) According to the deviation between the actual position and the desired position of the leading unmanned boat, design a non-singular terminal sliding mode controller based on the fixed-time convergence mechanism, use the super-twisting integral sliding mode observer for disturbance estimation, build the unmanned boat tracking control subsystem, and achieve the tracking of the leading unmanned boat to the desired trajectory within the preset time;

[0137] 3) Use the super-twisting integral sliding mode observer to estimate the wind-wave-current disturbances and model uncertainties in real time, based on the lag state information of the leading unmanned boat, online estimate the communication delay, and compensate for the time-delay information of the leading unmanned boat, build the unmanned boat formation control subsystem, and solve the communication delay problem;

[0138] 4) Combine the fixed-time convergence mechanism, the non-singular terminal sliding mode controller, and the super-twisting integral sliding mode observer under the communication delay, build the formation control system composed of the unmanned boat tracking control subsystem and the unmanned boat formation control subsystem, and achieve the maintenance of the unmanned boat formation;

[0139] Specifically, in the step S3, the specific steps of designing the desired positions of the unmanned boats by using the leader-follower method are as follows:

[0140] The unmanned boat formation control method designed by the leader-follower method selects the distance-angle-based following mode, and designs the desired positions of the unmanned boats according to the relative positions and azimuths with the leader. The specific design process is as follows:

[0141]

[0142] In the formula, the vector , respectively represent the desired positions / attitudes of the $i$-th unmanned boat in the three degrees of freedom of surge, sway, and heading relative to the reference point, represents the distance-related parameter between the $i$-th unmanned boat and the leading unmanned boat, represents the angle between the $i$-th unmanned boat and the leading unmanned boat, represents the heading angle (course angle) of the $i$-th unmanned boat itself.

[0143] Specifically, in step 1) of step S3, the specific steps for constructing the super-twisting integral sliding mode observer are as follows:

[0144] By defining the sliding mode surface as a linear combination of the state error and the integral error, and using the super-twisting algorithm to dynamically adjust the observer gain, the observation and control of the relevant states are realized to ensure that the formation of the unmanned boat formation can be better maintained in the case of communication delay. The specific formula is as follows:

[0145]

[0146] In the formula, , is the sliding mode surface, which is linearly combined by the state error and the integral error . The auxiliary variable is the estimated value of the observer for , is a matrix related to the position and velocity of the unmanned boat, is the integral gain, which is used to smooth the observation error; is the super-twisting gain; is the estimated value; is the sign function.

[0147] Specifically, in step 2) of step S3, the specific steps for building the unmanned boat tracking control subsystem are as follows:

[0148] Design of the fixed-time convergence mechanism: Based on the Lyapunov function, set the upper bound of the convergence time to ensure that the tracking error approaches zero within the preset time, regardless of the initial state. The specific design is

[0149]

[0150] where the gain parameter , is a positive odd number and satisfies , and Fractional power extension of the sign function;

[0151] Design of a non-singular terminal sliding mode controller: A non-singular terminal sliding mode surface is constructed using fractional power parameters, and the dynamic convergence of the tracking error is achieved through a linear combination of the integral error and the state estimation error. When moving on the sliding mode surface, it can operate according to the desired dynamic characteristics. The specific design of the sliding mode surface is as follows:

[0152]

[0153] where represents the tracking error between the actual position and velocity of the leader unmanned boat and the desired position and velocity after state space transformation. represents the sliding mode surface parameter, which adjusts the convergence speed of the error dynamics. represents the power parameter. represents with respect to nonlinear function of.

[0154] Design of a super-twisting integral sliding mode observer: The estimated value of the wind, wave, and current disturbance estimated by the super-twisting integral sliding mode observer is used as a feedforward input to cancel the influence of environmental disturbances on the trajectory tracking of the leader unmanned boat.

[0155] Integrate the sliding mode surface, tracking error, disturbance feedforward compensation, and desired trajectory acceleration to ensure the convergence of the tracking error within a fixed time. The specific process of building the tracking control subsystem of the unmanned boat based on the non-singular terminal sliding mode controller and the super-twisting integral sliding mode observer with fixed-time convergence is as follows:

[0156]

[0157] where is the mass matrix of the unmanned boat, is the rotation matrix, is the estimated value of the external disturbance estimated by the super-twisting observer, is the desired acceleration.

[0158] More specifically, the specific process of the parameter selection method of the non-singular terminal sliding mode controller is as follows:

[0159] Fractional power constraint: Set the numerator and denominator parameters of a specific odd number to avoid the singular point where the denominator of the derivative of the sliding mode surface is zero.

[0160] Disturbance boundary estimation: Use the output of the super-twisting integral sliding mode observer to dynamically update the disturbance boundary value, which is used as the robustness gain parameter of the super-twisting integral sliding mode observer. The specific design is as follows:

[0161]

[0162] where , which is a symbolic power function, is the tracking error, is the variable of the sliding mode surface function, is a very small positive odd number, the smoothing transition parameter , ;

[0163] Integral sliding mode surface coefficient , power parameter ;

[0164] When the system state is far from the equilibrium point, plays a major approaching role to ensure the rapid convergence of the system; when the system state is close to the equilibrium point, plays a major role, and the system reaches the steady state within a fixed time; the system maintains a relatively fast convergence speed during the entire dynamic process, and at the same time when approaches zero, the derivative of the sliding mode surface does not contain negative exponential terms, which avoids the singularity problem.

[0165] Specifically, in step 3) of step S3, the specific steps for building the unmanned boat formation control subsystem are as follows:

[0166] The wind, wave and current disturbances and model uncertainties are estimated in real time through a super-twisting integral sliding mode observer, the lag state signal of the leader unmanned boat is received and the lag state information of the leader unmanned boat is extracted, and an adaptive time-delay estimation method is designed based on the lag state information of the leader unmanned boat through the Lyapunov stability theory to estimate the communication time-delay online. The specific design is as follows:

[0167]

[0168] In the formula is the time-delay estimation value, is the adaptive gain coefficient, is the time-delay state estimation of the leader unmanned boat;

[0169] Compensate the time-delay information of the leader unmanned boat: Dynamically adjust the information of the leader unmanned boat according to the time-delay estimation value to ensure stability when the follower unmanned boat performs formation control.

[0170] Specifically, in step 4) of step S3, the specific steps for building the formation control system are as follows:

[0171] Construct a non-singular terminal sliding mode surface by using the fractional power parameter, and realize the dynamic convergence of the tracking error through the linear combination of the integral error and the state estimation error. The specific design of the sliding mode surface is as follows:

[0172]

[0173]

[0174]

[0175]

[0176] where the integral sliding mode surface coefficient , the fractional power parameter , and are the tracking error components; is a very small positive odd number, is a piecewise function;

[0177] Time convergence: Based on the Lyapunov function, set the upper bound of the convergence time to ensure that the tracking error approaches zero within the preset time, regardless of the initial state;

[0178] Disturbance feedforward compensation: Use the estimated value of the wind, wave and current disturbance estimated by the super-twisting integral sliding mode observer as the feedforward input to cancel the influence of the environmental disturbance on the trajectory tracking of the leader unmanned boat;

[0179] Time delay compensation: Compensate the time delay information of the leader unmanned boat with the time delay estimated by the adaptive time delay estimator to resist the influence of the time delay.

[0180] The design calculation formula for building the formation control system is:

[0181]

[0182] where , is a positive odd number and satisfies .

[0183] S4. Verify the stability of the unmanned boat formation through simulation experiments.

[0184] According to the obtained Figure 4 , Figure 5 , Figure 6 , Figure 7 and Figure 8 of the state trajectories shown, in the case of external environmental disturbances and communication time delays, the follower unmanned boat and the leader unmanned boat can form a formation; in addition, through Figure 9 it can be determined that the fixed-time nonsingular terminal sliding mode leader unmanned boat formation control strategy set in this embodiment based on the adaptive time delay compensator and the disturbance observer ensures the formation stability of the unmanned boat formation;

[0185] A method for maintaining the formation of unmanned surface vehicles (USVs) under communication delay is presented in this embodiment. This method aims to solve the problem of anti-interference formation maintenance control for USV formations under communication delay, while considering complex external environmental disturbances such as wind, waves, and currents. The method adopts a leader-follower formation control approach and, by combining the position and velocity information of USVs, establishes the formation position and velocity error equations between the follower USV and the leader USV. To estimate the time delay and compensate for the time-delay information, an adaptive time-delay estimation method is designed based on the Lyapunov stability theory. The disturbance is estimated using a super-twisting integral sliding mode observer, and a USV formation control method is designed by combining the fixed-time theory and non-singular terminal sliding mode control. The effectiveness and practicality of the control algorithm are verified through theoretical proofs and simulation experiments.

[0186] Although the preferred embodiments of the present application have been described, those skilled in the art can make additional changes and modifications once they learn the basic creative concepts. Therefore, the appended claims are intended to be construed as including the preferred embodiments as well as all changes and modifications that fall within the scope of the present application.

[0187] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalent technologies, the present application is also intended to include these modifications and variations.

Claims

1. A method for maintaining the formation of unmanned boat formations under communication delay, characterized in that, Including: S1. Based on the horizontal motion of the unmanned boat, construct a three-degree-of-freedom kinematic and dynamic model of the unmanned boat, and convert it into a state-space equation; S2. According to the Fossen manual, construct a wind-wave-current disturbance model of the unmanned boat, and combine it with the three-degree-of-freedom motion model of the unmanned boat to construct a motion model of the unmanned boat including environmental disturbances; S3. Use the leader-follower method to design the desired position of the unmanned boat according to the relative position and azimuth with the leading unmanned boat, build a tracking control subsystem and a formation control subsystem of the unmanned boat, and use the tracking control subsystem and the formation control subsystem of the unmanned boat to build a formation control system to achieve the maintenance of the formation shape of the unmanned boat; 1) Based on the motion model of the unmanned boat, construct a super-twisting integral sliding mode observer to observe and compensate for disturbances; 2) According to the deviation between the actual position and the desired position of the leading unmanned boat, design a non-singular terminal sliding mode controller based on the fixed-time convergence mechanism, use the super-twisting integral sliding mode observer to estimate disturbances, and build a tracking control subsystem of the unmanned boat to achieve the tracking of the leading unmanned boat to the desired trajectory within a preset time; 3) Use the super-twisting integral sliding mode observer to estimate the wind-wave-current disturbances and model uncertainties in real time, based on the lag state information of the leading unmanned boat, estimate the communication delay online, and compensate for the time-delay information of the leading unmanned boat, and build a formation control subsystem of the unmanned boat to solve the communication delay problem; 4) Combine the fixed-time convergence mechanism, the non-singular terminal sliding mode controller and the super-twisting integral sliding mode observer under the communication delay, build a formation control system composed of a tracking control subsystem and a formation control subsystem of the unmanned boat to achieve the maintenance of the formation shape of the unmanned boat; S4. Verify the stability of the unmanned boat formation through simulation experiments.

2. The method for maintaining the formation of unmanned boat formations under communication delay according to claim 1, characterized in that In the step S1, the process of constructing the three-degree-of-freedom motion model of the unmanned boat and converting it into a state-space equation is as follows: Based on the premise that the unmanned boat only has horizontal motion, construct a three-degree-of-freedom motion model of the unmanned boat according to the kinematics and dynamics of the three degrees of freedom of surge, sway and yaw, and then convert the three-degree-of-freedom motion model of the unmanned boat into a state-space equation according to the conversion relationship between speed and position. The calculation formula is as follows: ； where is the position-related variable among the state variables of the unmanned boat, is the speed-related variable, is related to the transformed speed-related variable; when it is, it is the leading unmanned boat; when it is, it is the following unmanned boat; is the position in the inertial coordinate system; is the control input of the unmanned boat; is the speed of the unmanned boat Where, ; ； ； ； where is the rotation matrix related to the heading angle of the unmanned boat , is the mass matrix is the inverse matrix; is the external environmental disturbance; is the skew-symmetric matrix is the Coriolis force and centripetal force matrix is the damping matrix.

3. A method for maintaining the formation of unmanned boat formations under communication delay, as claimed in claim 1, wherein In the step S2, the specific steps of constructing the motion model of the unmanned boat are as follows: S21. Construct a wind-wave-current disturbance model According to the Fossen manual, construct a wind-wave-current disturbance model for wind force, wave force and current force, including a wind force disturbance model, a wave force disturbance model and a current force disturbance model. The specific process is as follows: ① Wind force disturbance model: Adopt the six-component wind force coefficient method to calculate the lateral and longitudinal wind force components according to the windward area of the unmanned boat, air density and real-time wind speed, and convert the wind force distribution to the center of gravity position of the unmanned boat through the moment conversion formula. The specific formula is as follows: ； where respectively represent the total wind forces and moments generated in the surge, sway, and yaw directions; represents the air density, with the unit of ; represents the angle between the wind direction and the heading of the unmanned boat; represents the wind force and moment coefficient; , and respectively represent the projected area of the front part of the unmanned boat hull, the projected area of the side above the waterline, and the total length; ② Wave force disturbance model: Based on the linear model of the forces and moments caused by the first-order and second-order waves, adopt the wave frequency and amplitude parameters under the fourth-level sea state, and combine the hull geometric parameters of the unmanned boat to generate wave-induced forces and moments. The specific formula is as follows: ; where are the total wave forces and moments in the surge, sway, and yaw directions, respectively, is the wave-related coefficient, which adjusts the wave forces and moments through , is the Laplace operator, is the damping coefficient, is the encounter frequency, is the drift force;​ Among them, the drift forces in the surge, sway, and yaw directions are calculated through the Wiener process: ； where is Gaussian white noise; ③Hydrodynamic force disturbance model: Construct the forces and torques applicable to constant water flow velocity, decomposed into surge and sway direction components. Calculate the lateral and longitudinal hydrodynamic force components based on the contact area of the unmanned boat with the water flow, water density, and flow velocity, and equivalent the hydrodynamic force distribution to the center of gravity position of the unmanned boat through the torque conversion formula; ; In the formula are respectively the total forces and moments generated by the water flow in the surge, sway, and yaw directions; is the water density, with the unit of ; are the water flow force and moment coefficients; are respectively the projected area of the front part of the unmanned boat hull, the projected area of the side above the waterline, and the total length; is the angle between the forward direction of the unmanned boat and the water flow, represents the absolute flow velocity; S22. Construct the motion model of the unmanned boat Disturbance coupling mechanism: Linearly superimpose the wind, wave, and flow forces generated during the wind force disturbance model, wave force disturbance model, and hydrodynamic force disturbance model onto the three-degree-of-freedom motion model of the unmanned boat to construct a motion model of the unmanned boat including environmental disturbances. The specific formula is as follows: ； In the formula represents the environmental disturbance caused by wind, wave and current; among them, represents the sum of the wind disturbing forces and moments designed by the wind disturbance model, respectively represent the sum of the wind disturbing forces and moments generated by the wind in the surge, sway and yaw directions; represents the sum of the wave disturbing forces and moments designed by the wave disturbance model, , and respectively represent the sum of the wind disturbing forces and moments generated by the wave in the surge, sway and yaw directions; represents the sum of the current disturbing forces and moments designed by the current disturbance model, respectively represent the sum of the wind disturbing forces and moments generated by the current in the surge, sway and yaw directions.

4. A method for maintaining the formation of unmanned boat formations under communication delay according to claim 1, characterized in that, In step S3, the specific steps for designing the desired position of the unmanned boat using the leader-follower method are as follows: Select the distance - angle based following mode, and design the expected position of the unmanned boat according to the relative position and orientation with the leading unmanned boat. The specific design process is as follows: ; In the formula, the vectors , respectively represent the expected positions / attitudes of the i-th unmanned boat in the three degrees of freedom directions of surge, sway, and heading relative to the reference point, represents the distance-related parameter between the i-th unmanned boat and the leading unmanned boat, is related to the angle between the -th unmanned boat and the leading unmanned boat, represents the heading angle of the i-th unmanned boat itself.

5. A method for maintaining the formation of unmanned boat formations under communication delay, as claimed in claim 1, wherein In 1) of step S3, the specific steps for constructing the super-twisting integral sliding mode observer are as follows: By defining the sliding mode surface as a linear combination of the state error and the integral error, use the super-twisting algorithm to construct the super-twisting integral sliding mode observer and dynamically adjust the observer gain. The specific formula is as follows: ； where , is the sliding mode surface, which is composed of a linear combination of the state error and the integral error . The auxiliary variable is the estimated value of the observer for . is a matrix related to the position and velocity of the unmanned boat. is the integral gain, which is used to smooth the observation error; is the super-twisting gain; is the estimated value of the disturbance; is the sign function.

6. The method for maintaining the formation of unmanned boat formation under communication delay according to claim 1, characterized in that, In 2) of step S3, the specific construction steps of the unmanned boat tracking control subsystem are as follows: Design of the fixed-time convergence mechanism: Set an upper bound for the convergence time based on the Lyapunov function to ensure that the tracking error approaches zero within a preset time, independent of the initial state. The specific design is as follows: ; Among them, the gain parameter , is a positive odd number and satisfies , , and are fractional power expansions of the sign function; Design of the non-singular terminal sliding mode controller: Construct a non-singular terminal sliding mode surface using fractional power parameters, and achieve the dynamic convergence of the tracking error through the linear combination of the integral error and the state estimation error. The specific design of the sliding mode surface is as follows: ; where represents the tracking error between the actual position and velocity of the leader unmanned boat and the desired position and velocity after state - space transformation, represents the integral sliding - mode surface parameter, represents the power - order parameter, represents with respect to a non - linear function; Design of the super-twisting integral sliding mode observer: Use the estimated values of wind, wave, and flow disturbances estimated by the super-twisting integral sliding mode observer as the feedforward input to cancel the influence of environmental disturbances on the trajectory tracking of the leader unmanned boat; Based on the non-singular terminal sliding mode controller and the super-twisting integral sliding mode observer with fixed-time convergence, the specific process of building the unmanned boat tracking control subsystem is as follows: ； In the formula is the mass matrix of the unmanned boat, is the rotation matrix, is the disturbance estimation value estimated by the super-twisting observer, is the desired acceleration.

7. A method for maintaining the formation of unmanned boat formations under communication delay, according to claim 6, wherein The parameter selection method of the non-singular terminal sliding mode controller is as follows: Fractional power constraint: Set the numerator and denominator parameters of a specific odd number to avoid the singular point where the denominator of the derivative of the sliding mode surface is zero; Disturbance boundary estimation: Dynamically update the disturbance boundary value using the output of the super-twisting integral sliding mode observer as the robustness gain parameter of the super-twisting integral sliding mode observer. The specific design is as follows: ; In the formula, , which is a symbolic power function, is the tracking error, is the variable of the sliding mode surface function, is a very small positive odd number, the smooth transition parameter ; Integral sliding mode surface coefficient , power parameter ; When the system state is far from the equilibrium point, plays a major approaching role to ensure the rapid convergence of the system; when the system state approaches the equilibrium point, plays a major role and the system reaches the steady state within a fixed time; the system maintains a relatively fast convergence speed throughout the dynamic process, and at the same time when approaches zero, the derivative of the sliding mode surface does not contain negative exponential terms.

8. A method for maintaining the formation of unmanned boat formations under communication delay, according to claim 1, characterized in that In 3) of step S3, the specific construction steps of the unmanned boat formation control subsystem are as follows: Real-time estimate the wind, wave, and flow disturbances and model uncertainties through the super-twisting integral sliding mode observer, receive the lag state signal of the leader unmanned boat and extract the lag state information of the leader unmanned boat. Based on the lag state information of the leader unmanned boat, design an adaptive time-delay estimation method through the Lyapunov stability theory to estimate the communication time-delay online. The specific design is as follows: ； where is the estimated time delay value, is the adaptive gain coefficient, is the formation control error, is the lag state information of the leading unmanned boat; Compensate for the time-delay information of the leader unmanned boat: Dynamically adjust the information of the leader unmanned boat according to the time-delay estimation value to ensure stability when the follower unmanned boat performs formation control.

9. A method for maintaining the formation of unmanned boat formations under communication delay, according to claim 1, wherein In 4) of step S3, the specific construction steps of the formation control system are as follows: Construct a non-singular terminal sliding mode surface using fractional power parameters, and achieve the dynamic convergence of the tracking error through the linear combination of the integral error and the state estimation error. The specific design of the sliding mode surface is as follows: ; ; ； ； where the integral sliding mode surface coefficient , the fractional power parameter , and are the tracking error components; is a very small positive odd number, is a piecewise function; Time convergence: Set an upper bound on the convergence time based on the Lyapunov function to ensure that the tracking error approaches zero within the preset time, regardless of the initial state; Disturbance feedforward compensation: Use the estimated values of the wind, wave, and current disturbances estimated by the super-twisting integral sliding mode observer as the feedforward input to cancel the influence of environmental disturbances on the trajectory tracking of the leader unmanned boat; Time-delay compensation: Compensate the time-delay information of the leader unmanned boat with the time-delay estimated by the adaptive time-delay estimator to resist the influence of time-delay; The design calculation formula for building the formation control system is: ； where the gain parameter , is a positive odd number and satisfies , is the disturbance estimate value, is the lag state information.

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