Unmanned ship formation keeping control method under communication time delay

Abstract

The invention discloses an unmanned ship formation keeping control method under communication time delay, and belongs to the technical field of intelligent ship navigation control, and the method comprises the steps: building an unmanned ship motion model based on a built unmanned ship three-degree-of-freedom motion model, a state-space equation of the unmanned ship three-degree-of-freedom motion model, and an environment disturbance mathematical model; aiming at the problems of wind wave flow disturbance and communication time delay suffered by the unmanned ship formation, constructing a superhelix integral sliding mode observer and a self-adaptive time delay estimator; a formation control system is built by combining a fixed time theory, a formation controller of a nonsingular terminal sliding mode and a superhelix integral sliding mode observer, and formation keeping of the unmanned surface vehicle is achieved; and finally verifying through a simulation experiment. The formation control system is built based on the fixed time theory and the nonsingular terminal sliding mode control method for the unmanned surface vehicle formation, the unmanned surface vehicle formation control precision is effectively improved, unmanned surface vehicle formation shape keeping control under composite disturbance is achieved, and the method has great significance in promoting precise development of unmanned surface vehicle formation operation.

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 boats under communication delay. Background Art

[0002] An unmanned boat formation refers to two or more unmanned boats exchanging information, cooperating with each other or independently performing complex tasks, and forming 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-tolerant control capabilities, which can effectively improve the task completion rate and efficiency, making surface operations more large-scale, intelligent, and efficient. Based on the original single-boat operation tasks including marine environmental monitoring, resource exploration, maritime search and rescue, etc., the operation range and efficiency are significantly improved.

[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 non-linear 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 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 extension of the 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 delay. 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] In the process of unmanned boat formations performing tasks, with the increase of task complexity and the expansion of the size of the formation, the time it takes for signals to propagate in space increases, resulting in communication delays; the complex marine environment interferes with the propagation path and speed of acoustic signals, further exacerbating communication delays; limited computing resources on the device side cause network queuing delays. The existence of communication delay problems has a multi-faceted negative impact on the overall performance of the unmanned boat formation. In terms of formation control performance, communication delays cause information updates to lag between boats, reduce the accuracy of formation maintenance, and make it impossible for each boat to adjust its status in real time, ultimately destroying the consistency of the formation; in terms of system stability, feedback control information is delayed due to communication delays, greatly increasing the risk of control algorithm failure, making it impossible for control instructions to accurately match the actual operating status of the unmanned boat, which may cause unstable responses in the system, and even cause unstable phenomena such as oscillations in the entire formation system, seriously affecting the effective execution of the unmanned boat formation mission. Summary of the invention

[0005] In view of the shortcomings of the background technology, the purpose of the present invention is to propose a method for maintaining the formation of an unmanned boat under communication delay. The unmanned boat motion model is constructed based on the established three-degree-of-freedom motion model of the unmanned boat and its state space equation and the mathematical model of environmental disturbance. Then, in view of the wind, wave and flow disturbance and communication delay problems in the unmanned boat formation during actual navigation, a super-helical integral sliding mode observer is designed to estimate the disturbance and an adaptive delay estimator is designed to estimate the delay. Based on this, a fixed-time non-singular terminal sliding mode control method is combined to design a fixed-time non-singular terminal sliding mode formation controller. The stability of the designed method is verified through simulation experiments, and finally the formation maintenance control of the unmanned boat formation under communication delay is realized.

[0006] The specific technical solution adopted by the present invention is: S1, based on the kinematics and dynamics of the three degrees of freedom of the unmanned boat in the horizontal motion of the unmanned boat, a three-degree-of-freedom motion model of the unmanned boat is constructed and converted into a state space equation; S2, according to the Fossen manual, the wind, wave and current disturbance model of the unmanned boat is constructed, and the unmanned boat motion model including environmental disturbance is constructed by combining it with the three-degree-of-freedom motion model of the unmanned boat; S3, using the leader-follower method to design the expected position of the unmanned boat according to the relative position and orientation between the unmanned boat and the pilot 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 a formation control system to achieve the formation maintenance of the unmanned boat formation; 1) Based on the unmanned boat motion model, a super-helical integral sliding mode observer is constructed to observe disturbances and compensate for them; 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 the preset time; 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 time 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 time delay problem; 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 time 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; S4. Verify the stability of the unmanned boat formation through simulation experiments.

[0007] 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: Based on the premise that the unmanned boat only has horizontal motion, the three-degree-of-freedom motion model of the unmanned boat is constructed according to the kinematics and dynamics of the three degrees of freedom 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 then converted into a state space equation, and the calculation formula is as follows:

[0008] 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; Among them,

[0009]

[0010]

[0011] ; In the formula 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 a skew-symmetric matrix, is the Coriolis force and centripetal force matrix, is the damping matrix, including the forward thrust and the yaw moment.

[0012] Preferably, in the step S2, the unmanned boat motion model is constructed, and the specific steps are as follows: S21, constructing the wind-wave-current disturbance model 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: ① Wind force disturbance model: The six-component wind force coefficient method is adopted. The lateral and longitudinal wind force components are calculated 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:

[0013] In the formula 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 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; 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:

[0014] In the formula respectively are the sum of the wave force and moment in the surge, sway, and yaw directions, is the coefficient related to the wave, and the wave force and moment are adjusted through , , is the Laplace operator, is the damping coefficient, is the encounter frequency, is the drift force; Among them, the drift force Calculated through the Wiener process:

[0015] In the formula is Gaussian white noise; ③ Hydrodynamic force perturbation model: Construct the forces and moments 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 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;

[0016] 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 ; is the hydrodynamic 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; S22, construct the unmanned boat motion model 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 an unmanned boat motion model including environmental perturbations. The specific formula is as follows:

[0017] In the formula represents the environmental perturbation caused by wind, wave, and flow; among them, represents the total sum of the wind perturbation forces and moments designed by the wind perturbation model, , and represent the total sums of the wind perturbation forces and moments generated by the wind in the surge, sway, and yaw directions respectively; represents the total sum of the wave perturbation forces and moments designed by the wave perturbation model, , and represent the total sums of the wind perturbation forces and moments generated by the waves in the surge, sway, and yaw directions respectively; represents the total sum of the hydrodynamic perturbation forces and moments designed by the hydrodynamic perturbation model, represent the total sums of the wind perturbation forces and moments generated by the water flow in the surge, sway, and yaw directions respectively.

[0018] Preferably, in step S3, the specific steps for designing the desired position of the unmanned boat using the leader-following method are as follows: Select the distance-angle Following mode, design the desired position of the unmanned boat according to the relative position and orientation with the leading unmanned boat. The specific design process is as follows:

[0019] 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 of surge, sway, and yaw. represents the th unmanned boat and the distance-related parameter between the leading unmanned boat. represents the th unmanned boat and the angle between the leading unmanned boat, represents the th unmanned boat's own yaw angle.

[0020] Preferably, in step 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:

[0021] In the formula , is the sliding mode surface, which is composed of the linear combination of the state error and the integral error . The auxiliary variable is the observer's estimate of . is the matrix related to the position and speed of the unmanned boat. is the integral gain, which is used to smooth the observation error; is the super-twisting gain; is the disturbance estimate value; is the sign function.

[0022] Preferably, in step 2) of step S3, the specific steps for building the unmanned boat tracking control subsystem are as follows: Design of the fixed-time convergence mechanism: 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. The specific design is as follows:

[0023] Among them, the gain parameter , is a positive odd number and satisfies , , and is the fractional power extension of the sign function; Design of the nonsingular terminal sliding mode controller: A nonsingular terminal sliding mode surface is constructed using fractional power parameters, and the dynamic convergence of the tracking error is achieved through the linear combination of the integral error and the state estimation error. The specific design of the sliding mode surface is as follows:

[0024] wherein 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 parameter, represents with respect to nonlinear function; Design of the 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 the feedforward input to cancel the influence of the environmental disturbance on the trajectory tracking of the leader unmanned boat; Based on the nonsingular 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:

[0025] wherein 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.

[0026] Preferably, the parameter selection method of the nonsingular 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 sliding mode surface derivative is zero; 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:

[0027] wherein, , which is the sign 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 , 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 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.

[0028] Preferably, in step 3) of step S3, the specific steps for building the unmanned boat formation control subsystem are as follows: 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 leading unmanned boat is received and the lag state information of the leading unmanned boat is extracted, and an adaptive time-delay estimation method is designed 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:

[0029] wherein is the time-delay estimation value, is the adaptive gain coefficient, is the formation control error, is the lag state information of the leading unmanned boat; Compensate the time-delay information of the leading unmanned boat: Dynamically adjust the information of the leading unmanned boat according to the time-delay estimation value to ensure stability when the following unmanned boats perform formation control.

[0030] Preferably, in step 4) of step S3, the specific steps for building the formation control system are as follows: 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:

[0031]

[0032]

[0033]

[0034] where the integral sliding mode surface coefficient , the fractional power parameter , and is the tracking error component; is a very small positive odd number, is a piecewise function; 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; 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; 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.

[0035] The design calculation formula for building the formation control system is:

[0036] In the formula, the gain parameter , is a positive odd number and satisfies , is the disturbance estimated value, is the lag state information.

[0037] Compared with the prior art, the present invention proposes a method for maintaining the formation of unmanned boats under communication time-delay. The advantages of this method are: In the present invention, the sliding mode formation control, time-delay estimation, and disturbance estimation schemes are combined. Based on the fixed-time nonsingular fast terminal sliding mode leader unmanned boat formation control strategy of the adaptive time-delay compensator and the disturbance observer, the unmanned boat formation can overcome the problems of external disturbance and communication time-delay and realize the cooperative tasks of multiple unmanned boats; comprehensively considering the formation stability of the unmanned boat formation and the communication time-delay existing between unmanned boats, design an adaptive time-delay estimator to compensate the time-delay information of the unmanned boat; at the same time, set a nonlinear singular sliding mode surface, and the combination of the fixed-time theory and the sliding mode control can effectively cope with the external disturbance received by the unmanned boat, and the effective compensation of the disturbance is realized by designing a super-twisting sliding mode observer, which enables the unmanned boat formation to maintain stability during cooperative navigation and also ensures the stability of the unmanned boat formation system.

[0038] The advantages of the present invention and the advantages of the additional aspects will be described in detail in the following specific embodiments. Brief Description of the Drawings

[0039] Figure 1 is a flowchart of a method for maintaining the formation of unmanned boats under communication time-delay according to an embodiment of the present invention; Figure 2 is the reference coordinate system of the unmanned boat motion model according to an embodiment of the present invention; Figure 3Horizontal structure diagram of the leading unmanned boat - following unmanned boat according to the embodiment of the present invention; Figure 4 Curve trajectory diagram of the unmanned boat formation according to the simulation example of the embodiment of the present invention; Figure 5 Position and attitude change diagram of the unmanned boat formation trajectory tracking according to the simulation example of the embodiment of the present invention; Figure 6 Speed change diagram of the unmanned boat formation trajectory tracking according to the simulation example of the embodiment of the present invention; Figure 7 Control input change diagram of the unmanned boat formation trajectory tracking according to the simulation example of the embodiment of the present invention; Figure 8 Position and attitude error change diagram of the unmanned boat formation trajectory tracking according to the embodiment of the present invention; Figure 9 Position and attitude error change diagram of the unmanned boat formation trajectory tracking according to the simulation example of the embodiment of the present invention. Specific implementation manner

[0040] 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.

[0041] 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-mentioned purpose, features and advantages of the present invention, the advantages of the present invention will be further illustrated by comparing the embodiments in conjunction with the drawings and specific implementation manners.

[0042] The present invention proposes a method for maintaining the formation of unmanned boats under communication delay, as shown in Figure 1 and Figure 2 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 problems of wind - wave - current disturbance and communication delay in 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 of the unmanned boat formation under communication delay is maintained. The steps of this method are described in detail as follows: S1. Based on the horizontal motion of the unmanned boat, construct a three-degree-of-freedom (surge, sway, and yaw) kinematic and dynamic model of the unmanned boat, and convert it into a state-space equation; 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: During the motion of the unmanned boat, the original unmanned boat motion model has six degrees of freedom (surge, sway, yaw, heave, roll, and pitch). Based on the premise of only considering the horizontal motion of the unmanned boat, ignore the vertical motions of heave, roll, and pitch, and only retain the horizontal motion analysis. Only study the kinematics and dynamics of the three degrees of freedom of surge, sway, and yaw and conduct modeling. Then, according to the conversion relationship between velocity and position, convert the three-degree-of-freedom motion model of the unmanned boat into a state-space equation. The calculation formula of the state-space equation for unmanned boat modeling is as follows:

[0043] 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 velocity-related variable, is related to the converted velocity-related variables (such as surge velocity, sway velocity, 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 velocity of the unmanned boat; Among them,

[0044]

[0045]

[0046] ; In the formula is the rotation matrix related to the heading angle of the unmanned boat, which is 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 (the disturbing forces or torques generated by wind, waves, water currents, etc. on the unmanned boat); is the skew-symmetric matrix, is the Coriolis force and centripetal force matrix, is the damping matrix.

[0047] S2. According to the Fossen manual, construct the 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 the motion model of the unmanned boat including environmental disturbances; Specifically, in the step S2, constructing the wind-wave-current disturbance model and combining it with the three-degree-of-freedom motion model of the unmanned boat to construct the motion model of the unmanned boat including environmental disturbances, the specific steps are as follows: S21. Construct the wind-wave-current disturbance model According to the Fossen manual, the wind-wave-current disturbance model of the unmanned boat models the wind force, wave force and water current force respectively, including the wind force disturbance model, the wave force disturbance model and the water current force disturbance model. The specific process is as follows: 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:

[0048] In the formula respectively represent the total 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 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; 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 fourth sea state, and combine the geometric parameters of the unmanned boat hull to generate the wave-induced force and moment. The specific formula is as follows:

[0049] In the formula 、 and are respectively the total wave forces and moments 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; Among them, the drift force is calculated through the Wiener process:

[0050] In the formula is Gaussian white noise; 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 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;

[0051] In the formula are the total forces and moments generated by the water flow in the surge, sway, and yaw directions respectively; is the water density, with the unit of ; is the hydrodynamic 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; S22, construct the unmanned boat motion model 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 an unmanned boat motion model including environmental perturbations. The specific formula is as follows:

[0052] In the formula represents the environmental perturbation caused by wind, wave, and flow; among them, represents the total wind disturbance force and moment designed by the wind perturbation model, , and represent the total wind disturbance force and moment generated by the wind in the surge, sway, and yaw directions respectively; represents the total wave disturbance force and moment designed by the wave perturbation model, , and represent the total wind disturbance force and moment generated by the wave in the surge, sway, and yaw directions respectively; represents the total hydrodynamic disturbance force and moment designed by the hydrodynamic perturbation model, , and respectively represent the total wind disturbance forces and moments generated by the water flow in the surge, sway, and yaw directions.

[0053] S3. Using the leader-follower method, design the desired position of the unmanned boat according to the relative position and orientation 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; 1) Based on the unmanned boat motion model, construct a super-twisting integral sliding mode observer to observe the disturbance and compensate it; 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; 3) Use the super-twisting integral sliding mode observer to estimate the wind-wave-current disturbance and model uncertainty in real time, based on the lag state information of the leading unmanned boat, online estimate the communication delay, and compensate the time-delay information of the leading unmanned boat, build the unmanned boat formation control subsystem, and 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 the unmanned boat tracking control subsystem and the unmanned boat formation control subsystem, and achieve the maintenance of the unmanned boat formation; Specifically, in the step S3, the specific steps of designing the desired position of the unmanned boat using the leader-follower method are as follows: The unmanned boat formation control method designed by the leader-follower method selects the distance-angle following mode, and designs the desired position of the unmanned boat according to the relative position and orientation with the leader. The specific design process is as follows:

[0054] where 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 between the i-th unmanned boat and the leading unmanned boat, represents the heading angle (course angle) of the i-th unmanned boat itself.

[0055] Specifically, in step 1) of step S3, the specific steps for constructing a 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, and using the super-twisting algorithm to dynamically adjust the observer gain, the observation and control of relevant states are realized, so as to ensure that the formation of the unmanned boat fleet can be well maintained in the case of communication delay. The specific formula is as follows:

[0056] In the formula , 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 ; is the sign function.

[0057] Specifically, in step 2) of step S3, the specific steps for building the unmanned boat tracking control subsystem are as follows: 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

[0058] Among them, the gain parameter , is a positive odd number, and satisfies , and is the fractional power extension of the sign function; Design of the non-singular terminal sliding mode controller: Use the fractional power parameter to construct a non-singular terminal sliding mode surface, and realize the dynamic convergence of the tracking error through the linear combination of the integral error and the state estimation error. When moving on the sliding mode surface, it can operate according to the expected dynamic characteristics; the specific design of the sliding mode surface is:

[0059] In the formula represents the tracking error between the actual position and velocity of the leading unmanned boat and the expected position and velocity after the state space transformation, represents the sliding mode surface parameter, which adjusts the convergence speed of the error dynamics, represents the power parameter, represents a non - linear function with respect to ; Design of the super - twisting integral sliding - mode observer: The estimated value of the wind - wave - current disturbance estimated by the super - twisting integral sliding - mode observer is used as the feed - forward input to cancel the influence of environmental disturbances on the trajectory tracking of the leading unmanned boat; Integrate the sliding - mode surface, tracking error, disturbance feed - forward compensation, and desired trajectory acceleration to ensure that the tracking error converges within a fixed time. The specific process of building the tracking control subsystem of the unmanned boat based on the fixed - time - convergent non - singular terminal sliding - mode controller and the super - twisting integral sliding - mode observer is as follows:

[0060] 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.

[0061] More specifically, the specific process of 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 singularity point where the denominator of the sliding - mode surface derivative is zero; 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:

[0062] where , which is the sign - 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 , ; The integral - sliding - mode - 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. At the same time, when approaches zero, the derivative of the sliding - mode surface does not contain negative - exponent terms, which avoids the singularity problem.

[0063] Specifically, in step 3) of step S3, the specific steps for building the unmanned boat formation control subsystem are as follows: 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 leading unmanned boat is received and the lag state information of the leading unmanned boat is extracted, and an adaptive time-delay estimation method is designed 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:

[0064] In the formula is the time-delay estimation value, is the adaptive gain coefficient, is the time-delay state estimation of the leading unmanned boat; Compensate for the time-delay information of the leading unmanned boat: Dynamically adjust the information of the leading unmanned boat according to the time-delay estimation value to ensure stability when the following unmanned boat performs formation control.

[0065] Specifically, in step 4) of step S3, the specific steps for building the formation control system are as follows: A non-singular terminal sliding mode surface is constructed by using fractional power parameters, and the dynamic convergence of the tracking error is realized through the linear combination of the integral error and the state estimation error. The specific design of the sliding mode surface is as follows:

[0066]

[0067]

[0068]

[0069] 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; 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; Disturbance feedforward compensation: Use the estimated wind, wave and current disturbance value 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 leading unmanned boat; Time-delay compensation: Compensate the time-delay estimated by the adaptive time-delay estimator for the time-delay information of the leading unmanned boat to resist the influence of the time-delay.

[0070] The design calculation formula for building the formation control system is:

[0071] wherein , is a positive odd number and satisfies .

[0072] S4. Verify the stability of the unmanned boat formation through simulation experiments.

[0073] According to the Figure 4 , Figure 5 , Figure 6 , Figure 7 and Figure 8 state trajectories shown, in the case of external environmental disturbances and communication time delays, the following unmanned boat and the leading unmanned boat can form a formation; in addition, through Figure 9 it can be determined that the fixed-time nonsingular terminal sliding mode leaderless unmanned boat formation control strategy set in this embodiment ensures the formation stability of the unmanned boat formation; A method for maintaining the formation of an unmanned boat under a communication time delay in this embodiment is used to solve the problem of anti-interference formation maintenance control of an unmanned boat formation under a communication time delay, and at the same time consider complex external environmental disturbances such as wind, waves, and currents; this method adopts a leader-follower formation control method and combines the position and speed information of the unmanned boat to establish an error equation for the formation position and speed between the following unmanned boat and the leading unmanned boat; in order 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 by using a super-twisting integral sliding mode observer, and a fixed-time theory and a nonsingular terminal sliding mode control are combined to design an unmanned boat formation control method, and the effectiveness and practicability of the control algorithm are proved through theoretical proof and simulation experiments.

[0074] Although the preferred embodiments of the present application have been described, those skilled in the art can make additional changes and modifications to these embodiments once they learn the basic creative concepts. Therefore, the appended claims are intended to be construed to include the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0075] 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 an unmanned boat fleet under communication delay, characterized in that: include: S1, based on the kinematics and dynamics of the three degrees of freedom of the unmanned boat in the horizontal motion of the unmanned boat, a three-degree-of-freedom motion model of the unmanned boat is constructed and converted into a state space equation; S2, according to the Fossen manual, the wind, wave and current disturbance model of the unmanned boat is constructed, and the unmanned boat motion model including environmental disturbance is constructed by combining it with the three-degree-of-freedom motion model of the unmanned boat; S3, using the leader-follower method to design the expected position of the unmanned boat according to the relative position and orientation between the unmanned boat and the pilot 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 a formation control system to achieve the formation maintenance of the unmanned boat formation; 1) Based on the unmanned boat motion model, a super-helical integral sliding mode observer is constructed to observe disturbances and compensate for them; 2) According to the deviation between the actual position and the expected position of the pilot unmanned boat, a non-singular terminal sliding mode controller is designed based on the fixed time convergence mechanism, and the super helical integral sliding mode observer is used for disturbance estimation. The unmanned boat tracking control subsystem is built to enable the pilot unmanned boat to track the expected trajectory within the preset time; 3) Use the super-helical integral sliding mode observer to estimate the wind, wave and current disturbances and model uncertainty in real time. Based on the delayed state information of the pilot unmanned boat, estimate the communication delay online, compensate for the pilot unmanned boat delay information, build an unmanned boat formation control subsystem, and solve the communication delay problem. 4) Under the communication delay, a fixed-time convergence mechanism, a non-singular terminal sliding mode controller and a super-helical integral sliding mode observer are combined to build a formation control system consisting of an unmanned boat tracking control subsystem and an unmanned boat formation control subsystem to achieve the formation maintenance of the unmanned boat formation; S4, verify the stability of the unmanned boat formation through simulation experiments.

2. The method for maintaining the formation of an unmanned boat fleet under communication delay according to claim 1 is characterized in that: In 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 moves horizontally, the three-degree-of-freedom motion model of the unmanned boat is constructed according to the kinematics and dynamics of the three degrees of freedom: surge, sway and pitch. The three-degree-of-freedom motion model of the unmanned boat is converted into a state space equation according to the conversion relationship between speed and position. The calculation formula is as follows: ； In the formula is the position-related variable in the state variable of the unmanned boat, is the speed related variable, For Speed-related variables of conversion; When, it is the pilot unmanned boat; When following the 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; in, ; ； ； ； In the formula The heading angle of the unmanned boat The associated rotation matrix, is the mass matrix, For Inverse matrix; For external environmental disturbances; is a skew-symmetric matrix, is the Coriolis force and centripetal force matrix, is the damping matrix.

3. The method for maintaining the formation of an unmanned boat fleet under communication delay according to claim 1 is characterized in that: In step S2, the unmanned boat motion model is constructed, and the specific steps are as follows: S21, build wind wave current disturbance model According to the Fossen manual, a wind-wave-current disturbance model is constructed for wind force, wave force and water flow force, including wind disturbance model, wave force disturbance model and water flow disturbance model. The specific process is as follows: ① Wind disturbance model: The six-component wind coefficient method is used to calculate the lateral and longitudinal wind components according to the windward area of ​​the unmanned boat, air density and real-time wind speed, and the wind force distribution is equivalent to the center of gravity of the unmanned boat through the torque conversion formula. The specific formula is as follows: ； In the formula Respectively represent the sum of wind forces and moments generated in the surge, sway and pitch directions; Indicates wind density in units of ; Indicates the angle between the wind direction and the bow direction of the unmanned boat; represents the wind force and moment coefficients; , and They represent the front projection area of ​​the unmanned boat hull, the side projection area above the waterline and the total length respectively; ② Wave force disturbance model: Based on the linear model of forces and moments caused by first-order and second-order waves, the wave frequency and amplitude parameters under the fourth-level sea state are used, combined with the geometric parameters of the unmanned boat hull to generate wave induced forces and moments. The specific formula is as follows: ; In the formula are the sum of wave forces and moments in the surge, sway and pitch directions, is the wave correlation coefficient, through Adjust the wave forces and moments. , 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 pitch directions are Calculated by the Wiener process: ； In the formula is Gaussian white noise; ③ Water flow force disturbance model: construct the force and moment applicable to the constant speed of water flow, decompose it into longitudinal and transverse direction components, calculate the transverse 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 use the moment conversion formula to convert the water flow force distribution to the center of gravity of the unmanned boat; ; In the formula are the sum of the forces and moments generated by the water flow in the surge, sway and pitch directions respectively; is the water flow density, in units of ; are the flow force and moment coefficients; They are the front projection area of ​​the unmanned boat hull, the side projection area above the waterline and the total length; is the angle between the unmanned boat’s forward direction and the water flow, represents the absolute flow rate; S22, build the unmanned boat motion model Disturbance coupling mechanism: The wind, wave and current forces generated in the wind disturbance model, wave disturbance model and water flow disturbance model are linearly superimposed on the three-degree-of-freedom motion model of the unmanned boat to construct an unmanned boat motion model including environmental disturbances. The specific formula is as follows: ； In the formula represents the environmental disturbance caused by wind, waves and currents; represents the sum of wind disturbance forces and moments designed by the wind disturbance model, They represent the sum of wind disturbance forces and moments generated by wind in the surge, sway and pitch directions respectively; represents the sum of the wave disturbance forces and moments designed by the wave disturbance model, , and They represent the sum of wind disturbance forces and moments generated by waves in the surge, sway and pitch directions respectively; represents the sum of the water disturbance force and moment designed by the water disturbance model, They represent the sum of the wind disturbance forces and moments generated by the water flow in the longitudinal, transverse and yaw directions respectively.

4. The method for maintaining the formation of an unmanned boat fleet under communication delay according to claim 1 is characterized in that: In step S3, the specific steps of designing the desired position of the unmanned boat using the leader-follower method are as follows: Select based on distance-angle Following mode, the desired position of the unmanned boat is designed according to the relative position and orientation between the unmanned boat and the pilot unmanned boat. The specific design process is as follows: ; The vector , Respectively represent the expected position / attitude of the i-th unmanned boat relative to the reference point in the three degrees of freedom of longitudinal, transverse and bow directions, Representative The distance parameters between the unmanned boat and the pilot unmanned boat are: Representatives and The angle between the first unmanned boat and the pilot unmanned boat is related to Representative The bow angle of the unmanned boat itself.

5. The method for maintaining the formation of an unmanned boat fleet under communication delay according to claim 1, characterized in that: In step S3 1), the specific steps of constructing the super helical integral sliding mode observer are as follows: By defining the sliding surface as a linear combination of the state error and the integral error, the superhelical integral sliding mode observer is constructed using the superhelical algorithm, and the observer gain is dynamically adjusted. The specific formula is as follows: ； In the formula , is the sliding surface, and the state error and integral error Linear combination, auxiliary variables For the observer The estimated value of For the location of the unmanned boat and speed The relevant matrix, is the integral gain, used to smooth the observation error; is the superhelical gain; is the disturbance estimate; is a symbolic function.

6. The method for maintaining the formation of an unmanned boat fleet under communication delay according to claim 1 is characterized in that: In step S3 2), the specific steps of building the unmanned boat tracking control subsystem are as follows: Design of fixed time convergence mechanism: The upper bound of convergence time is set based on Lyapunov function to ensure that the tracking error approaches zero within the preset time, regardless of the initial state. The specific design is as follows: ; Among them, the gain parameter , is a positive odd number and satisfies , , and is the fractional power expansion of the symbolic function; Design of non-singular terminal sliding mode controller: The non-singular terminal sliding mode surface is constructed using fractional power parameters, and the dynamic convergence of the tracking error is achieved through the linear combination of the integral error and the state estimation error. The specific design of the sliding mode surface is: ; In the formula It represents the tracking error between the actual position and speed of the pilot unmanned boat and the expected position and speed after the state space transformation. represents the integral sliding surface parameters, represents the power parameter, Indicates about Nonlinear function of Design of super-helical integral sliding mode observer: The estimated value of wind, wave and flow disturbance estimated by the super-helical integral sliding mode observer is used as the feedforward input to offset the influence of environmental disturbance on the trajectory tracking of the pilot unmanned boat; Based on the fixed-time convergence non-singular terminal sliding mode controller and the super-helical integral sliding mode observer, 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 perturbation estimate from the superhelical observer, is the expected acceleration.

7. The method for maintaining the formation of an unmanned boat fleet under communication delay according to claim 6 is characterized in that: The parameter selection method of the non-singular terminal sliding mode controller is as follows: Fractional power constraint: set the numerator and denominator parameters to specific odd numbers to avoid singular points where the denominator of the sliding surface derivative is zero; Disturbance boundary estimation: The disturbance boundary value is dynamically updated using the output of the super-helical integral sliding mode observer as the robustness gain parameter of the super-helical integral sliding mode observer. The specific design is: ; In the formula, , which is a signed power function, is the tracking error, is the variable of the sliding surface function, is a very small positive odd number, smooth transition parameter ; Integral sliding surface coefficient , power parameter ; When the system state is far away from the equilibrium point, It plays a major role in approaching and ensuring rapid convergence of the system; when the system state approaches the equilibrium point, plays a major role, and the system reaches a steady state within a fixed time; the system maintains a fast convergence speed in the entire dynamic process, and at the same time When it approaches zero, the derivative of the sliding surface does not contain negative exponential terms.

8. The method for maintaining the formation of an unmanned boat fleet under communication delay according to claim 1, characterized in that: In step S3 3), the specific steps of building the unmanned boat formation control subsystem are as follows: The wind, wave and current disturbances and model uncertainty are estimated in real time through the super-helical integral sliding mode observer, the hysteresis state signal of the pilot unmanned boat is received and the hysteresis state information of the pilot unmanned boat is extracted. Based on the hysteresis state information of the pilot unmanned boat, an adaptive delay estimation method is designed through the Lyapunov stability theory to estimate the communication delay online. The specific design is as follows: ； In the formula is the estimated delay value, is the adaptive gain coefficient, is the formation control error, To provide the delayed status information of the pilot unmanned boat; Compensate for the time delay information of the pilot unmanned boat: Dynamically adjust the pilot unmanned boat information according to the estimated time delay value to ensure stability when following the unmanned boat for formation control.

9. The method for maintaining the formation of an unmanned boat fleet under communication delay according to claim 1, characterized in that: In step S3 (4), the specific steps of building the formation control system are as follows: The non-singular terminal sliding surface is constructed by using fractional power parameters. The dynamic convergence of the tracking error is achieved through the linear combination of the integral error and the state estimation error. The sliding surface is specifically designed as follows: ; ; ； ； In the formula, the integral sliding surface coefficient , fractional power parameter , and is the tracking error component; is a very small positive odd number, is a piecewise function; Time convergence: The upper bound of the convergence time is set 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: The estimated value of wind, wave and flow disturbance estimated by the super-helical integral sliding mode observer is used as the feedforward input to offset the influence of environmental disturbance on the trajectory tracking of the pilot unmanned boat; Delay compensation: The delay estimated by the adaptive delay estimator is used to compensate the delay information of the pilot unmanned boat to resist the influence of the delay; The design calculation formula for building a formation control system is: ； The gain parameter , is a positive odd number and satisfies , is the disturbance estimate, It is the delayed status information.

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