A fixed-time path following control method considering input delay

Abstract

The application discloses a fixed-time path tracking control method considering input delay, comprising the following steps: constructing a nonlinear mathematical model of a USV based on input delay; improving an input delay auxiliary system according to the control input of the USV under the input delay condition; generating a USV reference course by using LVS technology, constructing a LVS guidance law to obtain the position error and the heading angle error of the USV, and obtaining the dynamics error of the USV; designing a USV position error virtual control law, introducing a DSC technology to design a fixed-time filter; calculating the derivative of the attitude error signal of the USV, and designing an attitude error virtual control law; constructing a fixed-time path tracking controller and an adaptive law based on the input delay auxiliary system, and realizing the path tracking control of the USV under the input delay condition; the application can effectively predict and compensate the influence of the input delay signal, improve the convergence performance of the system, enhance the stability of the system, solve the input delay problem of the controller, and enhance the convergence precision and the robustness against external interference of the system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of ship motion control research, and particularly relates to a fixed-time path tracking control method considering input delay. BACKGROUND

[0002] In actual ship control tasks, in order to track the real-time changing desired path, the control system needs to solve the control command in real time and transmit it to the actuator. Although the control algorithm based on MLP and DSC is used in the controller-to-actuator channel, the control input is delayed in the actual scene, and the traditional path tracking algorithm does not solve the input delay problem of the control system. In addition, the path convergence time is one of the important indicators to reflect the performance of the path tracking controller. An ideal controller should be able to drive the ship from the current position to the preset coordinates within the desired time and complete the path tracking task with a specific attitude. At present, most control researches are carried out with the goal of asymptotic stability of the system. The time required for the system to converge from the initial state to the vicinity of the equilibrium point is theoretically infinite. In view of the above shortcomings, the generation of the fixed-time theory breaks this bondage. It not only has the performance of fast convergence but also the convergence time is independent of the initial state. Therefore, the research on the path tracking controller based on the fixed-time theory is more in line with engineering application.

[0003] Based on the above analysis, the existing path tracking control algorithm has the following two defects:

[0004] 1) The existing control strategy based on MLP and DSC does not consider the delay problem existing in actual signal transmission. If such an algorithm is directly applied, the control algorithm will not be able to compensate for system uncertainties and external disturbances in real time, which will lead to a decrease in the performance of the closed-loop control system or even divergence, which is not conducive to the engineering application of the algorithm.

[0005] 2) The traditional asymptotically stable path tracking control strategy is theoretically an infinite time convergence strategy, which cannot guarantee the demand for immediate control of ship motion in actual engineering, and is seriously dependent on the initial motion state of the ship, and the robustness is general. SUMMARY

[0006] The present application provides a fixed-time path tracking control method considering input delay to overcome the technical problems that the existing path tracking control algorithm does not consider the delay problem existing in actual signal transmission, cannot compensate for system uncertainties and external disturbances in real time, is seriously dependent on the initial motion state of the ship, the robustness is general, and cannot guarantee the demand for immediate control of ship motion in actual engineering.

[0007] In order to achieve the above purpose, the technical scheme of the present application is:

[0008] A fixed-time path tracking control method considering input delay, comprising:

[0009] S1: constructing a nonlinear mathematical model of the USV based on input delay as a subsequent controlled object; improving the input delay auxiliary system according to the control input of the USV under input delay to obtain an improved input delay auxiliary system;

[0010] S2: generating a reference route of the USV using LVS technology, constructing a LVS guidance law according to the reference route, and obtaining a position error and a heading angle error of the USV according to the LVS guidance law, and simultaneously obtaining a dynamics error of the USV under the improved input delay auxiliary system;

[0011] S3: designing a USV position error virtual control law, introducing DSC technology, and designing a fixed-time filter according to the USV position error virtual control law;

[0012] S4: calculating a derivative of an attitude error signal of the USV according to the dynamics error of the USV, the fixed-time filter, the position error and the heading angle error, and designing an attitude error virtual control law;

[0013] S5: constructing a fixed-time path tracking controller and an adaptive law based on the input delay auxiliary system according to the nonlinear mathematical model of the USV based on input delay, the improved input delay auxiliary system, the dynamics error of the USV and the fixed-time filter;

[0014] S6: realizing path tracking control of the USV under input delay according to the fixed-time path tracking controller of the input delay auxiliary system and the adaptive law based on the input delay auxiliary system.

[0015] Further, a nonlinear mathematical model of the USV based on input delay is constructed, the nonlinear mathematical model of the USV based on input delay is shown in formula (1),

[0016]

[0017] In the formula, x, y represent the position coordinates of the USV, ψ represents the heading angle of the USV, u, v, r respectively represent the forward speed, the transverse drift speed and the yaw angle speed of the ship, θ u , θ v , θ r are unknown time-varying functions of the forward, transverse drift and yaw degrees of freedom, f u (u), f v (v), f r (r) are known smooth nonlinear functions of the forward, transverse drift and yaw degrees of freedom, g u (v), g r (v) are control gains in the forward and yaw directions, dwu ,d wv ,d wr is the non-structured uncertainty of the measurement noise due to the ocean environment disturbance; T u (t-ξ),T r (t-ξ) represent the control inputs in the surge and yaw directions respectively under the input delay condition; ξ represents the time of the input delay.

[0018] Further, the input delay auxiliary system is improved according to the control inputs of the USV under the input delay condition, and an improved input delay auxiliary system is obtained, and the improved input delay auxiliary system comprises:

[0019] The input delay auxiliary system is improved according to the control inputs of the USV under the input delay condition, and the improved input delay auxiliary system is shown in formula (2),

[0020]

[0021] wherein, T i (t-ξ),i=u,r represent the control inputs in the surge and yaw directions under the delay condition, w u ,w r represent state variables in the input delay auxiliary system, and the initial value is zero; c u , c r represent design parameters of the surge and yaw degrees of freedom respectively, w u , w r represent state variables in the input delay auxiliary system of the surge and yaw degrees of freedom.

[0022] Further, the reference course of the USV is generated by using the LVS technology, the LVS guidance law is constructed according to the reference course, the position error and the heading angle error of the USV are obtained according to the LVS guidance law, and the dynamic error of the USV under the improved input delay auxiliary system is obtained, and the method comprises:

[0023] S21, the LVS guidance law is shown in formula (3),

[0024]

[0025] wherein, x d , y d represent the position coordinates of the LVS, ψ d represents the heading angle of the LVS, r d represents the expected yaw angular velocity of the LVS, u d represents the expected surge velocity.

[0026] S22, the position error and the heading angle error of the USV are obtained according to the LVS guidance law, and the position error and the heading angle error of the USV are shown in formula (4),

[0027]

[0028] where x e ,y e ,ψ e are position error and yaw error of the USV, J(ψ) is the rotation matrix related to the yaw angle, x, y, ψ represent the position coordinates and yaw angle of the USV in the earth coordinate system respectively;

[0029] S23, the dynamics error of the USV under the improved input delay auxiliary system is obtained, as shown in formula (5),

[0030]

[0031] Formula (5) represents the dynamics error after the input delay auxiliary system processing; represents the attitude error signal; u e represents the dynamics error of the forward freedom degree, r e represents the dynamics error of the yaw freedom degree, β u ,β r , represents the time signal after DSC filtering.

[0032] Further, a USV position error virtual control law is designed, DSC technology is introduced, and a fixed time filter is designed according to the USV position error virtual control law, including:

[0033] S31, in order to stabilize the USV position error, a USV position error virtual control law is designed, as shown in formula (6),

[0034]

[0035] wherein, is a design parameter, α u represents the virtual control law for stabilizing the position error x e , represents the virtual control law for stabilizing the position error y e , and v represents the transverse drift speed of the ship;

[0036] S32, DSC technology is introduced, and a fixed time filter is designed according to the USV position error virtual control law, and the fixed time filter is as shown in formula (7),

[0037]

[0038] wherein, t u , t r is a time constant, βu ,β r , is the time signal filtered by DSC; is the time signal filtered by the fixed time filter; α r is the attitude error signal is the virtual control law of the attitude error.

[0039] Further, the derivative of the attitude error signal of the USV is calculated according to the dynamic error of the USV, the fixed time filter, the position error and the heading error, and a virtual control law of the attitude error is designed, including:

[0040] S51, the derivative of the attitude error signal is obtained in combination with formulas (4), (5) and (7), as shown in formula (8),

[0041]

[0042] S52, a virtual control law of the attitude error is designed according to the attitude error signal of the USV and the derivative of the attitude error signal, as shown in formula (9),

[0043]

[0044] In the formula, k c2 is a design parameter, α r represents the virtual control law of the attitude error.

[0045] Further, the fixed time path tracking controller and adaptive law based on the input delay auxiliary system are constructed according to the nonlinear mathematical model of the USV based on the input delay, the improved input delay auxiliary system, the dynamic error of the USV and the fixed time filter, including:

[0046] The fixed time path tracking controller and adaptive law based on the input delay auxiliary system are constructed in combination with formulas (1), (2), (5), (7) and considering the input delay, as shown in formulas (10) and (11),

[0047]

[0048] In the formula, i=u,r is a controller design parameter, i=u,r represents a gain adaptive design parameter; T i represents the control input of the USV without delay, g i represents a non-zero control gain in the forward and yaw directions, ε i represents a design parameter, denotes a smooth function, denotes the control input of the fixed-time path following controller based on the input delay auxiliary system, denotes a time-varying function i adaptive law, denotes the adaptive law of the non-structural uncertainty term d wi adaptive law, f i (v) denotes a smooth nonlinear function as the forward, lateral drift and yaw freedom.

[0049] Beneficial effects: the present application provides a fixed-time path tracking control method considering input delay, improves the input delay auxiliary system, predicts and compensates the influence of the delay signal, ensures that the control command is timely delivered to the actuator, thereby eliminating the influence of input delay on system performance; a fixed-time filter is designed, a filtered signal is used instead of a virtual control signal, the "complexity explosion problem" caused by derivation of the virtual control law in the traditional Backstepping method is solved, the calculation amount in the process of designing the virtual control law is simplified, the structure of the controller is simpler, and the precision of real-time control of ship movement in actual engineering is ensured; a fixed-time path tracking controller and adaptive law based on the input delay auxiliary system are designed, which solves the problem of unknown non-structural uncertainty term and control gain in the model, and makes the signals in the closed-loop system realize fixed-time convergence. BRIEF DESCRIPTION OF DRAWINGS

[0050] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0051] Figure 1 The method flow chart of the fixed-time path tracking control method considering input delay provided by the present application;

[0052] Figure 2 The fixed-time path tracking control structure diagram of the USV of the present application;

[0053] Figure 3 The trajectory comparison curve diagram of the present application compared with the prior art in an embodiment;

[0054] Figure 4 The error change curve diagram of the present application compared with the prior art in an embodiment;

[0055] Figure 5 The control input change curve diagram of the present application compared with the prior art in an embodiment;

[0056] Figure 6 Input delay auxiliary system curve diagram for comparing the present application with prior art in an embodiment;

[0057] Figure 7 Controller adaptive parameter curve diagram for comparing the present application with prior art in an embodiment. DETAILED DESCRIPTION

[0058] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some 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 labor fall within the scope of protection of the present application.

[0059] The present embodiment provides a fixed-time path tracking control method considering input delay, as shown in Figure 1 , which comprises:

[0060] S1: Construct a nonlinear mathematical model of the USV based on input delay as a subsequent controlled object; improve the input delay auxiliary system according to the control input of the USV under input delay to obtain an improved input delay auxiliary system;

[0061] S2: Generate a reference course of the USV using LVS technology, construct a LVS guidance law according to the reference course, and obtain the position error and heading angle error of the USV according to the LVS guidance law, while obtaining the dynamic error of the USV under the improved input delay auxiliary system;

[0062] S3: Design a USV position error virtual control law, introduce DSC technology, and design a fixed-time filter according to the USV position error virtual control law;

[0063] S4: Calculate the derivative of the attitude error signal of the USV according to the dynamic error of the USV, the fixed-time filter, the position error and the heading angle error, and design an attitude error virtual control law;

[0064] S5: Construct a fixed-time path tracking controller based on input delay auxiliary system and an adaptive law according to the nonlinear mathematical model of the USV based on input delay, the improved input delay auxiliary system, the dynamic error of the USV and the fixed-time filter;

[0065] S6: Realize path tracking control of the USV under input delay according to the fixed-time path tracking controller of the input delay auxiliary system and the adaptive law based on the input delay auxiliary system.

[0066] Specifically, first, a nonlinear mathematical model of the USV based on input delay is constructed as a subsequent controlled object; an input delay auxiliary system is improved according to the control input of the USV under the input delay condition to obtain an improved input delay auxiliary system, the input delay auxiliary system can effectively predict and compensate the influence of the input delay signal, ensure that the control command can be timely transmitted to the actuator, and thus eliminate the negative influence of the input delay on the system performance; secondly, a reference route of the USV is generated using the LVS technology, a LVS guidance law is constructed according to the reference route, and the position error and the heading angle error of the USV are obtained according to the LVS guidance law, and meanwhile, the dynamic error of the USV under the improved input delay auxiliary system is obtained; the guidance law can balance the uncertainty caused by the error, and can make the USV more accurately track the preset path; a USV position error virtual control law is designed, the DSC technology is introduced, and a fixed-time filter is designed according to the USV position error virtual control law; through the virtual control law, the position coordinates, the speed size and the direction of the ship at different time points and other data can be obtained, the fixed-time filter is designed to use the filtered signal to replace the virtual control signal, the “complexity explosion problem” caused by the derivation of the virtual control law in the traditional Backstepping method is solved, and the calculation of the designed filter is simplified; thirdly, the derivative of the attitude error signal of the USV is calculated according to the dynamic error of the USV, the fixed-time filter, the position error and the heading angle error, an attitude error virtual control law is designed, a control law with low calculation load and fixed-time convergence is designed, and the rapid convergence of the USV to the expected geometric formation and the reference path is realized; a fixed-time path tracking controller and an adaptive law based on the input delay auxiliary system are constructed according to the nonlinear mathematical model of the USV based on input delay, the improved input delay auxiliary system, the dynamic error of the USV and the fixed-time filter, for the tracking control problem of the real ship, the error signal is modified by using fractional power, so that the kinematics loop and the dynamics loop of the underactuated ship reach double-ring fixed-time convergence, and the convergence accuracy and the robustness against external interference of the system are enhanced; finally, the path tracking control of the USV under the input delay is realized according to the fixed-time path tracking controller of the input delay auxiliary system and the adaptive law based on the input delay auxiliary system.

[0067] In specific embodiments, the scheme of constructing a nonlinear mathematical model of the USV based on input delay as a subsequent controlled object, and improving an input delay auxiliary system according to the control input of the USV under the input delay condition to obtain an improved input delay auxiliary system is as follows:

[0068] The nonlinear mathematical model of the USV based on input delay is shown in formula (12),

[0069]

[0070] where x, y represent the position coordinates of the USV in the earth coordinate system, ψ represents the heading angle of the USV, u, v, r represent the forward velocity, the cross drift velocity and the yaw angular velocity of the ship respectively, θ u , θ v , θ r are unknown time-varying functions of the forward, cross drift and yaw degrees of freedom, f u (u), f v (v), f r (r) are known smooth nonlinear functions of the forward, cross drift and yaw degrees of freedom, g u (v), g r (v) are unknown nonzero control gains in the forward and yaw directions, d wu , d wv , d wr are the ocean environment disturbances, the unstructured uncertain terms of measurement noise; T u (t-ξ), T r (t-ξ) represent the control inputs in the forward and yaw directions under the condition of input delay, respectively; ξ represents the time of input delay;

[0071] The input delay auxiliary system is improved according to the control input of the USV under the condition of input delay, and the improved input delay auxiliary system is shown in formula (13),

[0072]

[0073] where T i (t-ξ), i = u, r represent the control inputs in the forward and yaw directions under the condition of delay, w u , w r represent state variables in the input delay auxiliary system, and the initial values are zero; c u , c r represent design parameters of the forward and yaw degrees of freedom, respectively, w u , w r represent state variables in the input delay auxiliary system of the forward and yaw degrees of freedom, and the initial values are zero, and if the input signal has no delay, they will always remain zero values during the system operation.

[0074] The input delay auxiliary system can effectively predict and compensate the influence of the input delay signal, ensure that the control command can be timely transmitted to the actuator, and thus eliminate the negative influence of the input delay on the system performance; in the embodiment, the traditional delay auxiliary system is improved according to the control input of the ship, and the influence of the input delay of the ship on the system can be targetedly eliminated.

[0075] In specific embodiments, the reference course of the USV is generated using the LVS technology, the LVS guidance law is constructed according to the reference course, the position error and the heading angle error of the USV are obtained according to the LVS guidance law, and the dynamics error of the USV under the improved input delay auxiliary system is obtained, and the scheme is as follows:

[0076] S21, generating a reference course of the USV using the LVS technology;

[0077] S22, constructing a LVS guidance law according to the reference course, the LVS guidance law being shown in formula (14),

[0078]

[0079] wherein x d ,y d , and ψ d represent the position coordinates of the LVS, r d represents the desired yaw angle velocity of the LVS, u d represents the desired forward velocity;

[0080] S23, obtaining the position error and the heading angle error of the USV according to the LVS guidance law, the position error and the heading angle error of the USV being shown in formula (15),

[0081]

[0082] wherein x e ,y e , and ψ e are the position error and the heading angle error of the USV, J(ψ) is a rotation matrix related to the heading angle, x, y, and ψ represent the position coordinates and the heading angle of the USV in the geodetic coordinate system, respectively;

[0083] S24, obtaining the dynamics error of the USV under the improved input delay auxiliary system, as shown in formula (16),

[0084]

[0085] Formula (16) represents the dynamics error processed by the input delay auxiliary system; represents the attitude error signal; u e represents the dynamics error of the forward degree of freedom, r e represents the dynamics error of the yaw degree of freedom, β u , β r , represents the time signal filtered by the DSC, and at this time, the motion state of the USV control system is non-delayed.

[0086] In this embodiment, the method of generating a reference path according to the LVS technology is referred to, reference document Zhang G, Zhang X. Concise robust adaptive path-following control of underactuated ships using DSC and MLP [J]. IEEE Journal of Oceanic Engineering, 2013, 39(4): 685-694. The guidance law is obtained according to the reference path, which can balance the uncertainty caused by the error and make the USV more accurately track the preset path.

[0087] In a specific embodiment, a USV position error virtual control law is designed, and a DSC technology is introduced. The scheme for designing a fixed-time filter according to the USV position error virtual control law is as follows:

[0088] S31, in order to stabilize the USV position error, a USV position error virtual control law is designed, as shown in formula (17),

[0089]

[0090] In the formula, is a positive design parameter, and α u represents the virtual control law for stabilizing the position error x e , represents the virtual control law for stabilizing the error y e , and v represents the lateral drift speed of the ship; the reference path is generated by a virtual ship, in which the expected forward speed u d = 3 m / s;

[0091] S32, in order to avoid the complexity explosion caused by repeated differentiation of the virtual controller, a DSC technology is introduced, and a fixed-time filter is designed according to the USV position error virtual control law, the fixed-time filter is as shown in formula (18),

[0092]

[0093] In the formula, t u , t r is a time constant greater than zero, β u , β r , is a time signal filtered by DSC; represents the time signal of the fixed-time filter; α r is a virtual control law of the attitude error signal .

[0094] In this embodiment, a virtual control law is designed, through which the position coordinates, speed size and direction of the ship at different time points can be obtained, a fixed time filter is designed to replace the virtual control signal with a filtered signal, the "complexity explosion problem" caused by derivation of the virtual control law in the traditional Backstepping method is solved, the calculation amount in the process of designing the virtual control law is simplified, the structure of the controller is simpler, and the precision of the instantaneous control of the ship in the actual engineering is ensured.

[0095] In specific embodiments, a derivative of an attitude error signal of the USV is calculated according to the dynamic error of the USV, the fixed time filter, the position error and the heading error, and a scheme of designing an attitude error virtual control law is:

[0096] S51, in combination with formulas (15), (16) and (18), a derivative of an attitude error signal is obtained, as shown in formula (19),

[0097]

[0098] S52, an attitude error virtual control law is designed according to the attitude error signal of the USV and the derivative of the attitude error signal, as shown in formula (20),

[0099]

[0100] In the formula, k c2 is a positive design parameter, and α r represents the attitude error virtual control law.

[0101] In this embodiment, a control law with low calculation load and fixed time convergence is designed, and rapid convergence of the USV to the expected geometric formation and the reference path is realized.

[0102] In specific embodiments, a fixed time path tracking controller and an adaptive law based on the input delay auxiliary system are constructed according to the nonlinear mathematical model of the USV based on the input delay, the improved input delay auxiliary system, the dynamic error of the USV and the fixed time filter, including:

[0103] In combination with formulas (12), (13), (16) and (18), a fixed time path tracking controller and an adaptive law based on the input delay auxiliary system are constructed by considering the input delay, as shown in formulas (21) and (22),

[0104]

[0105] In the formula, i=u,r are positive controller design parameters, i=u, r represents the positive gain adaptive design parameter; T i Indicates the USV control input without delay, g i Denotes the non-zero control gain for forward and yaw directions, ε i represents the design parameters, represents a smooth function, represents the control input of the fixed-time path tracking controller for the input-delay-based auxiliary system, represents the time-varying function θ i The adaptive law of represents the non-structural uncertainty term d wi The adaptive law, f i (v) is expressed as a smooth nonlinear function of the forward, drift and pitch degrees of freedom.

[0106] In this embodiment, a fixed-time path tracking controller and adaptive law are designed to address the tracking control problem of a real ship. Fractional powers are used to modify the error signal, so that the kinematic loop and dynamic loop of the underactuated ship achieve dual-loop fixed-time convergence, enhancing the system's convergence accuracy and robustness against external interference.

[0107] In a specific embodiment, according to the fixed-time path tracking controller of the input delay auxiliary system and the adaptive law based on the input delay auxiliary system, the solution for implementing the path tracking control of the USV under input delay is:

[0108] The USV fixed time path tracking control process is as follows Figure 2 As shown, the whole system is divided into guidance module, control module and navigation module;

[0109] The guidance module takes waypoints as input, generates a desired route based on the waypoints, and generates guidance laws based on the LVS to obtain the LVS position coordinates, heading angle, and desired forward speed.

[0110] The control module multiplies the acquired coordinates, heading angle, and desired forward speed with the USV's position coordinates and heading angle acquired by GPS, performs coordinate conversion, obtains the position error, and obtains a virtual control law based on the position error. The data is then input into the improved input delay auxiliary system. The state variables in the input delay auxiliary system for forward and yaw degrees of freedom are input into the fixed-time path tracking controller, and the adaptive law of the control module design parameters is also implemented.

[0111] The navigation module controls the underactuated surface vessel based on a fixed-time path tracking controller and an adaptive law.

[0112] In order to verify the advantages and effectiveness of the application in solving input delay, numerical comparison simulation is carried out under simulated external marine environment. The application and the path tracking control technology based on DSC and MLP are compared and simulated under simulated external marine environment, and the difference is shown in Table 1,

[0113] Table 1 Similarities and differences between the method of the application and the prior art

[0114] Indicator Fixed time control Input delay assistance system Uniform ultimate boundedness Method of the invention Yes Yes Yes Prior art No No Yes

[0115] The method of the application and the prior art are compared and simulated on an industrial computer (Intel(R) Core(TM) i5-7300 HQ CPU @ 2.50 GHz, RAM: 8.00 GB), Figures 3-5 The main comparison results are shown, where algorithm A represents the prior art:

[0116] Figure 3 The path tracking trajectory comparison results of the two methods are shown, although both methods achieve satisfactory path tracking, the trajectory curve convergence speed of the method of the application is faster in the initial stage due to the good convergence performance of the fixed-time controller, as can be seen from the enlarged view, the tracking accuracy of the algorithm of the application is also higher, and the convergence speed of the prior art is slower;

[0117] Figure 4 The error curves of the two methods are described, as can be seen from the figure, the algorithm error of the application is relatively small and more stable, the position error and heading angle error between the real ship and the virtual ship can quickly converge to a small range near zero, having good transient and steady-state performance, which is the advantage of fixed-time control, and the error of the prior art is larger;

[0118] Figure 5 The control input change curves of the two methods are shown, as can be seen from the figure, the control input of the method of the application is more stable than that of the prior art, in addition, due to the effect of the input delay auxiliary system, the input delay problem is effectively solved, while the prior art cannot handle such problems;

[0119] Figure 6 The change curve of the input delay auxiliary system is shown, Figure 7 The adaptive parameter change curve of the controller is shown, due to the modification of the fractional power of the fixed time, the curve has the phenomenon of up and down oscillation, but it will eventually converge near the zero neighborhood.

[0120] Based on the existing path tracking control technology based on MLP and DSC, the following 3 beneficial effects are achieved in the control field:

[0121] 1) Compared with existing control algorithms, the method proposed in the present application has significant advantages in many aspects. First, the input delay auxiliary system adopted can effectively predict and compensate the influence of the input delay signal, ensuring that the control command can be timely delivered to the actuator, thereby eliminating the negative impact of input delay on system performance. This feature enables the USV to maintain high efficiency in a delay environment. Second, the designed fixed-time path tracking controller not only has fast convergence performance but also has convergence time independent of the initial state, which not only improves the convergence performance of the system but also significantly enhances the stability of the system.

[0122] Therefore, the fixed-time path tracking controller based on the input delay auxiliary system designed in the present application not only effectively solves the input delay problem of the controller, but also enhances the convergence accuracy and robustness against external disturbances of the system. By combining these two advanced technologies, the controller of the present application exhibits excellent performance and stability in various complex environments.

[0123] 2) Further, the fixed-time path tracking controller with input delay enables the USV to maintain good response characteristics even in the presence of input delay. Input delay often affects the response speed and accuracy of the ship, especially when rapid adjustment of the heading or avoidance of obstacles is required. The input delay auxiliary system ensures delay compensation during the transmission of the control signal, enabling the system to respond quickly to changes in instructions and avoiding adverse effects caused by input delay, improving the safety and stability of the operation, and optimizing the operation efficiency and dynamic performance of the USV. Existing control algorithms may take an infinite time to converge from the initial state to the vicinity of the equilibrium point when the initial position is far from the target path, which affects the convergence speed and performance of the system. The fixed-time path tracking controller solves this problem and can better and faster converge to the desired position regardless of the initial position.

[0124] 3) Numerical simulation verifies that the method of the present application can achieve excellent control performance in the task of fixed-time path tracking control of USV, not only solving the shortcomings of traditional control algorithms in input delay processing, but also significantly improving the adaptability and reliability of the system in complex environments, providing a more efficient, safe and stable solution for the field of USV motion control. USV has broad application prospects in modern marine logistics, global trade, large-scale ocean engineering, etc. Underactuated ship systems are widely used in actual ocean engineering and have the advantage of high economic benefit. The present application can accelerate the transformation of USV to be more intelligent, more energy-efficient and safer.

[0125] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, and are not intended to limit the present application; although the present application has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions recorded in the above embodiments can be modified, or some or all of the technical features can be replaced by equivalents; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A fixed-time path following control method that takes into account input delays, characterized by, Comprise: S1: Construct a nonlinear mathematical model of USV based on input delay as a subsequent controlled object; the nonlinear mathematical model of USV based on input delay is shown in formula (1), （1） wherein, denotes the position coordinates of the USV, denotes the heading angle of the USV, denote the forward speed, the sway speed and the yaw angular speed of the vessel, respectively, are unknown time-varying functions of the forward, sway and yaw degrees of freedom, , , are known smooth nonlinear functions of the forward, sway and yaw degrees of freedom, are control gains in the forward and yaw directions, is the ocean environment disturbance, a non-structured uncertainty term of the measurement noise; denote the control inputs in the forward and yaw directions, respectively, in the presence of input delays; denotes the time of the input delays. According to the control input of USV under input delay, improve the input delay auxiliary system to obtain an improved input delay auxiliary system, as shown in formula (2), （2） wherein denotes the control input in the forward and yawing direction with delay, , denote the design parameters for the forward and yawing degree of freedom, respectively, , denote the state variables in the input delay aided system for the forward and yawing degree of freedom, respectively; S2: Generate a reference route of USV using LVS technology, construct a LVS guidance law according to the reference route, and obtain the position error and heading angle error of USV according to the LVS guidance law, and at the same time obtain the dynamics error of USV under the improved input delay auxiliary system; S3: Design a USV position error virtual control law, introduce DSC technology, and design a fixed time filter according to the USV position error virtual control law, the specific steps are as follows: S31, in order to stabilize the USV position error, design a USV position error virtual control law, as shown in formula (3), （3） wherein are design parameters, denotes a virtual control law that stabilizes the position error denotes a virtual control law that stabilizes the position error denotes a virtual control law that stabilizes the position error denotes a virtual control law that stabilizes the position error denotes the cross drift velocity of the vessel; denotes the desired forward velocity; are the position error and the heading angle error of the USV; S32, introduce DSC technology, and design a fixed time filter according to the USV position error virtual control law, the fixed time filter is shown in formula (4), （4） wherein is a time constant, is a time signal filtered by a DSC filter; , , denotes a time signal of a fixed time filter; is a virtual control law for the attitude error signal . S4: Calculate the derivative of the attitude error signal of USV according to the dynamics error of USV, the fixed time filter, the position error and the heading angle error, and design an attitude error virtual control law; S5: Construct a fixed time path tracking controller and adaptive law based on input delay auxiliary system according to the nonlinear mathematical model of USV based on input delay, the improved input delay auxiliary system, the dynamics error of USV and the fixed time filter; S6: According to the fixed time path tracking controller of input delay auxiliary system and the adaptive law based on input delay auxiliary system, realize the path tracking control of USV under input delay.

2. The fixed-time path-following control method considering input delay according to claim 1, characterized by, Generate a reference route of USV using LVS technology, construct a LVS guidance law according to the reference route, and obtain the position error and heading angle error of USV according to the LVS guidance law, and at the same time obtain the dynamics error of USV under the improved input delay auxiliary system, comprising: S21, the LVS guidance law is shown in formula (5), （5） wherein, represents the position coordinates of the LVS, represents the heading angle of the LVS, represents the desired yaw rate of the LVS, represents the desired forward speed; S22, obtain the position error and heading angle error of USV according to the LVS guidance law, the position error and heading angle error of USV are shown in formula (6), （6） wherein is the position error and the heading error of the USV, is the rotation matrix related to the heading angle, respectively represent the position and the heading angle of the USV in the geodetic coordinate system. S23, obtain the dynamics error of USV under the improved input delay auxiliary system, as shown in formula (7), （7） Equation (5) represents the dynamics error after the input delay auxiliary system processing; represents the attitude error signal; represents the dynamics error of the forward freedom, represents the dynamics error of the yaw freedom, represents the time signal after DSC filtering.

3. The fixed-time path-following control method considering input delay according to claim 2, characterized by, According to the dynamics error of USV, the fixed time filter, the position error and the heading angle error, calculate the derivative of the attitude error signal of USV, and design an attitude error virtual control law, comprising: S51, combined with formula (4), (6) and (7), the derivative of the attitude error signal is obtained, as shown in formula (8), （8） S52, a pose error signal of the USV and a derivative of the pose error signal to design a pose error virtual control law as shown in equation (9), （9） wherein are design parameters, denotes the attitude error virtual control law.

4. The fixed-time path-following control method that takes into account input delay according to claim 3, characterized by, According to the input delay based USV nonlinear mathematical model, the improved input delay auxiliary system, the dynamics error of the USV and the fixed time filter, a fixed time path tracking controller and adaptive law based on the input delay auxiliary system are constructed, comprising: In combination with formulas (1), (2), (4) and (7), the fixed time path tracking controller and adaptive law based on the input delay auxiliary system are constructed by considering the input delay, as shown in formulas (10) and (11), In combination with formulas (1), (2), (4) and (7), the fixed time path tracking controller and adaptive law based on the input delay auxiliary system are constructed by considering the input delay, as shown in formulas (10) and (11), （10） （11） where is the controller design parameter, denotes the gain adaptive design parameter; denotes the USV control input without delay, denotes the non-zero control gain for the forward and yaw directions, denotes the design parameter, denotes the smooth function, denotes the control input of the fixed-time path following controller based on the input delay auxiliary system, denotes the time-varying function adaptive law, denotes the adaptive law for the unstructured uncertainty term denotes the adaptive law for the structured uncertainty term, denotes the smooth nonlinear function for the forward, sway, and yaw degrees of freedom.

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