Fixed time path tracking control method considering input delay

Abstract

The invention discloses a fixed time path tracking control method considering input delay. The method comprises the following steps: constructing a USV nonlinear mathematical model based on input delay; the input delay auxiliary system is improved according to the control input of the USV under the input delay condition; generating a USV reference route by using an LVS technology, constructing an LVS guidance law to obtain a position error and a heading angle error of the USV, and obtaining a dynamic error of the USV; designing a USV position error virtual control law, and 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 based on an input delay auxiliary system and an adaptive law, and realizing path tracking control of the USV under the input delay; the influence of the input delay signal can be effectively predicted and compensated, the convergence performance of the system is improved, the stability of the system is enhanced, the problem of input delay of the controller is solved, and the convergence precision of the system and the robustness of resisting external interference are enhanced.

Description

Technical Field

[0001] The present invention relates to the technical field of ship motion control research, and in particular to a fixed-time path tracking control method considering input delay. Background Art

[0002] In actual ship control tasks, in order to track the desired route that changes in real time, 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, there is a delay in the control input in the actual scenario, 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 that reflect the performance of the path tracking controller. The ideal controller should be able to drive the ship from the current position to the preset coordinates within the expected time and complete the path tracking task with a specific posture. At present, most control research is 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 equilibrium point is theoretically infinite. In view of the above shortcomings, the emergence of fixed time theory breaks this constraint. It not only has the performance of fast convergence but also the convergence time is independent of the initial state. Therefore, the study of path tracking controller based on fixed time theory is more in line with engineering applications.

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

[0004] 1) The existing control strategies based on MLP and DSC do not take into account the delay problem existing in actual signal transmission. If such algorithms are directly applied, the control algorithms will not be able to compensate for system uncertainty and external interference in real time, which will lead to the performance degradation or even divergence of the closed-loop control system, and the engineering application of the algorithm will not be utilized.

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

[0006] The present invention provides a fixed-time path tracking control method taking input delay into consideration, so as to overcome the technical problems that the existing path tracking control algorithm fails to take into consideration the delay problem existing in actual signal transmission, cannot compensate for system uncertainty and external interference in real time, is heavily dependent on the initial motion state of the ship, has relatively general robustness, and cannot guarantee the technical problems of the demand for real-time control of ship motion in actual engineering.

[0007] In order to achieve the above object, the technical solution of the present invention is:

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

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

[0010] S2: Generate a reference route of the USV using the LVS technology, construct an LVS guidance law according to the reference route, obtain a position error and a heading angle error of the USV according to the LVS guidance law, and simultaneously obtain a dynamic error of the USV under the improved input delay auxiliary system;

[0011] S3: Design a virtual control law for USV position error, introduce DSC technology, and design a fixed time filter according to the virtual control law for USV position error;

[0012] S4: calculating 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 designing an attitude error virtual control law;

[0013] S5: constructing a fixed-time path tracking controller and an adaptive law based on an input delay auxiliary system 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;

[0014] S6: Implement 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] Furthermore, 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 USV, ψ represents the heading angle of USV, u, v, r represent the forward speed, drift speed and bow angular velocity of the ship respectively, and θ u ,θ v ,θ r is the unknown time-varying function of the forward, drift and pitching degrees of freedom, f u (u), f v (v), f r (r) is a known smooth nonlinear function of the forward, drift and pitch degrees of freedom, g u (v),g r (v) is the control gain for forward and yaw directions, dwu ,d wv ,d wr is the unstructured uncertainty of the ocean environment disturbance and measurement noise; T u (t-ξ),T r (t-ξ) represents the control input of the forward and yaw directions under the condition of input delay, respectively; ξ represents the time of input delay.

[0018] Furthermore, the input delay auxiliary system is improved according to the control input of the USV under the input delay condition, and the improved input delay auxiliary system is obtained, including:

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

[0020]

[0021] Among them, T i (t-ξ), i = u, r represents the control input for the forward and yaw directions under delay conditions, w u ,w r represents the state variable in the input delay auxiliary system, with an initial value of zero; c u , c r denote the design parameters of forward and yaw freedom, respectively, w u , w r State variables in the input-delay auxiliary system representing the forward and yaw degrees of freedom.

[0022] Furthermore, the reference route of the USV is generated using the LVS technology, the LVS guidance law is constructed according to the reference route, and the position error and 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, including:

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

[0024]

[0025] Among them, x d ,y d represents the position coordinates of LVS, ψ d represents the heading angle of LVS, r d represents the desired yaw angular velocity of LVS, u d Indicates the expected forward speed;

[0026] S22. Obtain the position error and heading angle error of the USV according to the LVS guidance law. The position error and heading angle error of the USV are as shown in formula (4):

[0027]

[0028] In the formula, x e ,y e ,ψ e is the position error and heading angle error of USV, J(ψ) is the rotation matrix related to the heading angle, x, y, ψ represent the position coordinates and heading angle of USV in the geodetic coordinate system respectively;

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

[0030]

[0031] Formula (5) represents the dynamic error after being processed by the input delay assistance system; Represents the attitude error signal; u e represents the dynamic error of the forward degree of freedom, r e represents the dynamic error of the yaw degree of freedom, β u ,β r , Represents the time signal after DSC filtering.

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

[0033] S31. To stabilize the USV position error, a virtual control law for the USV position error is designed, as shown in formula (6):

[0034]

[0035] In the formula, is the design parameter, α u Denotes the stabilization position error x e The virtual control law, Denotes the stabilization position error y e The virtual control law is: v represents the ship's transverse drift speed;

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

[0037]

[0038] Where, t u , t r is the time constant, βu ,β r , is the time signal after DSC filtering; represents the time signal of the fixed time filter; α r is the attitude error signal Virtual control law.

[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 angle error, and the attitude error virtual control law is designed, including:

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

[0041]

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

[0043]

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

[0045] Furthermore, a fixed-time path tracking controller and an adaptive law based on an 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, including:

[0046] Combining formulas (1), (2), (5), 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).

[0047]

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

[0049] Beneficial effects: The present invention provides a fixed-time path tracking control method taking input delay into consideration, improves the input delay auxiliary system, predicts and compensates for the influence of delayed signals, ensures that control instructions are transmitted to the actuator in a timely manner, and thus eliminates the influence of input delay on system performance; designs a fixed-time filter, uses filtered signals instead of virtual control signals, solves the "complexity explosion problem" caused by the derivation of virtual control laws in traditional Backstepping methods, simplifies the amount of calculation in the process of designing virtual control laws, makes the structure of the controller simpler, and ensures the accuracy of real-time control of ship motion in actual engineering; designs a fixed-time path tracking controller and adaptive law based on an input delay auxiliary system, while solving the problems of non-structural uncertainties and unknown control gains in the model, so that the signals in the closed-loop system achieve fixed-time convergence. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0051] Figure 1 A method flow chart of a fixed time path tracking control method considering input delay provided by the present invention;

[0052] Figure 2 This is a USV fixed time path tracking control structure diagram of the present invention;

[0053] Figure 3 A trajectory comparison curve diagram of the present invention and the prior art in an embodiment;

[0054] Figure 4 is an error variation curve diagram comparing the present invention with the prior art in an embodiment;

[0055] Figure 5 A control input variation curve diagram comparing the present invention with the prior art in one embodiment;

[0056] Figure 6 is a graph of an input delay assistance system comparing the present invention with the prior art in one embodiment;

[0057] Figure 7 It is a controller adaptive parameter curve diagram comparing the present invention with the prior art in an embodiment. DETAILED DESCRIPTION

[0058] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0059] This embodiment provides a fixed-time path tracking control method considering input delay, such as Figure 1 As shown, including:

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

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

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

[0063] S4: calculating 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 designing an attitude error virtual control law;

[0064] S5: constructing a fixed-time path tracking controller and an adaptive law based on an input delay auxiliary system 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;

[0065] S6: Implement 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, firstly, a nonlinear mathematical model of a USV based on input delay is constructed as the subsequent controlled object; the 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, which can effectively predict and compensate for the influence of the input delay signal, ensure that the control command can be transmitted to the actuator in time, and thus eliminate the negative impact of the input delay on the system performance; secondly, the reference route of the USV is generated by using the LVS technology, the LVS guidance law is constructed according to the reference route, and the position error and 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 at the same time; the guidance law can balance the uncertainty caused by the error, and enable the USV to track the preset path more accurately; a virtual control law for the USV position error is designed, and the DSC technology is introduced, and a fixed time filter is designed according to the virtual control law for the USV position error; the position coordinates, speed and direction of the ship at different time points can be obtained through the virtual control law, and the fixed time filter is designed to use the filter signal instead of the virtual control signal to solve the traditional Back The "complexity explosion problem" caused by the derivation of the virtual control law in the stepping method is simplified to simplify the calculation of the design filter; secondly, 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, and the attitude error virtual control law is designed. A control law with low computational load and fixed time convergence is designed, which realizes the rapid convergence of the USV to the desired geometric formation and reference path; 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. For the tracking control problem of the real ship, the error signal is modified by fractional power, so that the kinematic loop and the dynamic loop of the under-actuated ship achieve double-loop fixed time convergence, which enhances the convergence accuracy of the system and the robustness against external interference; finally, 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 path tracking control of the USV under input delay is realized.

[0067] In a specific embodiment, a nonlinear mathematical model of a USV based on input delay is constructed as a subsequent controlled object; the input delay auxiliary system is improved according to the control input of the USV under input delay conditions, and the scheme of the improved input delay auxiliary system is:

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

[0069]

[0070] In the formula, x, y represent the position coordinates of USV in the geodetic coordinate system, ψ represents the heading angle of USV, u, v, r represent the forward speed, drift speed and bow angular velocity of the ship respectively, and θ u ,θ v ,θ r is the unknown time-varying function of the forward, drift and pitching degrees of freedom, f u (u), f v (v), f r (r) is a known smooth nonlinear function of the forward, drift and pitch degrees of freedom, g u (v),g r (v) is the unknown non-zero control gain in the forward and yaw directions, d wu ,d wv ,d wr is the unstructured uncertainty of the ocean environment disturbance and measurement noise; T u (t-ξ),T r (t-ξ) represents the control input of the forward and yaw directions under the input delay condition, respectively; ξ represents the time of the input delay;

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

[0072]

[0073] Among them, T i (t-ξ), i = u, r represents the control input for the forward and yaw directions under delay conditions, w u ,w r represents the state variable in the input delay auxiliary system, with an initial value of zero; c u , c r denote the design parameters of forward and yaw freedom, respectively, w u , w r The state variables in the input-delay auxiliary system representing the forward and yaw degrees of freedom are initially zero and will remain zero during system operation if there is no delay in the input signal.

[0074] The input delay auxiliary system can effectively predict and compensate for the impact of input delay signals, ensuring that control instructions can be transmitted to the actuator in a timely manner, thereby eliminating the negative impact of input delay on system performance; in this embodiment, the traditional delay auxiliary system is improved according to the control input of the ship, which can specifically eliminate the impact of the ship's input delay on the system.

[0075] In a specific embodiment, the LVS technology is used to generate a reference route of the USV, the LVS guidance law is constructed according to the reference route, and the position error and 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 at the same time. The scheme is:

[0076] S21. Generate a reference route for USV using LVS technology;

[0077] S22. Construct an LVS guidance law according to the reference route. The LVS guidance law is as shown in formula (14):

[0078]

[0079] Among them, x d ,y d represents the position coordinates of LVS, ψ d represents the heading angle of LVS, r d represents the desired yaw angular velocity of LVS, u d Indicates the expected forward speed;

[0080] S23. Obtain the position error and heading angle error of the USV according to the LVS guidance law. The position error and heading angle error of the USV are as shown in formula (15):

[0081]

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

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

[0084]

[0085] Formula (16) represents the dynamic error after being processed by the input delay assistance system; Represents the attitude error signal; u e represents the dynamic error of the forward degree of freedom, r e represents the dynamic error of the yaw degree of freedom, β u ,β r , It represents the time signal after DSC filtering. For the USV control system, the motion state at this time is without delay.

[0086] In this embodiment, referring to the method of generating a reference route based on the LVS technology, reference is made to 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., and a guidance law is obtained according to the reference route. The guidance law can balance the uncertainty caused by the error and enable the USV to track the preset path more accurately.

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

[0088] S31. To stabilize the USV position error, a virtual control law for the USV position error is designed, as shown in formula (17):

[0089]

[0090] In the formula, is a positive design parameter, α u Denotes the stabilization position error x e The virtual control law, represents the stabilization error y e The virtual control law is: v represents the ship's drift speed; the reference path is generated by the virtual ship, where the expected forward speed u d =3m / s;

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

[0092]

[0093] Where, t u , t r is a time constant greater than zero, β u ,β r , is the time signal after DSC filtering; represents the time signal of the fixed time filter; α r is the attitude error signal Virtual control law.

[0094] In this embodiment, a virtual control law is designed, through which data such as the position coordinates, speed and direction of the ship at different time points can be obtained. A fixed-time filter is designed to use filtered signals instead of virtual control signals, so as to solve the "complexity explosion problem" caused by the derivation of the virtual control law in the traditional Backstepping method, simplify the amount of calculation in the process of designing the virtual control law, make the structure of the controller simpler, and ensure the accuracy of real-time control of ship motion in actual engineering.

[0095] In a specific embodiment, 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, and the scheme for designing the attitude error virtual control law is:

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

[0097]

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

[0099]

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

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

[0102] In a specific embodiment, a fixed-time path tracking controller and an adaptive law based on an 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] Combining formulas (12), (13), (16) and (18) to consider the input delay, a fixed-time path tracking controller and adaptive law based on the input delay auxiliary system are constructed, as shown in formulas (21) and (22):

[0104]

[0105] In the formula, i=u, r is a positive controller design parameter, 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 in the forward and yaw directions, ε i represents the design parameters, represents a smooth function, represents the control input to the fixed-time path-following controller for the input-delay-based auxiliary system, represents the time-varying function θ i The adaptive law of represents the non-structural uncertainty 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 an adaptive law are designed. Aiming at the tracking control problem of a real ship, the error signal is modified by using fractional powers, so that the kinematic loop and the dynamic loop of the underactuated ship can achieve double-loop fixed-time convergence, thereby enhancing the convergence accuracy of the system and its 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 is divided into a guidance module, a control module and a navigation module;

[0109] The guidance module inputs waypoints, generates the 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 expected forward speed with the position coordinates and heading angle of the USV acquired by the GPS, performs coordinate conversion, obtains the position error, and obtains the virtual control law according to the position error, and then inputs the data into the improved input delay auxiliary system, inputs the state variables in the input delay auxiliary system of the forward and yaw degrees of freedom into the fixed time path tracking controller, and at the same time, the adaptive law of the control module design parameters;

[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 superiority and effectiveness of the present invention in solving input delay, numerical comparison simulation was carried out in a simulated external ocean environment. The present invention and the path tracking control technology based on DSC and MLP were numerically compared and simulated in a simulated external ocean environment. The differences are shown in Table 1.

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

[0114] index Fixed time control Input Lag Assist Uniformly eventually bounded Method of the present invention yes yes yes Prior art no no yes

[0115] The method of the present invention was compared with the prior art on an industrial computer (Intel(R) Core(TM) i5-7300 HQ CPU@2.50GHz, RAM: 8.00GB). Figure 3-Figure 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 present invention is faster in the initial stage due to the good convergence performance of the fixed time controller. It can be seen from the enlarged figure that the tracking accuracy of the algorithm of the present invention is also higher, while the convergence speed of the prior art is slower.

[0117] Figure 4 The error curves of the two methods are described. It can be seen from the figure that the error of the algorithm of the present invention 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, and have better transient and steady-state performance. These are the advantages of fixed time control, while the error of the existing technology is larger;

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

[0119] Figure 6 It shows the change curve of the input delay assistance system. 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 oscillates up and down, but eventually converges near the zero point.

[0120] By combining the existing MLP-based and DSC-based path tracking control technologies for numerical comparison simulation, the present invention has achieved the following three beneficial effects in the control field:

[0121] 1) Compared with the existing control algorithms, the method proposed in the present invention shows significant advantages in many aspects. First, the input delay auxiliary system adopted can effectively predict and compensate for the influence of the input delay signal, ensuring that the control instructions can be transmitted to the actuator in time, thereby eliminating the negative impact of the input delay on the system performance. This feature enables the USV to maintain efficient operation in a delayed environment. Secondly, the designed fixed-time path tracking controller not only has the performance of fast convergence but also the convergence time is 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 by the present invention can not only effectively solve the input delay problem of the controller, but also enhance the convergence accuracy of the system and the robustness against external interference. By combining these two advanced technologies, the controller of the present invention exhibits excellent performance and stability in a variety of complex environments.

[0123] 2) Furthermore, the fixed-time path tracking controller with input delay enables the USV to maintain good response characteristics in the case of input delay. Input delay often affects the response speed and accuracy of the ship, especially when it is necessary to quickly adjust the course or avoid obstacles. The input delay auxiliary system ensures the delay compensation of the control signal during the transmission process, so that the system can respond quickly to command changes, avoid the adverse effects caused by input delays, improve the safety and stability of operations, and optimize the operating efficiency and dynamic performance of the USV. When the existing control algorithm encounters an initial position that is far from the target path, the time required for the system to converge from the initial state to the vicinity of the equilibrium point may be infinite, which will affect the convergence speed and convergence performance of the system. The fixed-time path tracking controller solves this problem. It is not limited by the initial position and can converge to the desired position better and faster.

[0124] 3) Through numerical simulation, it is verified that the method of the present invention can achieve excellent control performance in the USV fixed time path tracking control task, which not only solves the shortcomings of the traditional control algorithm in input delay processing, but also significantly improves the adaptability and reliability of the system in complex environments, providing a more efficient, safe and stable solution for the USV motion control field. USV has broad application prospects in modern shipping logistics, global trade, large-scale marine engineering, etc. The underactuated ship system is widely present in actual marine engineering and has the advantage of high economic benefits. The present invention can accelerate the transformation of USV to a smarter, more energy-saving and safer aspect.

[0125] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A fixed-time path tracking control method considering input delay, characterized in that: include: S1: Construct a nonlinear mathematical model of the USV based on input delay as the subsequent controlled object; improve the input delay auxiliary system according to the control input of the USV under the input delay condition to obtain the improved input delay auxiliary system; S2: Generate a reference route of the USV using the LVS technology, construct an LVS guidance law according to the reference route, obtain a position error and a heading angle error of the USV according to the LVS guidance law, and simultaneously obtain a dynamic error of the USV under the improved input delay auxiliary system; S3: Design a virtual control law for USV position error, introduce DSC technology, and design a fixed time filter according to the virtual control law for USV position error; S4: calculating 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 designing an attitude error virtual control law; S5: constructing a fixed-time path tracking controller and an adaptive law based on an input delay auxiliary system 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; S6: Implement 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.

2. The fixed-time path tracking control method considering input delay according to claim 1, characterized in that: 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): In the formula, x, y represent the position coordinates of USV, ψ represents the heading angle of USV, u, v, r represent the forward speed, drift speed and bow angular velocity of the ship respectively, and θ u ,θ v ,θ r is the unknown time-varying function of the forward, drift and pitching degrees of freedom, f u (u), f v (v), f r (r) is a known smooth nonlinear function of the forward, drift and pitch degrees of freedom, g u (v),g r (v) is the control gain for forward and yaw directions, d wu ,d wv ,d wr is the unstructured uncertainty of the ocean environment disturbance and measurement noise; T u (t-ξ),T r (t-ξ) represents the control input of the forward and yaw directions under the condition of input delay, respectively; ξ represents the time of input delay.

3. The fixed time path tracking control method considering input delay according to claim 2, characterized in that: The input delay auxiliary system is improved according to the control input of the USV under the input delay condition, and the improved input delay auxiliary system is obtained, including: The input delay auxiliary system is improved according to the control input of the USV under the input delay condition. The improved input delay auxiliary system is shown in formula (2): Among them, T i (t-ξ), i = u, r represents the control input for the forward and yaw directions under delay conditions, w u ,w r represents the state variable in the input delay auxiliary system, with an initial value of zero; c u , c r denote the design parameters of forward and yaw freedom, respectively, w u , w r State variables in the input-delay auxiliary system representing the forward and yaw degrees of freedom.

4. The fixed-time path tracking control method considering input delay according to claim 3, characterized in that: Generate a reference route of the USV using the LVS technology, construct an LVS guidance law according to the reference route, obtain a position error and a heading angle error of the USV according to the LVS guidance law, and simultaneously obtain a dynamic error of the USV under the improved input delay auxiliary system, including: S21, the LVS guidance law is as shown in formula (3), Among them, x d ,y d represents the position coordinates of LVS, ψ d represents the heading angle of LVS, r d represents the desired yaw angular velocity of LVS, u d Indicates the expected forward speed; S22. Obtain the position error and heading angle error of the USV according to the LVS guidance law. The position error and heading angle error of the USV are as shown in formula (4): In the formula, x e ,y e ,ψ e is the position error and heading angle error of USV, J(ψ) is the rotation matrix related to the heading angle, x, y, ψ represent the position coordinates and heading angle of USV in the geodetic coordinate system respectively; S23, obtaining the dynamic error of the USV under the improved input delay auxiliary system, as shown in formula (5), Formula (5) represents the dynamic error after being processed by the input delay assistance system; Represents the attitude error signal; u e represents the dynamic error of the forward degree of freedom, r e represents the dynamic error of the yaw degree of freedom, β u ,β r , Represents the time signal after DSC filtering.

5. The fixed time path tracking control method considering input delay according to claim 4, characterized in that: A virtual control law for USV position error is designed, DSC technology is introduced, and a fixed time filter is designed according to the virtual control law for USV position error, including: S31. To stabilize the USV position error, a virtual control law for the USV position error is designed, as shown in formula (6): In the formula, is the design parameter, α u Denotes the stabilization position error x e The virtual control law, Denotes the stabilization position error y e The virtual control law is: v represents the ship's transverse drift speed; S32, introducing DSC technology, designing a fixed time filter according to the virtual control law of the USV position error, the fixed time filter is as shown in formula (7), In the formula, t u , t r is the time constant, β u ,β r , is the time signal after DSC filtering; represents the time signal of the fixed time filter; α r is the attitude error signal Virtual control law.

6. The fixed-time path tracking control method considering input delay according to claim 5, characterized in that: 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, and the attitude error virtual control law is designed, including: S51. Combining formulas (4), (5) and (7), the derivative of the attitude error signal is obtained, as shown in formula (8): S52, according to the posture error signal of the USV The virtual control law of attitude error is designed by the derivative of attitude error signal, as shown in formula (9): In the formula, k c2 is the design parameter, α r Represents the virtual control law of attitude error.

7. The fixed-time path tracking control method considering input delay according to claim 6, characterized in that: A fixed-time path tracking controller and an adaptive law based on an 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: Combining formulas (1), (2), (5), 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 the formula, i=u, r is the controller design parameter, i=u, r represents the gain adaptive design parameter; T i Indicates the USV control input without delay, g i Denotes the non-zero control gain in the forward and yaw directions, ε i represents the design parameters, represents a smooth function, represents the control input to the fixed-time path-following controller for the input-delay-based auxiliary system, represents the time-varying function θ i The adaptive law of represents the non-structural uncertainty d wi The adaptive law, f i (v) is expressed as a smooth nonlinear function of the forward, drift and pitch degrees of freedom.

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