Autonomous tugboat event triggering quantitative towing control method based on command filtering

Abstract

The invention discloses an autonomous tugboat event-triggered quantitative towing control method based on command filtering, and the method comprises the steps: constructing a nonlinear system model of AT and a tugboat, and obtaining a reference route of AT and the tugboat through a guidance virtual ship; constructing a guidance law according to the positions of the guidance virtual ship and the real ship to generate AT and an expected trajectory of the tugged ship; designing a virtual control law of the AT and the tugboat on the forward freedom degree and the yawing freedom degree, and introducing a filter to compensate the dynamic error to obtain the compensated dynamic error; designing AT and updating laws of an intermediate control law and a self-adaptive law of the tugboat on the forward degree of freedom and the yawing degree of freedom according to the compensated dynamic error; designing an event trigger quantization AT controller based on command filtering and a tugboat controller based on command filtering based on the AT and an updating law of an intermediate control law and a self-adaptive law of the tugboat on the forward freedom degree and the yawing freedom degree; two controllers are used for realizing towing control of the AT on the towed boat; according to the method, the response speed of the system can be improved, frequent adjustment caused by tiny fluctuation is avoided, unnecessary signal transmission and calculation amount are remarkably reduced, and therefore limited communication bandwidth and calculation resources are saved.

Description

Technical Field

[0001] The present invention relates to the technical field of ship motion control research, and in particular to an event-triggered quantitative towing control method for an autonomous towing boat based on command filtering. Background Art

[0002] In existing ship path tracking control systems, continuous-time control algorithms are usually relied on to achieve real-time control of dynamic systems. However, this approach has significant defects, especially in resource-constrained network control systems (such as sensor networks, embedded systems, etc.), where periodic updates of control signals lead to unnecessary waste of resources and are difficult to cope with complex environmental dynamic changes. In addition, the influence of filter errors in the signal processing process of existing systems has not been effectively compensated. Specifically, existing control technologies face the following major problems:

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

[0004] In the continuous-time algorithm, the control signal is updated periodically, and the control signal must be calculated and sent regularly regardless of whether the system state changes significantly. Although the controller uses a control algorithm based on MLP and DOB, which can effectively estimate disturbances and is robust to model uncertainties, this mode may lead to a large amount of invalid calculations and communications in actual engineering contexts, wasting precious bandwidth and computing resources. Especially in systems with limited network bandwidth and high communication costs, this waste of resources will significantly affect system performance.

[0005] Existing control algorithms based on MLP and DOB lack the ability to effectively deal with external interference and noise. Since the control signal is continuously updated indiscriminately, the system may produce frequent signal adjustments when facing small noise or uncertainty, resulting in system jitter, further affecting the stability and dynamic response performance of the system. In addition, this control algorithm often uses a first-order filter to avoid the "complexity explosion phenomenon" caused by the derivation of the virtual controller, but the first-order filter will introduce errors in the signal processing process, thereby affecting the control accuracy. These errors are not effectively compensated, resulting in delays and error accumulation when the system responds to rapidly changing signals, further reducing the performance and stability of the system. Summary of the invention

[0006] The present invention provides an event-triggered quantitative towing control method for an autonomous tugboat based on command filtering, so as to overcome the technical problems that the existing path tracking control algorithm will cause a large amount of resource waste when realizing control, and the control algorithm lacks effective response capabilities to external interference and noise, which will cause system jitter, and the introduction of filters to deal with interference and noise will introduce errors, thereby reducing the performance and stability of the control system.

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

[0008] An event-triggered quantitative towing control method for an autonomous tugboat based on command filtering, comprising:

[0009] S1: construct nonlinear system models of the AT and the towed ship respectively as the control objects of the controller designed in the subsequent steps, and use the guided virtual ships of the AT and the towed ship to obtain the reference routes of the AT and the towed ship;

[0010] S2: constructing a guidance law according to the positions of the guided virtual ship and the actual AT and the towed ship in the reference route, and generating the expected trajectories of the AT and the towed ship according to the guidance law;

[0011] S3: respectively design virtual control laws for the AT and the towed vessel in terms of forward freedom and bow pitch freedom, introduce filters to compensate for the dynamic errors between the actual trajectories and the expected trajectories of the AT and the towed vessel in the virtual control laws, and obtain the compensated dynamic errors of the AT and the towed vessel;

[0012] S4: designing intermediate control laws of the AT and the towed ship in the forward degree of freedom and the pitching degree of freedom respectively according to the compensated dynamic errors of the AT and the towed ship, and designing update laws of the adaptive laws of the AT and the towed ship respectively according to the compensated dynamic errors of the AT and the towed ship and the two intermediate control laws;

[0013] S5: designing an event-triggered quantized AT controller based on command filtering and a towed vessel controller based on command filtering based on the intermediate control law of the AT and the towed vessel in the forward degree of freedom and the pitching degree of freedom and the update law of the AT and the towed vessel adaptive law;

[0014] S6: Using the command filtering-based event-triggered quantized AT controller and the command filtering-based towed ship controller to implement AT towing control of the towed ship.

[0015] Furthermore, nonlinear system models of the AT and the towed ship are constructed respectively as control objects of the controller designed in the subsequent steps, and the reference routes of the AT and the towed ship are obtained using the guided virtual ships of the AT and the towed ship, including:

[0016] S11. Construct nonlinear mathematical models of the AT and the towed vessel respectively, as shown in formula (1) and formula (2).

[0017]

[0018]

[0019] In the formula, T represents the autonomous tugboat, i.e. AT, S represents the towed ship, and x i ,y i ,i=T,S represents the position coordinates of AT and the towed ship, ψ i represents AT and the heading angle of the towed vessel, u i represents AT and the forward speed of the towed vessel, v i represents AT and the transverse drift speed of the towed vessel, r i represents AT and the yaw angular velocity of the towed vessel, represents the hydrodynamic added mass of AT and the towed vessel in the forward degree of freedom, represents the hydrodynamic additional mass of AT and the towed vessel in the drifting degree of freedom, represents the hydrodynamic added mass of AT and the towed vessel in the pitching degree of freedom, f vi (v), f ri (v) represent the nonlinear terms of AT and the towed vessel in the forward, drift and pitch degrees of freedom, respectively, d wui ,d wvi ,d wri is the disturbance force and moment of the external environment acting on the AT and the towed vessel’s forward, sideways and yaw degrees of freedom, T u (·),F r (·) respectively represent the control gains of the main engine speed and rudder angle of the tugboat, n p represents the main engine speed of the tugboat, δ p represents the rudder angle of the tugboat, Q(n p |n p |),Q(δ r ) represent the quantization input of the hysteresis quantizer in the forward degree of freedom and the bow degree of freedom of the tugboat, respectively, H u represents the towing force acting on the towed vessel, L1 represents the length of the tugboat, L2 represents the length of the towed vessel, θ2 represents the angle between the tow rope and the tugboat, and θ1 represents the angle between the tow rope and the towed vessel;

[0020] The hysteresis quantizer is shown in formula (3),

[0021] Q(k)=G(k)k+D (3)

[0022] Wherein, Q(k) represents the hysteresis quantizer, k represents the actual hysteresis quantization input of AT, G(k) represents the quantization control gain, as shown in formula (4), and D represents the additional interference term, as shown in formula (5);

[0023]

[0024]

[0025] The hysteresis quantizer is piecewise linearized, as shown in formula (6):

[0026]

[0027] Among them, k j =ρ (1-j) k min , is a constant, is the derivative of k, sgn is the sign function, k j is the threshold of the hysteresis quantizer, j is the quantization level, k min is the quantization dead zone, ρ is the quantization density, Q(k(t - )) represents the quantized value of the actual input k at the left limit moment of time t;

[0028] S12. Use the guided virtual ship to obtain the reference route of AT and the towed ship, as shown in formula (7):

[0029]

[0030] In the formula, x d (t),y d (t) represents the position coordinates of the guided virtual ship on the reference route, ψ d (t) represents the heading angle of the guided virtual ship, r d (t) represents the expected bow angular velocity of the guided virtual ship, and t represents the continuous motion time of the virtual guided ship.

[0031] Furthermore, a guidance law is constructed according to the positions of the guided virtual ship, the actual AT and the towed ship in the reference route, including:

[0032] The guidance law is shown in formula (8):

[0033]

[0034] In the formula, ψ ri It represents the AT and the azimuth of the towed ship relative to the guided virtual ship, with the lateral distance between the towed ship and the tugboat as the x-axis and the longitudinal distance as the y-axis. ei represents the position error of the AT and the towed ship relative to the guided virtual ship on the x-axis, and yei represents the position error of the AT and the towed ship relative to the guided virtual ship on the y-axis, z ei Indicates the distance between the AT and the towed ship relative to the guided virtual ship.

[0035] Furthermore, a filter is introduced to compensate for the dynamic error between the actual trajectory and the expected trajectory of the AT and the towed vessel in the virtual control law, and the compensated dynamic error of the AT and the towed vessel is obtained, including:

[0036] S31. Define the position error and heading error of AT and the towed vessel, as shown in formula (9):

[0037]

[0038] In the formula, represents the derivative of AT and the distance between the towed ship and the guided virtual ship, represents the derivative of AT and the heading error of the towed vessel, ψ ri represents AT and the azimuth of the towed ship relative to the guided virtual ship, r i Indicates AT and the pitching angular velocity of the towed vessel; i = T, S, where T represents AT and S represents the towed vessel;

[0039] S32, design the virtual control law of AT and the towed vessel in the forward degree of freedom and bow pitch degree of freedom, as shown in formula (10),

[0040]

[0041] In the formula, α ui represents the virtual control law of AT and the towed vessel in the forward degree of freedom, α ri represents the virtual control law of AT and the towed vessel in the bow pitch degree of freedom, represents the design parameters of the virtual control law for the AT and the towed vessel in the forward and bow degrees of freedom, represents the constant of the virtual control law of AT and the towed vessel in the forward degree of freedom;

[0042] S33, introducing a filter to compensate for the dynamic errors of the AT and the towed vessel, the filter is as shown in formula (11),

[0043]

[0044] In the formula, β ιi , ι=u,r represents the filter variables of AT and the towed vessel in the forward and bow degrees of freedom; ∈ ιi is a time constant greater than zero, α ιi (0), β ιi (0) is α ιi , βιi The initial value of q ιi =α ιi -β ιi , represents the first-order filter error;

[0045] S34, defining the dynamic error of the AT and the towed vessel according to formula (11), as shown in formula (12),

[0046] ι ei =β ιi -ι i (12)

[0047] In the formula, ι ei represents the dynamic error between AT and the towed vessel;

[0048] S35, designing a filter error compensation signal according to the filter variables of the AT and the towed vessel in the forward degree of freedom and the pitching degree of freedom, as shown in formula (13),

[0049]

[0050] In the formula, ζ ιi represents the filter error compensation signal of AT and the towed vessel, and the variable ζ ιi The initial value of k is zero, ιi are the design parameters of the AT and towed vessel filter error compensation signals;

[0051] S36, compensating the dynamic error according to the filter error compensation signal to obtain a compensated dynamic error, as shown in formula (14),

[0052] χ ei =β ιi -ι ei -ζ ιi (14)

[0053] In the formula, χ ei Represents the compensated dynamic error, χ=U,R.

[0054] Furthermore, according to the compensated dynamic errors of the AT and the towed vessel, the intermediate control laws of the AT and the towed vessel in the forward degree of freedom and the bow pitch degree of freedom are designed respectively, including:

[0055] S41. Combining formulas (1), (2), (11), (13) and (14), the dynamic errors of AT and the towed vessel are derived, as shown in formula (24):

[0056]

[0057] In the formula, are the neural network weights of AT and the towed vessel in the forward and bow freedom, respectively. uT (v),S rT (v) and S uS (v),S rS (ν) represents the Gaussian function of the AT and the towed vessel on the forward and yaw degrees of freedom, ν represents the input of the neural network of the AT and the towed vessel on the forward and yaw degrees of freedom, ε uT ,ε uS and ε uT ,ε rS represents the approximation error of AT and the towed vessel in the forward and bow freedom, respectively. G(N u ) represents the quantized control gain of AT on the forward degree of freedom, G(δ r ) represents the quantitative control gain N of AT on the yaw degree of freedom u =n p |n p |, represents the control input of AT in the forward degree of freedom without hysteresis quantization;

[0058] S42. Design the intermediate control law of the AT in the forward and yaw degrees of freedom and the intermediate control law of the towed vessel in the forward and yaw degrees of freedom, as shown in formulas (16) and (17),

[0059]

[0060]

[0061] In the formula, represents the design parameters of the intermediate control law of AT, k uT ,k rT represents the design parameters of the AT filter compensation signal, is the design parameter of the intermediate control law of the towed vessel, k uS ,k rS represents the design parameters of the towed vessel filter compensation signal, u=T, S is the estimate of the external disturbance boundary of AT and the towed vessel in the forward and bow degrees of freedom, respectively. ui ,b ri ,i=T,S are the design constants of interference estimation of AT and the towed vessel in forward freedom and bow freedom, respectively, U ei represents the forward speed error between AT and the towed vessel in the forward degree of freedom, R ei represents the angular velocity error of AT and the towed vessel in the yaw degree of freedom, ∈ ui represents the time constant of the filter variables of AT and the towed vessel in the forward degree of freedom, ∈ rirepresents the time constant of the filter variables of AT and the towed vessel in the pitching degree of freedom, represents the derivative of the filter variables of AT and the towed vessel in the forward degree of freedom, represents the derivative of the filter variables of AT and the towed vessel in the pitching degree of freedom, ζ ui represents the filter error compensation signal of AT and the towed vessel in the forward degree of freedom, ζ ri represents the filter error compensation signal of AT and the towed vessel in the pitching degree of freedom, S ui represents the basis function of the neural network of AT and the towed vessel in the forward degree of freedom, S ri Represents the basis functions of the neural network for AT and the tugboat’s pitching degree of freedom.

[0062] Furthermore, the update laws of the AT and the towed ship adaptive law are designed respectively according to the compensated dynamic errors of the AT and the towed ship and the two intermediate control laws, including:

[0063] S43, defining the event trigger measurement error and event trigger condition of AT in the forward degree of freedom and the pitching degree of freedom according to the dynamic error and the position error, as shown in formulas (18) and (19),

[0064]

[0065]

[0066] In formula (18), e n represents the event-triggered measurement error of AT in the forward degree of freedom, e δ represents the event-triggered measurement error of AT on the pitching degree of freedom, represents the sampling time of the event triggering moment in the forward and yaw degrees of freedom, k = n, δ represents the sampling time of the next event triggering moment in the forward degree of freedom and the pitching degree of freedom;

[0067] In formula (19), Indicates the event triggering condition of AT on the forward degree of freedom, represents the event triggering condition of AT on the pitching degree of freedom, W is the sign of event triggering, inf represents the infimum, Indicates the event triggering conditions on the forward and forward degrees of freedom The trigger threshold, and It is the event triggering condition on the forward freedom and the pitching freedom The design parameters, ‖S r (v)‖ represents the neural network basis function S on the yaw degree of freedomr The norm of (v), ‖S u (v)‖ represents the neural network basis function S on the forward degree of freedom u (v) norm;

[0068] S44. In the time period between the sampling time of the event triggering moment and the sampling time of the next event triggering moment, the updating law of the adaptive law of the neural network weight estimator at the AT event triggering moment is designed according to the intermediate control law of the AT, as shown in formula (20),

[0069]

[0070] In the formula, α k represents the intermediate control law of AT in forward and yaw degrees of freedom, and represents the adaptive law of the neural network weight estimator at the time of AT event triggering; S uT (ν) and S rT (ν) represents the Gaussian function of AT in the forward and forward degrees of freedom;

[0071] S45. Design an update law of the AT adaptive law according to the intermediate control law of the AT. The update law of the AT adaptive law is shown in formula (21):

[0072]

[0073] In the formula, represents the update law of the AT adaptive law, represents the gain adaptive design parameter of AT in forward and yaw degrees of freedom; for The initial value of

[0074] S46. Design an update law for the adaptive law of the towed ship according to the intermediate control law of the towed ship. The update law for the adaptive law of the towed ship is shown in formula (22):

[0075]

[0076] In the formula, represents the update law of the towed ship’s adaptive law; represents the gain adaptive design parameters of the towed vessel in the forward and bow freedom; for The initial value of

[0077] S47. Design an update law for the adaptive law of the neural network weight estimator at the event triggering moment of the towed ship according to the intermediate control law of the towed ship, as shown in formula (23):

[0078]

[0079] In the formula, represents the update law of the adaptive law of the neural network weight estimator at the time of the towed ship event triggering, is the design constant of the weighted adaptive law for the forward and bow freedom of the towed vessel; S uS (v) and S rS (ν) represents the Gaussian function of the towed vessel in the forward and forward degrees of freedom;

[0080] S48. Design the updating law of the adaptive law of AT and the external disturbance of the towed vessel, as shown in formula (24),

[0081]

[0082] In the formula, represents the design constants of the adaptive law for external disturbances of the AT and the towed vessel in the forward and bow degrees of freedom; is the estimate of the external disturbance boundary between AT and the towed vessel; for The initial value of .

[0083] Furthermore, based on the intermediate control law of the AT and the towed vessel in the forward degree of freedom and the pitching degree of freedom and the update law of the AT and the towed vessel adaptive law, an event-triggered quantized AT controller based on command filtering and a towed vessel controller based on command filtering are designed, including:

[0084] S51. Based on the intermediate control law of the AT and the towed vessel in the forward degree of freedom and the pitching degree of freedom and the update law of the AT and the towed vessel adaptive law, an event-triggered quantized AT controller based on command filtering and a towed vessel controller based on command filtering are designed, as shown in formulas (25) and (26).

[0085]

[0086]

[0087] Where n p represents the speed of the controller of AT in the forward degree of freedom, α U represents the intermediate control law of the towed vessel in the forward degree of freedom, represents the control law of the controller of the towed vessel in the forward degree of freedom, represents the adaptive law of the intermediate control law of AT on the forward degree of freedom, α n represents the intermediate control law of AT on the forward degree of freedom, δ r represents the rudder angle of the AT controller in the pitching degree of freedom, represents the adaptive law of AT on the yaw degree of freedom, α δ represents the intermediate control law of AT on the yaw degree of freedom, represents the adaptive law of the towed ship in the forward degree of freedom, α R represents the intermediate control law of the towed vessel in the bow pitch degree of freedom, represents the control law of the controller of the towed vessel in the pitching degree of freedom, It represents the adaptive law of the towed vessel in the bow pitch degree of freedom.

[0088] Beneficial effects: The present invention provides an event-triggered quantitative towing control method for an autonomous tugboat based on command filtering. By designing virtual control laws for AT and the towed ship and introducing filters to compensate for errors in the virtual control laws, the delay and error caused by the first-order filter are eliminated. By designing intermediate control laws and adaptive update laws for AT and the towed ship, and designing event-triggered controllers for AT and the towed ship according to the intermediate control laws and the adaptive update laws, the response speed of the system can be improved, frequent adjustments caused by small fluctuations can be avoided, and unnecessary signal transmission and calculation can be significantly reduced, thereby saving limited communication bandwidth and computing resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] 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.

[0090] Figure 1 A method flow chart of an autonomous tugboat event-triggered quantitative towing control method based on command filtering according to the present invention;

[0091] Figure 2 A coordinate system diagram of a tugboat and a towed ship in an embodiment of the present invention;

[0092] Figure 3 This is a control structure diagram of the tugboat event-triggered quantitative control path tracking control of the present invention;

[0093] Figure 4 A trajectory comparison curve diagram comparing the present invention with the prior art in an embodiment of the present invention;

[0094] Figure 5 is an error variation curve diagram comparing the present invention and the prior art in an embodiment of the present invention;

[0095] Figure 6 The control input variation curve diagram comparing the present invention and the prior art in the embodiment of the present invention is shown. DETAILED DESCRIPTION

[0096] 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.

[0097] This embodiment provides an event-triggered quantitative towing control method for an autonomous towing vessel based on command filtering, such as Figure 1 As shown, including:

[0098] S1: construct nonlinear system models of the AT and the towed ship respectively as the control objects of the controller designed in the subsequent steps, and use the guided virtual ships of the AT and the towed ship to obtain the reference routes of the AT and the towed ship;

[0099] S2: constructing a guidance law according to the positions of the guided virtual ship and the actual AT and the towed ship in the reference route, and generating the expected trajectories of the AT and the towed ship according to the guidance law;

[0100] S3: respectively design virtual control laws for the AT and the towed vessel in terms of forward freedom and bow pitch freedom, introduce filters to compensate for the dynamic errors between the actual trajectories and the expected trajectories of the AT and the towed vessel in the virtual control laws, and obtain the compensated dynamic errors of the AT and the towed vessel;

[0101] S4: designing intermediate control laws of the AT and the towed ship in the forward degree of freedom and the pitching degree of freedom respectively according to the compensated dynamic errors of the AT and the towed ship, and designing update laws of the adaptive laws of the AT and the towed ship respectively according to the compensated dynamic errors of the AT and the towed ship and the two intermediate control laws;

[0102] S5: designing an event-triggered quantized AT controller based on command filtering and a towed vessel controller based on command filtering based on the intermediate control law of the AT and the towed vessel in the forward degree of freedom and the pitching degree of freedom and the update law of the AT and the towed vessel adaptive law;

[0103] S6: Using the command filtering-based event-triggered quantized AT controller and the command filtering-based towed ship controller to implement AT towing control of the towed ship.

[0104] Specifically, firstly, nonlinear system models of the AT and the towed ship are constructed respectively as the control objects of the controller designed in the subsequent steps, and the reference routes of the AT and the towed ship are obtained by using the guided virtual ship of the AT and the towed ship. The AT is an autonomous tugboat, and a reference route of the AT and the towed ship is formed by using the guided virtual ship. The AT and the towed ship need to track the reference route, and the reference route is used as a reference for obtaining the expected trajectory; secondly, a guidance law is constructed according to the positions of the guided virtual ship and the actual AT and the towed ship in the reference route, and the expected trajectory of the AT and the towed ship is generated according to the guidance law. The guidance law is constructed and the expected trajectory is generated for the subsequent construction of the controller to control the AT and The towed vessel moves along the desired trajectory, providing a path reference to eliminate the error between the actual trajectory and the desired trajectory; secondly, virtual control laws for the AT and the towed vessel in the forward degree of freedom and the bow pitch degree of freedom are designed respectively, and a filter is introduced to compensate for the dynamic error between the actual trajectory and the desired trajectory of the AT and the towed vessel in the virtual control law, so as to obtain the compensated dynamic error of the AT and the towed vessel. The introduction of the filter can avoid the complexity explosion caused by the repeated differentiation of the virtual control law, and the design of the compensation signal can eliminate the influence of the first-order filter error on the control system, thus avoiding the performance degradation caused by the filter error; secondly, according to the compensated AT and the dynamic error of the towed vessel The intermediate control laws of the AT and the towed ship in the forward degree of freedom and the bow pitch degree of freedom are designed respectively according to the compensated dynamic errors of the AT and the towed ship and the two intermediate control laws. The update laws of the adaptive laws of the AT and the towed ship are designed respectively according to the dynamic errors of the AT and the towed ship after compensation and the two intermediate control laws. This can effectively reduce the influence of the error on the control effect, improve the performance of the control system, improve the control accuracy of the AT and the towed ship, effectively deal with the time-varying or unknown dynamic characteristics of the AT and the towed ship system, and enhance the robustness of the AT and the towed ship. Thirdly, based on the intermediate control laws of the AT and the towed ship in the forward degree of freedom and the bow pitch degree of freedom and the update laws of the adaptive laws of the AT and the towed ship, an event trigger based on command filtering is designed. The quantized AT controller and the towed ship controller based on command filtering set event trigger mechanisms for position error, heading error and dynamic error to ensure that the system updates the control signal only when the signal change exceeds a certain threshold, thereby realizing the synchronous update of the controller and the neural network weights, thereby improving the response speed of the system; in addition, combined with the hysteresis quantization mechanism, the system can avoid frequent adjustments caused by small fluctuations, significantly reduce unnecessary signal transmission and calculation, thereby saving limited communication bandwidth and computing resources; finally, the event-triggered quantized AT controller based on command filtering and the towed ship controller based on command filtering are used to realize AT towing control of the towed ship.

[0105] In a specific embodiment, nonlinear system models of the AT and the towed ship are constructed respectively as control objects of the controller designed in the subsequent steps, and the scheme of using the guided virtual ships of the AT and the towed ship to obtain the reference routes of the AT and the towed ship is:

[0106] S11. Construct nonlinear mathematical models of the AT and the towed vessel respectively, as shown in formula (27) and formula (28).

[0107]

[0108]

[0109] In the formula, T represents the autonomous tugboat, i.e. AT, S represents the towed ship, and x i ,y i ,i=T,S represents the position coordinates of AT and the towed ship, ψ i represents AT and the heading angle of the towed vessel, u i represents AT and the forward speed of the towed vessel, v i represents AT and the transverse drift speed of the towed vessel, r i represents AT and the yaw angular velocity of the towed vessel, represents the hydrodynamic added mass of AT and the towed vessel in the forward degree of freedom, represents the hydrodynamic additional mass of AT and the towed vessel in the drifting degree of freedom, represents the hydrodynamic added mass of AT and the towed vessel in the pitching degree of freedom, are the nonlinear terms of AT and the towed vessel in the forward, drift and pitching degrees of freedom, respectively, and d wui ,d wvi ,d wri is the disturbance force and moment of the external environment acting on the AT and the towed vessel’s forward, sideways and yaw degrees of freedom, T u (·),F r (·) respectively represent the control gains of the main engine speed and rudder angle of the tugboat, n p represents the main engine speed of the tugboat, δ p represents the rudder angle of the tugboat, Q(n p |n p |),Q(δ r ) represent the quantization input of the hysteresis quantizer in the forward degree of freedom and the bow degree of freedom of the tugboat, respectively, H u represents the towing force acting on the towed vessel, L1 represents the length of the tugboat, L2 represents the length of the towed vessel, θ2 represents the angle between the tow rope and the tugboat, and θ1 represents the angle between the tow rope and the towed vessel;

[0110] The hysteresis quantizer is shown in formula (29),

[0111] Q(k)=G(k)k+D (29)

[0112] Wherein, Q(k) represents the hysteresis quantizer, k represents the actual hysteresis quantization input of AT, G(k) represents the quantization control gain, as shown in formula (30), and D represents the additional interference term, as shown in formula (31);

[0113]

[0114]

[0115] The hysteresis quantizer is piecewise linearized, as shown in formula (32),

[0116]

[0117] Among them, k j =ρ (1-j) k min , is a design constant greater than 0, is the derivative of k, sgn is the sign function, k j is the threshold of the hysteresis quantizer, j is the quantization level, k min is the quantization dead zone, ρ is the quantization density, Q(k(t - )) represents the quantized value of the actual input k at the left limit moment of time t;

[0118] S12. Use the guided virtual ship to obtain the reference route of AT and the towed ship, as shown in formula (33),

[0119]

[0120] In the formula, x d (t),y d (t) represents the position coordinates of the guided virtual ship on the reference route, ψ d (t) represents the heading angle of the guided virtual ship, r d (t) represents the expected bow angular velocity of the guided virtual ship, t represents the continuous motion time of the virtual guided ship; the angular velocity r d The curvature of the virtual guided ship can be controlled to produce a straight or curved trajectory. d = 0, the heading angle of the virtual ship is ψ d remains unchanged, the virtual ship is guided to move in a straight line, and the reference route is a straight line. If r d ≠0, the heading angle of the guided virtual ship ψ d As time changes, the virtual ship is guided to move along a curve, and the reference route is a curve.

[0121] Specifically, the coordinate system diagram of AT and the towed vessel is as follows: Figure 2As shown in the figure, the tugboat is AT, l1 is half of the tugboat's length, l2 is half of the tugboat's length, and x b ,y b are the abscissa axes of AT and the coordinate system of the towed vessel, respectively. The abscissa axis is based on the direction of the lateral distance between the towed vessel and the tugboat, and the ordinate axis is based on the direction of the longitudinal distance between the towed vessel and the tugboat. E ,Y E ,O E They are the horizontal axis, vertical axis and origin of the geodetic coordinate system respectively;

[0122] The steps to obtain the reference route of AT and the towed vessel using the guided virtual ship are as follows:

[0123] First, initialize the state of the virtual guided ship and set the initial position of the virtual guided ship (x d0 ,y d0 ) and the initial heading angle ψ d0 , set the speed u of the virtual guided ship d and angular velocity r d ,These parameters are usually determined by the desired mission or trajectory planning goals;

[0124] Secondly, according to formula (33), the numerical integration method is used to update x at each time t d (t),y d (t) and ψ d (t), as shown in formula (34),

[0125]

[0126] By iterating the above formula, the continuous motion trajectory of the virtual guided ship (x d (t),y d (t));

[0127] Finally, set the reference route and the position trajectory of the virtual guided ship (x d (t),y d (t)) is the required reference route.

[0128] In this scheme, nonlinear system models of AT and the towed vessel are designed as the control objects of the controller in the subsequent steps. A hysteresis quantizer is introduced to ensure that the control signal is updated only when the system state changes significantly, avoiding frequent adjustments caused by small fluctuations.

[0129] In a specific embodiment, a guidance law is constructed according to the positions of the guided virtual ship and the actual AT and the towed ship in the reference route, and a scheme for generating the desired trajectory of the AT and the towed ship according to the guidance law is:

[0130] A guidance law is constructed according to the positions of the guided virtual ship, the actual AT and the towed ship in the reference route. The guidance law is shown in formula (35):

[0131]

[0132] In the formula, ψ ri represents AT and the azimuth of the towed ship relative to the guided virtual ship, Figure 2 The lateral distance between the towed vessel and the tugboat is the x-axis, and the longitudinal distance is the y-axis. ei represents the position error of the AT and the towed ship relative to the guided virtual ship on the x-axis, and y ei represents the position error of the AT and the towed ship relative to the guided virtual ship on the y-axis, z ei Indicates the distance between the AT and the towed ship relative to the guided virtual ship.

[0133] The desired trajectory of the AT and the towed vessel is generated according to the guidance law. For details, see Zhang G, Liu S, Zhang X, et al. Event-triggered cooperative formation control for autonomous surface vehicles under the maritime search operation[J]. IEEE Transactions on Intelligent Transportation Systems, 2022, 23(11): 21392-21404.

[0134] In this embodiment, a guidance law is constructed and a desired trajectory is generated to provide a path reference for the subsequent construction of a controller to control the AT and the towed vessel to move along the desired trajectory, thereby eliminating the error between the actual trajectory and the desired trajectory.

[0135] In a specific embodiment, virtual control laws of the AT and the towed vessel in the forward degree of freedom and the pitching degree of freedom are designed respectively, and a filter is introduced to compensate for the dynamic errors between the actual trajectories and the expected trajectories of the AT and the towed vessel in the virtual control law. The scheme for obtaining the compensated dynamic errors of the AT and the towed vessel is:

[0136] S31. Define the position error and heading error of AT and the towed vessel, as shown in formula (36):

[0137]

[0138] In the formula, represents the derivative of AT and the distance between the towed ship and the guided virtual ship, represents the derivative of AT and the heading error of the towed vessel, ψ ri represents AT and the azimuth of the towed ship relative to the guided virtual ship, r i Indicates AT and the pitching angular velocity of the towed vessel; i = T, S, where T represents AT and S represents the towed vessel;

[0139] S32, design the virtual control law of AT and the towed vessel in the forward degree of freedom and bow pitch degree of freedom, as shown in formula (37),

[0140]

[0141] In the formula, α ui represents the virtual control law of AT and the towed vessel in the forward degree of freedom, α ri represents the virtual control law of AT and the towed vessel in the bow pitch degree of freedom, represents the design parameters of the virtual control law for the AT and the towed vessel in the forward and bow degrees of freedom, It represents the constant of the virtual control law of AT and the towed vessel in the forward degree of freedom; the design parameters and constants are both greater than 0;

[0142] S33, introducing a filter to compensate for the dynamic errors of the AT and the towed vessel, the filter is as shown in formula (38),

[0143]

[0144] In the formula, β ιi , ι=u,r represents the filter variables of AT and the towed vessel in the forward and bow degrees of freedom; ∈ ιi is a time constant greater than zero, α ιi (0), β ιi (0) is α ιi , β ιi The initial value of q ιi =α ιi -β ιi , represents the first-order filter error;

[0145] S34. Define the dynamic error of the AT and the towed vessel according to formula (38), as shown in formula (39),

[0146] ι ei =β ιi -ι i (39)

[0147] In the formula, ι ei represents the dynamic error between AT and the towed vessel;

[0148] S35, designing a filter error compensation signal according to the filter variables of the AT and the towed vessel in the forward degree of freedom and the bow pitch degree of freedom, as shown in formula (40),

[0149]

[0150] In the formula, ζ ιi represents the filter error compensation signal of AT and the towed vessel, and the variable ζ ιi The initial value of k is zero, ιi The design parameters for the AT and towed vessel filter error compensation signals are greater than 0;

[0151] S36, compensating the dynamic error according to the filter error compensation signal to obtain a compensated dynamic error, as shown in formula (41),

[0152] χ ei =β ιi -ι ei -ζ ιi (41)

[0153] In the formula, χ ei It represents the dynamic error after compensation, χ=U,R, and the motion state at this time has eliminated the influence of the filter error.

[0154] In this embodiment, virtual control laws for the AT and the towed vessel in the forward and yaw degrees of freedom are designed respectively, which can stabilize the position error and heading error generated by the AT and the towed vessel. The introduction of filters can avoid the complexity explosion caused by repeated differentiation of the virtual control law; the compensation signal is designed to eliminate the first-order filter error q ιi =α ιi -β ιi The impact on the control system not only enables the system to effectively smooth the control signal, but also maintains high-precision control performance and avoids performance degradation due to filtering errors.

[0155] In a specific embodiment, according to the compensated dynamic errors of the AT and the towed ship, the intermediate control laws of the AT and the towed ship in the forward degree of freedom and the pitching degree of freedom are designed respectively, and according to the compensated dynamic errors of the AT and the towed ship and the two intermediate control laws, the scheme of designing the update law of the adaptive law of the AT and the towed ship respectively is:

[0156] S41. Combining formulas (27), (28), (38), (40) and (41), the dynamic errors of AT and the towed ship are derived as shown in formula (42):

[0157]

[0158] In the formula, are the neural network weights of AT and the towed vessel in the forward and bow freedom, respectively. uT (v),S rT (ν) and S uS (ν),S rS (ν) represents the Gaussian function of the AT and the towed vessel on the forward and yaw degrees of freedom, ν represents the input of the neural network of the AT and the towed vessel on the forward and yaw degrees of freedom, ε uT ,ε uS and ε rT ,ε rS represents the approximation error of AT and the towed vessel in the forward and bow freedom, respectively. G(N u ) represents the quantized control gain of AT on the forward degree of freedom, G(δ r ) represents the quantitative control gain N of AT on the yaw degree of freedom u =n p |n p |, represents the control input of AT in the forward degree of freedom without hysteresis quantization;

[0159] S42. Design the intermediate control law of the AT in the forward and yaw degrees of freedom and the intermediate control law of the towed vessel in the forward and yaw degrees of freedom, as shown in formulas (43) and (44),

[0160]

[0161]

[0162] In the formula, represents the design parameter greater than 0 of the intermediate control law of AT, k uT ,k rT represents the design parameter greater than 0 of the AT filter compensation signal, is the design parameter greater than 0 of the intermediate control law of the towed vessel, k uS ,k rS represents the design parameter greater than 0 of the towed vessel filter compensation signal, i=T, S is the estimate of the external disturbance boundary of AT and the towed vessel in the forward and bow degrees of freedom, respectively. ui ,b ri , i=T, S are the design constants greater than 0 for the interference estimation of AT and the towed vessel in the forward and bow degrees of freedom, respectively, U ei represents the forward speed error between AT and the towed vessel in the forward degree of freedom, R ei represents the angular velocity error of AT and the towed vessel in the yaw degree of freedom, ∈ ui represents the time constant of the filter variables of AT and the towed vessel in the forward degree of freedom, ∈ri represents the time constant of the filter variables of AT and the towed vessel in the pitching degree of freedom, represents the derivative of the filter variables of AT and the towed vessel in the forward degree of freedom, represents the derivative of the filter variables of AT and the towed vessel in the pitching degree of freedom, ζ ui represents the filter error compensation signal of AT and the towed vessel in the forward degree of freedom, ζ ri represents the filter error compensation signal of AT and the towed vessel in the pitching degree of freedom, S ui represents the basis function of the neural network of AT and the towed vessel in the forward degree of freedom, S ri represents the basis functions of the neural network for AT and the tugboat’s pitching degrees of freedom;

[0163] S43. Define the event trigger measurement error and event trigger condition of AT in the forward degree of freedom and the pitching degree of freedom according to the dynamic error and the position error, as shown in formulas (45) and (46),

[0164]

[0165]

[0166] In formula (45), e n represents the event-triggered measurement error of AT in the forward degree of freedom, e δ represents the event-triggered measurement error of AT on the pitching degree of freedom, represents the sampling time of the event triggering moment in the forward and yaw degrees of freedom, k = n, δ represents the sampling time of the next event triggering moment in the forward degree of freedom and the pitching degree of freedom;

[0167] In formula (46), Indicates the event triggering condition of AT on the forward degree of freedom, represents the event triggering condition of AT on the pitching degree of freedom, W is the sign of event triggering, inf represents the infimum, Indicates the event triggering conditions on the forward and forward degrees of freedom The trigger threshold, and It is the event triggering condition on the forward freedom and the pitching freedom The design parameters are greater than 0, ‖S r (v)‖ represents the neural network basis function S on the yaw degree of freedom r The norm of (v), ‖S u (v)‖ represents the neural network basis function S on the forward degree of freedom u(v) norm;

[0168] S44. In the time period between the sampling time of the event triggering moment and the sampling time of the next event triggering moment, the updating law of the adaptive law of the neural network weight estimator at the AT event triggering moment is designed according to the intermediate control law of the AT, as shown in formula (47).

[0169]

[0170] In the formula, α k represents the intermediate control law of AT in forward and yaw degrees of freedom, and represents the adaptive law of the neural network weight estimator at the time of AT event triggering; S uT (v) and S rT (v) represents the Gaussian function of AT in the forward and forward degrees of freedom;

[0171] S45. Design an update law of the AT adaptive law according to the intermediate control law of the AT. The update law of the AT adaptive law is shown in formula (48):

[0172]

[0173] In the formula, represents the update law of the AT adaptive law, represents the gain adaptive design parameter of AT in forward and yaw degrees of freedom; for The initial value of

[0174] S46. Design an update law for the adaptive law of the towed ship according to the intermediate control law of the towed ship. The update law for the adaptive law of the towed ship is shown in formula (49):

[0175]

[0176] In the formula, represents the update law of the towed ship’s adaptive law; represents the gain adaptive design parameters of the towed vessel in the forward and bow freedom; for The initial value of

[0177] S47. Design an update law for the adaptive law of the neural network weight estimator at the event triggering moment of the towed ship according to the intermediate control law of the towed ship, as shown in formula (50):

[0178]

[0179] In the formula, represents the update law of the adaptive law of the neural network weight estimator at the time of the towed ship event triggering, is the design constant greater than 0 of the weighted adaptive law of the towed vessel in the forward and bow degrees of freedom; S uS (v) and S rS (v) represents the Gaussian function of the towed vessel in the forward and forward degrees of freedom;

[0180] S48. Design the updating law of the adaptive law of AT and the external disturbance of the towed vessel, as shown in formula (51),

[0181]

[0182] In the formula, represents the design constant greater than 0 of the adaptive law of external disturbances of the AT and the towed vessel in the forward and yaw degrees of freedom; is the estimate of the external disturbance boundary between AT and the towed vessel; for The initial value of .

[0183] In this embodiment, the nonlinear terms in the autonomous tugboat system are approximated online by a neural network approximator, and the intermediate control law is designed by compensating the dynamic error, which can effectively reduce the influence of the error on the control effect, improve the performance of the control system, and improve the control accuracy of the AT and the towed ship; and the actuator and quantizer gain adaptive law and the update law of the adaptive law are designed through adaptive technology, which can effectively cope with the time-varying or unknown dynamic characteristics of the AT and the towed ship system, and enhance the robustness of the AT and the towed ship.

[0184] In a specific embodiment, the scheme for designing an event-triggered quantized AT controller based on command filtering and a towed vessel controller based on command filtering based on the intermediate control law of the AT and the towed vessel in the forward degree of freedom and the pitching degree of freedom and the update law of the AT and the towed vessel adaptive law is:

[0185] S51. Based on the intermediate control law of the AT and the towed vessel in the forward degree of freedom and the pitching degree of freedom and the update law of the AT and the towed vessel adaptive law, an event-triggered quantized AT controller based on command filtering and a towed vessel controller based on command filtering are designed, as shown in formulas (52) and (53).

[0186]

[0187]

[0188] Where n p represents the speed of the controller of the AT in the forward degree of freedom (the input of the controller of the AT in the forward degree of freedom is expressed in speed), α Urepresents the intermediate control law of the towed vessel in the forward degree of freedom, represents the control law of the controller of the towed vessel in the forward degree of freedom, represents the adaptive law of the intermediate control law of AT on the forward degree of freedom, α n represents the intermediate control law of AT on the forward degree of freedom, δ r represents the rudder angle of the controller of the AT in the pitching degree of freedom (the input of the controller of the AT in the pitching degree of freedom is expressed in rudder angle), represents the adaptive law of AT on the yaw degree of freedom, α δ represents the intermediate control law of AT on the yaw degree of freedom, represents the adaptive law of the towed ship in the forward degree of freedom, α R represents the intermediate control law of the towed vessel in the bow pitch degree of freedom, represents the control law of the controller of the towed vessel in the pitching degree of freedom, It represents the adaptive law of the towed vessel in the bow pitch degree of freedom.

[0189] The controller can adaptively adjust the weights of the neural network to improve the stability and control effect of the system, and adjust the update law of the adaptive law according to the value of the system state v, thereby ensuring that the system can achieve optimal performance in different states.

[0190] In a specific embodiment, the scheme for implementing the towing control of the towed vessel by the AT using the event-triggered quantized AT controller based on command filtering and the towed vessel controller based on command filtering is:

[0191] like Figure 3 As shown, the tugboat event-triggered quantitative control path tracking control is divided into guidance system, control system and navigation system;

[0192] The guidance system performs initial state setting and waypoint setting, and generates the relevant path, i.e., the desired trajectory;

[0193] The control system multiplies the expected trajectory with the data of the actual navigation system to obtain and generate the dynamic error, transform the dynamic error into coordinates, generate adaptive and tugboat controllers, add hysteresis quantizers and event triggers to the tugboat controller, perform neural network weight estimation and radial basis neural network approximation on the system, eliminate the dynamic error, and realize path tracking control of the tugboat.

[0194] In this embodiment, an event trigger mechanism is set for the position error, heading error and dynamic error to ensure that the system updates the control signal only when the signal change exceeds a certain threshold, thereby achieving synchronous updating of the controller and the neural network weights, thereby improving the response speed of the system; in addition, combined with the hysteresis quantization mechanism, the system can avoid frequent adjustments caused by small fluctuations, significantly reduce unnecessary signal transmission and calculation, thereby saving limited communication bandwidth and computing resources.

[0195] The scheme of the present invention and the path tracking technology based on MLP and DOB were used to conduct numerical comparison simulation in a simulated external ocean environment. The differences are shown in Table 1.

[0196] Table 1 Similarities and differences between the solution of the present invention and the prior art

[0197] index Disturbance Observer Filter Error Compensation Event-triggered quantitative control Method of the present invention no yes yes Prior art yes no no

[0198] The method of the present invention and the prior art were compared and simulated on an industrial computer (Intel(R) Core(TM) i5-7300 HQ CPU@2.50GHz, RAM: 8.00GB). Figure 4-Figure 6 The main comparison results are shown:

[0199] Figure 4 The comparison results of ship path tracking under the two methods are shown. Although both methods achieve satisfactory control effects, the trajectory of the method of the present invention is more stable due to the effect of the filter error compensation signal, while the prior art fails to solve the input filter error problem;

[0200] Figure 5 The error curves of the two methods are described. It can be seen from the figure that the error of the method of the present invention is relatively small and more stable, which means that the method of the present invention has more advantages in terms of smoothness and accuracy of path tracking;

[0201] from Figure 6 It can be seen that the method of the present invention performs step control action at each triggering moment, which effectively reduces the execution frequency of the actuator. In addition, thanks to the introduction of the hysteresis quantizer, the problem of frequent jitter of the input is effectively solved, while the existing technology cannot cope with such problems. Such improvements improve the stability and responsiveness of the system.

[0202] Therefore, by combining the existing MLP-based and DOB-based path tracking control technologies for numerical comparison simulation, the present invention has achieved the following three beneficial effects in the field of AT motion control:

[0203] 1) Compared with the existing control algorithms, the event-triggered quantitative control method based on command filtering proposed in this invention shows significant advantages in many aspects. First, by introducing the filter compensation signal, the influence of the filter error can be effectively predicted and compensated, ensuring that the control signal can respond accurately in the process of rapid changes. This feature eliminates the delay and error accumulation problems caused by the traditional first-order filter, allowing the control system to maintain high-precision control performance while smoothing the control signal to avoid performance degradation caused by filtering errors.

[0204] 2) Secondly, by setting event trigger mechanisms for position error, heading error and dynamic error, the present invention ensures that the system updates the control signal only when the signal change exceeds a certain threshold. This mechanism realizes the synchronous update of the controller and the neural network weights, thereby improving the response speed of the system. In addition, combined with the hysteresis quantization mechanism, the system can avoid frequent adjustments caused by small fluctuations, significantly reduce unnecessary signal transmission and calculation, thereby saving limited communication bandwidth and computing resources.

[0205] 3) Through numerical simulation verification, the control method of the present invention shows superior control performance in the towing control task of the autonomous tugboat, which not only overcomes the shortcomings of the traditional control algorithm in processing filter errors and signal triggering, but also significantly improves the adaptability and reliability of the system in complex environments, and provides a more energy-saving, efficient, safe and stable solution for the motion control of the autonomous tugboat. This innovation has laid a solid foundation for the application of autonomous tugboats in marine engineering and other fields.

[0206] 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. An event-triggered quantitative towing control method for autonomous tugboat based on command filtering, characterized in that: include: S1: construct nonlinear system models of the AT and the towed ship respectively as the control objects of the controller designed in the subsequent steps, and use the guided virtual ships of the AT and the towed ship to obtain the reference routes of the AT and the towed ship; S2: constructing a guidance law according to the positions of the guided virtual ship and the actual AT and the towed ship in the reference route, and generating the expected trajectories of the AT and the towed ship according to the guidance law; S3: respectively design virtual control laws for the AT and the towed vessel in terms of forward freedom and bow pitch freedom, introduce filters to compensate for the dynamic errors between the actual trajectories and the expected trajectories of the AT and the towed vessel in the virtual control laws, and obtain the compensated dynamic errors of the AT and the towed vessel; S4: designing intermediate control laws of the AT and the towed ship in the forward degree of freedom and the pitching degree of freedom respectively according to the compensated dynamic errors of the AT and the towed ship, and designing update laws of the adaptive laws of the AT and the towed ship respectively according to the compensated dynamic errors of the AT and the towed ship and the two intermediate control laws; S5: designing an event-triggered quantized AT controller based on command filtering and a towed vessel controller based on command filtering based on the intermediate control law of the AT and the towed vessel in the forward degree of freedom and the pitching degree of freedom and the update law of the AT and the towed vessel adaptive law; S6: Using the command filtering-based event-triggered quantized AT controller and the command filtering-based towed ship controller to implement AT towing control of the towed ship.

2. The method for autonomous tugboat event-triggered quantitative towing control based on command filtering according to claim 1, characterized in that: The nonlinear system models of the AT and the towed ship are respectively constructed as the control objects of the controller designed in the subsequent steps, and the reference routes of the AT and the towed ship are obtained using the guided virtual ships of the AT and the towed ship, including: S11. Construct nonlinear mathematical models of the AT and the towed vessel respectively, as shown in formula (1) and formula (2). In the formula, T represents the autonomous tugboat, i.e. AT, S represents the towed ship, and x i ,y i ,i=T,S represents the position coordinates of AT and the towed ship, ψ i represents AT and the heading angle of the towed vessel, u i represents AT and the forward speed of the towed vessel, v i represents AT and the transverse drift speed of the towed vessel, r i represents AT and the yaw angular velocity of the towed vessel, represents the hydrodynamic added mass of AT and the towed vessel in the forward degree of freedom, represents the hydrodynamic additional mass of AT and the towed vessel in the drifting degree of freedom, represents the hydrodynamic added mass of AT and the towed vessel in the pitching degree of freedom, f vi (v), f ri (v) represent the nonlinear terms of AT and the towed vessel in the forward, drift and pitch degrees of freedom, respectively, d wui ,d wvi ,d wri is the disturbance force and moment of the external environment acting on the AT and the towed vessel’s forward, sideways and yaw degrees of freedom, T u (·),F r (·) respectively represent the control gains of the main engine speed and rudder angle of the tugboat, n p represents the main engine speed of the tugboat, δ p represents the rudder angle of the tugboat, Q(n p |n p |),Q(δ r ) represent the quantization input of the hysteresis quantizer in the forward degree of freedom and the bow degree of freedom of the tugboat, respectively, H u represents the towing force acting on the towed vessel, L1 represents the length of the tugboat, L2 represents the length of the towed vessel, θ2 represents the angle between the tow rope and the tugboat, and θ1 represents the angle between the tow rope and the towed vessel; The hysteresis quantizer is shown in formula (3), Q(k)=G(k)k+D (3) Wherein, Q(k) represents the hysteresis quantizer, k represents the actual hysteresis quantization input of AT, G(k) represents the quantization control gain, as shown in formula (4), and D represents the additional interference term, as shown in formula (5); The hysteresis quantizer is piecewise linearized, as shown in formula (6): Among them, k j =ρ (1-j) k min , is a constant, is the derivative of k, sgn is the sign function, k j is the threshold of the hysteresis quantizer, j is the quantization level, k min is the quantization dead zone, ρ is the quantization density, Q(k(t - )) represents the quantized value of the actual input k at the left limit moment of time t; S12. Use the guided virtual ship to obtain the reference route of AT and the towed ship, as shown in formula (7): In the formula, x d (t),y d (t) represents the position coordinate of the guided virtual ship on the reference route, ψ d (t) represents the heading angle of the guided virtual ship, r d (t) represents the expected bow angular velocity of the guided virtual ship, and t represents the continuous motion time of the virtual guided ship.

3. The method for autonomous tugboat event-triggered quantitative towing control based on command filtering according to claim 2, characterized in that: A guidance law is constructed according to the positions of the guided virtual ship, the actual AT and the towed ship in the reference route, including: The guidance law is shown in formula (8): In the formula, ψ ri It represents the AT and the azimuth of the towed ship relative to the guided virtual ship, with the lateral distance between the towed ship and the tugboat as the x-axis and the longitudinal distance as the y-axis. ei represents the position error of the AT and the towed ship relative to the guided virtual ship on the x-axis, and y ei represents the position error of the AT and the towed ship relative to the guided virtual ship on the y-axis, z ei Indicates the distance between the AT and the towed ship relative to the guided virtual ship.

4. The method for autonomous tugboat event-triggered quantitative towing control based on command filtering according to claim 3 is characterized in that: The virtual control laws of the AT and the towed ship in the forward degree of freedom and the bow pitch degree of freedom are designed respectively, and the filter is introduced to compensate the dynamic errors between the actual trajectory and the expected trajectory of the AT and the towed ship in the virtual control law, and the compensated dynamic errors of the AT and the towed ship are obtained, including: S31. Define the position error and heading error of AT and the towed vessel, as shown in formula (9): In the formula, represents the derivative of AT and the distance between the towed ship and the guided virtual ship, represents the derivative of AT and the heading error of the towed vessel, ψ ri represents AT and the azimuth of the towed ship relative to the guided virtual ship, r i Indicates AT and the pitching angular velocity of the towed vessel; i = T, S, where T represents AT and S represents the towed vessel; S32, design the virtual control law of AT and the towed vessel in the forward degree of freedom and bow pitch degree of freedom, as shown in formula (10), In the formula, α ui represents the virtual control law of AT and the towed vessel in the forward degree of freedom, α ri represents the virtual control law of AT and the towed vessel in the bow pitch degree of freedom, represents the design parameters of the virtual control law for the AT and the towed vessel in the forward and bow degrees of freedom, represents the constant of the virtual control law of AT and the towed vessel in the forward degree of freedom; S33, introducing a filter to compensate for the dynamic errors of the AT and the towed vessel, the filter is as shown in formula (11), In the formula, β ιi , ι=u,r represents the filter variables of AT and the towed vessel in the forward and bow degrees of freedom; ∈ ιi is a time constant greater than zero, α ιi (0), β ιi (0) is α ιi , β ιi The initial value of q ιi =α ιi -β ιi , represents the first-order filter error; S34, defining the dynamic error of the AT and the towed vessel according to formula (11), as shown in formula (12), ι ei ＝β ιi -ι i (12) In the formula, ι ei represents the dynamic error between AT and the towed vessel; S35, designing a filter error compensation signal according to the filter variables of the AT and the towed vessel in the forward degree of freedom and the pitching degree of freedom, as shown in formula (13), In the formula, ζ ιi represents the filter error compensation signal of AT and the towed vessel, and the variable ζ ιi The initial value of k is zero, ιi are the design parameters of the AT and towed vessel filter error compensation signals; S36, compensating the dynamic error according to the filter error compensation signal to obtain a compensated dynamic error, as shown in formula (14), x ei =b ιi -i ei -g ιi (14) In the formula, χ ei Represents the compensated dynamic error, X=U,R.

5. The method for autonomous tugboat event-triggered quantitative towing control based on command filtering according to claim 4, characterized in that: According to the compensated dynamic errors of the AT and the towed vessel, the intermediate control laws of the AT and the towed vessel in the forward degree of freedom and the bow pitch degree of freedom are designed respectively, including: S41. Combining formulas (1), (2), (11), (13) and (14), the dynamic errors of AT and the towed vessel are derived, as shown in formula (15): In the formula, are the neural network weights of AT and the towed vessel in the forward and bow freedom, respectively. uT (v),S rT (v) and S uS (v),S rS (v) represents the Gaussian function of the AT and the towed vessel in the forward and forward degrees of freedom, ν represents the input of the neural network of the AT and the towed vessel in the forward and forward degrees of freedom, ε uT ,ε uS and ε uT ,ε rS represents the approximation error of AT and the towed vessel in the forward and bow freedom, respectively. G(N u ) represents the quantized control gain of AT on the forward degree of freedom, G(δ r ) represents the quantitative control gain N of AT on the yaw degree of freedom u =n p |n p |, represents the control input of AT in the forward degree of freedom without hysteresis quantization; S42. Design the intermediate control law of the AT in the forward and yaw degrees of freedom and the intermediate control law of the towed vessel in the forward and yaw degrees of freedom, as shown in formulas (16) and (17), In the formula, represents the design parameters of the intermediate control law of AT, k uT ,k uT represents the design parameters of the AT filter compensation signal, is the design parameter of the intermediate control law of the towed vessel, k uS ,k uS represents the design parameters of the towed vessel filter compensation signal, u=T, S is the estimate of the external disturbance boundary of AT and the towed vessel in the forward and bow degrees of freedom, respectively. ui ,b ri ,i=T,S are the design constants of interference estimation of AT and the towed vessel in forward freedom and bow freedom, respectively, U ei represents the forward speed error between AT and the towed vessel in the forward degree of freedom, R ei represents the angular velocity error of AT and the towed vessel in the yaw degree of freedom, ∈ ui represents the time constant of the filter variables of AT and the towed vessel in the forward degree of freedom, ∈ ri represents the time constant of the filter variables of AT and the towed vessel in the pitching degree of freedom, represents the derivative of the filter variables of AT and the towed vessel in the forward degree of freedom, represents the derivative of the filter variables of AT and the towed vessel in the pitching degree of freedom, ζ ui represents the filter error compensation signal of AT and the towed vessel in the forward degree of freedom, ζ ri represents the filter error compensation signal of AT and the towed vessel in the pitching degree of freedom, S ui represents the basis function of the neural network of AT and the towed vessel in the forward degree of freedom, S ri Represents the basis functions of the neural network for AT and the tugboat’s pitching degree of freedom.

6. The method for autonomous tugboat event-triggered quantitative towing control based on command filtering according to claim 5, characterized in that: According to the compensated dynamic errors of the AT and the towed vessel and the two intermediate control laws, the update laws of the AT and the towed vessel adaptive laws are designed respectively, including: S43, defining the event trigger measurement error and event trigger condition of AT in the forward degree of freedom and the pitching degree of freedom according to the dynamic error and the position error, as shown in formulas (18) and (19), In formula (18), e n represents the event-triggered measurement error of AT in the forward degree of freedom, e δ represents the event-triggered measurement error of AT on the pitching degree of freedom, represents the sampling time of the event triggering moment in the forward and yaw degrees of freedom, k = n, δ represents the sampling time of the next event triggering moment in the forward degree of freedom and the pitching degree of freedom; In formula (19), Indicates the event triggering condition of AT on the forward degree of freedom, represents the event triggering condition of AT on the pitching degree of freedom, W is the sign of event triggering, inf represents the infimum, Indicates the event triggering conditions on the forward and forward degrees of freedom The trigger threshold, and It is the event triggering condition on the forward degree of freedom and the pitching degree of freedom The design parameters, ‖S r (v)‖ represents the neural network basis function S on the yaw degree of freedom r The norm of (v), ‖S u (v)‖ represents the neural network basis function S on the forward degree of freedom u (v) norm; S44. In the time period between the sampling time of the event triggering moment and the sampling time of the next event triggering moment, the updating law of the adaptive law of the neural network weight estimator at the AT event triggering moment is designed according to the intermediate control law of the AT, as shown in formula (20), In the formula, α k represents the intermediate control law of AT in forward and yaw degrees of freedom, and represents the adaptive law of the neural network weight estimator at the time of AT event triggering; S uT (v) and S rT (v) represents the Gaussian function of AT in the forward and forward degrees of freedom; S45. Design an update law of the AT adaptive law according to the intermediate control law of the AT. The update law of the AT adaptive law is shown in formula (21): In the formula, represents the update law of the AT adaptive law, represents the gain adaptive design parameter of AT in forward and yaw degrees of freedom; for The initial value of S46. Design an update law for the adaptive law of the towed ship according to the intermediate control law of the towed ship. The update law for the adaptive law of the towed ship is shown in formula (22): In the formula, represents the update law of the towed ship’s adaptive law; represents the gain adaptive design parameters of the towed vessel in the forward and bow freedom; for The initial value of S47. Design an update law for the adaptive law of the neural network weight estimator at the event triggering moment of the towed ship according to the intermediate control law of the towed ship, as shown in formula (23): In the formula, represents the update law of the adaptive law of the neural network weight estimator at the time of the towed ship event triggering, is the design constant of the weighted adaptive law for the forward and bow freedom of the towed vessel; S uS (v) and S rS (ν) represents the Gaussian function of the towed vessel in the forward and forward degrees of freedom; S48. Design the updating law of the adaptive law of AT and the external disturbance of the towed vessel, as shown in formula (24), In the formula, represents the design constants of the adaptive law of external disturbances of the AT and the towed vessel in the forward and bow degrees of freedom; is the estimate of the external disturbance boundary between AT and the towed vessel; for The initial value of .

7. The method for autonomous tugboat event-triggered quantitative towing control based on command filtering according to claim 6, characterized in that: Based on the intermediate control law of the AT and the towed ship on the forward degree of freedom and the pitching degree of freedom and the update law of the AT and the towed ship's adaptive law, an event-triggered quantized AT controller based on command filtering and a towed ship controller based on command filtering are designed, including: S51. Based on the intermediate control law of the AT and the towed vessel in the forward degree of freedom and the pitching degree of freedom and the update law of the AT and the towed vessel adaptive law, an event-triggered quantized AT controller based on command filtering and a towed vessel controller based on command filtering are designed, as shown in formulas (25) and (26). Where n p represents the speed of the controller of AT in the forward degree of freedom, α U represents the intermediate control law of the towed vessel in the forward degree of freedom, represents the control law of the controller of the towed vessel in the forward degree of freedom, represents the adaptive law of the intermediate control law of AT on the forward degree of freedom, α n represents the intermediate control law of AT on the forward degree of freedom, δ r represents the rudder angle of the AT controller in the pitching degree of freedom, represents the adaptive law of AT on the yaw degree of freedom, α δ represents the intermediate control law of AT on the yaw degree of freedom, represents the adaptive law of the towed ship in the forward degree of freedom, α R represents the intermediate control law of the towed vessel in the bow pitch degree of freedom, represents the control law of the controller of the towed vessel in the pitching degree of freedom, It represents the adaptive law of the towed vessel in the bow pitch degree of freedom.

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