A trajectory tracking control method and system for underactuated ships based on identification modeling

Abstract

The invention discloses a trajectory tracking control method and system for an underactuated ship based on identification modeling, and designs an identification model, an improved extended state observer and a trajectory tracking controller; the method comprises: S1. according to the motion characteristics of the underactuated ship, a three-degree-of-freedom model structure is determined by mechanism analysis, and model parameters are identified by using an extended Kalman filter algorithm through ship navigation data to obtain an identification model; S2. the model identification error and the environmental disturbance error are regarded as total disturbance, and an improved extended state observer is designed to estimate the total disturbance of the system; S3. based on the sliding mode control theory, a trajectory tracking controller is designed, and according to the complexity of the ship control task, an exponential reaching law and a linear sliding mode surface are adopted, and disturbance compensation is added in the design of the controller to obtain a trajectory tracking controller; the invention can still realize high-precision trajectory tracking control without the need for complex modeling, and has strong anti-interference ability.

Description

Technical Field

[0001] The present invention relates to the technical field of ship motion control, and more particularly to a method and system for tracking and controlling an underactuated ship trajectory based on identification modeling. Background Art

[0002] At present, in order to ensure that ships can complete actual navigation tasks as required, ship trajectory tracking control technology has been widely studied. Trajectory tracking control has higher requirements for ship navigation control and has strong time constraints. It is necessary to control the ship to sail along the set route and arrive at the designated location within the specified time.

[0003] The actuators of an under-driven ship only have propellers and rudders, which can only provide longitudinal thrust and bow torque, avoiding control system failure due to thrust failure of a fully-driven ship and increasing navigation stability and safety.

[0004] However, due to the constraints of under-actuated characteristics, the trajectory tracking control of the ship is also more difficult; in addition, the ship modeling work is complicated and many model parameters are approximate calculations. When there are disturbances such as wind and waves in the navigation environment, the ship will exhibit unknown nonlinear dynamic parameter changes.

[0005] Therefore, how to provide a ship trajectory tracking control method that is highly robust to model parameter uncertainty and environmental disturbances is an urgent problem that technicians in this field need to solve. Summary of the invention

[0006] In view of this, the present invention aims at the problems of complex ship modeling, uncertain model parameters and external environmental disturbances, performs model parameter identification based on the extended Kalman filter algorithm, combines sliding mode control and anti-disturbance theory, and designs an under-actuated ship trajectory tracking control method based on identification modeling to solve the problem of high-precision trajectory tracking control under the condition of uncertain ship model.

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

[0008] A trajectory tracking control method for an underactuated ship based on identification modeling comprises the following steps:

[0009] S1. According to the motion characteristics of the underactuated ship, the three-degree-of-freedom model structure is determined through mechanism analysis, and the model parameters are identified by using the extended Kalman filter algorithm through the ship's navigation data to obtain the identification model;

[0010] S2. Treat the model identification error and environmental disturbance error as the total disturbance, and design an improved extended state observer to estimate the total disturbance of the system;

[0011] S3. Based on the sliding mode control theory, the trajectory tracking controller is designed. According to the complexity of the ship control task, the exponential reaching law and the linear sliding surface are adopted, and disturbance compensation is added to the controller design to obtain the trajectory tracking controller;

[0012] S4. Obtain the navigation data of the underactuated ship in real time, use the ship's three-degree-of-freedom identification model to identify the internal disturbance of the model parameter error, obtain the external environmental disturbance, use the improved extended state observer based on the external environmental disturbance and the internal disturbance of the model parameter error to estimate the total disturbance in the ship trajectory tracking process, and use the trajectory tracking controller to compensate for the disturbance of the underactuated ship based on the total disturbance, so as to perform trajectory tracking control in real time.

[0013] Preferably, the identification model in step S1 is:

[0014]

[0015] Where q = [xy ψ] T Define the ship position variable in the attached coordinate system. is the speed variable, is the acceleration variable, τ=[n1 δ n2] T is the output of the control transmitter, d is the design of all disturbance information received by the system as an expansion state, n1 and n2 are propeller speeds, δ is the rudder angle, m is the ship mass, u is the longitudinal speed of the ship, v is the sway speed, r is the bow angular velocity, a i ,b i ,c i are identification parameters respectively.

[0016] Preferably, the improved extended state observer in step S2 is:

[0017]

[0018] Among them, z i is the estimated value of the ship state variable, i = 1, 2, 3, e1 represents the error between the expected trajectory and the actual trajectory, e2 represents the error between the derivative of the expected trajectory and the derivative of the actual trajectory, α1 = α1I3, α2 = α2I3, α1>0, α2>0 are constant coefficients, β1, β2, β3 are the gains of the extended state observer respectively, ω o is the system bandwidth;

[0019] The disturbance estimate of the improved extended state observer is:

[0020]

[0021] Preferably, the trajectory tracking controller in step S3 is in the form of:

[0022]

[0023] Among them, the sliding mode switching surface is:

[0024]

[0025] The exponential reaching law is:

[0026]

[0027] The saturation function is:

[0028]

[0029] Where e = q wd -q w , q wd is the expected trajectory in the world coordinate system, is the expected velocity, 1 / b is the time constant, k1 and k2 are reaching law parameters, k1>0, k2>0, Δ is the thickness of the saturation function boundary layer.

[0030] Preferably, the identification model is obtained by:

[0031] According to the typical MMG separation model, the model structure of identification modeling is determined as follows:

[0032]

[0033] Among them, n1n2 is the propeller speed, δ is the rudder angle, and a i ,b i ,c i is the parameter to be identified;

[0034] Use a specific random sequence to simulate the output dynamic noise and measurement noise of the actual system, and transform the model into a general system equation:

[0035]

[0036] y(t)=Hx(t)+e(t)

[0037] in:

[0038]

[0039] Discretize the system equations:

[0040] x(k+1)=f a (x(k),k)+w(k)

[0041] y(k)=Hx(k)+e(k)

[0042]

[0043] Where w(k) and e(k) are zero-mean white noise sequences with variances Q and R respectively;

[0044] Then, f1 a arrive The expression is:

[0045]

[0046] In summary, the extended Kalman filter recursive formula is:

[0047]

[0048] Among them, P(k+1|k) is the prediction error covariance matrix, P(k+1) is the estimation error covariance matrix, K(k+1) is the filter gain matrix, For status forecast, is the state estimation;

[0049] According to the extended Kalman filter recursive formula, the system reaches a convergence state after a certain number of times, thereby obtaining the state value x(k) and finally obtaining the model parameter a i 、b i and c i An estimated value of

[0050] The total disturbance information of the system is designed as an expansion state d, and the ship position variable is defined as q = [xy ψ] in the attached coordinate system. T The speed variable is Acceleration variable The output of the control input is τ=[n1 δ n2] T , and obtain the identification model.

[0051] Preferably, the ship state equation is:

[0052]

[0053] The error between the true value and the estimated value of the system state variable is:

[0054] e i =x i -z i

[0055] Among them, the state variable x1 = q w , x3=D(t),D(t)=-d,q w is the position of the ship in a fixed coordinate system.

[0056] An underactuated ship trajectory tracking control system based on identification modeling, based on the underactuated ship trajectory tracking control method based on identification modeling, comprising: an identification model, an improved extended state observer and a trajectory tracking controller;

[0057] Identification model, which is used to determine the three-degree-of-freedom model structure through mechanism analysis for the motion characteristics of underactuated ships, and identify model parameters using the extended Kalman filter algorithm through ship navigation data;

[0058] Improved extended state observer, which is used to treat the model identification error and environmental disturbance error as the total disturbance and estimate the total disturbance of the system;

[0059] The trajectory tracking controller is used to perform trajectory tracking control based on the sliding mode control theory, using the exponential reaching law and the linear sliding surface according to the complexity of the ship control task, and adding disturbance compensation in the design of the controller.

[0060] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the underactuated ship trajectory tracking control method based on identification modeling.

[0061] A processing terminal comprises a memory and a processor. The memory stores a computer program that can be run on the processor. When the processor executes the computer program, the underactuated ship trajectory tracking control method based on identification modeling is implemented.

[0062] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses a trajectory tracking control method and system for an underactuated ship based on identification modeling. The model parameter identification algorithm based on the extended Kalman filter can solve the problems of complex mechanism modeling process and uncertain model parameters. The improved extended state observer is used to identify modeling errors and estimate system internal and external disturbances such as environmental disturbances, and a strong robustness control algorithm sliding mode control is used to design a trajectory tracking controller, which further improves the control capability of the ship under environmental disturbances and realizes high-precision trajectory tracking control without the need for complex modeling process and strong environmental disturbances. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0064] Figure 1 The accompanying drawing is a schematic diagram of a trajectory tracking control method for an underactuated ship based on identification modeling provided by the present invention;

[0065] Figure 2 The accompanying drawings are schematic diagrams of an inertial coordinate system and an attached coordinate system provided by the present invention;

[0066] Figure 3 The accompanying drawing is a schematic diagram of a parameter convergence curve in a model parameter identification process provided by an embodiment of the present invention;

[0067] Figure 4 The accompanying drawing is a schematic diagram of a trajectory tracking control response curve provided by an embodiment of the present invention;

[0068] Figure 5 The accompanying drawings are schematic diagrams of trajectory tracking control response curves of various degrees of freedom provided by an embodiment of the present invention;

[0069] Figure 6 The accompanying drawing is a schematic diagram of trajectory tracking control errors of each degree of freedom provided by an embodiment of the present invention;

[0070] Figure 7 The accompanying drawing is a schematic diagram of a vehicle rudder control instruction in a trajectory tracking process provided by an embodiment of the present invention;

[0071] Figure 8 The accompanying drawing is a schematic diagram of estimated disturbance and actual disturbance curves provided by an embodiment of the present invention;

[0072] Fig. 9 The accompanying drawing is a schematic diagram of the underactuated ship trajectory tracking control system provided by the present invention. DETAILED DESCRIPTION

[0073] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only 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.

[0074] The embodiment of the present invention discloses a trajectory tracking control method for an underactuated ship based on identification modeling, such as Figure 1 , including the following steps:

[0075] S1. According to the motion characteristics of the underactuated ship, the three-degree-of-freedom model structure is determined through mechanism analysis, and the model parameters are identified by using the extended Kalman filter algorithm through the ship's navigation data to obtain the identification model;

[0076] S2. Treat the model identification error and environmental disturbance error as the total disturbance, and design an improved extended state observer to estimate the total disturbance of the system;

[0077] S3. Based on the sliding mode control theory, the trajectory tracking controller is designed. According to the complexity of the ship control task, the exponential reaching law and the linear sliding surface are adopted, and disturbance compensation is added to the controller design to obtain the trajectory tracking controller;

[0078] S4. Obtain the navigation data of the underactuated ship in real time, use the ship's three-degree-of-freedom identification model to identify the internal disturbance of the model parameter error, obtain the external environmental disturbance, use the improved extended state observer based on the external environmental disturbance and the internal disturbance of the model parameter error to estimate the total disturbance in the ship trajectory tracking process, and use the trajectory tracking controller to compensate for the disturbance of the underactuated ship based on the total disturbance, so as to perform trajectory tracking control in real time.

[0079] In this embodiment, considering the three-degree-of-freedom ship mechanism model, the typical MMG separation model is:

[0080]

[0081] Among them, m is the mass of the ship, u is the longitudinal velocity of the ship, v is the sway velocity, r is the bow angular velocity, and the right side of the equation is the force on the bare ship, the oar force, the rudder force and the disturbance force caused by wind and waves;

[0082] The modeling work through mechanism analysis method is complicated. In addition, many parameters are obtained by empirical formulas or approximate calculations, and the results have certain errors, which further affects the ship control performance.

[0083] In order to further implement the above technical solution, the identification model is obtained by:

[0084] According to the typical MMG separation model, the model structure of identification modeling is determined as follows:

[0085]

[0086] Among them, n1n2 is the propeller speed, δ is the rudder angle, and a i ,b i ,c i is the parameter to be identified;

[0087] A specific random sequence is used to simulate the output dynamic noise and measurement noise of the actual system. The sequences do not interfere with each other. This embodiment uses a Gaussian white noise sequence to transform the model into a general system equation:

[0088]

[0089] y(t)=Hx(t)+e(t)

[0090] in:

[0091]

[0092] Discretize the system equations:

[0093] x(k+1)=f a (x(k),k)+w(k)

[0094] y(k)=Hx(k)+e(k)

[0095]

[0096] Where w(k) and e(k) are zero-mean white noise sequences with variances Q and R respectively;

[0097] Then, f1 a arrive The expression is:

[0098]

[0099] In summary, the extended Kalman filter recursive formula is:

[0100]

[0101] Among them, P(k+1|k) is the prediction error covariance matrix, P(k+1) is the estimation error covariance matrix, K(k+1) is the filter gain matrix, For status forecast, is the state estimation;

[0102] According to the extended Kalman filter recursive formula, the system reaches a convergence state after a certain number of times, thereby obtaining the state value x(k) and finally obtaining the model parameter a i 、b i and c i An estimated value of

[0103] The total disturbance information of the system is designed as an expansion state d, and the ship position variable is defined as q = [xy ψ] in the attached coordinate system. T The speed variable is Acceleration variable The output of the control input is τ=[n1 δ n2] T , and obtain the identification model.

[0104] In order to further implement the above technical solution, the identification model in step S1 is:

[0105]

[0106] Where q = [xy ψ] T Define the ship position variable in the attached coordinate system. is the speed variable, is the acceleration variable, τ=[n1 δ n2] T is the output of the control transmitter, d is the design of all disturbance information received by the system as an expansion state, n1 and n2 are propeller speeds, δ is the rudder angle, m is the ship mass, u is the longitudinal speed of the ship, v is the sway speed, r is the bow angular velocity, a i ,b i ,c i are identification parameters respectively.

[0107] In practical applications, the model identification results are obtained in the ship's body coordinate system, and in actual control, they need to be converted to the inertial coordinate system, such as Figure 2 .

[0108] In order to further implement the above technical solution, the internal and external disturbances d(t) of the ship are designed as an expanded state, and all the disturbance information of the system is designed as an expanded state d. The ship state equation is:

[0109]

[0110] The error between the true value and the estimated value of the system state variable is:

[0111] e i =x i -z i Among them, the state variable x1 = q w , x3=D(t),D(t)=-d,q w is the position of the ship in a fixed coordinate system.

[0112] In order to further implement the above technical solution, the improved extended state observer in step S2 is:

[0113]

[0114] Among them, z i is the estimated value of the ship state variable, i = 1, 2, 3, e1 represents the error between the expected trajectory and the actual trajectory, e2 represents the error between the derivative of the expected trajectory and the derivative of the actual trajectory, α1 = α1I3, α2 = α2I3, α1>0, α2>0 are constant coefficients, β1, β2, β3 are the gains of the extended state observer respectively, ω o is the system bandwidth;

[0115] The disturbance estimate of the improved extended state observer is:

[0116]

[0117] In order to further implement the above technical solution, the design method of the trajectory tracking controller in step S3 is:

[0118] Design the sliding surface, that is, the state space manifold, and the selected sliding mode switching surface is:

[0119]

[0120] The derivative is:

[0121]

[0122] When s→0, Then e(t) converges exponentially, the time constant is 1 / b, and the exponential convergence law is:

[0123]

[0124] Due to the discontinuity of the sign function sgn(), the system may suffer from a jitter problem. Therefore, the saturation function used in this embodiment is:

[0125]

[0126] Reasonable setting of the reaching law parameters k1 and k2 can adjust the dynamic arrival process of the sliding surface and achieve the purpose of reducing chattering;

[0127] Further, according to the derivative of the sliding mode switching surface, the exponential reaching law and the saturation function, and the identification model, we can get:

[0128]

[0129] By compensating the disturbance estimated by the observer in the controller, the final controller form can be obtained:

[0130]

[0131] Where e = q wd -q w , q wd is the expected trajectory in the world coordinate system, is the expected velocity, 1 / b is the time constant, k1 and k2 are reaching law parameters, k1>0, k2>0, Δ is the thickness of the saturation function boundary layer.

[0132] In this embodiment, a trajectory tracking control method for an underactuated ship based on identification modeling is simulated and verified:

[0133] In the simulation test, the patrol ship was taken as the research object. The ship is 47 meters long, 8 meters wide, and has a draft of 2.4 meters. It is a typical under-driven twin-propeller and twin-rudder ship with good maneuverability and maneuverability.

[0134] Firstly, the parameter identification method of the three-degree-of-freedom model of the under-actuated ship proposed in the present invention is tested, and the identification environment is designed as the third-level sea condition; in the trajectory tracking control task, based on the above identification model, the trajectory control accuracy and anti-interference ability of the sliding mode control and sliding mode anti-disturbance control algorithms are tested.

[0135] The reference trajectory is set to a circular trajectory with a radius of 200 meters and a period of 800 seconds:

[0136]

[0137] From the simulation results of the identification model Figure 3 It can be seen that when the identification program runs for 200 seconds, the model parameters stabilize to a certain fixed value, and this model parameter is used as the controller design; from the trajectory tracking control response results Figure 4 It can be seen that both control methods can achieve arc trajectory tracking, but the SMC method has obvious trajectory control errors, while the SMC-ESO almost coincides with the desired trajectory.

[0138] from Figure 5 and Figure 6 It can be seen that in the trajectory tracking of the three degrees of freedom, longitudinal, lateral and bow, the control performance of the SMC-ESO method is better than that of the SMC method.

[0139] from Figure 7 It can be seen that the rudder control instructions of the SMC control method change dramatically, which will damage the actuators of the ship during actual navigation. Compared with the linear SMC-ESO control method, the rudder output instructions are smoother and the control effect is better.

[0140] from Figure 8 It can be seen that the disturbance estimation value of the observer is basically consistent with the actual added disturbance, which verifies the effectiveness of the ship sliding mode active disturbance rejection control method proposed in the present invention under environmental disturbances.

[0141] A trajectory tracking control system for an underactuated ship based on identification modeling, based on a trajectory tracking control method for an underactuated ship based on identification modeling, such as Fig. 9 , including: identification model, improved extended state observer and trajectory tracking controller;

[0142] Identification model, which is used to determine the three-degree-of-freedom model structure through mechanism analysis for the motion characteristics of underactuated ships, and identify model parameters using the extended Kalman filter algorithm through ship navigation data;

[0143] Improved extended state observer, which is used to treat the model identification error and environmental disturbance error as the total disturbance and estimate the total disturbance of the system;

[0144] The trajectory tracking controller is used to perform trajectory tracking control based on the sliding mode control theory, using the exponential reaching law and the linear sliding surface according to the complexity of the ship control task, and adding disturbance compensation in the design of the controller.

[0145] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements a trajectory tracking control method for an underactuated ship based on identification modeling.

[0146] A processing terminal comprises a memory and a processor. The memory stores a computer program that can be run on the processor. When the processor executes the computer program, an underactuated ship trajectory tracking control method based on identification modeling is implemented.

[0147] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0148] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A trajectory tracking control method for an underactuated ship based on identification modeling, characterized in that: The following steps are involved: S1. According to the motion characteristics of underactuated ships, the three-degree-of-freedom model structure is determined through mechanism analysis, and the model parameters are identified by using the extended Kalman filter algorithm through the ship navigation data to obtain the three-degree-of-freedom identification model of the ship; S2. Treat the model identification error and environmental disturbance error as the total disturbance, and design an improved extended state observer to estimate the total disturbance of the system; S3. Based on the sliding mode control theory, the trajectory tracking controller is designed. According to the complexity of the ship control task, the exponential reaching law and the linear sliding surface are adopted, and disturbance compensation is added to the controller design to obtain the trajectory tracking controller; S4. Real-time acquisition of navigation data of the underactuated ship, identification of internal disturbances of model parameter errors using the ship's three-degree-of-freedom identification model, acquisition of external environmental disturbances, estimation of total disturbances in the ship's trajectory tracking process using an improved extended state observer based on external environmental disturbances and internal disturbances of model parameter errors, and disturbance compensation of the underactuated ship using a trajectory tracking controller based on the total disturbances, so as to perform trajectory tracking control in real time; The identification model in step S1 is: Where q = [xy ψ] T Define the ship position variable in the attached coordinate system. is the speed variable, is the acceleration variable, τ=[n1 δ n2] T is the output of the control transmitter, d is the design of all disturbance information received by the system as an expansion state, n1 and n2 are propeller speeds, δ is the rudder angle, m is the ship mass, u is the longitudinal speed of the ship, v is the sway speed, r is the bow angular velocity, a i ,b i ,c i are the identification parameters respectively; The improved extended state observer in step S2 is: Among them, z i is the estimated value of the ship state variable, i = 1, 2, 3, e1 represents the error between the expected trajectory and the actual trajectory, e2 represents the error between the derivative of the expected trajectory and the derivative of the actual trajectory, α1 = α1I3, α2 = α2I3, α1>0, α2>0 are constant coefficients, β1, β2, β3 are the gains of the extended state observer respectively, ω o is the system bandwidth; The disturbance estimate of the improved extended state observer is: The trajectory tracking controller in step S3 is in the form of: Among them, the sliding mode switching surface is: The exponential reaching law is: The saturation function is: Where e = q wd -q w , q w is the position of the ship in the fixed coordinate system, q wd is the expected trajectory in the world coordinate system, is the expected velocity, 1 / b is the time constant, k1 and k2 are reaching law parameters, k1>0, k2>0, Δ is the thickness of the saturation function boundary layer.

2. The underactuated ship trajectory tracking control method based on identification modeling according to claim 1 is characterized in that: The identification model is obtained by: According to the typical MMG separation model, the model structure of identification modeling is determined as follows: Use a specific random sequence to simulate the output dynamic noise and measurement noise of the actual system, and transform the model into a general system equation: in: Discretize the system equations: x(k+1)=f a (x(k),k)+w(k) y(k)=Hx(k)+e(k) Where w(k) and e(k) are zero-mean white noise sequences with variances Q and R respectively; but, arrive The expression is: In summary, the extended Kalman filter recursive formula is: Among them, P(k+1|k) is the prediction error covariance matrix, P(k+1) is the estimation error covariance matrix, K(k+1) is the filter gain matrix, For status forecast, is the state estimation; According to the extended Kalman filter recursive formula, the system reaches a convergence state after a certain number of times, thereby obtaining the state value x(k) and finally obtaining the model parameter a i , b i and c i The estimated value of .

3. The underactuated ship trajectory tracking control method based on identification modeling according to claim 1 is characterized in that: The ship state equation is: The error between the true value and the estimated value of the system state variable is: e i =x i -z i Among them, the state variable x1 = q w , x3=D(t),D(t)=-d.

4. An underactuated ship trajectory tracking control system based on identification modeling, characterized in that: A trajectory tracking control method for an underactuated ship based on identification modeling according to any one of claims 1 to 3, comprising: an identification model, an improved extended state observer and a trajectory tracking controller; Identification model, which is used to determine the three-degree-of-freedom model structure through mechanism analysis for the motion characteristics of underactuated ships, and identify model parameters using the extended Kalman filter algorithm through ship navigation data; Improved extended state observer, which is used to treat the model identification error and environmental disturbance error as the total disturbance and estimate the total disturbance of the system; The trajectory tracking controller is used to perform trajectory tracking control based on the sliding mode control theory, using the exponential reaching law and the linear sliding surface according to the complexity of the ship control task, and adding disturbance compensation in the design of the controller.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the underactuated ship trajectory tracking control method based on identification modeling as described in any one of claims 1 to 3 is implemented.

6. A processing terminal, comprising a memory and a processor, wherein the memory stores a computer program that can be run on the processor, characterized in that: When the processor executes the computer program, the underactuated ship trajectory tracking control method based on identification modeling as described in any one of claims 1 to 3 is implemented.

Images