Unmanned ship trajectory tracking control method based on shear mapping function

Abstract

The invention discloses an unmanned ship trajectory tracking control method based on a shear mapping function. Converting an error transformation function in a traditional preset performance framework through two-dimensional shear mapping, and based on a preset performance boundary, obtaining an error transformation variable capable of realizing singularity avoidance and overcoming an initial value constraint after applying the two-dimensional shear mapping; and establishing an unmanned ship trajectory tracking controller based on a shear mapping function in combination with the unmanned ship trajectory tracking error and the estimated value of the adaptive parameter, so as to obtain a virtual control law and an actual control law and complete tracking control of the unmanned ship. According to the invention, through two-dimensional shear mapping, the system can keep stable even if the state trajectory deviates from the preset performance constraint area and the initial value of the state trajectory is not in the preset performance constraint area. The conservative property of preset performance control is remarkably reduced, and the problem of singularity of the controller can be avoided, so that the control method has wider applicability and higher effectiveness in actual engineering application.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned ship control, and in particular to an unmanned ship trajectory tracking control method based on a shear mapping function. Background Art

[0002] As an intelligent surface navigation system, unmanned ships have attracted widespread attention due to their important role in marine resource exploration, development, maritime transportation and national defense construction. These ships usually have the ability to navigate remotely or autonomously, and can perform various maritime tasks without human intervention. Among many practical applications, trajectory tracking is a key area in unmanned ship control technology and is the basis for its wide application in fields such as marine surveillance, rescue and military missions. The trajectory tracking capability of unmanned ships not only reflects their maneuverability and adaptability, but is also an important indicator of their degree of automation and intelligence. Research on unmanned ship trajectory tracking technology has important strategic value for promoting the development of the marine industry.

[0003] In recent years, the requirements for ship operation tasks have gradually increased, and higher requirements and standards have been put forward for the transient and steady-state performance of unmanned ship trajectory tracking control. In this context, the field of unmanned ship trajectory tracking control with preset performance has received widespread attention from industry scholars. The core of preset performance control lies in the following two points: the design of performance function and the implementation of error transformation. The role of the performance function is to ensure that the convergence speed and overshoot of the tracking error can meet the expected standards, while the error transformation converts the problem of system control performance into the problem of ensuring that the error transformation function remains within certain limits. At present, most research focuses on optimizing the characteristics of the performance function and has achieved remarkable results. However, the existing results still have the following key problems:

[0004] First, in the control system design process, in order to ensure that the error transformation function is properly defined at the initial moment, the initial value of the performance function is usually closely related to the initial value of the tracking error, which means that the initial value is subject to certain constraints. The existence of this constraint limits the flexibility of the system's initial state, making it difficult for the system to start from certain specific initial conditions. In addition, if the initial value is not selected properly, it may cause large errors or instability in the system during the startup phase, affecting the control effect and the overall performance of the system.

[0005] Second, in the traditional preset performance control system, the effectiveness of the control system is achieved only when the state trajectory remains within the established boundary conditions. Although it is possible to ensure that the state trajectory complies with these boundaries during the system startup phase, it is difficult to ensure the stability of this state during the control cycle, especially in the face of strong interference. In addition, due to the limited control capabilities of the actual actuator, once a sudden disturbance occurs, the state trajectory may be pulled out of the constraint area, which may lead to controller singularity or even system instability. This conservatism limits the scope of application and effectiveness of traditional preset performance control in actual engineering. Summary of the invention

[0006] The present invention provides an unmanned ship trajectory tracking control method based on a shear mapping function to overcome the above technical problems.

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

[0008] A trajectory tracking control method for an unmanned ship based on a shear mapping function comprises the following steps:

[0009] S1: Establish an unmanned ship model considering environmental interference;

[0010] S2: establishing an unmanned ship trajectory tracking error according to the unmanned ship model considering environmental interference; constructing a preset performance boundary of a preset performance function according to the unmanned ship trajectory tracking error, and determining an error transformation function based on the preset performance boundary of the preset performance function;

[0011] S3: establishing a 2D shear mapping, and obtaining an error conversion variable capable of achieving singularity avoidance after applying the 2D shear mapping according to the 2D shear mapping and the error transformation function;

[0012] S4: obtaining fuzzy weights of adaptive parameters based on the fuzzy logic system to establish a fuzzy predictor, and then obtaining estimated values ​​of the adaptive parameters;

[0013] S5: According to the error conversion variables that can achieve singularity avoidance after applying the two-dimensional shear mapping, the unmanned ship trajectory tracking error and the estimated values ​​of the adaptive parameters, based on the second-order nonlinear tracking differentiator, an unmanned ship trajectory tracking controller based on the shear mapping function is established to obtain the virtual control law and the actual control law to complete the tracking control of the unmanned ship.

[0014] Furthermore, in S3, the 2D shear mapping is established as follows:

[0015]

[0016] Where: m 0 ,n 0Respectively represent the horizontal and vertical coordinates in the original space, m 1 Represents the transformation space with m 0 The corresponding horizontal axis, n 1 Represents the transformation space with n 0 The corresponding vertical coordinate; Indicates the shear angle of the shear mapping.

[0017] Furthermore, in S3, the formula used to obtain the error conversion variable after applying the 2D shear mapping is as follows;

[0018]

[0019] in,

[0020]

[0021] Where: z 1h (t) represents z 1 The hth (h=1,2,3)th component of (t); z 1 (t) represents the transformation variable that can achieve singularity-avoiding error after applying 2D shear mapping; represents the shear angle of the shear mapping; Represents auxiliary variables The hth component of ; represents the hth component of the unmanned ship trajectory tracking error e(t); represents a preset performance function; and All are positive numbers; h (t) represents the hth (h=1,2,3)th component of z(t); Indicates the independent variable The error conversion variable calculated by the error transformation function; Represents the hth (h=1, 2, 3)th component of the new auxiliary variable that satisfies the two-dimensional shear mapping condition.

[0022] Furthermore, in S1, the method for establishing an unmanned ship model considering environmental interference is as follows:

[0023] Introducing a three-degree-of-freedom nonlinear model with kinematics and dynamics:

[0024]

[0025] Where: η represents the position vector of the unmanned ship in the earth coordinate system, where x, y represent the horizontal and vertical coordinates of the 3-DOF position of the unmanned ship in the earth coordinate system, ψ represents the heading angle, and T represents the transposition; Δ represents the velocity vector of the unmanned ship in the ship coordinate system; Among them, u, v, and r represent the sway velocity, drift velocity, and bow angular velocity in the ship coordinate system, respectively; represents the rotation matrix; Represents the inertia matrix of the unmanned ship; represents the derivative of Δ with respect to time; represents the control input of the unmanned ship; represents the Coriolis centripetal matrix; represents the nonlinear damping matrix; represents the unknown hydrodynamic damping; represents the unknown external disturbance caused by wind, waves and currents; represents three-dimensional real number space; represents the set of 3x3 real matrices; represents the derivative of v with respect to time;

[0026] Let x 1 =η and Then the unmanned ship model considering environmental interference is further transformed into the following form:

[0027]

[0028] in,

[0029] f(x 1 ,x 2 )=(M * ) -1 [-C * x 2 -D * x 2 +g(η,Δ)]

[0030] M * =R(ψ)MR T (ψ)

[0031]

[0032] τ u =(M * ) -1 R(ψ)τ

[0033] D * =R(ψ)D(Δ)R T (ψ)

[0034] Where: x 1 Represents the position vector information of the unmanned ship in the earth coordinate system; x 2 Represents the velocity vector information of the unmanned ship in the earth coordinate system; represents the derivative of η with respect to time; Represents x 1Derivative with respect to time; Represents x 2 Derivative with respect to time; represents the system input, i.e. the actual control law; f(x 1 ,x 2 ) represents the unknown nonlinear function that does not contain the unknown external disturbance; M * , C * , D * All represent intermediate calculation parameters; g(η,Δ) represents unknown hydrodynamic damping; R T (ψ) represents the transpose of R(ψ); C(Δ) represents the Coriolis centripetal matrix; represents the time derivative of R(ψ); D(Δ) represents the nonlinear damping matrix.

[0035] Furthermore, in S2, the method for constructing the preset performance boundary of the preset performance function is as follows:

[0036] S21: Establish the unmanned ship trajectory tracking error as follows:

[0037] e(t)=y(t)-y r (t)

[0038] Where: y(t) represents the system output, where represents the reference signal, i.e. the expected trajectory; e(t) represents the tracking error of the unmanned ship trajectory;

[0039] S22: According to the unmanned ship trajectory tracking error, a preset performance boundary of a preset performance function is constructed as follows:

[0040]

[0041] Where: and All are normal numbers; represents a preset performance function; represents the hth component of the unmanned ship trajectory tracking error e(t); h represents the index of the component of the unmanned ship trajectory tracking error; represents the set of real numbers;

[0042] in,

[0043]

[0044] Where: h (·) is locally Lipschitz continuous function, represents a continuously strictly increasing function with a domain of [0,∞); Indicates the preset performance function The initial value of Indicates the preset performance function The final value of express The derivative with respect to time.

[0045] Furthermore, in S4, the method for obtaining the estimated value of the adaptive parameter is as follows:

[0046] S41: The unknown nonlinear function in the unmanned ship model considering environmental interference is approximated by the fuzzy logic system as follows:

[0047] f(x 1 ,x 2 )+ω(t)=W T β+∈

[0048] Where: W represents the fuzzy weight of the adaptive parameter; β represents the fuzzy basis vector used to approximate the unknown nonlinear function; ∈ represents the error generated by using the fuzzy logic system to approximate the unknown nonlinear function; f(x 1 ,x 2 ) represents the unknown nonlinear function that does not contain the unknown external disturbance; represents the unknown external disturbance caused by wind, waves and currents;

[0049] S42: Establish the system fuzzy estimator as follows:

[0050]

[0051] Where: is x 2 The estimate of the speed information of the unmanned ship in the earth coordinate system; τ u is the system input; W represents the fuzzy weight of the adaptive parameter, is the estimated value of W; β represents the fuzzy basis vector used to approximate the unknown nonlinear function; Adjust parameters for the fuzzy estimator; is the fuzzy predictor control gain; represents the estimation error;

[0052] S43: According to the designed fuzzy predictor, a fuzzy adaptive law is designed as follows:

[0053]

[0054] Where: is the adaptive gain; β represents the fuzzy basis vector used to approximate the unknown nonlinear function; is x 2 The estimation of , that is, the estimated value of the speed information of the unmanned ship in the earth coordinate system; Adjust the parameters for the fuzzy adaptive law.

[0055] Furthermore, in S5, the second-order nonlinear tracking differentiator is established as follows:

[0056]

[0057] Where: μ 1h The virtual control law μ after filtering is 1 The h(i=1,2,3)th component of The virtual control law μ after filtering is 1 The time derivative of the hth (h=1,2,3)th component of is the adjustment parameter of the second-order nonlinear tracking differentiator, represents the set of positive real numbers; α 1h Denotes the virtual control law α 1 The hth (h=1,2,3) component of Represents μ 1h The second derivative of .

[0058] Furthermore, in S5, the unmanned ship trajectory tracking controller based on the shear mapping function is established as follows:

[0059]

[0060] Where: α 1h Virtual control law The hth (h=1,2,3) component of is the control gain of the virtual control law, Indicates k 1 The hth (h=1,2,3) component of h Indicates z 1h (t) for auxiliary variables The ratio of the derivative obtained by the derivation to the preset performance function, where represents a preset performance function; Indicates z 1h (t) for auxiliary variables The derivative obtained by taking the derivative is and are all normal numbers, represents the hth (h=1,2,3) component of the new auxiliary variable that satisfies the two-dimensional shear mapping condition; z 1h (t) represents z 1 The hth (h=1,2,3)th component of (t); represents the shear angle of the shear mapping; z 1(t) represents the error transformation variable that can achieve singularity avoidance after applying the 2D shear mapping; W represents the fuzzy weight of the adaptive parameter, is an estimate of W, express The hth (h=1,2,3) component of ; β represents the fuzzy basis vector used to approximate the unknown nonlinear function, β h represents the hth (h=1,2,3)th component of β; represents the reference signal, i.e. the expected trajectory, Represents y r The derivative of (t), e(t) represents the tracking error of the unmanned ship trajectory; express The hth (h=1,2,3) component of h represents the hth component of the intermediate variable ζ calculated by the preset performance function, Indicates the preset performance function The derivative of z 2 =x 2 -μ 1 represents the dynamic surface error, z 2h Indicates z 2 The hth (h=1,2,3) component of 1 represents the virtual control law after filtering; is the adaptive gain; is x 2 The estimate of is the estimated value of the speed information of the unmanned ship in the earth coordinate system; Adjust parameters for the fuzzy adaptive law; The virtual control law μ after filtering is 1 The second derivative of represents the system input, i.e., the actual control law; is the fuzzy predictor control gain.

[0061] Beneficial effects: The present invention provides an unmanned ship trajectory tracking control method based on a shear mapping function; the error transformation function in the traditional preset performance control framework is transformed through a 2D shear mapping, and based on the preset performance boundary, an error transformation variable that can achieve singularity avoidance and overcome the initial value constraint after applying the 2D shear mapping is obtained; and an unmanned ship trajectory tracking controller based on a shear mapping function is established in combination with the unmanned ship trajectory tracking error and the estimated value of the adaptive parameter to obtain a virtual control law and an actual control law, and complete the tracking control of the unmanned ship. The present invention establishes a 2D shear mapping, and combines the error change function determined by the preset boundary of the preset performance function of the present invention, so that the system can ensure that it can remain stable even when the state trajectory deviates from the preset performance constraint area and the initial value of the state trajectory is not within the preset performance constraint area. This improvement not only significantly reduces the conservatism of the preset performance control, but also avoids the singularity problem of the controller, so that the control method has a wider applicability and stronger effectiveness in actual engineering applications. At the same time, by introducing a preset performance constraint strategy, it is ensured that the trajectory tracking error of the unmanned ship can converge to a preset error range. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] 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.

[0063] Figure 1 It is a flow chart of the unmanned ship trajectory tracking control method based on the shear mapping function of the present invention;

[0064] Figure 2 is a schematic structural diagram of an unmanned ship trajectory tracking control system in an embodiment of the present invention;

[0065] Figure 3 is a schematic diagram of a calculation process of an error transformation function based on a shear mapping function in an embodiment of the present invention;

[0066] Figure 4 is a schematic diagram of tracking error and preset performance constraints in an embodiment of the present invention;

[0067] Figure 5 is a schematic diagram of an expected circular trajectory and an actual trajectory in a circular tracking plane in an embodiment of the present invention;

[0068] Figure 6 It is a schematic diagram of the tracking error change when the initial value of the tracking error is not within the preset performance constraint range in an embodiment of the present invention. DETAILED DESCRIPTION

[0069] 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.

[0070] This embodiment provides a trajectory tracking control method for an unmanned ship based on a shear mapping function. Figure 1 , including the following steps:

[0071] S1: Establish an unmanned ship model considering environmental interference;

[0072] Preferably, in S1, the method for establishing an unmanned ship model considering environmental interference is as follows:

[0073] Introducing a three-degree-of-freedom nonlinear model with kinematics and dynamics:

[0074]

[0075] Where: η represents the position vector of the unmanned ship in the earth coordinate system, where x, y represent the horizontal and vertical coordinates of the 3-DOF position of the unmanned ship in the earth coordinate system, ψ represents the heading angle, and T represents the transposition; Δ represents the velocity vector of the unmanned ship in the ship coordinate system; Among them, u, v, and r represent the sway velocity, drift velocity, and bow angular velocity in the ship coordinate system, respectively; represents the rotation matrix; Represents the inertia matrix of the unmanned ship; represents the derivative of Δ with respect to time; represents the control input of the unmanned ship; represents the Coriolis centripetal matrix; represents the nonlinear damping matrix; represents the unknown hydrodynamic damping; represents the unknown external disturbance caused by wind, waves and currents; represents three-dimensional real number space; represents the set of 3x3 real matrices; represents the time derivative of v.

[0076] Let x 1 =η and Then the unmanned ship model considering environmental interference is further transformed into the following form:

[0077]

[0078] in,

[0079] f(x 1 ,x 2 )=(M * ) -1 [-C * x 2 -D * x 2 +g(η,Δ)]

[0080] M * =R(ψ)MR T (ψ)

[0081]

[0082] τ u =(M * ) -1 R(ψ)τ

[0083] D * =R(ψ)D(Δ)R T (ψ)

[0084] Where: x 1 Represents the position vector information of the unmanned ship in the earth coordinate system; x 2 Represents the velocity vector information of the unmanned ship in the earth coordinate system; represents the derivative of η with respect to time; Represents x 1 Derivative with respect to time; Represents x 2 Derivative with respect to time; represents the system input, i.e. the actual control law; f(x 1 ,x 2 ) represents the unknown nonlinear function that does not contain the unknown external disturbance; M * , C * , D * Both represent intermediate calculation parameters. In this embodiment, M * is the new matrix obtained by calculating the inertia matrix M, C * is the new matrix obtained by calculating the Coriolis centripetal matrix C(Δ) and the inertia matrix M, D * is the new matrix obtained by calculating the nonlinear damping matrix; g(η,Δ) represents the unknown hydrodynamic damping; R T (ψ) represents the transpose of R(ψ); C(Δ) represents the Coriolis centripetal matrix; represents the time derivative of R(ψ); D(Δ) represents the nonlinear damping matrix;

[0085] Specifically, since f(x 1 ,x 2 ) contains the unknown hydrodynamic damping g(η,Δ), so f(x 1 ,x 2 ) and ω(t) can be regarded as unknown nonlinear functions as a whole.

[0086] S2: establishing an unmanned ship trajectory tracking error according to the unmanned ship model considering environmental interference; constructing a preset performance boundary of a preset performance function according to the unmanned ship trajectory tracking error, and determining an error transformation function based on the preset performance boundary of the preset performance function;

[0087] Preferably, in S2, the method for constructing the preset performance boundary of the preset performance function is as follows:

[0088] S21: Establish the unmanned ship trajectory tracking error e(t) as follows:

[0089] e(t)=y(t)-y r (t)

[0090] Where: y(t) represents the system output, where represents the reference signal, i.e. the expected trajectory; e(t) represents the tracking error of the unmanned ship trajectory;

[0091] S22: According to the unmanned ship trajectory tracking error, a preset performance boundary of a preset performance function is constructed as follows:

[0092]

[0093] Where: and All are normal numbers; represents a preset performance function; represents the hth (h=1, 2, 3) component of the unmanned ship trajectory tracking error e(t); h represents the index of the component of the unmanned ship trajectory tracking error; represents the set of real numbers;

[0094] Among them, select the preset performance function

[0095]

[0096] Where: h (·) is locally Lipschitz continuous function, represents a continuously strictly increasing function with a domain of [0,∞); Indicates the preset performance function The initial value of Indicates the preset performance function The terminal value of express Derivative with respect to time;

[0097] Among them, the method adopted for determining the error transformation function based on the preset performance boundary of the preset performance function is a conventional technology in the field and will not be described in detail here.

[0098] In this embodiment, auxiliary variables are constructed The hth (h=1,2,3) component of the auxiliary variable The definition is as follows:

[0099]

[0100] Without loss of generality, according to the preset performance boundary, the error transformation function under the traditional preset performance control framework is selected And the error transformation process is as follows:

[0101]

[0102] Where: Artanh represents the inverse hyperbolic tangent function.

[0103] S3: establishing a 2D shear mapping, and obtaining an error conversion variable capable of achieving singularity avoidance after applying the 2D shear mapping according to the 2D shear mapping and the error transformation function;

[0104] Preferably, the 2D shear mapping is established as follows:

[0105] Specifically, in order to avoid the singularity problem existing in the traditional preset performance control, this embodiment defines the following linear mapping as 2D shear mapping:

[0106]

[0107] Where: m 0 ,n 0 Respectively represent the horizontal and vertical coordinates in the original space, m 1 Represents the transformation space with m 0 The corresponding horizontal axis, n 1 Represents the transformation space with n 0 The corresponding vertical coordinate; The shear angle of the shear mapping, which affects the tilt of the mapped space relative to the original space;

[0108] Preferably, the formula used to obtain the error conversion variable after applying the 2D shear mapping is as follows:

[0109]

[0110] Where: z h (t) represents the hth (h=1,2,3)th component of z(t); Indicates the independent variable The error conversion variable calculated by the error transformation function; z 1h (t) represents z 1 The h(i=1,2,3)th component of (t), z 1 (t) represents the error transformation variable obtained after applying the 2D shear mapping; Represents auxiliary variables The hth (h=1,2,3) component of represents the hth (h=1,2,3)th component of the new auxiliary variable that satisfies the two-dimensional shear mapping condition; The shear angle of the shear mapping, which affects the tilt of the mapped space relative to the original space;

[0111] Furthermore, the error transformation process after applying the shear mapping can be expressed as:

[0112]

[0113] in,

[0114]

[0115] Where: z 1h (t) represents z 1 The hth (h=1,2,3)th component of (t); z 1 (t) represents the error transformation variable after applying the 2D shear mapping, i.e., the error transformation variable based on the singularity avoidance; z h (t) represents the hth (h=1,2,3)th component of z(t); Indicates the independent variable The error conversion variable calculated by the error transformation function; represents the hth (h=1,2,3)th component of the new auxiliary variable that satisfies the two-dimensional shear mapping condition; represents the shear angle of the shear mapping; Represents auxiliary variables The hth (h=1,2,3) component of Represents the i-th (i=1, 2, 3) component of the unmanned ship trajectory tracking error e(t); represents a preset performance function; and All are normal numbers;

[0116] S4: Approximating an unknown nonlinear function in the unmanned ship model considering environmental interference based on a fuzzy logic system, obtaining fuzzy weights of adaptive parameters to establish a fuzzy predictor, and designing a fuzzy adaptive law based on the fuzzy predictor to obtain estimated values ​​of adaptive parameters;

[0117] Specifically, the input end of the fuzzy predictor is connected to the fuzzy logic system, and the output end is connected to the unmanned ship trajectory tracking controller based on the shear mapping function. The input signal of the fuzzy predictor includes the estimated error of the unmanned ship speed information in the earth coordinate system Output of fuzzy logic system and the system input τ of the unmanned ship trajectory tracking controller u ; The output signal is the estimated speed information of the unmanned ship in the earth coordinate system and fuzzy adaptive law

[0118] Preferably, the method for obtaining the estimated value of the adaptive parameter is as follows:

[0119] S41: The unknown nonlinear function in the unmanned ship model considering environmental interference is approximated by the fuzzy logic system as follows:

[0120] f(x 1 ,x 2 )+ω(t)=W T β+∈

[0121] Where: W represents the fuzzy weight of the adaptive parameter; β represents the fuzzy basis vector used to approximate the unknown nonlinear function; ∈ represents the error generated by using the fuzzy logic system to approximate the unknown nonlinear function; f(x 1 ,x 2 ) represents the unknown nonlinear function that does not contain the unknown external disturbance; represents the unknown external disturbance caused by wind, waves and currents;

[0122] S42: Establish the system fuzzy estimator as follows:

[0123]

[0124]

[0125] Where: is x 2 The estimate of the speed information of the unmanned ship in the earth coordinate system; τ u is the system input; W represents the fuzzy weight of the adaptive parameter, is the estimated value of W; β represents the fuzzy basis vector used to approximate the unknown nonlinear function; Adjust parameters for the fuzzy estimator; is the fuzzy predictor control gain; represents the estimation error,

[0126] S43: According to the designed fuzzy predictor, a fuzzy adaptive law is designed as follows:

[0127]

[0128] Where: is the adaptive gain; β represents the fuzzy basis vector used to approximate the unknown nonlinear function; is x 2 The estimation of , that is, the estimated value of the speed information of the unmanned ship in the earth coordinate system; Adjust the parameters for the fuzzy adaptive law.

[0129] S5: According to the error conversion variables after applying the two-dimensional shear mapping, the unmanned ship trajectory tracking error and the estimated values ​​of the adaptive parameters, based on the second-order nonlinear tracking differentiator, an improved dynamic surface control method of the second-order nonlinear tracking differentiator is adopted, and based on the fuzzy predictor, an unmanned ship trajectory tracking controller based on the shear mapping function is established to obtain the virtual control law and the actual control law, so as to complete the tracking control of the unmanned ship.

[0130] Specifically, the input end of the unmanned ship trajectory tracking controller based on the shear mapping function of this embodiment is based on the shear mapping function, and the second-order nonlinear tracking differentiator, the fuzzy predictor and the desired trajectory y r (t), and the output end is connected to the unmanned ship control system and the fuzzy predictor. Its input signal includes the derivative of the filtered virtual control law And the second-order derivative Fuzzy Adaptive Law Expected trajectory y r (t) and the transformation variable z calculated by the shear mapping function 1 (t); the output signal includes the system input τ u .

[0131] Preferably, in S5, the second-order nonlinear tracking differentiator is established as follows:

[0132]

[0133] Where: μ 1h The virtual control law μ after filtering is 1 The hth (h=1,2,3)th component of The virtual control law μ after filtering is 1 The time derivative of the hth (h=1,2,3)th component of is the adjustment parameter of the second-order nonlinear tracking differentiator, represents the set of positive real numbers; α 1h Denotes the virtual control law α 1 The hth (h=1,2,3) component of Represents μ 1h The second derivative of .

[0134] Preferably, according to the The unmanned ship trajectory tracking controller based on the shear mapping function is established as follows:

[0135]

[0136] Where: α 1n Virtual control law The hth (h=1,2,3) component of is the control gain of the virtual control law, Indicates k 1 The hth (h=1,2,3) component of h Indicates z 1h (t) for auxiliary variables The ratio of the derivative obtained by the derivation to the preset performance function, where represents a preset performance function; Indicates z 1h (t) for auxiliary variables The derivative obtained by taking the derivative is and are all normal numbers, represents the hth (h=1,2,3) component of the new auxiliary variable that satisfies the two-dimensional shear mapping condition; z 1h (t) represents z 1 The hth (h=1,2,3)th component of (t); represents the shear angle of the shear mapping; z 1 (t) represents the error transformation variable after applying the 2D shear mapping, i.e., the transformation variable based on the error transformation function that can achieve singularity avoidance; W represents the fuzzy weight of the adaptive parameter, is an estimate of W, express The hth (h=1,2,3) component of ; β represents the fuzzy basis vector used to approximate the unknown nonlinear function, β h represents the hth (h=1,2,3)th component of β; represents the reference signal, i.e. the expected trajectory, Represents y r The derivative of (t), e(t) represents the tracking error of the unmanned ship trajectory; express The hth (h=1,2,3) component of h represents the hth component of the intermediate variable ζ calculated by the preset performance function, Indicates the preset performance function The derivative of z 2 =x 2 -μ 1 represents the dynamic surface error, z 2h Indicates z 2 The hth (h=1,2,3) component of 1 represents the virtual control law after filtering; is the adaptive gain; is x 2 The estimate of is the estimated value of the speed information of the unmanned ship in the earth coordinate system; Adjust parameters for the fuzzy adaptive law; The virtual control law μ after filtering is 1 The second derivative of represents the system input, i.e., the actual control law; is the fuzzy predictor control gain;

[0137] Specifically, the unmanned ship trajectory tracking control system in this embodiment has a shear mapping function, a fuzzy predictor, a fuzzy logic system, and a second-order nonlinear tracking differentiator. The input end of the unmanned ship control system is connected to the output end of the unmanned ship trajectory tracking controller; the output end is connected to the fuzzy logic system. The input signal of the unmanned ship control system is the system input τ u ; The output signal includes the position information x of the unmanned ship in the earth coordinate system 1 , unmanned ship speed information x 2 , Estimation error of unmanned ship speed information in the earth coordinate system As well as unknown nonlinear functions generated by the unmanned ship itself and external disturbances.

[0138] This embodiment introduces a preset performance constraint strategy to ensure that the trajectory tracking error of the unmanned ship can converge to a preset, smaller error range. In addition, the method of this embodiment allows the speed of error convergence to be controlled by adjusting the preset performance function to adapt to different practical application requirements. In addition, in the traditional preset performance control framework, this embodiment incorporates the shear mapping function. The system can ensure that it remains stable even when the state trajectory deviates from the preset performance constraint area and the initial value of the state trajectory is not within the preset performance constraint area. This improvement not only significantly reduces the conservatism of the preset performance control, but also avoids the singularity problem of the controller, so that the control method has a wider applicability and stronger effectiveness in practical engineering applications. Through this method, the unmanned ship can achieve more accurate and reliable trajectory tracking in a complex marine environment, and at the same time, the flexibility of its controller design has been improved, so that it can adapt to changing marine conditions and mission requirements. In general, the unmanned ship trajectory tracking control method of this embodiment provides strong technical support for the further development of unmanned ships in the field of automation and intelligence.

[0139] A specific embodiment of the present invention is as follows:

[0140] like Figure 2 The structure of the unmanned ship trajectory tracking control system based on the shear mapping function of this embodiment is demonstrated, including an unmanned ship control system, a fuzzy predictor, a fuzzy adaptive law, a second-order nonlinear tracking differentiator, and an unmanned ship trajectory tracking controller based on the shear mapping function.

[0141] The model and related parameters of the unmanned ship selected in this embodiment are:

[0142]

[0143] Where: Represents the position vector of the unmanned ship in the earth coordinate system, including the 3-DOF position (x, y) and the heading angle ψ; represents the velocity vector of the unmanned ship in the hull coordinate system, including the longitudinal velocity u, the transverse velocity v and the bow angular velocity r; represents the control input of the unmanned ship; represents the unknown hydrodynamic damping; Represents the unknown external disturbance caused by wind, waves and currents.

[0144]

[0145] d11(Δ)=0.7225+1.3274×|u|+5.8664×u 2 ,

[0146] d22(Δ)=0.8612+36.2823×|v|+0.805×|r|,

[0147] d23(Δ)=-0.1079+0.845×|v|+3.45×|r|,

[0148] d32(Δ)=-0.1052-5.0437×|v|-0.13×|r|,

[0149] d33(Δ)=1.9-0.08×|v|+0.75×|r|.

[0150] Select the state variable x 1 =η and The unmanned ship model is further transformed into the following form:

[0151]

[0152] Where: f(x 1 ,x 2 )=(M * ) -1 [-C * x 2 -D * x 2 +g(η,Δ)];M * =R(ψ)MR T (ψ); τ u =(M * ) -1 τ * ,τ * =R(ψ)τ; Indicates system input; D * =R(ψ)D(Δ)R T (ψ).

[0153] Furthermore, the specific parameters designed in this embodiment are as follows: 1 =[1.2 1.2 0.2], k 2 =[500 500 500],κ 2 =[500 500 500], Select the preset performance function to meet

[0154] Among them, k 1 is the specific parameter of the control gain of the virtual control law of this embodiment, k 2 is the specific parameter of the control gain of the fuzzy predictor in this embodiment, κ 2are the specific parameters of the adjustment parameters of the fuzzy predictor of this embodiment, are all positive scalar specific parameters of this embodiment, These are all specific parameters of the adjustment parameters of the second-order nonlinear tracking differentiator of this embodiment.

[0155] Let the initial value be: x 1 (0) = [1 2.5 -1.5], x 2 (0) = [0 0 0],

[0156] Among them, x 1 (0) represents the initial position information of the unmanned ship in the earth coordinate system, x 2 (0) represents the initial velocity information of the unmanned ship in the earth coordinate system, and Indicates the initial values ​​of the 1st, 2nd and 3rd preset performance functions.

[0157] Furthermore, the simulation results of this embodiment are as follows: Figure 4 , 5 As shown: Figure 4 is a schematic diagram of the estimated tracking error and the preset performance constraint in an embodiment of the present invention, from Figure 4 It can be seen that the tracking error can approach zero at a faster speed, showing good tracking performance. Figure 5 is a schematic diagram of the expected circular trajectory and the actual trajectory in the circular tracking plane in an embodiment of the present invention. Figure 5 It can be seen that the unmanned ship can accurately track the predetermined trajectory in a relatively short time and maintain a high tracking accuracy throughout the process. Figure 6 It can be seen that even if the initial value of the tracking error is not within the preset performance constraint range, the tracking effect can still be guaranteed.

[0158] In this embodiment, an unmanned ship trajectory tracking control method based on a shear mapping function is provided. The error transformation function in the traditional preset performance control framework is transformed through a 2D shear mapping, and based on the preset performance boundary of the preset performance function, an error transformation variable that can achieve singularity avoidance and overcome the initial value constraint after applying the 2D shear mapping is obtained; and an unmanned ship trajectory tracking controller based on a shear mapping function is established in combination with the unmanned ship trajectory tracking error and the estimated value of the adaptive parameter to obtain a virtual control law and an actual control law to complete the tracking control of the unmanned ship. In this embodiment, by establishing a 2-dimensional shear mapping, the system can ensure that it remains stable even when the state trajectory deviates from the preset performance constraint area and the initial value of the state trajectory is not within the preset performance constraint area. This improvement not only significantly reduces the conservatism of the preset performance control, but also avoids the singularity problem of the controller, so that the control method has a wider applicability and stronger effectiveness in actual engineering applications. At the same time, by introducing a preset performance constraint strategy, it is ensured that the trajectory tracking error of the unmanned ship can converge to a preset, smaller error range. In addition, the method allows the speed of error convergence to be controlled by adjusting the performance function to adapt to different practical application requirements.

[0159] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A trajectory tracking control method for an unmanned ship based on a shear mapping function, characterized in that: The steps include: S1: Establish an unmanned ship model considering environmental interference; S2: establishing an unmanned ship trajectory tracking error according to the unmanned ship model considering environmental interference; constructing a preset performance boundary of a preset performance function according to the unmanned ship trajectory tracking error, and determining an error transformation function based on the preset performance boundary of the preset performance function; S3: establishing a 2D shear mapping, and obtaining an error conversion variable capable of achieving singularity avoidance after applying the 2D shear mapping according to the 2D shear mapping and the error transformation function; S4: obtaining fuzzy weights of adaptive parameters based on the fuzzy logic system to establish a fuzzy predictor, and then obtaining estimated values ​​of the adaptive parameters; S5: According to the error conversion variables that can achieve singularity avoidance after applying the two-dimensional shear mapping, the unmanned ship trajectory tracking error and the estimated values ​​of the adaptive parameters, based on the second-order nonlinear tracking differentiator, an unmanned ship trajectory tracking controller based on the shear mapping function is established to obtain the virtual control law and the actual control law to complete the tracking control of the unmanned ship.

2. The unmanned ship trajectory tracking control method based on shear mapping function according to claim 1 is characterized in that: In S3, the 2D shear mapping is established as follows: Where: m0, n0 represent the horizontal coordinate and vertical coordinate in the original space respectively, m1 represents the horizontal coordinate corresponding to m0 in the transformed space, and n1 represents the vertical coordinate corresponding to n0 in the transformed space; Indicates the shear angle of the shear mapping.

3. The unmanned ship trajectory tracking control method based on shear mapping function according to claim 1 is characterized in that: In S3, the formula used to obtain the error conversion variable after applying the 2D shear mapping is as follows: in, Where: z 1h (t) represents the hth (h=1, 2, 3) component of z1(t); z1(t) represents the error-avoiding transformation variable after applying the 2D shear mapping; represents the shear angle of the shear mapping; Represents auxiliary variables The hth component of ; represents the hth component of the unmanned ship trajectory tracking error e(t); represents a preset performance function; and All are positive numbers; h (t) represents the hth (h=1,2,3)th component of z(t); Indicates the independent variable The error conversion variable calculated by the error transformation function; Represents the hth (h=1, 2, 3)th component of the new auxiliary variable that satisfies the two-dimensional shear mapping condition.

4. The unmanned ship trajectory tracking control method based on shear mapping function according to claim 1 is characterized in that: In S1, the method for establishing the unmanned ship model considering environmental interference is as follows: Introducing a three-degree-of-freedom nonlinear model with kinematics and dynamics: Where: η represents the position vector of the unmanned ship in the earth coordinate system, where x, y represent the horizontal and vertical coordinates of the 3-DOF position of the unmanned ship in the earth coordinate system, ψ represents the heading angle, and T represents the transposition; Δ represents the velocity vector of the unmanned ship in the ship coordinate system; Among them, u, v, and r represent the sway velocity, drift velocity, and bow angular velocity in the ship coordinate system, respectively; represents the rotation matrix; Represents the inertia matrix of the unmanned ship; represents the derivative of Δ with respect to time; represents the control input of the unmanned ship; represents the Coriolis centripetal matrix; represents the nonlinear damping matrix; represents the unknown hydrodynamic damping; represents the unknown external disturbance caused by wind, waves and currents; represents three-dimensional real number space; represents the set of 3x3 real matrices; represents the derivative of v with respect to time; Let x1 = η and Then the unmanned ship model considering environmental interference is further transformed into the following form: in, f(x1,x2)=(M * ) -1 [-C * x2-D * x2+g(η,Δ)] M * =R(ψ)MR T (ψ) t u =(M * ) -1 R(ψ)t D * =R(ψ)D(Δ)R T (ψ) Where: x1 represents the position vector information of the unmanned ship in the earth coordinate system; x2 represents the velocity vector information of the unmanned ship in the earth coordinate system; represents the derivative of η with respect to time; represents the derivative of x1 with respect to time; represents the derivative of x2 with respect to time; represents the system input, i.e., the actual control law; f(x1,x2) represents the unknown nonlinear function that does not contain the unknown external disturbance; M * , C * , D * All represent intermediate calculation parameters; g(η,Δ) represents unknown hydrodynamic damping; R T (ψ) represents the transpose of R(ψ); C(Δ) represents the Coriolis centripetal matrix; represents the time derivative of R(ψ); D(Δ) represents the nonlinear damping matrix.

5. The unmanned ship trajectory tracking control method based on shear mapping function according to claim 1 is characterized in that: In S2, the method for constructing the preset performance boundary of the preset performance function is as follows: S21: Establish the unmanned ship trajectory tracking error as follows: e(t)=y(t)-y r (t) Where: y(t) represents the system output, where represents the reference signal, i.e. the expected trajectory; e(t) represents the tracking error of the unmanned ship trajectory; S22: According to the unmanned ship trajectory tracking error, a preset performance boundary of a preset performance function is constructed as follows: Where: and All are normal numbers; represents a preset performance function; represents the hth component of the unmanned ship trajectory tracking error e(t); h represents the index of the component of the unmanned ship trajectory tracking error; represents the set of real numbers; in, Where: h (·) is locally Lipschitz continuous function, represents a continuous and strictly increasing function with a domain of [0,∞); θ h (0) represents the preset performance function θ h The initial value of (t); θ h (∞) represents the preset performance function θ h (t) the final value; Represents θ h (t) The time derivative.

6. The unmanned ship trajectory tracking control method based on shear mapping function according to claim 1 is characterized in that: In S4, the method for obtaining the estimated value of the adaptive parameter is as follows: S41: The unknown nonlinear function in the unmanned ship model considering environmental interference is approximated by the fuzzy logic system as follows: f(x1,x2)+ω(t)=W T β+∈ Where: W represents the fuzzy weight of the adaptive parameter; β represents the fuzzy basis vector used to approximate the unknown nonlinear function; ∈ represents the error generated by using the fuzzy logic system to approximate the unknown nonlinear function; f(x1,x2) represents the unknown nonlinear function that does not contain the unknown external disturbance; represents the unknown external disturbance caused by wind, waves and currents; S42: Establish the system fuzzy estimator as follows: Where: is the estimate of x2, that is, the estimated value of the speed information of the unmanned ship in the earth coordinate system; τ u is the system input; W represents the fuzzy weight of the adaptive parameter, is the estimated value of W; β represents the fuzzy basis vector used to approximate the unknown nonlinear function; Adjust parameters for the fuzzy estimator; is the fuzzy predictor control gain; represents the estimation error; S43: According to the designed fuzzy predictor, a fuzzy adaptive law is designed as follows: Where: is the adaptive gain; β represents the fuzzy basis vector used to approximate the unknown nonlinear function; is the estimate of x2, that is, the estimated value of the speed information of the unmanned ship in the earth coordinate system; Adjust the parameters for the fuzzy adaptive law.

7. The unmanned ship trajectory tracking control method based on shear mapping function according to claim 1 is characterized in that: In S5, the second-order nonlinear tracking differentiator is established as follows: Where: μ 1h represents the hth (i=1,2,3)th component of the filtered virtual control law μ1, represents the time derivative of the hth (h=1,2,3)th component of the filtered virtual control law μ1; is the adjustment parameter of the second-order nonlinear tracking differentiator, represents the set of positive real numbers; α 1h represents the hth (h=1,2,3)th component of the virtual control law α1; Represents μ 1h The second derivative of .

8. The unmanned ship trajectory tracking control method based on shear mapping function according to claim 1 is characterized in that: In S5, the unmanned ship trajectory tracking controller based on the shear mapping function is established as follows: Where: α 1h Virtual control law The hth (h=1,2,3) component of is the control gain of the virtual control law, represents the hth (h=1,2,3) component of k1; ψ h Indicates z 1h (t) for auxiliary variables The ratio of the derivative obtained by the derivation to the preset performance function, where represents a preset performance function; Indicates z 1h (t) for auxiliary variables The derivative obtained by taking the derivative is and are all normal numbers, represents the hth (h=1,2,3) component of the new auxiliary variable that satisfies the two-dimensional shear mapping condition; z 1h (t) represents the hth (h=1,2,3)th component of z1(t); represents the shear angle of the shear mapping; z1(t) represents the error transformation variable that can achieve singularity avoidance after applying the 2D shear mapping; W represents the fuzzy weight of the adaptive parameter, is an estimate of W, express The hth (h=1,2,3) component of ; β represents the fuzzy basis vector used to approximate the unknown nonlinear function, β h represents the hth (h=1,2,3)th component of β; represents the reference signal, i.e. the expected trajectory, Represents y r The derivative of (t), e(t) represents the tracking error of the unmanned ship trajectory; express The hth (h=1,2,3) component of h represents the hth component of the intermediate variable ζ calculated by the preset performance function, Represents the preset performance function θ h The derivative of (t); z2 = x2-μ1 represents the dynamic surface error, z 2h represents the hth (h=1,2,3) component of z2; μ1 represents the virtual control law after filtering; is the adaptive gain; It is the estimate of x2, that is, the estimated value of the speed information of the unmanned ship in the earth coordinate system; Adjust parameters for the fuzzy adaptive law; represents the second-order derivative of the filtered virtual control law μ1; represents the system input, i.e., the actual control law; is the fuzzy predictor control gain.

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