Under-actuated unmanned surface vehicle path following control method based on model-free adaptive sliding mode

Abstract

The application discloses a kind of underactuated unmanned ship path tracking control methods based on model-free adaptive sliding mode, steps are as follows: step 1: the discrete motion model of underactuated unmanned ship in horizontal plane three degrees of freedom motion is built;Step 2: construct the tracking error dynamic equation based on discrete time;Step 3: according to the tracking error dynamic equation based on discrete time, as well as the expected error angle of preset, the desired value of the bow angle velocity in trajectory tracking guidance law and the local path coordinate system origin moving speed are obtained;Step 4: according to the desired bow angle velocity and the local path coordinate system origin moving speed, the tracking control law of forward speed and the tracking control law of bow angle velocity are constructed, and unmanned ship is controlled by the tracking control law of forward speed and the tracking control law of bow angle velocity.The application adopts discretization technology for unmanned ship motion control system, designs path tracking guidance law and tracking control law, and is more in line with the needs of practical application.

Description

Technical Field

[0001] This invention relates to the field of motion control technology for underactuated unmanned surface vessels (USVs), and specifically to a path tracking control method for USVs based on model-free adaptive sliding mode. Background Technology

[0002] Unmanned surface vessels (USVs) possess strong flexibility, high intelligence, and wide applicability, making them promising candidates for both military and civilian applications. Safe and effective autonomous navigation is a prerequisite for completing relevant missions, and this autonomous navigation relies primarily on robust and precise control.

[0003] For unmanned surface vessels (USVs) navigating the ocean, ensuring safe navigation along desired routes is fundamental to achieving their various predetermined strategies and tactics. This makes path tracking control a crucial task in the field of USV motion control. Since most USVs are controlled by digital computers, their controllers are discrete in nature. Current control method research often employs continuous system-based control designs for most USV controllers, which can lead to poor control performance or the generation of additional complex and uncontrollable dynamic behaviors.

[0004] Path tracking only requires geometric position tracking and is independent of time information. Under the control of the control system, the unmanned surface vessel (USV) tracks a predetermined path until the mission is completed. Controllers for path tracking control problems typically employ mathematical model-based design methods. The design of such controllers heavily relies on accurate dynamic mathematical models. Furthermore, considering the effects of uncertainties such as model perturbations and marine environmental disturbances, the designed control schemes are often overly complex. The controller also requires high-order derivatives of the system state, which are difficult to obtain in practice. Therefore, the path tracking control problem for USVs faces challenges such as the difficulty in establishing accurate mathematical models and the difficulty in guaranteeing the system's robustness, adaptability, and control performance under uncertainties. Mathematical model-based controller design methods are difficult to apply in practical engineering. Summary of the Invention

[0005] This invention provides a path tracking control method for underactuated unmanned surface vessels based on model-free adaptive sliding mode, in order to solve the technical problems of difficulty in accurate modeling of unmanned surface vessel dynamics, unknown upper bound of system disturbance, and easy system chattering in the prior art.

[0006] This invention provides a path tracking control method for underactuated unmanned surface vessels based on model-free adaptive sliding mode, comprising the following steps:

[0007] Step 1: Construct a discrete motion model of the underactuated unmanned surface vessel in three degrees of freedom motion on the horizontal plane, including constructing a set of discrete kinematic equations and a set of discrete dynamic equations;

[0008] Step 2: Based on the discrete motion model of the unmanned surface vessel, construct the dynamic equation of tracking error based on discrete time. Specifically, select a point on the given path as the local coordinate origin, establish a local path movement coordinate system, obtain the dynamic equation of tracking error based on continuous time, and then discretize the dynamic equation of tracking error based on continuous time to obtain the dynamic equation of tracking error based on discrete time.

[0009] Step 3: Based on the dynamic equation of the tracking error in discrete time and the preset expected error angle, combined with Lyapunov stability theory, obtain the expected value of the heading angular velocity and the moving speed of the origin of the local path coordinate system in the trajectory tracking guidance law.

[0010] Step 4: Based on the compact form model-free adaptive algorithm and the double power discrete sliding mode control algorithm, construct the forward velocity tracking control law and the forward angular velocity tracking control law according to the desired forward angular velocity and the local path coordinate system origin movement speed, and control the unmanned surface vessel through the forward velocity tracking control law and the forward angular velocity tracking control law.

[0011] Furthermore, the set of discrete kinematic equations in step 1 is as follows:

[0012]

[0013] The discrete equations of the dynamics are:

[0014]

[0015] Furthermore, the dynamic equation for the discrete-time tracking error in step 2 is:

[0016]

[0017] In the formula, c(ω) is the curvature of the local coordinate origin of the given path.

[0018] Furthermore, step 3 also includes obtaining the sideslip angle in the dynamic equation of the tracking error in discrete time, specifically through the following method:

[0019] The lateral and longitudinal velocities acquired by the sensor are filtered and denoised using an improved tracking differentiator, and the sideslip angle is calculated based on the processed lateral and longitudinal velocities.

[0020] Furthermore, the improved tracking differentiator is formulated as follows:

[0021] x1(k+1)=x1(k)+T s x2(k)

[0022] x2(k+1)=x2(k)+Ts f r (k)

[0023]

[0024] In the formula, y1 is the input signal, i.e., the lateral or longitudinal velocity acquired by the sensor; x1 is the output signal tracking y1; x2 is the differential signal of the tracking system outputting y1; positive gain parameters a1, a2, a1 > 1, β; R is an adjustable parameter for changing the tracking speed, K is the discrete time, and Ts is the discrete time step.

[0025] Furthermore, in the improved tracking differentiator formula, a2 > 1. β > 1.

[0026] Furthermore, in step 3, the preset desired heading error angle is:

[0027]

[0028] The desired heading angular velocity is:

[0029] r d，k =(-ψ e，k +δ k+1 -(Δβ k -c(ω k )Δω k )) / T s

[0030] The speed at which the origin of the local path coordinate system moves is:

[0031] ω k+1 =ω k +T s (cosψ e，k U k +k2x e，k )

[0032] In the formula, the gain parameter k2 > 0, k δ >0;

[0033] Furthermore, in step 4, the forward velocity and bow angular velocity in the dynamic model of the unmanned surface vessel are first converted into dynamic linearized equations in a tight-form format using a model-free adaptive algorithm. Then, the tracking control laws for the forward velocity and bow angular velocity are constructed using a double-power adaptive discrete sliding mode method.

[0034] Furthermore, the tracking control law for the forward velocity is:

[0035] τ u，k =τu，k-1 +Δτ u，k

[0036] In the formula,

[0037] Where, σ u It is an estimated value. Additional correction terms; gain parameters ε1 > 0, ε2 > 0; gain parameter q1 > 0 and satisfies 1 - q1T s >0, 0<β1<1, 0<β2<1, sgn(·) denotes the sign function;

[0038] The tracking control law for the heading angular velocity is:

[0039] τ r，k =τ r，k-1 +Δτ r，，k

[0040] In the formula,

[0041] Where, σ r It is an estimated value. Additional correction terms; gain parameter ε3 > 0, ε4 > 0, gain parameter q2 > 0 and 1-q2T s >0, 0<β3<1, 0<β4<1.

[0042] The beneficial effects of this invention are:

[0043] This invention employs discretization technology in the motion control system of unmanned surface vessels (USVs) to design path-following guidance and tracking control laws, making it more suitable for practical applications. Based on a model-free adaptive control method, this invention transforms the unknown dynamics of the USV into a dynamically linearized data model. This invention eliminates the need for precise modeling of the controlled object and estimation of external disturbances, reducing control complexity while maintaining the original performance. This invention uses a double-power discrete sliding mode control algorithm to achieve tracking of the desired velocity within a finite time, exhibiting a certain degree of anti-interference capability. Attached Figure Description

[0044] The features and advantages of the invention will be more clearly understood by referring to the accompanying drawings, which are schematic and should not be construed as limiting the invention in any way. In the drawings:

[0045] Figure 1 This is a block diagram of the unmanned surface vessel path tracking system, which includes the guidance subsystem and control subsystem in a specific embodiment of the present invention.

[0046] Figure 2 This is a block diagram of the control subsystem designed based on the dynamic linearized model-free adaptive control algorithm and the double power discrete sliding mode control algorithm in a specific embodiment of the present invention;

[0047] Figure 3 This is a system block diagram of underactuated unmanned surface vessel path tracking based on model-free double power discrete sliding mode in a specific embodiment of the present invention. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0049] This invention provides a path tracking control method for underactuated unmanned surface vessels based on model-free adaptive sliding mode.

[0050] Figure 1 As shown, the desired path is given to the unmanned surface vessel (USV) guidance system. Using a moving local track coordinate system and Lyapunov stability theory, the desired heading angular velocity of the USV is calculated. Then, the current actual speed and heading angular velocity of the USV are measured using sensors such as GPS and a compass, and the error between the desired value and the current value is calculated. Figure 2 A model-free path tracking controller for an unmanned surface vessel (USV) is designed. A compact-format model-free adaptive control algorithm is used to estimate the pseudo-derivative of the dynamically linearized model. Simultaneously, based on the current tracking error, a double-power discrete sliding mode control algorithm is used to calculate the control input at the current moment. Figure 3 A detailed block diagram of the underactuated unmanned surface vessel (USV) path-tracking control system of this invention is presented, particularly illustrating the connection between the guidance subsystem and the model-free discrete sliding mode adaptive controller. The filtered forward velocity and sway velocity are obtained through an improved tracking differentiator, and the sideslip angle is calculated. The desired heading angular velocity is then calculated using a guidance law designed based on Lyapunov stability theory. This signal is transmitted to the controller to guide the USV to follow a predetermined path.

[0051] Includes the following steps:

[0052] Step 1: Establish a discrete motion model for the unmanned surface vessel:

[0053] First, establish the kinematic model of the unmanned surface vessel (USV). Considering the USV's three-degree-of-freedom motion on the horizontal plane, in the NED inertial navigation coordinate system, the kinematic model can be expressed as:

[0054]

[0055] In the formula, (x, y) is the position of the unmanned surface vessel; ψ is the heading angle; u is the forward velocity; v is the sway velocity; and r is the heading angular velocity.

[0056] Secondly, establish the dynamic model of the unmanned surface vessel:

[0057]

[0058] In the formula, f u =, f v f r For unknown system dynamics; τ u τ r These are the longitudinal thrust and steering torque of the unmanned surface vessel, respectively; τ wu τ wv τ wr External interferences during the unmanned surface vessel's navigation must satisfy the constraint |τ wu |≤D u ,|τ wv |≤D v ,|τ wr |≤D r D u D v D r It is an unknown positive constant.

[0059] Finally, by using the forward Euler method to discretize the kinematic and dynamic models, the discrete kinematic equations are obtained:

[0060]

[0061] Discrete equations of dynamics:

[0062]

[0063] Step 2: Establish a discrete-time guidance subsystem:

[0064] First, select a point on the given path as the local coordinate origin and establish a local path movement coordinate system. Based on geometric relationships and basic kinematics theory, obtain the dynamic equations of the tracking error based on continuous time:

[0065]

[0066] In the formula, x e y e For tracking error, it is also the coordinate of the unmanned surface vessel in the local coordinate system; ψ is the speed of the unmanned surface vessel. e =ψ+β-ψ d , ψ d The path tangential angle; c(ω) represents the speed at which the local coordinate origin moves along the path; c(ω) represents the curvature of the path.

[0067] Discretize the dynamic equation of the tracking error as follows:

[0068]

[0069] Further simplification and organization yield:

[0070]

[0071] In the formula, Δω k =ω k -ω k-1 Δβ k =β k -β k-1 .

[0072] Step 3: The lateral and longitudinal velocities acquired by the sensor are filtered and denoised using an improved tracking differentiator to suppress noise interference in the lateral and longitudinal velocity data, and the sideslip angle is calculated based on the processed lateral and longitudinal velocities.

[0073] The sideslip angle can be calculated by measuring the lateral and longitudinal velocities using sensors, and then performing the calculations.

[0074]

[0075] However, the measurement data obtained by the sensor contains noise, affecting the accuracy of the sideslip angle calculation. The angle deviation further affects the accuracy of the tracking error through the guidance law. Therefore, an improved tracking differentiator filter is used to filter the forward velocity and sway velocity measurement signals to suppress the effects of measurement interference.

[0076] The improved tracking differentiator is as follows:

[0077] x1(k+1)=x1(k)+T s x2(k)

[0078] x2(k+1)=x2(k)+T s f r (k)

[0079]

[0080] In the formula, y1 is the input signal, which is the measurement signal of forward velocity or sway velocity; x1 is the output signal tracking y1; x2 is the differential signal of the tracking system output y1; generally, a1 > 1 and a2 > 1 are taken. β > 1, R is an adjustable parameter. Increasing R will speed up the tracking speed and amplify the noise.

[0081] The velocity estimate is obtained using an improved tracking differentiator. The sideslip angle was calculated as follows:

[0082]

[0083] Step 4: Design the trajectory tracking guidance law for the discrete-time system:

[0084] To describe the heading angle error ψ of an unmanned surface vessel in the path tracking problem e，k The motion changes, and the discrete expected error angle of the system is designed as follows:

[0085]

[0086] In the formula, k δ >0, and for any y e，k , all have y e，k δ k ≤0 holds true only if y e，k When =0, the equality sign is true.

[0087] By tracking the dynamic equation of the error, it can be found that as long as the heading angle error ψ e，k Converging to δ k And x e，k It also converges to 0 at the same time. At this point, y e，k It will naturally converge to 0. If y e，k If it converges to 0, then by the definition of the expected angle, δ k It also converges to 0. Therefore, the following kinematic control law is designed, where the desired heading angular velocity r... d，k and the speed ω of the local path coordinate system origin. k+1 :

[0088]

[0089] In the formula, k2 > 0.

[0090] Define Lyapunov function V nav (k+1)=(ψ e，k+1 -δ k+1 ) 2 ,

[0091] Then ΔV nav (k+1)=(ψ e，k+1 -δ k+1 ) 2 -(ψ e，k -δ k ) 2

[0092] =(ψ e，k +Ts r k +(Δβ k -c(ω k )Δω k )-δ k+1 ) 2 -(ψ e，k -δ k ) 2

[0093] =(2ψ e，k +T s r k +(Δβ k -c(ω k )Δω k )-δ k+1 -δ k (T) s r k +(Δβ k -c(ω k )Δω k )-δ k+1 +δ k )

[0094] When r k =r d，k At that time,

[0095] ΔV nav =-(ψ e，k -δ k ) 2 ≤0

[0096] At this time, the unmanned surface vessel's bow angle tracking error ψ e It will asymptotically converge to the desired angle δ.

[0097] At the same time, define the Lyapunov function:

[0098]

[0099] If ω k The adaptive law design is as follows:

[0100] ω k+1 =ω k +T s (cosψ e，k U k +k2x e，k )

[0101] but

[0102]

[0103]

[0104] A speed tracker for an unmanned surface vessel is designed using a model-free adaptive algorithm based on a compact scheme and a double-power discrete sliding mode control algorithm.

[0105] The control system of the unmanned surface vessel is divided into a forward velocity control subsystem and a forward angular velocity control subsystem, and is written in the form of a single-input single-output discrete-time nonlinear system:

[0106]

[0107] The first step is to design the tracking control law for the forward velocity. Based on the compact scheme model-free adaptive algorithm, the compact scheme dynamic linearization model of the forward velocity can be written as:

[0108]

[0109] In the formula, the adaptive parameter The pseudo-partial derivative of this subsystem is the input change Δτ. u，k =τ u，k -τ u，k-1 The specific process is as follows:

[0110] First, calculate the pseudo-partial derivatives. Design the following pseudo-partial derivative criterion function:

[0111]

[0112] In the formula, μ1 is the weighting factor; for The estimated value;

[0113] Based on the criterion function, then find the information about... The extreme value of the pseudo-partial derivative can be obtained by the following algorithm:

[0114]

[0115] In the formula, η1∈(0,1] is the step size factor, which increases the flexibility of the algorithm.

[0116] if or |Δτ u，k-1 |≤∈or but

[0117] Secondly, a double-power discrete sliding mode control algorithm is used to obtain the corresponding system input τ. u，k .

[0118] The discrete integral terminal sliding mode function is defined as follows:

[0119] s u，k =e x，k +c uE u，k-1

[0120] In the formula, c u >0, α is the ratio of two odd numbers, and 0 < α < 1. The output tracking error e is defined as follows. u，k The difference between the desired speed and the current speed:

[0121] e u，k =u d，k -u k

[0122] In the formula, u d，k It is the desired speed, u k This is the current speed.

[0123] To force the sliding surface to be reached at a single sampling time, a discrete sliding mode control strategy is adopted:

[0124] Δs(k)=s u，k+1 -s u，k =0

[0125] Equivalent control is achieved through reorganization:

[0126]

[0127] In the formula, σ u It is an additional correction term for the estimated value. To avoid When it is very small, control τ uea，k It became very big.

[0128] The switching control design is as follows:

[0129]

[0130] In the formula, ε1>0, ε2>0, q1>0, 1-q1T s >0, 0<β1<1, 0<β2<1, sgn(·) denotes the sign function.

[0131] Therefore, the change in the control quantity of forward speed is:

[0132] Δτ u，k =Δτ uea，k +iΔτ udis，k

[0133] Then the control input for the forward velocity at time k is:

[0134] τ u，k =τ u，k-1 +Δτ u，k

[0135] At this point, the velocity subsystem satisfies the double power-law approach:

[0136]

[0137] The second step is to design the tracking control law for the bow angular velocity. Similar to the design method for the tracking control law for the forward velocity, the compact-form dynamic linearized model of the discrete system for the bow angular velocity can be written as:

[0138]

[0139] Design the pseudo-partial derivative criterion function for this model:

[0140]

[0141] but The estimated value for:

[0142]

[0143] if or |Δτ r，k-1 |≤∈or

[0144] The discrete integral terminal sliding mode function is defined as follows:

[0145] s r，k =e r，k +c r E r，k-1 ,

[0146] In the formula, c r >0,

[0147] Define the output tracking error e r，k The difference between the desired heading angular velocity and the current heading angular velocity:

[0148] e r，k =r d，k -r k

[0149] Discrete sliding mode control strategy is adopted:

[0150] s r，k+1 -s r，k =0

[0151] Derive the equivalent control law:

[0152]

[0153] Then, design the switching control law:

[0154]

[0155] In the formula, ε3>0, s4>0, q2>0, 1-q2T s >0, 0<β3<1, 0<β4<1.

[0156] The change in the control quantity of the bow angular velocity is then:

[0157] Δτ r，k+1 =Δτ req，k +Δτ rdis，k

[0158] Then the control input for the heading angular velocity at time k is:

[0159] τ r，k =τ r，k-1 +Δτ r，k

[0160] The heading angular velocity subsystem satisfies the double power-law approach:

[0161]

[0162] Although embodiments of the invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the invention, and such modifications and variations all fall within the scope defined by the appended claims.

Claims

1. A path tracking control method for underactuated unmanned surface vessels based on model-free adaptive sliding mode, characterized in that, The process includes the following steps: Step 1: Constructing a discrete motion model of the underactuated unmanned surface vessel (USV) in three degrees of freedom motion on the horizontal plane, including constructing a set of discrete kinematic equations and a set of discrete dynamic equations; Step 2: Based on the USV's discrete motion model, constructing a dynamic equation for tracking error based on discrete time, specifically: selecting a point on a given path as the local coordinate origin, establishing a local path movement coordinate system, obtaining the dynamic equation for tracking error based on continuous time, and then discretizing the dynamic equation for tracking error based on continuous time to obtain the dynamic equation for tracking error based on discrete time; Step 3: Filtering and denoising the lateral and longitudinal velocities collected by the sensors using an improved tracking differentiator, and calculating the lateral and longitudinal velocities based on the processed lateral and longitudinal velocities. Calculate the sideslip angle and introduce it into the dynamic equation of the tracking error in discrete time. Based on the dynamic equation of the tracking error in discrete time and the preset expected error angle, combined with the discrete domain Lyapunov stability theory, obtain the expected value of the bow angular velocity and the moving speed of the origin of the local path coordinate system in the trajectory tracking guidance law. Step 4: First, convert the forward velocity and bow angular velocity in the dynamic model of the unmanned surface vessel into a compact form dynamic linearized equation through a compact form model-free adaptive algorithm. Then, based on the double power discrete sliding mode control algorithm, design the equivalent control law and the switching control law, construct the tracking control law of forward velocity and the tracking control law of bow angular velocity, and control the unmanned surface vessel through the tracking control law of forward velocity and the tracking control law of bow angular velocity.

2. The path tracking control method for underactuated unmanned surface vessels based on model-free adaptive sliding mode as described in claim 1, characterized in that, The set of discrete kinematic equations in step 1 is as follows: ； The discrete equations of the dynamics are: ； In the formula, Let k be the position coordinates of the unmanned surface vessel in the inertial coordinate system at time k. Let k be the bow angle of the unmanned surface vessel. Let k be the forward velocity. Let k be the sway velocity at time k. Let k be the heading angular velocity; The discrete time step; , , This refers to the unknown nonlinear dynamic term of the system. , These are the longitudinal thrust control input and the steering torque control input, respectively. , , This refers to external marine environmental disturbances.

3. The path tracking control method for underactuated unmanned surface vessels based on model-free adaptive sliding mode as described in claim 1, characterized in that, The dynamic equation for the discrete-time tracking error in step 2 is as follows: ； In the formula, , Let k be the position tracking error of the unmanned surface vessel in the local path coordinate system at time k; Let k be the net velocity of the unmanned surface vessel at time k; Let k be the heading angle tracking error at time k; This represents the change in the speed of the origin of the local path coordinate system along the path. Let be the curvature of the given path at the local coordinate origin; This represents the change in sideslip angle. Let k be the sideslip angle of the unmanned surface vessel at time k.

4. The path tracking control method for underactuated unmanned surface vessels based on model-free adaptive sliding mode as described in claim 1, characterized in that, The improved tracking differentiator in step 3 is as follows: ； ； ； In the formula, The input signal is the lateral or longitudinal velocity measurement value acquired by the sensor. The filtered output signal is used to track the input signal; The differential estimate of the input signal; the positive gain parameter satisfies , ; Fractional order satisfies The gain coefficient satisfies R is an adjustable parameter for adjusting the tracking speed. is the discrete time step.

5. The path tracking control method for underactuated unmanned surface vessels based on model-free adaptive sliding mode as described in claim 1, characterized in that, In step 3, the preset expected heading error angle is: ； The desired bow angular velocity is: ； The update law for the velocity of the origin of the local path coordinate system is: ； In the formula, the gain parameter satisfies , The angle parameters satisfy .

6. The path tracking control method for underactuated unmanned surface vessels based on model-free adaptive sliding mode as described in claim 1, characterized in that, In step 4, the compact-form model-free adaptive algorithm converts the forward velocity and heading angular velocity subsystems into compact-form dynamic linearized equations: ； ； In the formula, , These are the pseudo-partial derivatives of the forward velocity and bow angular velocity subsystems, respectively. , These represent the control input changes for the two subsystems, respectively.

7. The path tracking control method for underactuated unmanned surface vessels based on model-free adaptive sliding mode as described in claim 6, characterized in that, The adaptive estimation algorithm for the pseudo-partial derivative is as follows: ； ； In the formula, Step size factor; As a weighting factor; , They are respectively , The estimated value; when satisfying or Reset When satisfied or Reset ,in It is a preset minimum positive number.

8. The path tracking control method for underactuated unmanned surface vessels based on model-free adaptive sliding mode as described in claim 6, characterized in that, In step 4, the tracking control law for the forward velocity is: ； In the formula: ； in, This is an additional correction term for the pseudo-partial derivative estimate, used to avoid abrupt changes in the control quantity due to an excessively small denominator; The desired forward velocity; Forward velocity tracking error; The discrete integral terminal sliding mode function; the gain parameter satisfies , , and , , , Represents a symbolic function.

9. The path tracking control method for underactuated unmanned surface vessels based on model-free adaptive sliding mode as described in claim 6, characterized in that, In step 4, the tracking control law for the heading angular velocity is: ； In the formula: ； in, This is an additional correction term for the pseudo-partial derivative estimate; The desired heading angular velocity; For heading angular velocity tracking error; The discrete integral terminal sliding mode function; the gain parameter satisfies , , and , , , Represents a symbolic function.

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