An unmanned ship path tracking control method based on a sliding mode control

Abstract

The application discloses a path tracking control method for an unmanned surface vehicle based on a sliding mode control, and the method comprises the following steps: establishing a kinematics and dynamics mathematical model of the unmanned surface vehicle; designing expected longitudinal and transverse velocities of the unmanned surface vehicle in a navigation process, so as to realize tracking of an expected path of the unmanned surface vehicle; adopting a saturation function to design an improved longitudinal thrust sliding mode control law and a bow moment sliding mode control law, so that the longitudinal and transverse velocities of the unmanned surface vehicle relative to an inertial coordinate system can track virtual control inputs in the navigation process; designing an auxiliary system to eliminate influences of internal disturbances and input saturation on control performance; introducing an event triggering mechanism into the control law to save the calculation amount of the controller and reduce the loss of an actuator; and adopting the designed path tracking controller of the unmanned surface vehicle to track and control the path of the unmanned surface vehicle. The application combines the sliding mode control, the event triggering mechanism anti-disturbance strategy and the anti-saturation strategy, so that the tracking precision is improved, and the calculation amount is reduced.

Description

Technical Field

[0001] This invention relates to unmanned surface vessel (USV) path tracking technology, and in particular to a USV path tracking control method based on sliding mode control. Background Technology

[0002] In recent years, with the rise and development of unmanned driving technology, unmanned surface vessels (USVs), as miniaturized, intelligent, and multi-purpose unmanned marine transport platforms, have attracted widespread attention from scholars. Among them, path tracking technology has important application value in both military and civilian fields. The motion control of USVs faces research challenges such as control input saturation limitations, model uncertainty, nonlinearity, and strong external disturbances, posing challenges to effective and reliable target tracking control. Qin H et al. used the hyperbolic tangent function to solve the control input saturation problem, employed neural networks to estimate model uncertainty and environmental disturbances, and designed a finite-time stable underactuated USV trajectory tracking control method. Simulation experiments and analysis demonstrated the effectiveness of the proposed control method, but this scheme has a high computational cost and limited practical application performance. B. Bernhardsson et al. compared the control performance based on time-period sampling and event-triggered mechanisms for some simple systems. Experimental results showed that event-triggered control can reduce the number of control signal updates in the system, but its application in the field of USV control is limited. Currently, theories such as sliding mode variable structure control and active disturbance rejection control have been successfully applied to practical projects, but problems such as input saturation limitations of USV controllers and actuator losses have not been adequately addressed.

[0003] Existing methods for path tracking control of underactuated unmanned surface vessels (USVs) combine robust control and sliding mode control. First, a three-degree-of-freedom mathematical model of the USV, including kinematic and dynamic models, is constructed. Then, robust control and sliding mode control are used to design the path tracking controller. Finally, stability analysis and simulation experiments are used to verify the stability and effectiveness of the control strategy. While this existing technology has clear advantages, such as strong adaptability to changes in inherently uncertain parameters and external environments, it suffers from excessive computational load, lacks further processing and optimization for disturbance input saturation, does not adequately consider chattering elimination, and is overly complex, requiring frequent controller updates, making it difficult to apply in practical engineering. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide a path tracking control method for unmanned surface vessels based on sliding mode control.

[0005] Technical solution: The present invention provides a path tracking control method for unmanned surface vessels based on sliding mode control, comprising:

[0006] S1. Establish an inertial coordinate system and an unmanned surface vessel appendage coordinate system, and establish a three-degree-of-freedom kinematic and dynamic mathematical model of the underactuated surface unmanned surface vessel;

[0007] S2. Design a kinematic controller, including establishing the unmanned surface vessel's position tracking error and velocity tracking error, and designing the desired velocity u for the longitudinal velocity u and lateral velocity v during the unmanned surface vessel's navigation in the attached coordinate system. d v d The desired path of the unmanned surface vessel is tracked by the desired speed;

[0008] S3. Design a dynamic controller, including an improved longitudinal thrust sliding mode control law τ using a saturation function. u and the heading moment sliding mode control law τ r This allows the unmanned surface vessel's longitudinal and lateral velocities relative to the inertial coordinate system to track the virtual control input u during navigation. d v d ;

[0009] S4. Design an auxiliary system to eliminate the impact of internal disturbances and input saturation on control performance;

[0010] S5. Introduce an event triggering mechanism into the control law to save the computational load of the controller and reduce the wear and tear on the actuator;

[0011] S6. Use the unmanned surface vessel path tracking controller designed in steps S2 to S5 to track and control the unmanned surface vessel path, and determine whether the desired target point has been reached. If the desired target point has been reached, switch the target point and continue tracking and control; otherwise, return to step S2 to redesign the unmanned surface vessel path tracking controller.

[0012] Furthermore, the kinematic model of the unmanned surface vessel established in step S1 is as follows:

[0013]

[0014] The dynamic model of the unmanned surface vessel is as follows:

[0015]

[0016] Among them, (x,y, () represents the forward displacement, lateral displacement, and heading angle of the unmanned surface vessel in the inertial coordinate system. x, y, The derivatives; (u,v,r) represent the forward velocity, lateral drift velocity, and bow angular velocity in the attached coordinate system. The differentials of u, v, and r are respectively; (τ) u ,τ v ,τ r ) is the thrust control input, τ uFor longitudinal thrust, τ v For lateral thrust, τ v =0; τ r For the bow moment; (τ) wu τ wv τ wr ) represents time-varying disturbance in the attached coordinate system; m 11 m 22 m 33 d 11 d 22 d 33 All of these are parameters of the coefficient matrix.

[0017] Furthermore, the desired speed u designed in step S2 d v d for:

[0018]

[0019] Where, k x ,k y >0 represents the controller gain, l x ,l y >0 is the saturation constant, x e y e For position tracking error, x d y d Let be the desired position, and tanh(·) be the hyperbolic tangent function.

[0020] Furthermore, the improved longitudinal thrust sliding mode control law in step S3 is as follows:

[0021]

[0022] The heading moment sliding mode control law is:

[0023]

[0024] Where k2≥0 is the coefficient of the exponential approach term of the unmanned surface vessel's bow roll rate sliding mode control; W2≥0 is the switching gain of the unmanned surface vessel's bow roll rate sliding mode control.

[0025] Furthermore, the auxiliary system in step S4 is:

[0026]

[0027] Where, θ i As auxiliary system state variables, For θ i The differential; i = u, r, Δτ i μ represents the difference between the actual input and the maximum input. iδ i θ g It is a constant greater than 0, θ g →0,χ、 It is a positive odd number and satisfies

[0028] The longitudinal thrust control law and the bow moment sliding mode control law after adding the auxiliary system are as follows:

[0029]

[0030] σ u σ r To adjust the parameters.

[0031] Furthermore, the event triggering condition for the event triggering mechanism in step S5 is as follows:

[0032]

[0033] Where t represents time, t b At time k, t b+1 At time k+1, x is the estimated value of the state variable. r The reference value is Υ, and the trigger threshold is Υ.

[0034] The initial update time t0 is defined as follows:

[0035]

[0036] The present invention provides a path tracking control system for unmanned surface vessels based on sliding mode control, comprising:

[0037] The model building module is used to build a three-degree-of-freedom kinematic and dynamic mathematical model of an unmanned surface vessel based on an inertial coordinate system and an unmanned surface vessel attached coordinate system.

[0038] The controller establishment module is used to establish a tracking controller for unmanned surface vessels. This includes designing a kinematic controller and a dynamic controller, and adding an auxiliary system to the controller to eliminate the impact of internal disturbances and input saturation on control performance. At the same time, an event triggering mechanism is incorporated into the control law to save the computational load of the controller and reduce the wear and tear on the actuators.

[0039] The tracking control module uses the designed unmanned surface vessel (USV) path tracking controller to track and control the USV's path, and determines whether the desired target point has been reached. If the desired target point has been reached, the target point is switched and tracking control is continued; otherwise, the process returns to redesigning the USV path tracking controller.

[0040] An apparatus of the present invention includes a memory and a processor, wherein:

[0041] Memory is used to store computer programs that can run on a processor;

[0042] The processor is used to execute the steps of the above-described unmanned surface vessel path tracking control method based on sliding mode control when running the computer program.

[0043] Furthermore, a storage medium storing a computer program, which, when executed by at least one processor, implements the steps of the aforementioned unmanned surface vessel path tracking control method based on sliding mode control.

[0044] Beneficial Effects: Compared with the prior art, the significant technical effects of this invention are as follows: This invention considers the problems of unknown environmental disturbances, controller input saturation, chattering near the conventional sliding mode switching surface, and frequent controller updates, and designs an improved sliding mode controller for the path tracking control problem of unmanned surface vessels; it adopts an improved reaching law based on an anti-saturation function, which improves control accuracy, enhances system robustness, and effectively weakens the impact of chattering; it designs an auxiliary system to address the controller input saturation problem, thereby improving control performance; considering the excessive number of controller updates and actuator wear, it introduces an event triggering mechanism and designs threshold event triggering conditions for the control law, which can effectively reduce the number of controller updates, reduce computational load, and alleviate actuator wear. Attached Figure Description

[0045] Figure 1 This is a flowchart of the control method of the present invention. Detailed Implementation

[0046] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0047] The present invention provides a path tracking control method for an underactuated unmanned surface vessel, which involves the control design of the underactuated unmanned surface vessel under sliding mode control, including disturbances, controller input saturation and actuator losses, and combines sliding mode control, event triggering mechanism anti-disturbance strategy and anti-saturation strategy.

[0048] like Figure 1 As shown, the present invention provides a path tracking control method for unmanned surface vessels based on sliding mode control, comprising the following steps:

[0049] S1. Establish the inertial coordinate system O-XYZ and the unmanned surface vessel's attached coordinate system O1-k1Y1Z1, and establish the three-degree-of-freedom kinematic and dynamic mathematical model of the underactuated surface unmanned vessel.

[0050] The kinematic model of the unmanned surface vessel is as follows:

[0051]

[0052] The dynamic model of the unmanned surface vessel is as follows:

[0053]

[0054] Where: (x,y, () represents the forward displacement, lateral displacement, and heading angle of the unmanned surface vessel in the inertial coordinate system. x, y, The derivatives; (u,v,r) represent the forward velocity, lateral drift velocity, and bow angular velocity in the attached coordinate system. The differentials of u, v, and r are respectively; (τ) u ,τ v ,τ r ) is the thrust control input, τ u For longitudinal thrust, τ v For lateral thrust, τ r For bow torque, generally USVs do not have lateral thrust, so τ v =0; (τ) wu τ wv τ wr The ) represents time-varying disturbance in the attached coordinate system. And... d 11 =X u d 22 =X v d 33 =N r ;m 11 ,m, m 22 , m 33 I y , d 11 X u d 22 X v d 33 N r All of these are parameters of the coefficient matrix.

[0055] The unmanned surface vessel path tracking controller includes the design of kinematic controllers and dynamic controllers. The design methods of each controller are described in detail below.

[0056] S2. Design a kinematic controller; in the kinematic controller, design the desired velocity u. d v d To achieve the tracking of the desired path;

[0057] First, define the position tracking error:

[0058]

[0059] Where, x e ye These represent the position tracking errors along the x and y axes in the inertial coordinate system, where x and y are the actual coordinates of the unmanned surface vessel during path tracking in the inertial coordinate system. d y d These are the desired trajectory coordinates for a given target trajectory.

[0060] Differentiating equation (3) yields the dynamic equation for the position tracking error during the actual navigation of the unmanned surface vessel:

[0061]

[0062] Among them, parameters x e y e x d y d The differential.

[0063] Simultaneously define the velocity tracking error:

[0064]

[0065] Among them, u e and v e These represent the velocity tracking errors of the longitudinal velocity u and lateral velocity v during the navigation of the unmanned surface vessel in the attached coordinate system, respectively. d v d Let be the expected velocities of the longitudinal velocity *u* and lateral velocity *v* during the unmanned surface vessel's navigation in the attached coordinate system, respectively. In the inertial coordinate system, these are represented as... and

[0066] The desired speed u designed in this invention d v d for:

[0067]

[0068] Where, k x ,k y >0 represents the controller gain, l x ,l y >0 is the saturation constant, x e y e For position tracking error, x d y d For the desired position, tanh(·) is a hyperbolic tangent function that is smooth and continuous. Therefore, choosing the hyperbolic tangent function tanh as the input of the virtual velocity quantity can effectively reduce chattering in the sliding mode controller of the unmanned surface vessel.

[0069] S3. Design a dynamic controller; in the dynamic controller, design the control law τ using an improved reaching law based on the saturation function. u τ r This allows the unmanned surface vessel's longitudinal and lateral velocities relative to the inertial coordinate system to track the virtual control input u during navigation. d v d .

[0070] This section focuses on the design of the dynamic loop controller for the unmanned surface vessel (USV). The main task is to design the sliding mode controller τ. u and τ r This allows the unmanned surface vessel's longitudinal velocity u and lateral velocity v relative to the inertial coordinate system to track the virtual control input u during navigation. d and v d .

[0071] (1) Design of longitudinal thrust sliding mode control law;

[0072] Define the following longitudinal first-order integral sliding surface:

[0073]

[0074] Where λ1 is the sliding surface parameter and t is time;

[0075] The time derivative of the sliding surface S1 is:

[0076]

[0077] in, u e and u d The differential, A u These are the parameters of the sliding surface;

[0078] Longitudinal thrust sliding mode control law selection: Exponential approach control law:

[0079]

[0080] Where, τ u For longitudinal thrust sliding mode control law, All are parameters. All are parameters. k1>0 is the coefficient of the exponential approach term of the longitudinal velocity sliding mode control of the unmanned surface vessel, W1>0 is the switching gain of the longitudinal velocity sliding mode control of the unmanned surface vessel, and sgn(S1) is the sign function.

[0081] To improve the accuracy of the control system and reduce chattering, an improved reaching law based on a saturation function is adopted, with the following expression:

[0082]

[0083] The improved saturation function is as follows:

[0084]

[0085] Where σ>1, 0<Δ<1, as σ increases, The corresponding increase in σ also increases the system's control accuracy. In the above equation, the introduction of parameter σ improves the system's control accuracy while maintaining the saturation width Δ. In other words, a parameter Δ is first set to reduce system chattering, and then the control accuracy is improved by adjusting parameter σ.

[0086] Therefore, the improved longitudinal thrust control law is designed as follows:

[0087]

[0088] Finally, a Lyapunov function is constructed to determine the range of W1.

[0089] (2) Sliding mode control law for bow torque;

[0090] The following second-order sliding surface is defined to represent the tracking error of the unmanned surface vessel's lateral motion:

[0091]

[0092] Among them, λ3, λ2, v e (τ) are all parameters of the transverse second-order sliding surface, and t is time;

[0093] Calculate the heading control law under zero dynamics, let get:

[0094]

[0095] in, Let v be the first and second derivatives, respectively. v d The first and second derivatives;

[0096] In the dynamic model of unmanned surface vessels Taking the derivative again, we get For the desired velocity u d v d Differentiation yields:

[0097]

[0098] in, x d y dThe second-order differential; γ1 and γ2 are parameters;

[0099]

[0100]

[0101] Where, k x l x k y l y All are parameters;

[0102] From the formula, we get:

[0103]

[0104] Differentiating the above equation again, we get:

[0105]

[0106] in, for The derivative of These are the derivatives of parameters r and Λ, respectively;

[0107] Substituting equations (15), (18), and (19) into... The equivalent control law can be obtained:

[0108]

[0109] in, The corresponding estimates for h and b are expressed as follows:

[0110] b = m 22 u d -m 11 u (21)

[0111]

[0112] Among them, b, h, f r As a substitute variable;

[0113] In summary, the sliding mode control law for the bow torque can be obtained as follows:

[0114]

[0115] Where k2≥0 is the coefficient of the exponential approach term of the unmanned surface vessel's bow roll rate sliding mode control; W2≥0 is the switching gain of the unmanned surface vessel's bow roll rate sliding mode control, and the range of W2 is determined in the same way as W1.

[0116] S4. Design an auxiliary system to eliminate the impact of internal disturbances and input saturation on control performance;

[0117] Considering that system saturation has a significant impact on control performance, the auxiliary dynamic system is designed as follows:

[0118]

[0119] Where, θ i As auxiliary system state variables, For θ i The differential; i = u, r, Δτ i μ represents the difference between the actual input and the maximum input. i δ i θ g It is a constant greater than 0, θ g →0,χ、 It is a positive odd number and satisfies

[0120] The control law after adding the auxiliary system is:

[0121]

[0122] Where, σ u σ r To adjust the parameters.

[0123] S5. Introduce an event triggering mechanism into the control law to save the computational load of the controller and reduce the wear and tear on the actuator;

[0124] To address the issues of excessive controller updates and actuator wear, an event-triggered mechanism is introduced:

[0125] The event is triggered by the following conditions:

[0126]

[0127] Where t represents time, t b At time k, t b+1 At time k+1, x is the estimated value of the state variable. r Υ is a reference value, and Y is the trigger threshold.

[0128] The initial update time t0 is defined as follows:

[0129]

[0130] S6. Use the unmanned surface vessel path tracking controller designed in steps S2 to S5 to track and control the unmanned surface vessel path, and determine whether the desired target point has been reached. If the desired target point has been reached, switch the target point and continue tracking and control; otherwise, return to step S2 to redesign the unmanned surface vessel path tracking controller.

[0131] This invention also proposes a path tracking control system for unmanned surface vessels based on sliding mode control, comprising:

[0132] The model building module is used to build a three-degree-of-freedom kinematic and dynamic mathematical model of an unmanned surface vessel based on an inertial coordinate system and an unmanned surface vessel attached coordinate system.

[0133] The controller establishment module is used to establish a tracking controller for unmanned surface vessels. This includes designing a kinematic controller and a dynamic controller, and adding an auxiliary system to the controller to eliminate the impact of internal disturbances and input saturation on control performance. At the same time, an event triggering mechanism is incorporated into the control law to save the computational load of the controller and reduce the wear and tear on the actuators.

[0134] The tracking control module uses the designed unmanned surface vessel (USV) path tracking controller to track and control the USV's path, and determines whether the desired target point has been reached. If the desired target point has been reached, the target point is switched and tracking control is continued; otherwise, the process returns to redesigning the USV path tracking controller.

[0135] An apparatus of the present invention includes a memory and a processor, wherein:

[0136] Memory is used to store computer programs that can run on a processor;

[0137] The processor is configured to execute the steps of the above-described unmanned surface vessel path tracking control method based on sliding mode control when running the computer program.

[0138] The present invention provides a storage medium storing a computer program, which, when executed by at least one processor, implements the steps of the above-described unmanned surface vessel path tracking control method based on sliding mode control.

Claims

1. A path tracking control method for an unmanned surface vehicle based on sliding mode control, characterized in that, Comprise: S1, establish the inertial coordinate system and the unmanned surface vehicle appendage coordinate system, establish the kinematics, dynamics mathematical model of three degrees of freedom of the underactuated unmanned surface vehicle; S2, design kinematic controller, including establishing unmanned ship position tracking error and speed tracking error, designing the desired speed of longitudinal speed and lateral speed of unmanned ship in the process of sailing in the appendage coordinate system , , , , realizing the tracking of the desired path of the unmanned ship through the desired speed S3. Designing a dynamics controller, including designing an improved longitudinal thrust sliding mode control law using a saturation function and a yaw moment sliding mode control law such that the longitudinal and lateral velocities of the USV relative to the inertial coordinate frame track the virtual control inputs during navigation , ; The improved longitudinal thrust sliding mode control law is: ； The bow moment sliding mode control law is: ； wherein, is the exponential reaching term coefficient for the yaw angle velocity sliding mode control of the unmanned surface vehicle; is the switching gain for the yaw angle velocity sliding mode control of the unmanned surface vehicle; S4, design an auxiliary system for eliminating the influence of internal disturbance and input saturation on control performance; the auxiliary system is: ； wherein is a state variable of the auxiliary system, is a differential of , , represents a difference between the actual input and the maximum input, is a constant greater than 0, , is a positive odd number and satisfies , > 0; The longitudinal thrust control law and the bow moment sliding mode control law after adding the auxiliary system are: ； , to adjust the parameters; S5, introduce an event-triggered mechanism in the control law for saving the calculation amount of the controller and reducing the loss of the actuator; S6, use the unmanned surface vehicle path tracking controller designed in steps S2 to S5 to track the path of the unmanned surface vehicle, judge whether the desired target point is reached, if the desired target point is reached, switch the target point for continuous tracking control; otherwise, return to step S2 to redesign the unmanned surface vehicle path tracking controller.

2. The path tracking control method for an unmanned surface vehicle based on sliding mode control according to claim 1, characterized in that, The kinematics model of the unmanned surface vehicle established in step S1 is: ； The dynamics model of the unmanned surface vehicle is: ； wherein, is the forward displacement, lateral displacement and heading angle of the unmanned surface vehicle in the inertial coordinate frame, are the differentials of is the forward velocity, lateral velocity and heading velocity of the appendage in the body coordinate frame, are the differentials of is the thrust control input, is the longitudinal thrust, is the lateral thrust, is the heading moment; represents the time-varying disturbance in the body coordinate frame; are coefficient matrix parameters.​​​​​​​​ 3. The path tracking control method for an unmanned surface vehicle based on sliding mode control according to claim 1, characterized in that, The desired speed designed in step S2 , is: ； wherein, Kp is a controller gain, Ks is a saturation constant, , e is a position tracking error, , x is a desired position, is a hyperbolic tangent function.

4. The path tracking control method for an unmanned surface vehicle based on sliding mode control according to claim 1, characterized in that, The event-triggered condition of the event-triggered mechanism in step S5 is: ； wherein, represents a time instant, is a time instant, is a time instant, is an estimated value of a state variable, is a reference value, is a triggering threshold; Initial update time Is defined as follows: 。 5. A control system for the path following control method of the unmanned surface vehicle based on the sliding mode control according to any one of claims 1-4, characterized in that, Comprise: The model establishment module is used to establish the kinematics, dynamics mathematical model of three degrees of freedom of the unmanned surface vehicle based on the inertial coordinate system and the unmanned surface vehicle appendage coordinate system; The controller establishment module is used to establish the unmanned surface vehicle tracking controller, including designing the kinematics controller, the dynamics controller, adding the auxiliary system in the controller to eliminate the influence of internal disturbance and input saturation on control performance, and introducing the event-triggered mechanism in the control law to save the calculation amount of the controller and reduce the loss of the actuator; The tracking control module uses the designed unmanned surface vehicle path tracking controller to track the path of the unmanned surface vehicle, judges whether the desired target point is reached, if the desired target point is reached, switches the target point for continuous tracking control; Otherwise, return to redesign the unmanned surface vehicle path tracking controller.

6. An apparatus device comprising: Comprise a memory and a processor, wherein: The memory is used to store a computer program capable of running on the processor; The processor is used to execute the steps of the unmanned surface vehicle path tracking control method based on sliding mode control according to any one of claims 1-4 when running the computer program.

7. A storage medium, characterized by The storage medium has a computer program stored thereon, and the computer program is executed by at least one processor to implement the steps of the unmanned surface vehicle path tracking control method based on sliding mode control according to any one of claims 1-4.

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