An event-triggered autonomous underwater vehicle trajectory tracking control method

Abstract

The application discloses an event-triggered autonomous underwater vehicle trajectory tracking control method, comprising the following steps: constructing a kinematic model and a dynamic model of an autonomous underwater vehicle according to the system structure characteristics of a three-degree-of-freedom autonomous underwater vehicle; designing a motion controller of the autonomous underwater vehicle based on a backstepping method, obtaining a virtual control input, and obtaining a tracking error equation; designing a dynamic controller for stabilizing the tracking error by using a global sliding mode control method; and introducing an event-triggered mechanism, tracking controlling the trajectory of the autonomous underwater vehicle based on the fixed threshold strategy for triggering the control, and avoiding the Zeno phenomenon. The application avoids continuous action of the controller, reduces the burden of the control straight line mechanism, alleviates the problem of limited onboard energy of the AUV, and indicates that the system does not appear the Zeno phenomenon.

Description

Technical Field

[0001] This invention belongs to the field of autonomous underwater vehicle trajectory tracking and control, specifically an event-triggered autonomous underwater vehicle trajectory tracking and control method. Background Technology

[0002] With the rapid development of science and technology, autonomous underwater vehicles (AUVs) have the advantage of being able to operate without human intervention. In the marine underwater environment, due to their high degree of autonomy, AUVs have been widely used in recent years in areas such as marine surveying, emergency rescue, and military applications.

[0003] In recent years, many control methods have been applied to the trajectory tracking problem of autonomous underwater vehicles (AUVs). These include PID control, model predictive control, neural network adaptive control, and sliding mode control. Sliding mode control, including terminal sliding mode control, integral sliding mode control, and non-singular terminal sliding mode control, is widely used in various intelligent control systems due to its insensitivity to external disturbances and its rapid response. During the movement of underactuated AUVs, the precise model parameters are extremely difficult to determine due to external ocean currents and the complex and ever-changing marine environment. The complex and variable marine environment, including meteorological, sea state, geological, and ecological factors, severely interferes with the movement and control of AUVs, increasing the difficulty of achieving high-precision and stable control. AUVs typically need to reach a pre-set position smoothly without human intervention; therefore, achieving high-precision trajectory tracking is a key problem to be solved in AUV control systems.

[0004] Event-triggered control is a control strategy that can efficiently utilize resources. In traditional periodic sampling control, the system transmits information and updates control at fixed time intervals, which inevitably leads to a waste of system resources. In event-triggered control, however, the transmission of system information is triggered by specific events within the system; that is, information sampling and control updates only occur when the system needs them, which can effectively save communication and computing resources.

[0005] The invention disclosed in CN115016257A describes a fuzzy event-triggered sliding mode control method for longitudinally tracking unmanned underwater vehicles (UUVs), belonging to the field of UUV control engineering. This invention solves the problems of high energy consumption and significant actuator wear in existing UUV depth tracking control methods. The invention designs an event triggering mechanism using an integral sliding surface and a time-varying threshold to trigger the integral sliding mode controller at the event trigger time, thereby controlling the UUV system state and achieving intermittent updating of the integral sliding mode controller. During this process, an equivalent sliding mode control law is obtained through the integral sliding surface, and then the integral sliding mode controller is constructed based on the equivalent sliding mode control law. This invention can effectively reduce UUV control energy consumption and alleviate actuator wear during the control process. This invention is mainly used for intermittent control of the UUV's trajectory in the depth direction. The invention disclosed in CN113009831A provides an event-triggered adaptive fuzzy fault-tolerant performance-preserving control method for an underwater robot. The method involves acquiring the underwater robot's operational status data and inputting this data into a preset adaptive fuzzy fault-tolerant control model to control the underwater robot's position vector to track a given trajectory. The adaptive fuzzy fault-tolerant control model includes a funnel-tracking controller, and the underwater robot's position tracking error is limited within a preset performance funnel. This invention introduces the funnel control method into an adaptive control strategy based on a tan-type obstacle Lyapunov function, enabling the controlled underwater robot to achieve tracking performance with a specified accuracy.

[0006] However, neither of them considered how a three-degree-of-freedom autonomous underwater vehicle can achieve trigger-based trajectory tracking while ensuring that Zeno's phenomenon does not occur. Summary of the Invention

[0007] Technical problem solved: This invention discloses an event-triggered trajectory tracking control method for autonomous underwater vehicles, which avoids continuous controller operation, reduces the burden on the control linear mechanism, alleviates the problem of limited onboard energy of AUVs, and shows that the system does not exhibit the Zeno phenomenon.

[0008] Technical solution:

[0009] An event-triggered trajectory tracking control method for an autonomous underwater vehicle, the trajectory tracking control method comprising the following steps:

[0010] S1. Based on the system structural characteristics of the three-degree-of-freedom autonomous underwater vehicle, construct the kinematic and dynamic models of the autonomous underwater vehicle;

[0011] S2. Based on the backstepping method, a motion controller for an autonomous underwater vehicle is designed, and a virtual control input is obtained to derive the tracking error equation. A dynamic controller for stabilizing the tracking error is designed using a global sliding mode control method.

[0012] S3 introduces an event-triggered mechanism to track and control the trajectory of the autonomous underwater vehicle based on a fixed threshold strategy for triggering control, while avoiding the Zeno phenomenon.

[0013] Further, in step S1, the horizontal kinematic equations and dynamic equations of the three-degree-of-freedom autonomous underwater vehicle are:

[0014]

[0015] Where x and y represent the horizontal position coordinates of the autonomous underwater vehicle in the inertial coordinate system; ψ and r represent the yaw angle and yaw rate, respectively; and u and v represent the surge and sway rates, respectively.

[0016] Furthermore, in step S1, the dynamic model of the autonomous underwater vehicle is as follows:

[0017]

[0018] In the formula, m1, m2, and m3 represent the generalized mass of the autonomous underwater vehicle; X u Y v and N r Represents the linear damping coefficient; x u|u| Y v|v| and N r|r| τ represents the secondary damping coefficient; u and τ r These represent surge moment and yaw moment, respectively; the parameters satisfy the following conditions:

[0019]

[0020]

[0021]

[0022] Where: ∧ represents the nominal value of the parameter; - represents the upper limit of the parameter perturbation.

[0023] Furthermore, in step S2, the process of designing a dynamic controller for stabilizing the tracking error using a global sliding mode control method includes the following steps:

[0024] S21, the system's position error equation is defined as follows:

[0025]

[0026] Where: x R and y R Let x represent the desired position coordinates, and both x and y be smooth functions. e and ye These represent the positional error values ​​for the x-axis and y-axis, respectively.

[0027] S22, Design a motion controller, and obtain the virtual input as follows:

[0028]

[0029] In the formula, u d For virtual control input of surge velocity; r d For virtual control input of yaw speed; u R ψ is the desired surge velocity. e For the steady-state error of the angle; k x r is the adjustable gain coefficient. R k is the angular velocity. ψ The gain coefficient is adjustable.

[0030] S23, Design a dynamic controller, and obtain the dynamic control law as follows:

[0031]

[0032]

[0033] In the formula, λ1 is an adjustable coefficient; λ2 is an adjustable coefficient; η1 is the gain coefficient of the upper limit of parameter perturbation; η2 is the gain coefficient of the upper limit of parameter perturbation; S1 is the global sliding surface; S2 is the global sliding surface.

[0034] Furthermore, in step S3, an event-triggered mechanism is introduced. Based on the fixed threshold strategy for triggering control, the process of tracking and controlling the trajectory of the autonomous underwater vehicle includes the following steps:

[0035] S31, the event triggering controller is designed as follows:

[0036]

[0037] In the formula, w1(t) is the event trigger controller; For event-triggered controllers, w2(t) is the trigger time sequence; w2(t) is the event trigger controller. For event-triggered controllers, For the trigger time sequence;

[0038] S32, the event triggering condition is designed as follows:

[0039]

[0040]

[0041] in c1 and c2 are both positive constants and ε1>0, ε2>0, k∈N + When the event-triggered mechanism is triggered in the system, the input changes from τ(t) φ，k Update to τ(t) φ，k+1 ), t φ，k+1 - It is the moment the event is triggered, t φ，k+1 It is the instant the controller updates;

[0042] S33 verifies the stability of the autonomous underwater vehicle system based on Lyapunov stability theory. By analyzing and ensuring that the internal event time is greater than a normal number, it ensures that the control signal is updated discontinuously.

[0043] Furthermore, in step S33, the process of verifying the stability of the autonomous underwater vehicle system based on Lyapunov stability theory includes:

[0044] Define the Lyapunov function V:

[0045]

[0046] In the formula, V d1 For Lyapunov functions; V d2 For Lyapunov functions;

[0047] Take the derivatives of the Lyapunov function V and combine them. get:

[0048]

[0049]

[0050] because: so: in,

[0051] That is, all state variables of the system are bounded, and the system is asymptotically stable.

[0052] Beneficial effects:

[0053] First, the event-triggered trajectory tracking control method of this invention designs a kinematic controller based on backstepping and obtains virtual control input. Then, a sliding mode control method is used to design a dynamic controller to stabilize the tracking error.

[0054] Secondly, the event-triggered autonomous underwater vehicle trajectory tracking control method of the present invention introduces an event-triggered control mechanism, which saves more communication resources of the system and avoids the Zeno phenomenon. Attached Figure Description

[0055] Figure 1 This is a flowchart of the event-triggered trajectory tracking and control method for autonomous underwater vehicles according to an embodiment of the present invention;

[0056] Figure 2 This is a schematic diagram illustrating how an autonomous underwater vehicle tracks changes.

[0057] Figure 3 This is a schematic diagram illustrating the changes in position tracking error of an autonomous underwater vehicle.

[0058] Figure 4 A schematic diagram illustrating the error changes of virtual control variables for an autonomous underwater vehicle.

[0059] Figure 5 This is a diagram illustrating the trigger interval of the event triggering mechanism. Detailed Implementation

[0060] The following embodiments are provided to enable those skilled in the art to more fully understand the present invention, but do not limit the invention in any way.

[0061] See Figure 1 This embodiment discloses an event-triggered trajectory tracking and control method for autonomous underwater vehicles (AUVs), which includes the following steps:

[0062] (1) The kinematic equations and dynamic equations of the three-degree-of-freedom horizontal plane of the autonomous underwater vehicle in this example are as follows:

[0063]

[0064] Where x and y represent the horizontal position coordinates of the autonomous underwater vehicle in the inertial coordinate system; ψ and r represent the yaw angle and yaw rate, respectively; and u and v represent the surge and sway rates, respectively.

[0065] Neglecting higher-order hydrodynamic drag terms, the center of gravity of the autonomous underwater vehicle (AUV) coincides with its center of buoyancy. The dynamic equations of the underactuated AUV are expressed as:

[0066]

[0067] Where m1, m2, and m3 represent the generalized quality of the AUV; X u Y v and N r X represents the linear damping coefficient; u|u| Y v|v| and N r|r| τ represents the secondary damping coefficient; u and τ r These represent surge torque and yaw torque, respectively.

[0068] Considering the perturbation of the parameters, the parameters satisfy the following conditions:

[0069]

[0070]

[0071]

[0072] Where: "∧" represents the nominal value of the parameter; "-" represents the upper limit of the parameter perturbation.

[0073] (2) Based on the autonomous underwater vehicle model, establish the position error equation:

[0074]

[0075] Where: x R and y R It represents the desired position coordinates and is a sufficiently smooth function.

[0076] (3) In order to stabilize the error x e y e and ψ e Define the following Lyapunov function to obtain the virtual control input:

[0077]

[0078]

[0079] Therefore, the virtual control input is obtained as follows:

[0080]

[0081] (4) To design a dynamic controller, first define the speed error:

[0082]

[0083] (5) Design the integral sliding surface and differentiate it to obtain the dynamic control law:

[0084]

[0085]

[0086]

[0087] (6) By introducing an event-triggered control mechanism, the designed controller will only sample or perform operations when a specific event of the system is triggered, that is, information transmission and control updates will only be performed when the system needs them.

[0088] The designed event-triggered controller is as follows:

[0089]

[0090] The event triggering conditions are designed as follows:

[0091]

[0092] in c1 and c2 are both positive constants and ε1>0, ε2>0, k∈N + When the event-triggered mechanism is triggered in the system, the input changes from τ(t) φ，k Update to τ(t) φ，k+1 Assume that t φ，k+1 - It is the moment the event is triggered, t φ，k+1 It's the instant the controller updates.

[0093] (7) Ensure the stability of the system under the event triggering mechanism and avoid Zeno's phenomenon. Verify the stability of the autonomous underwater vehicle system based on Lyapunov stability theory. By analyzing and ensuring that the internal event time is greater than a normal number, ensure that the control signal is updated discontinuously, thereby avoiding Zeno's phenomenon.

[0094] Define the Lyapunov function V:

[0095]

[0096] Differentiate them separately and combine them The following results were obtained:

[0097]

[0098]

[0099] because: so: in: That is, all state variables of the system are bounded, and the system is asymptotically stable.

[0100] (8) To verify the effectiveness of the proposed AUV trajectory tracking control method based on the event-triggered mechanism, simulations were performed on an underactuated AUV. Specific parameters are as follows:

[0101] m1=215kg; m2=265kg; m3=80kg; u =70kg / s; Y u =100kg / s;

[0102] N r=100kg / s; X u|u| =100kg / s; Y v|v| =200kg / s; N r|r| =100kg / s;

[0103] The controller parameters are:

[0104] k x =1.5, k ψ =3.5, k u =3.5, k r =0.8,

[0105] λ1=0.1, λ2=0.1, γ1=0.5, γ2=0.3.

[0106] The expression for the expected trajectory of a straight line:

[0107]

[0108] The initial value is set as follows:

[0109] In the Simulink environment, an autonomous underwater vehicle (AUV) tracking system is simulated. Under the given conditions, the linear tracking performance of the underactuated AUV is as follows: Figure 2-5 As shown, Figure 2 The AUV's tracking performance under the event-triggered mechanism demonstrates that the AUV can track the desired signal very well. Figure 3 The error between the actual trajectory and the expected trajectory of the AUV under event-triggered control can be calculated. It can be concluded that the tracking error converges rapidly to zero throughout the entire control process, achieving a good tracking effect. Figure 4 This refers to the error of the virtual control variable throughout the entire control process. Figure 5 The simulation diagram shows the triggering time and triggering interval under event-triggered control, which avoids continuous action of the controller, reduces the burden on the control linear mechanism, alleviates the problem of limited airborne energy of the AUV, and shows that the system does not exhibit the Zeno phenomenon.

[0110] The above embodiments are merely illustrative of the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solutions based on the technical concept proposed in this invention shall fall within the scope of protection of this invention.

Claims

1. A trajectory tracking and control method for an event-triggered autonomous underwater vehicle, characterized in that, The trajectory tracking control method includes the following steps: S1. Based on the system structural characteristics of the three-degree-of-freedom autonomous underwater vehicle, construct the kinematic and dynamic models of the autonomous underwater vehicle; S2. Based on the backstepping method, a motion controller for an autonomous underwater vehicle is designed, and a virtual control input is obtained to derive the tracking error equation. A dynamic controller for stabilizing the tracking error is designed using a global sliding mode control method. S3 introduces an event-triggered mechanism to track and control the trajectory of the autonomous underwater vehicle based on a fixed threshold strategy for triggering control, while avoiding the Zeno phenomenon. In S3, an event-triggered mechanism is introduced. Based on the fixed threshold strategy for triggering control, the process of tracking and controlling the trajectory of the autonomous underwater vehicle includes the following steps: S31, the event triggering controller is designed as follows: ； In the formula, For event-triggered controllers; For event-triggered controllers, For the trigger time sequence; For event-triggered controllers; For event-triggered controllers, For the trigger time sequence; S32, the event triggering condition is designed as follows: ； in , and , All are positive constants and , , , , When the event-triggered mechanism is triggered in the system, the input from... Updated to , It is the moment the event is triggered. It is the instant the controller updates; S33 verifies the stability of the autonomous underwater vehicle system based on Lyapunov stability theory. By analyzing and ensuring that the internal event time is greater than a normal number, it ensures that the control signal is updated discontinuously.

2. The event-triggered trajectory tracking and control method for autonomous underwater vehicles according to claim 1, characterized in that, In step S1, the horizontal kinematics equations and dynamic equations of the three-degree-of-freedom autonomous underwater vehicle are as follows: ； in, and This represents the horizontal position coordinates of the autonomous underwater vehicle in the inertial coordinate system; and These represent the yaw angle and yaw rate, respectively. and These represent surge and oscillation speeds, respectively.

3. The event-triggered trajectory tracking and control method for autonomous underwater vehicles according to claim 2, characterized in that, In step S1, the dynamic model of the autonomous underwater vehicle is as follows: ； In the formula, , and The generalized mass representing an autonomous underwater vehicle; , and Represents the linear damping coefficient; , and Represents the secondary damping coefficient; and These represent surge moment and yaw moment, respectively; the parameters satisfy the following conditions: ； in: The nominal value of the representative parameter; This represents the upper limit of parameter perturbation.

4. The event-triggered trajectory tracking and control method for autonomous underwater vehicles according to claim 3, characterized in that, In step S2, the process of designing a dynamic controller for stabilizing tracking error using a global sliding mode control method includes the following steps: S21, the system's position error equation is defined as follows: ； in: and Let represent the desired position coordinates, and both are smooth functions. and These represent the positional error values ​​for the x-axis and y-axis, respectively. S22, Design a motion controller, and obtain the virtual input as follows: ； In the formula, Virtual control input for surge velocity; Virtual control input for yaw speed; The desired surge velocity; This refers to the steady-state error of the angle. The gain coefficient is adjustable. Angular velocity; The gain coefficient is adjustable. S23, Design a dynamic controller, and obtain the dynamic control law as follows: ； In the formula, This is an adjustable coefficient; This is an adjustable coefficient; The gain coefficient is the upper limit of the parameter perturbation. The gain coefficient is the upper limit of the parameter perturbation. For global sliding surface; This is the global sliding surface.

5. The event-triggered trajectory tracking and control method for autonomous underwater vehicles according to claim 1, characterized in that, Step S33, the process of verifying the stability of the autonomous underwater vehicle system based on Lyapunov stability theory, includes: Define Lyapunov functions : ； In the formula, For Lyapunov functions; For Lyapunov functions; For the Lyapunov function respectively Differentiate and combine get: ； ； because: ,so: ;in, ; That is, all state variables of the system are bounded, and the system is asymptotically stable.

Images