Unmanned underwater vehicle finite time trajectory tracking control method based on event triggering

Abstract

The invention relates to the field of unmanned underwater vehicles, and discloses an unmanned underwater vehicle finite time trajectory tracking control method based on event triggering, which comprises the following steps: establishing two coordinate systems to describe the motion state of an unmanned underwater vehicle, and constructing a kinematical equation and a kinetic equation of a six-degree-of-freedom full-drive unmanned underwater vehicle; the method comprises the following steps: establishing an underwater unmanned vehicle kinematics and dynamics model, determining a control target, setting an event triggering finite time backstepping controller and event triggering conditions in combination with the underwater unmanned vehicle kinematics and dynamics model, and adopting a virtual controller of the event triggering finite time backstepping controller and the event triggering controller to control the event triggering conditions. Enabling the kinematics and dynamics model of the underwater unmanned vehicle to reach a stable state within the convergence time, and enabling the trajectory tracking error of the underwater unmanned vehicle to obtain a convergence time upper bound within the convergence time; according to the method, rapid convergence in finite time is realized, so that the accuracy and rapidity of trajectory tracking control of the underwater vehicle are realized.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned underwater vehicles, and in particular to a finite-time trajectory tracking control method for an unmanned underwater vehicle based on event triggering. Background Art

[0002] An underwater unmanned vehicle (UUV) is a submersible equipped with an energy system and an autonomous controller. It can autonomously complete underwater exploration, underwater search, and carrying submarine-launched missiles in the deep sea without direct human control, depending on the specific equipment. Underwater UUVs integrate a variety of advanced technologies, such as automatic control, path planning, hydroacoustic communication, instrumentation, artificial intelligence, etc. In recent years, underwater UUVs have been widely used in the marine field. Due to the complexity and variability of the underwater environment, with the gradual deepening of marine resource exploration and development and the increasing importance of the marine field, underwater UUVs need to undertake more and more complex and diverse underwater tasks, so the requirements for their control accuracy and maneuverability are also getting higher and higher. However, due to their high integration and small size, underwater UUVs can only carry limited energy and communication bandwidth. In order to enable underwater UUVs to perform underwater operations for a long time under complex conditions, it is necessary to compare and track the actual motion trajectory of the underwater UUV with the expected set trajectory in real time while efficiently utilizing the communication bandwidth and energy, so as to achieve fast and accurate trajectory tracking control of the underwater UUV.

[0003] At present, the methods used for underwater unmanned vehicle trajectory tracking control mainly include PID control, sliding mode control, backstepping control, adaptive control, fuzzy control, finite time control, etc.; however, due to the high complexity and uncertainty of the actual underwater environment, the requirements for the accuracy and maneuverability of underwater unmanned vehicle trajectory tracking control are further improved; in order to ensure the performance of the controller, the traditional underwater unmanned vehicle control strategy based on time triggering is usually set with a very small sampling period, resulting in the need to transmit control signals at a high frequency all the time, but high-frequency control signal transmission may lead to excessive consumption of communication bandwidth and increase energy loss, and is also one of the reasons for actuator failure; and the amount of data and delay in each communication may still affect the control performance, especially in a communication environment with high delay or limited bandwidth; even if there are underwater unmanned vehicle control methods such as PID based on event triggering, because of its slow convergence speed, it is not finite time convergence, resulting in low control accuracy and speed, which cannot meet the requirements of reducing communication bandwidth consumption and energy loss while ensuring control accuracy and fast convergence. Summary of the invention

[0004] The purpose of the present invention is to solve the above problems and designs a finite-time trajectory tracking control method for an unmanned underwater vehicle based on event triggering.

[0005] The present invention provides an event-triggered unmanned underwater vehicle finite-time trajectory tracking control method, the event-triggered unmanned underwater vehicle finite-time trajectory tracking control method is characterized in that the method includes the following process: S1. Establish two coordinate systems to describe the motion state of the underwater unmanned vehicle, wherein the two coordinate systems are an inertial coordinate system and a motion coordinate system for describing position and attitude information; S2. Based on the momentum and angular momentum theorem and Newton's kinematics theorem, construct the kinematic equations and dynamic equations of the six-degree-of-freedom fully-driven underwater unmanned vehicle, and establish the kinematic and dynamic models of the underwater unmanned vehicle; S3, determine the control target, set the event-triggered finite-time backstepping controller and the event triggering condition in combination with the kinematic and dynamic model of the underwater unmanned vehicle, when the triggering moment of the event triggering condition is met, the control signal will be updated immediately, when the event triggering condition is not met, the control signal will be maintained at the value updated at the last triggering moment, wherein the control signal is used to control the underwater unmanned vehicle; S4. A virtual controller and an event-triggered controller of an event-triggered finite-time backstepping controller are used to make the kinematic and dynamic models of the underwater unmanned vehicle reach a stable state within the convergence time, and the trajectory tracking error of the underwater unmanned vehicle obtains a convergence time upper bound within the convergence time, thereby completing the trajectory tracking control of the underwater unmanned vehicle.

[0006] Optionally, in the first implementation of the present invention, in step S2, the kinematic equation and the dynamic equation of the six-degree-of-freedom fully-driven underwater unmanned vehicle are expressed as follows: In the formula, is the time derivative of the position and attitude vector in the inertial coordinate system, is the transformation matrix, are the linear velocity and angular velocity in the motion coordinate system, Represents the linear velocity in the longitudinal, transverse and vertical directions in the motion coordinate system, Represents the angular velocity of roll, pitch and yaw in the motion coordinate system, is the inertia matrix caused by the rigid body and the additional mass, is the acceleration vector, is the Coriolis centripetal force matrix, is the fluid damping matrix, are the restoring force and torque vectors generated by the combined effect of gravity and buoyancy, Represents the position and attitude vector in the inertial coordinate system, Expressed in an inertial coordinate system Position under direction, Indicates the roll, pitch and yaw attitudes in the inertial coordinate system. is the control force and control torque vector generated by the propulsion system of the fully-driven underwater unmanned vehicle, Represents the force generated by the propeller of the fully-driven unmanned vehicle in the longitudinal, transverse and vertical directions, Represents the moment generated in the rolling, pitching and yaw directions.

[0007] Optionally, in a second implementation of the present invention, the conversion matrix The expression is: Where, the linear velocity conversion matrix The expression is: Angular velocity conversion matrix The expression is: In the formula, Indicates the roll, pitch and yaw attitudes in the inertial coordinate system.

[0008] Optionally, in a third implementation of the present invention, the inertia matrix It consists of two parts: the hydrodynamic added mass matrix and rigid body mass and inertia matrix , the hydrodynamic added mass matrix The expression is: in, 、 、 、 、 、 represents different values ​​of the hydrodynamic added mass in the longitudinal direction, 、 、 、 、 、 represents different values ​​of the hydrodynamic added mass in the sway direction, 、 、 、 、 、 represents different values ​​of the hydrodynamic added mass in the heave direction, 、 、 、 、 、 represents different values ​​of the hydrodynamic added mass in the rolling direction, 、 、 、 、 、 represents different values ​​of the hydrodynamic added mass in the pitch direction, 、 、 、 、 、 Indicates different values ​​of the hydrodynamic added mass in the bow roll direction; Rigid body mass and inertia matrix The expression is: In the formula, is the mass of the underwater unmanned vehicle, , , represents the center of gravity of the underwater unmanned vehicle, 、 、 represents the moment of inertia of the underwater unmanned vehicle body around the x, y, and z axes, 、 、 、 、 、 It represents the product of inertia of the underwater unmanned vehicle body around different axes.

[0009] Optionally, in a fourth implementation of the present invention, the Coriolis centripetal force matrix The Coriolis centripetal force matrix of the added mass and the rigid body Coriolis centripetal force matrix Composition, additional mass Coriolis centripetal force matrix The expression is: In the formula, , 、 、 、 、 They represent the coupling effect between velocities in different directions respectively; Rigid body Coriolis centripetal force matrix The expression is: In the formula, is the mass of the underwater unmanned vehicle, 、 、 represents the center of gravity of the underwater unmanned vehicle, 、 、 represents the moment of inertia of the underwater unmanned vehicle body around the x, y, and z axes, 、 、 It represents the product of inertia of the underwater unmanned vehicle body around different axes.

[0010] Optionally, in a fifth implementation of the present invention, the fluid damping matrix is the linear damping term and the nonlinear damping term The superposition of the fluid damping matrix The expression is: In the formula, is the linear damping coefficient, is the nonlinear damping coefficient.

[0011] Optionally, in a sixth implementation of the present invention, the restoring force and torque vector generated by the combined action of gravity and buoyancy are The expression is: Where W is gravity, B is buoyancy, 、 、 The center of gravity of the underwater unmanned vehicle is The location of the direction, 、 、 Indicates that the buoyancy center of the underwater unmanned vehicle is The location of the direction.

[0012] Optionally, in a seventh implementation of the present invention, in step S2, the expression for establishing the kinematic and dynamic model of the underwater unmanned vehicle is: make , , the expression is: The expression of the error function is: In the formula, For virtual controllers, is the position error, is the speed error, are the position and attitude vectors in the inertial coordinate system, is the expected value of the position and attitude vector in the inertial coordinate system, is the time derivative of the position and attitude vector in the inertial coordinate system, is the second-order derivative of the position and attitude vector in the inertial coordinate system, is the inverse of the transformation matrix, is the inertia caused by the rigid body and the additional mass, is the Coriolis centripetal force, is the fluid damping, is the inertia matrix caused by the rigid body and the additional mass, is the Coriolis centripetal force matrix, is the fluid damping matrix, are the restoring force and torque vectors generated by the combined effect of gravity and buoyancy, Represents the control force and control torque vector generated by the thruster of the full-drive underwater unmanned vehicle.

[0013] Optionally, in an eighth implementation of the present invention, in step S3, the process of setting an event-triggered finite-time backstepping controller and an event-triggered condition includes: Position error The expression to be derived is: In the formula, For virtual controllers, is the expected value of the time derivative of the position and attitude vector in the inertial coordinate system, is the speed error; The expressions of designed virtual controller and adaptive law are: In the formula, represents diagonal matrix operations, represents the regularization parameter, T represents the transposition operation, represents the adaptive law, is the parameter to be designed and , represents an exponent that adjusts the convergence speed and , Represents the absolute value of the element. For any R, constant , , we get the following inequality: ; The expression of the Lyapunov function is: In the formula, Indicates the deviation between the actual trajectory and the expected trajectory; Taking the derivative of the Lyapunov function and substituting it into the inequality, we get the following expression: Simplifying the above inequality, we get the following expression: Further simplification based on the properties of vectors: Speed ​​error The expression to be derived is: In the formula, , , is the inertia caused by the rigid body and the additional mass, is the Coriolis centripetal force, is the fluid damping, are the restoring force and torque vectors generated by the combined effect of gravity and buoyancy, represents the control force and control torque vector generated by the thruster of the fully-driven underwater unmanned vehicle, represents the derivation of the virtual controller; Design the following controller: in , , is the parameter to be designed; because , and get the controller as follows: The event trigger conditions are: In the formula, Indicates in the collection Find the minimum time that satisfies the event triggering conditions ; in , A subset of the time trigger condition set; In the interval Internal, Controller satisfy: in, , is a time-varying constant; The final expression of the event-triggered finite-time backstepping controller is: In the formula, The current event triggering time, The next event trigger time, The threshold of the time trigger condition.

[0014] Optionally, in a ninth implementation of the present invention, in step S4, the upper limit of the convergence time is to converge to a preset region near the zero point, and the convergence time is: In the formula, is the convergence time, indicating that the Lyapunov function is in the initial state The value below represents the exponent for adjusting the convergence speed, is the negative exponential decay rate of the Lyapunov function.

[0015] In the technical solution provided by the present invention, two coordinate systems are established to describe the motion state of the underwater unmanned vehicle; based on the momentum and angular momentum theorem and Newton's kinematics theorem, the kinematic equation and dynamic equation of the six-degree-of-freedom fully-driven underwater unmanned vehicle are constructed, and the kinematic and dynamic model of the underwater unmanned vehicle is established; the control target is determined, and the event-triggered finite-time backstepping controller and the event triggering condition are set in combination with the kinematic and dynamic model of the underwater unmanned vehicle. When the triggering moment of the event triggering condition is met, the control signal will be updated immediately, and when the event triggering condition is not met, the control signal will be maintained at the value updated at the last triggering moment; using the event triggering condition The virtual controller and event-triggered controller of the finite-time backstepping controller are triggered by the event triggering method, so that the kinematic and dynamic models of the underwater unmanned vehicle reach a stable state within the convergence time, and the trajectory tracking error of the underwater unmanned vehicle obtains a convergence time upper bound within the convergence time, thereby completing the trajectory tracking control of the underwater unmanned vehicle; the present invention simultaneously uses event triggering and finite-time control methods to realize the trajectory tracking control of the unmanned underwater vehicle, aims to reduce the communication bandwidth, reduce the control energy consumption, and correspondingly reduce the loss caused by the actuator changing the output, and realize rapid convergence within a finite time, thereby realizing the accuracy and rapidity of the trajectory tracking control of the underwater vehicle. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Various other advantages and benefits will become apparent to those of ordinary skill in the art by reading the following detailed description of the preferred embodiment.The drawings are only for the purpose of illustrating the preferred embodiments and are not to be construed as limiting the invention.

[0017] Figure 1 A conversion relationship diagram describing the inertial coordinate system and the motion coordinate system of position and posture information provided by an embodiment of the present invention; Figure 2 A flow chart of a method for controlling an unmanned underwater vehicle's finite-time trajectory tracking based on event triggering provided by an embodiment of the present invention; Figure 3 A simulation diagram of the event triggering time interval provided by an embodiment of the present invention; Figure 4 A three-dimensional trajectory simulation diagram provided by an embodiment of the present invention; Figure 5 The x, y, and z direction trajectory error convergence curves provided by the embodiment of the present invention; Figure 6 The embodiment of the present invention provides ,ψ, Direction trajectory error convergence curve; Figure 7 An output force simulation diagram provided by an embodiment of the present invention; Figure 8 This is a simulation diagram of the output torque provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0018] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0019] (Lyapunov stability) for generalized nonlinear systems is as follows: 【1】 In the formula, is the state quantity of the nonlinear system, is a time variable. If for any , If it is always established, then it is called is the equilibrium point of the nonlinear system, and the following conclusions can be drawn: (1) There is any , if it exists , so that when , the state quantity converges to the following set: ,and 【2】 Equilibrium Point is a stable equilibrium point; (2) There is any , if it exists , so that inequality [2] holds, then it is called an equilibrium point A consistent and stable equilibrium point; (3) If the equilibrium point is a stable equilibrium point, and there exists a constant , so that for any ,when When If it is established, it is called an equilibrium point is an asymptotically stable equilibrium point; (4) If the equilibrium point is an asymptotically stable equilibrium point, and , for any , both have Established, so that the state quantity converges to the following set: , Equilibrium Point is a uniformly asymptotically stable equilibrium point.

[0020] Lemma 1: Assume there exists a continuous positive definite function , and there is Where: , then the system [1] converges in finite time, and the convergence time satisfy Lemma 2: For any , , , , the following inequality holds: Lemma 3: For any ,constant , the following inequality holds: .

[0021] See also Figure 1 and Figure 2The present embodiment is described. The event-triggered unmanned underwater vehicle finite-time trajectory tracking control method described in the present embodiment is used to simultaneously use the event triggering and finite-time control method to realize the trajectory tracking control of the unmanned underwater vehicle. The method includes the following process: S1. Establish two coordinate systems to describe the motion state of the underwater unmanned vehicle, wherein the two coordinate systems are an inertial coordinate system and a motion coordinate system for describing position and attitude information; S2. Based on the momentum and angular momentum theorem and Newton's kinematics theorem, construct the kinematic equations and dynamic equations of the six-degree-of-freedom fully-driven underwater unmanned vehicle, and establish the kinematic and dynamic models of the underwater unmanned vehicle; S3, determine the control target, set the event-triggered finite-time backstepping controller and the event triggering condition in combination with the kinematic and dynamic model of the underwater unmanned vehicle, when the triggering moment of the event triggering condition is met, the control signal will be updated immediately, when the event triggering condition is not met, the control signal will be maintained at the value updated at the last triggering moment, wherein the control signal is used to control the underwater unmanned vehicle; S4. A virtual controller and an event-triggered controller of an event-triggered finite-time backstepping controller are used to make the kinematic and dynamic models of the underwater unmanned vehicle reach a stable state within the convergence time, and the trajectory tracking error of the underwater unmanned vehicle obtains a convergence time upper bound within the convergence time, thereby completing the trajectory tracking control of the underwater unmanned vehicle.

[0022] See also Figure 1 Coordinate system conversion relationship, in the figure, E is the origin of the fixed coordinate system, ξ, b, ζ are the three axes of the fixed coordinate system, pointing to the north position, east position and center of the earth of the underwater unmanned vehicle respectively, O is the origin of the hull coordinate system, X, Y, Z are the three axes of the hull coordinate system, u, h, w represent the linear velocity of the underwater unmanned vehicle in the longitudinal, transverse and vertical directions respectively, p, q, r represent the angular velocity of the roll angle, pitch angle and bow angle of the underwater unmanned vehicle in the hull coordinate system respectively; in order to establish the kinematic and dynamic models of the underwater unmanned vehicle, it is necessary to establish two different coordinate systems to describe the motion state of the underwater unmanned vehicle, that is, the inertial coordinate system describing the position and attitude information (Earth coordinate system) and motion coordinate system (Carrier coordinate system).

[0023] The underwater unmanned vehicle needs to perform three-dimensional motion during underwater operation tasks. Therefore, in order to describe the motion state of the underwater unmanned vehicle system, a vector with six degrees of freedom is required. In this embodiment, Represents the linear velocity and angular velocity vector of the underwater unmanned vehicle system in the motion coordinate system; Represents the position and attitude vector of the underwater unmanned vehicle system in the inertial coordinate system.

[0024] This embodiment is aimed at studying a six-degree-of-freedom fully-driven underwater unmanned vehicle. Based on the momentum and angular momentum theorem and Newton's kinematics theorem, and considering the conversion relationship between the inertial coordinate system and the motion coordinate system, the kinematic equation and dynamic equation of the six-degree-of-freedom fully-driven underwater unmanned vehicle are defined as follows: In the formula, is the time derivative of the position and attitude vector in the inertial coordinate system, is the transformation matrix, are the linear velocity and angular velocity in the motion coordinate system, Represents the linear velocity in the longitudinal, transverse and vertical directions in the motion coordinate system, Represents the angular velocity of roll, pitch and yaw in the motion coordinate system, is the inertia matrix caused by the rigid body and the additional mass, is the acceleration vector, is the Coriolis centripetal force matrix, is the fluid damping matrix, are the restoring force and torque vectors generated by the combined effect of gravity and buoyancy, Represents the position and attitude vector in the inertial coordinate system, Expressed in an inertial coordinate system Position under direction, Indicates the roll, pitch and yaw attitudes in the inertial coordinate system. is the control force and control torque vector generated by the propulsion system of the fully-driven underwater unmanned vehicle, Represents the force generated by the propeller of the fully-driven unmanned vehicle in the longitudinal, transverse and vertical directions, Represents the moment generated in the rolling, pitching and yaw directions.

[0025] Transformation Matrix The expression is: Where, the linear velocity conversion matrix The expression is: Angular velocity conversion matrix The expression is: In the formula, Indicates the roll, pitch and yaw attitudes in the inertial coordinate system.

[0026] Inertial matrix of underwater unmanned vehicle It consists of two parts: the hydrodynamic added mass matrix and rigid body mass and inertia matrix , the hydrodynamic added mass matrix The expression is: in, 、 、 、 、 、 represents different values ​​of the hydrodynamic added mass in the longitudinal direction, 、 、 、 、 、 represents different values ​​of the hydrodynamic added mass in the sway direction, 、 、 、 、 、 represents different values ​​of the hydrodynamic added mass in the heave direction, 、 、 、 、 、 represents different values ​​of the hydrodynamic added mass in the rolling direction, 、 、 、 、 、 represents different values ​​of the hydrodynamic added mass in the pitch direction, 、 、 、 、 、 Indicates different values ​​of the hydrodynamic added mass in the bow roll direction; Rigid body mass and inertia matrix The expression is: In the formula, is the mass of the underwater unmanned vehicle, , , represents the center of gravity of the underwater unmanned vehicle, 、 、 represents the moment of inertia of the underwater unmanned vehicle body around the x, y, and z axes, 、 、 、 、 、 It represents the product of inertia of the underwater unmanned vehicle body around different axes.

[0027] Coriolis Centripetal Force Matrix The Coriolis centripetal force matrix of the added mass and the rigid body Coriolis centripetal force matrix Composition, additional mass Coriolis centripetal force matrix The expression is: In the formula, , 、 、 、 、 They represent the coupling effect between velocities in different directions.

[0028] Rigid body Coriolis centripetal force matrix The expression is: In the formula, is the mass of the underwater unmanned vehicle, 、 、 represents the center of gravity of the underwater unmanned vehicle, 、 、 represents the moment of inertia of the underwater unmanned vehicle body around the x, y, and z axes, 、 、 It represents the product of inertia of the underwater unmanned vehicle body around different axes.

[0029] Fluid Damping Matrix is the linear damping term and the nonlinear damping term The superposition of the fluid damping matrix The expression is: .

[0030] In the formula, is the linear damping coefficient, is the nonlinear damping coefficient.

[0031] Restoring force and torque vectors resulting from the combined effects of gravity and buoyancy The expression is: Where W is gravity, B is buoyancy, 、 、 The center of gravity of the underwater unmanned vehicle is The location of the direction, 、 、 Indicates that the buoyancy center of the underwater unmanned vehicle is The location of the direction.

[0032] The force (torque) vector generated by the six-degree-of-freedom control thruster of the fully-driven underwater unmanned vehicle It can be expressed as: This embodiment is based on the event-triggered underwater unmanned vehicle finite time trajectory tracking control problem. Based on the kinematics and dynamics model of the underwater unmanned vehicle, the following mathematical model can be obtained: (1) (2) To facilitate the derivation and writing of the control algorithm in this paper, substitute equation (1) into (2) and we can get (3) in make , , substituting into (3), we can get: (4) (5) (6) In order to facilitate subsequent calculations and writing, it can be simplified to: (7) (8) (9) Define the following error function: (10) (11) in, For virtual controllers, is the position error, is the speed error, are the position and attitude vectors in the inertial coordinate system, is the expected value of the position and attitude vector in the inertial coordinate system, is the time derivative of the position and attitude vector in the inertial coordinate system, is the second-order derivative of the position and attitude vector in the inertial coordinate system, is the second-order derivative of the position and attitude vector in the inertial coordinate system, is the inverse of the transformation matrix, is the inertia caused by the rigid body and the additional mass, is the Coriolis centripetal force, is the fluid damping, is the inertia matrix caused by the rigid body and the additional mass, is the Coriolis centripetal force matrix, is the fluid damping matrix, are the restoring force and torque vectors generated by the combined effect of gravity and buoyancy, Represents the control force and control torque vector generated by the thruster of the full-drive underwater unmanned vehicle.

[0033] Backstepping control is a nonlinear control method. Its basic principle is to decompose the nonlinear dynamics of the system into two parts: one part is the part that can be designed with a stable control law, and the other part is the unstable part; then, a feedback controller is designed to suppress the unstable part, so as to achieve the stability of the entire system; backstepping control has the advantages of controllable nonlinear systems, robustness, optimizability and scalability, and is a very effective control method.

[0034] first step: Combining equations (7)-(9), and taking the derivative of (10), we get: (12) In the formula, in the formula, For virtual controllers, is the expected value of the time derivative of the position and attitude vector in the inertial coordinate system, is the speed error; Design the virtual controller and adaptive law as follows: (13) (14) In the formula, represents diagonal matrix operations, represents the regularization parameter, T represents the transposition operation, represents the adaptive law, is the parameter to be designed and , represents an exponent that adjusts the convergence speed and , Representation vector The elements of take the absolute value, From (13), according to Lemma 3, we can get the following inequality: (15) Design the Lyapunov function of the first subsystem as follows: (16) In the formula, Indicates the deviation between the actual trajectory and the expected trajectory; Deriving equation (16) and substituting (12) into it, we can obtain: (17) According to inequality (15) and equation (17), the following inequality can be obtained: (18) Substituting equation (14) into inequality (18), we can obtain: (19) Simplifying, we can get: (20) Further simplification based on the properties of vectors: (twenty one) Step 2: Combining the underwater unmanned vehicle dynamic model (3) and formula (8), the error function (11) is derived to obtain (twenty two) In the formula, , , is the inertia caused by the rigid body and the additional mass, is the Coriolis centripetal force, is the fluid damping, are the restoring force and torque vectors generated by the combined effect of gravity and buoyancy, represents the control force and control torque vector generated by the thruster of the fully-driven underwater unmanned vehicle, represents the derivation of the virtual controller; Design the following controller: (twenty three) (twenty four) in , , is the parameter to be designed; To facilitate derivation and writing, it is known that , combined with the event trigger mechanism, the actual controller is designed as follows: (25) The event trigger conditions are: (26) In the formula, Indicates in the collection Find the minimum time that satisfies the event triggering conditions ; in .

[0035] Therefore, in the interval In the controller, due to the event triggering related equations (25) and (26), satisfy: (27) in, , is a time-varying constant From formula (27), we can get: (28) Designed controller for In the formula, The current event triggering time, The next event trigger time, The threshold of the time trigger condition.

[0036] Stability proof: For the kinematic and dynamic model (3) of the underwater unmanned vehicle, the virtual controller (13), (22), event-triggered controller (25), (26), (38) and appropriate design parameters are selected to make the closed-loop system model (3) stable within a limited time. The stable state is reached within a limited time, and the trajectory tracking error of the underwater unmanned vehicle is The inner part converges to an arbitrarily small area near the zero point, and the time trajectory tracking control of the underwater unmanned vehicle is completed.

[0037] prove: Consider the following Lyapunov function: (29) By taking the derivative of formula (29), we get: (30) Substituting equation (24) into equation (30), we can obtain the following inequality: (31) Further simplifying, we can get: (32) Combining inequalities (21) and (32), we can obtain: (33) By further simplifying Lemma 2, we can obtain: (34) in , ; Combining formula (34), we can get the following form: (35) According to Lemma 1, by using virtual controllers (13), (22), event-triggered controllers (25), (26), (38), and selecting appropriate design parameters, the closed-loop system model (3) can be realized in a finite time. The stable state is reached within a limited time, and the trajectory tracking error of the underwater unmanned vehicle is It converges to an arbitrarily small region near zero, and the convergence time is: (36) In the formula, is the convergence time, indicating that the Lyapunov function is in the initial state The value below represents the exponent for adjusting the convergence speed, is the negative exponential decay rate of the Lyapunov function; the finite-time stability is proved.

[0038] Next, it will be proved that the proposed control scheme can effectively avoid the occurrence of Zeno phenomenon. If the Zeno phenomenon does not occur, then there exists And satisfy: (37) By definition It is known that Taking the derivative, we get: (38) because is a differentiable function, is a bounded composite function, so there exists a positive vector ,satisfy: (39) And, according to as well as You can get: (40) Therefore there is , it can be proved that the proposed control scheme can effectively avoid the occurrence of Zeno phenomenon.

[0039] A simulation experiment was conducted on the unmanned underwater vehicle finite time trajectory tracking control method based on event triggering in this embodiment. Figure 3 The event trigger time interval simulation diagram shows the horizontal axis of the time change and the vertical axis of the Indicates the time interval between two adjacent event triggering times. Figure 3 The figure shows the changes in the intervals between event triggering moments in different time periods. In some time periods, the intervals between event triggering are shorter, indicating that the system needs to adjust or respond to changes in the external environment more frequently during this period; while in other time periods, the intervals between event triggering are longer, indicating that the system is relatively stable during this period and does not require frequent adjustments. This helps to optimize resource utilization and reduce unnecessary computing and communication overhead, especially under the limited time and energy constraints of unmanned underwater vehicles, and can effectively improve the efficiency and performance of the system.

[0040] from Figure 4 It can be seen that the actual trajectory is very close to the reference trajectory, especially in the spiral shape part in the three-dimensional space, which shows that this embodiment can effectively track the target trajectory within the convergence time and achieve high-precision path following with good control effect, which proves the effectiveness and practicality of the proposed method.

[0041] from Figure 5 , Figure 6 It can be seen that Figure 5 The horizontal axis represents time , the unit is seconds ( ), the ordinate represents the trajectory error , the unit is meter ( ), the blue curve ( ) represents the unmanned underwater vehicle The trajectory error in the direction, the red curve ( ) represents the unmanned underwater vehicle The trajectory error in the direction, the yellow curve ( ) represents the unmanned underwater vehicle Trajectory error in direction; Figure 6 The horizontal axis represents time , the unit is seconds ( ), the ordinate represents the trajectory error , the unit is radians ( ), the blue curve ( ): represents the unmanned underwater vehicle in The trajectory error in the direction, the red curve ( ): represents the unmanned underwater vehicle in The trajectory error in the direction, the yellow curve ( ) represents the unmanned underwater vehicle Trajectory errors in the three directions; as time goes by, the trajectory errors in these three directions gradually decrease and tend to zero, indicating that the deviation between the actual trajectory of the unmanned underwater vehicle in each direction and the expected trajectory is getting smaller and smaller, and finally a good tracking effect is achieved, proving that the proposed method has high accuracy and robustness, and is suitable for performing precise mission requirements in complex and changeable marine environments.

[0042] from Figure 7 , Figure 8 It can be seen that Figure 7 The horizontal axis represents time , the unit is seconds ( ), the ordinate represents the output force , in Newtons ( ); Figure 8 The horizontal axis represents time , the unit is seconds ( ), the ordinate represents the output force , in Newton meters ( ); Each output force / output torque has large fluctuations in the initial stage, but quickly converges to a stable value in a very short time (about a few seconds), indicating that the controller can effectively adjust the output force in a short time to ensure that the unmanned underwater vehicle moves along the predetermined trajectory. All output forces / output torques fluctuate within a small range during the entire simulation process, indicating that the control strategy has good stability and robustness, and can ensure the normal operation of the system even in the face of uncertain disturbances or nonlinear dynamic effects.

[0043] As shown in the simulation, the method proposed in this embodiment uses both event triggering and finite time control methods to achieve trajectory tracking control of unmanned underwater vehicles; using the event triggering control method, sampling or control signal update is performed only when the event condition is met. In event triggering control, the time of the next control signal update depends on the event triggering mechanism. A trigger condition based on the system state is set in advance. When the relevant state parameter in the system reaches the threshold set by the trigger condition, the control signal will be updated immediately; if the system does not meet the trigger condition, the control signal will be maintained at the value updated at the last trigger moment, that is, the zero-order holder can reduce the communication bandwidth, reduce the control energy consumption, and correspondingly reduce the loss caused by the actuator changing the output; The use of finite-time control methods can make the trajectory tracking error of the underwater vehicle converge quickly within the convergence time to achieve rapid response. According to the requirements of underwater unmanned vehicle control accuracy, the finite-time convergence theory can obtain an upper bound of the convergence time when the system converges, and the faster the convergence speed, the higher the control accuracy, thereby realizing rapid and accurate trajectory tracking control of the underwater unmanned vehicle.

[0044] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. The above embodiments and descriptions are only preferred examples of the present invention and are not intended to limit the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. An event-triggered unmanned underwater vehicle finite-time trajectory tracking control method, characterized in that: The method includes the following steps: S1. Establish two coordinate systems to describe the motion state of the underwater unmanned vehicle, wherein the two coordinate systems are an inertial coordinate system and a motion coordinate system for describing position and attitude information; S2. Based on the momentum and angular momentum theorem and Newton's kinematics theorem, construct the kinematic equations and dynamic equations of the six-degree-of-freedom fully-driven underwater unmanned vehicle, and establish the kinematic and dynamic models of the underwater unmanned vehicle; S3, determine the control target, set the event-triggered finite-time backstepping controller and the event triggering condition in combination with the kinematic and dynamic model of the underwater unmanned vehicle, when the triggering moment of the event triggering condition is met, the control signal will be updated immediately, when the event triggering condition is not met, the control signal will be maintained at the value updated at the last triggering moment, wherein the control signal is used to control the underwater unmanned vehicle; S4. A virtual controller and an event-triggered controller of an event-triggered finite-time backstepping controller are used to make the kinematic and dynamic models of the underwater unmanned vehicle reach a stable state within the convergence time, and the trajectory tracking error of the underwater unmanned vehicle obtains a convergence time upper bound within the convergence time, thereby completing the trajectory tracking control of the underwater unmanned vehicle.

2. The event-triggered finite-time trajectory tracking control method for an unmanned underwater vehicle according to claim 1, characterized in that: In step S2, the kinematic equation and dynamic equation of the six-degree-of-freedom fully-driven underwater unmanned vehicle are expressed as follows: In the formula, is the time derivative of the position and attitude vector in the inertial coordinate system, is the transformation matrix, are the linear velocity and angular velocity in the motion coordinate system, Represents the linear velocity in the longitudinal, transverse and vertical directions in the motion coordinate system, Represents the angular velocity of roll, pitch and yaw in the motion coordinate system, is the inertia matrix caused by the rigid body and the additional mass, is the acceleration vector, is the Coriolis centripetal force matrix, is the fluid damping matrix, are the restoring force and torque vectors generated by the combined effect of gravity and buoyancy, Represents the position and attitude vector in the inertial coordinate system, Expressed in an inertial coordinate system Position under direction, Indicates the roll, pitch and yaw attitudes in the inertial coordinate system. is the control force and control torque vector generated by the propulsion system of the fully-driven underwater unmanned vehicle, Represents the force generated by the propeller of the fully-driven unmanned vehicle in the longitudinal, transverse and vertical directions, Represents the moment generated in the rolling, pitching and yaw directions.

3. The event-triggered finite-time trajectory tracking control method for an unmanned underwater vehicle according to claim 2, characterized in that: Transformation Matrix The expression is: Where, the linear velocity conversion matrix The expression is: Angular velocity conversion matrix The expression is: In the formula, Indicates the roll, pitch and yaw attitudes in the inertial coordinate system.

4. The event-triggered finite-time trajectory tracking control method for an unmanned underwater vehicle according to claim 2, characterized in that: The inertia matrix It consists of two parts: the hydrodynamic added mass matrix and rigid body mass and inertia matrix , the hydrodynamic added mass matrix The expression is: in, 、 、 、 、 、 represents different values ​​of the hydrodynamic added mass in the longitudinal direction, 、 、 、 、 、 represents different values ​​of the hydrodynamic added mass in the sway direction, 、 、 、 、 、 represents different values ​​of the hydrodynamic added mass in the heave direction, 、 、 、 、 、 represents different values ​​of the hydrodynamic added mass in the rolling direction, 、 、 、 、 、 represents different values ​​of the hydrodynamic added mass in the pitch direction, 、 、 、 、 、 Indicates different values ​​of the hydrodynamic added mass in the bow roll direction; Rigid body mass and inertia matrix The expression is: In the formula, is the mass of the underwater unmanned vehicle, , , represents the center of gravity of the underwater unmanned vehicle, 、 、 represents the moment of inertia of the underwater unmanned vehicle body around the x, y, and z axes, 、 、 、 、 、 It represents the product of inertia of the underwater unmanned vehicle body around different axes.

5. The event-triggered finite-time trajectory tracking control method for an unmanned underwater vehicle according to claim 4, characterized in that: The Coriolis centripetal force matrix The Coriolis centripetal force matrix of the added mass and the rigid body Coriolis centripetal force matrix Composition, additional mass Coriolis centripetal force matrix The expression is: In the formula, , 、 、 、 、 They represent the coupling effect between velocities in different directions respectively; Rigid body Coriolis centripetal force matrix The expression is: In the formula, is the mass of the underwater unmanned vehicle, 、 、 represents the center of gravity of the underwater unmanned vehicle, 、 、 represents the moment of inertia of the underwater unmanned vehicle body around the x, y, and z axes, 、 、 It represents the product of inertia of the underwater unmanned vehicle body around different axes.

6. The event-triggered finite-time trajectory tracking control method for an unmanned underwater vehicle according to claim 2, characterized in that: Fluid Damping Matrix is the linear damping term and the nonlinear damping term The superposition of the fluid damping matrix The expression is: In the formula, is the linear damping coefficient, is the nonlinear damping coefficient.

7. The event-triggered finite-time trajectory tracking control method for an unmanned underwater vehicle according to claim 2, characterized in that: Restoring force and torque vectors resulting from the combined effects of gravity and buoyancy The expression is: Where W is gravity, B is buoyancy, 、 、 The center of gravity of the underwater unmanned vehicle is The position of the direction, 、 、 Indicates that the buoyancy center of the underwater unmanned vehicle is The location of the direction.

8. The event-triggered finite-time trajectory tracking control method for an unmanned underwater vehicle according to claim 1, characterized in that: In step S2, the expressions for establishing the kinematic and dynamic models of the underwater unmanned vehicle are: make , , the expression is: The expression of the error function is: In the formula, For virtual controllers, is the position error, is the speed error, are the position and attitude vectors in the inertial coordinate system, is the expected value of the position and attitude vector in the inertial coordinate system, is the time derivative of the position and attitude vector in the inertial coordinate system, is the second-order derivative of the position and attitude vector in the inertial coordinate system, is the inverse of the transformation matrix, is the inertia caused by the rigid body and the additional mass, is the Coriolis centripetal force, is the fluid damping, is the inertia matrix caused by the rigid body and the additional mass, is the Coriolis centripetal force matrix, is the fluid damping matrix, are the restoring force and torque vectors generated by the combined effect of gravity and buoyancy, Represents the control force and control torque vector generated by the thruster of the full-drive underwater unmanned vehicle.

9. The event-triggered finite-time trajectory tracking control method for an unmanned underwater vehicle according to claim 1, characterized in that: In step S3, the process of setting the event-triggered finite-time backstepping controller and the event-triggered condition includes: Position error The expression to be derived is: In the formula, For virtual controllers, is the expected value of the time derivative of the position and attitude vector in the inertial coordinate system, is the speed error; The expressions of designed virtual controller and adaptive law are: In the formula, represents diagonal matrix operations, represents the regularization parameter, T represents the transposition operation, represents the adaptive law, is the parameter to be designed and , represents an exponent that adjusts the convergence speed and , Represents the absolute value of the element. For any R, constant , , we get the following inequality: ； The expression of the Lyapunov function is: In the formula, Indicates the deviation between the actual trajectory and the expected trajectory; Taking the derivative of the Lyapunov function and substituting it into the inequality, we get the following expression: Simplifying the above inequality, we get the following expression: Further simplification based on the properties of vectors: Speed ​​error The expression to be derived is: In the formula, , , is the inertia caused by the rigid body and the additional mass, is the Coriolis centripetal force, is the fluid damping, are the restoring force and torque vectors generated by the combined effect of gravity and buoyancy, represents the control force and control torque vector generated by the thruster of the fully-driven underwater unmanned vehicle, represents the derivation of the virtual controller; Design the following controller: in , , is the parameter to be designed; because , and get the controller as follows: The event trigger conditions are: In the formula, Indicates in the collection Find the minimum time that satisfies the event triggering conditions ; in , A subset of the time trigger condition set; In the interval Internal, Controller satisfy: in, , is a time-varying constant; The final expression of the event-triggered finite-time backstepping controller is: In the formula, The current event triggering time, The next event trigger time, The threshold of the time trigger condition.

10. The event-triggered finite-time trajectory tracking control method for an unmanned underwater vehicle according to claim 1, characterized in that: In step S4, the upper limit of the convergence time is to converge to a preset area near the zero point, and the convergence time is: In the formula, is the convergence time, Indicates that the Lyapunov function is in the initial state The value below represents the exponent for adjusting the convergence speed, is the negative exponential decay rate of the Lyapunov function.

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