Underwater vehicle fixed time sliding mode tracking control method based on all-wheel-drive system theory

Abstract

The invention discloses an underwater vehicle fixed time sliding mode tracking control method based on an all-wheel-drive system theory. Aiming at the problem that an underwater vehicle executes an accurate trajectory tracking task under unknown external interference and internal model uncertainty, a second-order all-wheel-drive system model of the underwater vehicle is constructed based on a six-degree-of-freedom tracking error, so that excessive simplification of coupling characteristics by a traditional decoupling method is avoided; meanwhile, a fixed time disturbance observer based on an all-drive system model is designed, external disturbance and internal parameter perturbation are estimated, the system is compensated in real time, and a fixed time sliding mode controller is provided by further combining a fixed time stability theory. The provided sliding mode control method based on the all-wheel-drive system theory can effectively cope with disturbance in the underwater environment, enables tracking errors to converge to zero within fixed time, and achieves accurate trajectory tracking control over the position and attitude of an underwater vehicle system.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of underwater vehicle motion control, and particularly relates to a fixed-time sliding mode tracking control method for underwater vehicles based on a full-drive system theory. BACKGROUND

[0002] Underwater vehicles play an irreplaceable role in the fields of marine resource exploration, environmental monitoring, and military reconnaissance. However, the inherent nonlinearity and six-degree-of-freedom strong coupling characteristics of the dynamic model of underwater vehicles make it difficult for traditional tracking control methods to meet the requirements of precision and robustness for complex tasks. Especially in deep sea operations, underwater vehicles need to achieve high-precision trajectory tracking under unknown disturbances (such as ocean waves and ocean currents, sensor noise) and model parameter perturbations (such as changes in added mass). This poses a severe challenge to the design of the controller. How to build a framework that takes into account model accuracy and controller design efficiency has become a key problem in improving the autonomous operation capability of underwater vehicles.

[0003] Trajectory tracking control of underwater vehicles is one of the core technologies for ocean exploration, resource exploration, and other tasks, and the design of the controller determines the tracking accuracy and robustness of the system in a complex disturbance environment. However, the complex characteristics of the underwater vehicle dynamics model and external disturbances together exacerbate the difficulty of control system design. First, the nonlinearity (such as Coriolis force, damping force) and multi-degree-of-freedom coupling (such as longitudinal sway-lateral roll dynamic interaction) make it difficult to linearize the model, resulting in insufficient stability of traditional control methods. Second, the time-varying characteristics of unknown disturbances in complex underwater environments and model parameter uncertainties (such as changes in buoyancy coefficient) can significantly reduce control accuracy and even cause instability. To meet the requirements of trajectory tracking control, researchers are continuously exploring new technical approaches and striving to build more efficient control strategies, such as adaptive control, fuzzy logic control, backstepping control, and neural network control. These methods have made some progress in suppressing the strong nonlinearity of underwater vehicles, actuator saturation, and ocean environmental disturbances.

[0004] The above methods are all based on the first-order state space method. However, the traditional controller design method based on the first-order state space model is limited in terms of freedom, making it difficult to fully coordinate the dynamic response of multiple thrusters, further limiting the optimization space of control performance.

[0005] In recent years, the control method based on the high-order full-drive system theory has attracted widespread attention due to its effectiveness in solving second-order or high-order nonlinear systems. The advantage of this method is that it can directly solve the control variable, simplify the design process of the control law, provide more design freedom, allow parameterized design of the system controller, not only improve the intuitiveness and flexibility of control design, but also enhance the adaptability of the controller to system nonlinearities and uncertainties, which helps to overcome the limitations of designing the controller under the framework of the first-order system. SUMMARY

[0006] In view of the problems existing in the prior art, the purpose of the present application is to provide an underwater vehicle fixed-time sliding mode tracking control method based on full-drive system theory, which is used to solve the trajectory tracking control problem of underwater vehicle system with internal uncertainty and unknown disturbance.

[0007] Based on the above problems, the present application provides the following technical solutions:

[0008] The first aspect of the present application provides an underwater vehicle fixed-time sliding mode tracking control method based on full-drive system theory, comprising the following steps:

[0009] Step one: establish a six-degree-of-freedom kinematic model and a six-degree-of-freedom dynamic model of the underwater vehicle, and establish a six-degree-of-freedom underwater vehicle full-drive system error model based on the full-drive system theory.

[0010] Step two: design a fixed-time disturbance observer for the problem that the underwater vehicle is disturbed by external disturbances and the internal model parameters change due to environmental influences.

[0011] Step three: use the fixed-time sliding mode control to ensure that the underwater vehicle tracks the desired trajectory within a fixed time, and construct a fixed-time sliding mode surface.

[0012] Step four: combine the full-drive system error model to simplify the design steps of the controller, design a fixed-time sliding mode controller based on the full-drive system theory, calculate the fixed time and ensure that the system error converges to zero within the fixed time.

[0013] Step five: use the disturbance observer and the controller to realize tracking control.

[0014] The second aspect of the present application provides an electronic device for underwater vehicle fixed-time sliding mode tracking control based on full-drive system theory, comprising a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to realize the above-mentioned underwater vehicle fixed-time sliding mode tracking control method based on full-drive system theory.

[0015] The third aspect of the present application provides a computer readable storage medium, the storage medium stores a computer program, the computer program is used for executing the underwater vehicle fixed time sliding mode tracking control method based on the full drive system theory.

[0016] Based on the above technical solutions, the present application has the following beneficial effects:

[0017] (1) In view of the problem that the nonlinear and multi-degree-of-freedom coupling characteristics of the underwater vehicle dynamics model increase the difficulty of tracking controller design, the present application establishes a second-order full-drive system model based on the six-degree-of-freedom tracking error of the underwater vehicle. Unlike the way of directly designing a controller based on the underwater vehicle dynamics model in traditional sliding mode control research, the present application converts the traditional six-degree-of-freedom model of the underwater vehicle into a full-drive system model, retains the full-drive characteristics of the original six-degree-of-freedom system, and reduces the difficulty of controller design.

[0018] (2) In view of the problem that unknown disturbances exist in the complex underwater environment and the system internal model parameters change, the present application designs a fixed time disturbance observer to estimate the lumped disturbance in real time. The disturbance observer is based on the full-drive system model, which simplifies the observer design structure, and the observer estimates the unknown lumped disturbance in a fixed time, ensuring that the system can still achieve high-precision control in the presence of external disturbances and model uncertainties, while effectively suppressing the chattering phenomenon.

[0019] (3) In view of the problem that the high-frequency switching of the traditional sliding mode control method based on the first-order state space model leads to chattering of the control signal, the present application proposes a fixed time sliding mode controller based on the full-drive system model. The controller combines the full-drive system theory with the fixed time sliding mode control method, so that the position and attitude errors converge to zero in a fixed time, and the convergence time is independent of the initial state. The full-drive system model simplifies the design process of the controller and provides all the design degrees of freedom in the system. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 is a flowchart of the underwater vehicle fixed time sliding mode tracking control method based on the full-drive system theory provided by the present application.

[0021] Figure 2 is a three-dimensional trajectory tracking diagram provided by the present application.

[0022] Figure 3 is a six-degree-of-freedom tracking curve diagram provided by the present application.

[0023] Figure 4 is a disturbance estimation error curve diagram provided by the present application.

[0024] Figure 5The six-degree-of-freedom tracking error map is provided by the application. DETAILED DESCRIPTION

[0025] The technical solutions of the application will be described clearly and completely below in conjunction with the drawings. Obviously, the described embodiments are part of the embodiments of the application, rather than all the embodiments. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative work belong to the protection scope of the application.

[0026] As Figure 1 shown, the embodiment of the application provides a fixed-time sliding mode tracking control method for an underwater vehicle based on a full-drive system theory, including the following steps.

[0027] Step 1: Establish a six-degree-of-freedom kinematics model and a dynamics model of the underwater vehicle, and establish a six-degree-of-freedom underwater vehicle full-drive system error model based on the full-drive system theory. The specific steps are as follows.

[0028] The six-degree-of-freedom kinematics model and the dynamics model of the underwater vehicle are established.

[0029]

[0030] wherein, ; , , respectively represent position coordinates, respectively represent roll angle, pitch angle and yaw angle; respectively represent linear velocity components, respectively represent angular velocity components; is a coordinate transformation matrix; is a generalized mass matrix; is a water dynamic Coriolis force and centripetal force matrix; is a water dynamic damping matrix; is a restoring force (torque) vector; is a force and torque generated by the underwater vehicle; is an interference force and torque generated by the external environment.

[0031] The ground coordinate system is a fixed inertial system, which can provide a stable and unified reference for the control target. The body coordinate system of the underwater vehicle needs to be converted into the form of the ground coordinate system. The system transformation The dynamics model of the underwater vehicle is rewritten as:

[0032]

[0033] In the formula,

[0034]

[0035] wherein denotes the transpose of denotes the parameter the second derivative of time. Considering the internal uncertainty of the system model, the system model is transformed as

[0036]

[0037] wherein are the nominal terms of are the uncertain terms of

[0038] The underwater vehicle model itself has the full-drive characteristic, which is a typical full-drive system. The subsequent observer and controller design can directly design the controller according to the full-drive system model to achieve the control requirements, without further processing based on the traditional state space method.

[0039] The core goal of the present application is to realize the accurate tracking of the desired trajectory of the underwater vehicle, and to ensure that the tracking error converges to zero within a fixed time. Therefore, the position and attitude error is defined as wherein is the preset desired position and attitude. Based on the full-drive system theory, the full-drive system error model of the six-degree-of-freedom underwater vehicle is established as

[0040]

[0041] The established full-drive system error model conforms to the full-drive system form. Wherein, is the inverse matrix of the matrix corresponds to the continuous vector function in the full-drive system model, is the variable containing the related underwater vehicle model. is the lumped disturbance containing external disturbances and model internal uncertainties, which corresponds to the nonlinear uncertain term in the full-drive system model. Step two: in view of the problem that the underwater vehicle is disturbed by external disturbances and the internal model parameters change due to environmental influence, a fixed-time disturbance observer is designed. The specific steps are as follows:

[0042] According to the established full-drive system error model of the underwater vehicle, the auxiliary variables

[0043] and are introduced:

[0044]

[0045] wherein,​​​ . is the observer gain parameter, and are the design parameters related to fixed time, is a small positive number. All the above parameters are adjustable according to the control requirements.

[0046] A fixed time disturbance observer is designed for the problem that the internal model parameters of underwater vehicles change due to external disturbances and environmental influences:

[0047]

[0048] where, represents the observer estimate of the lumped disturbance .

[0049] The optimal estimate is obtained by adjusting the parameters, and the observer estimate value is compensated into the controller design through the feedback compensation mechanism, so as to minimize the influence of the lumped disturbance.

[0050] Taking the derivative of can get:

[0051]

[0052] The Lyapunov function is constructed , and its derivative can be obtained:

[0053]

[0054] where, , , , . , , and are fixed time parameters, and by adjusting the parameters, , satisfy the numerical condition, is the upper bound of the lumped disturbance. Finally, the result is obtained , according to the fixed time stability theory, will converge to zero within a fixed time and is bounded. Further, the disturbance estimation error is bounded, and can be made to converge to a neighborhood of the origin by adjusting the parameters. The full-drive system model does not need to design state space equations for multiple variables to be estimated separately, simplifying the design process of the fixed-time disturbance observer. At the same time, the output of the fixed-time disturbance observer is used in the estimation part of the lumped disturbance in the controller design, providing support for the controller to compensate for disturbances and improve system robustness.

[0055] Step three: use fixed-time sliding mode control to ensure that the underwater vehicle tracks the desired trajectory in a fixed time, and construct a fixed-time sliding mode surface. The specific steps are as follows:

[0056] A fixed-time control sliding mode surface is constructed as follows:

[0057]

[0058]

[0059] wherein, . An auxiliary variable is designed for the sliding mode surface, is the sliding mode surface gain parameter, and are design parameters related to fixed time, and the above parameters are parameters that can be adjusted according to control requirements. is the error of six degrees of freedom, , is a very small positive number. The smooth switching function is used in the embodiment of the application to avoid singularity problems, and appropriate parameters and are selected to make and its derivative continuous.

[0060] Step four: simplify the design steps of the controller by combining the full-drive system error model, and design a fixed-time sliding mode controller based on the full-drive system theory to ensure that the system error converges to zero in a fixed time. The specific steps are as follows:

[0061] Design a fixed-time sliding mode controller based on the full-drive system error model:

[0062]

[0063] wherein, ; and are controller gain parameters, and are design parameters related to fixed time, and are parameters that can be adjusted according to control requirements.

[0064] Lyapunov function is constructed for fixed time control sliding mode surface , with respect to time The derivative is

[0065]

[0066] where , , , , , and are fixed time parameters, which are adjusted to make , , , satisfy numerical conditions; the final result is According to the fixed time stability theory, after the estimation of the lumped disturbance is completed, the sliding mode surface converges to zero within fixed time , and the convergence time is independent of the initial state. After the system state reaches the sliding mode surface, it enters the sliding motion stage. The convergence of the system error in the sliding motion stage is analyzed below.

[0067] Lyapunov function is constructed for system error , and according to the size of , the discussion is expanded as follows:

[0068] Case 1: When , the derivative of the system tracking error can be written as , with respect to time The derivative is

[0069]

[0070] where , , , , , and are fixed time parameters, which are adjusted to make satisfy numerical conditions; the final result is According to the fixed time stability theory, after the system error reaches the sliding mode surface, it converges to zero within fixed time , and the convergence time is independent of the initial state.

[0071] Case 2: When , the derivative of the system tracking error can be written as​​​ , the system error about time , the derivative is:

[0072]

[0073] wherein, , , , . , , and are fixed time parameters, by adjusting the parameters so that , satisfy the numerical conditions. The final result is , according to the fixed time stability theory, the system error to the sliding mode surface in fixed time Converge to zero, the convergence time is independent of the initial state. The convergence time of the system tracking error is .

[0074] Step five: use the designed disturbance observer and controller to realize tracking control. Calculate the system error combined with the expected trajectory, estimate the lumped disturbance by the disturbance observer, and generate control commands according to the error signal and disturbance estimate value. Controller distributes to each thruster to drive the underwater vehicle to realize stable tracking of the expected trajectory in fixed time.

[0075] In order to verify the effectiveness of the method, the application embodiment carries out the following numerical simulation experiment:

[0076] The kinematic model of underwater vehicle contains coordinate transformation matrix , expressed in block form as:

[0077]

[0078] wherein, is the rotation matrix (convert the body translation velocity to the inertial system), is the Euler angle rate matrix, which is specifically expressed as:

[0079]

[0080]

[0081] wherein, , , .

[0082] The kinematic model of underwater vehicle contains inertia matrix , Coriolis matrix , damping matrix , and restoring force vector . Where inertia matrix is diagonalized as: . The simplified model of Coriolis matrix is:

[0083]

[0084] where is the mass of the underwater vehicle; are the moments of inertia about axis, axis, axis, respectively.

[0085] The hydrodynamic damping matrix is modeled as a combination of linear and second order damping terms . Where, is the linear damping term, is the second order damping term. The hydrodynamic damping matrix is specifically expressed as:

[0086]

[0087] where, is the inertia hydrodynamic coefficient for the corresponding degree of freedom, is the hydrodynamic coupling coefficient for the corresponding degree of freedom.

[0088] The restoring force vector is generated by the imbalance of gravity and buoyancy, and the simplified model is: . The specific parameter values are shown in Table 1:

[0089] Table 1 Parameter values

[0090]

[0091] The above is only for nominal values, and for uncertain terms, set: , , .

[0092] The desired trajectory is designed to be a spiral ascending trajectory, and the desired trajectory to be tracked is set as:

[0093]

[0094] For external disturbances, set the disturbance as:

[0095]

[0096] The simulation duration is defined as 30s, and the disturbance period .

[0097] The obtained three-dimensional trajectory tracking results of the underwater vehicle system are shown in Figure 2 、 Figure 3 From the curve fitting, the actual motion trajectory of the underwater vehicle is consistent with the expected trajectory curve. Although there is a certain deviation between the initial state of the underwater vehicle and the expected trajectory, the fixed-time sliding mode controller based on the full-drive system model can drive the underwater vehicle to achieve rapid and accurate tracking of the expected trajectory within about 1s, and the process is stable, which preliminarily proves the feasibility of the control method.

[0098] For the established error model of the underwater vehicle full-drive system, a fixed-time disturbance observer is further designed to estimate the lumped disturbance, and the convergence curve of the obtained lumped disturbance estimation error is shown in Figure 4 .

[0099] The simulation experiment shows that under the condition of a certain significant deviation in the initial state, the observation errors of the six degrees of freedom of the underwater vehicle can quickly converge to the steady state interval within 1s, and the convergence process is smooth and has no obvious oscillation, which effectively verifies that the designed fixed-time disturbance observer has high dynamic response characteristics. By reasonably adjusting the parameters, the observer effectively balances the rapidity and robustness of disturbance estimation, and can provide high-precision disturbance estimation information for the disturbance compensation link of the underwater vehicle control system under complex ocean environment disturbance, ensuring the stable execution of the control strategy.

[0100] Figure 5 The position and attitude tracking error curves of the underwater vehicle in six degrees of freedom are shown in the figure, from which it can be seen that the tracking trajectory error in each degree of freedom is small, and the tracking error can quickly converge to within 2% of the error band. Combining the experimental results of three-dimensional trajectory tracking, disturbance observation error convergence and six-degree-of-freedom tracking error convergence, it is fully proved that the method has significant comprehensive advantages in convergence speed, steady-state accuracy and anti-interference ability.

[0101] The embodiment of the application further discloses an electronic device for underwater vehicle fixed-time sliding mode tracking control based on a full drive system theory, including a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor executes the computer program to realize steps of the underwater vehicle fixed-time sliding mode tracking control method based on the full drive system theory, wherein the memory can include an internal memory such as a high-speed random memory, and can also include a non-volatile memory such as at least one disk memory; the processor, the network interface, and the memory are connected with each other through an internal bus, which can be an industry standard architecture bus, a peripheral component interconnect standard bus, an extended industry standard structure bus, etc., and the bus can be divided into an address bus, a data bus, a control bus, etc. The memory is used for storing a program, specifically, the program can include program codes, and the program codes include computer operation instructions. The memory can include an internal memory and a non-volatile memory, and provide instructions and data for the processor.

[0102] The embodiment of the application further discloses a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to realize steps of the underwater vehicle fixed-time sliding mode tracking control method based on the full drive system theory, specifically, the computer readable storage medium includes but is not limited to, for example, a volatile memory and / or a non-volatile memory. The volatile memory can include a random access memory (RAM) and / or a cache memory, etc. The non-volatile memory can include a read-only memory (ROM), a hard disk, a flash memory, an optical disc, a magnetic disc, etc.

[0103] In the application, specific examples are applied to describe the principles and implementation manners of the application, and the above embodiment descriptions are only used to help understand the method and core idea of the application; meanwhile, for those skilled in the art, according to the idea of the application, the specific implementation manners and application ranges can be changed. In conclusion, the content of the specification should not be understood as a limitation of the application.

Claims

1. An underwater vehicle fixed-time sliding mode tracking control method based on the theory of overactuated system, characterized in that, The method comprises the following steps: Step 1: establishing a six-degree-of-freedom kinematics model and a dynamics model of the underwater vehicle, and establishing a six-degree-of-freedom full-drive system error model of the underwater vehicle based on a full-drive system theory; Step 2: designing a fixed-time disturbance observer for the problem that the internal model parameters of the underwater vehicle change due to external interference and environmental influence; Step 3: ensuring that the underwater vehicle tracks the expected trajectory within a fixed time by using a fixed-time sliding mode control, and constructing a fixed-time sliding mode surface; Step 4: simplifying the design steps of the controller by combining the full-drive system error model, designing a fixed-time sliding mode controller based on the full-drive system theory, calculating the fixed time and ensuring that the system error converges to zero within the fixed time; Step 5: realizing tracking control by using the disturbance observer and the controller.

2. The method of claim 1, wherein, The step 1 comprises: establishing a six-degree-of-freedom kinematics model and a dynamics model of the underwater vehicle; ； wherein, , , and denote position coordinates, , and are roll, pitch and yaw angles, respectively; , , and denote linear velocity components, , and are angular velocity components; is a coordinate transformation matrix, is a generalized mass matrix, is a hydrodynamic Coriolis and centripetal force matrix, is a hydrodynamic damping matrix, is a moment vector, is a force and moment generated by the underwater vehicle, is an external disturbance force and moment. The underwater vehicle body coordinates are converted into a ground coordinate system form, and a system transformation is used The underwater vehicle dynamics model is rewritten; considering the internal uncertainty of the system model, and transforming the rewritten dynamics model by using an uncertainty term; Definitions is the position and attitude error, where is the preset desired position and attitude, and a six-degree-of-freedom underwater vehicle full-drive system error model is established based on a full-drive system theory: ； wherein is the inverse matrix of the matrix , , corresponds to a continuous vector function in the model of the full drive system, is a variable containing the model of the relevant underwater vehicle, , denotes the transpose of ; is a lumped disturbance containing external disturbances and model internal uncertainties, corresponding to a nonlinear uncertainty term in the model of the full drive system.

3. The method of claim 2, wherein, The step 2 comprises: According to the established error model of the full-drive system of underwater vehicles, auxiliary variables and are introduced designing a fixed-time disturbance observer for the problem that the internal model parameters of the underwater vehicle change due to external interference and environmental influence; ； wherein represents an observer estimate of the aggregate disturbance , , and are observer gain parameters, and are prescribed fixed time correlation parameters, is a prescribed positive parameter; obtaining an optimal estimate by adjusting parameters, and compensating the estimated value of the observer into the controller design through a feedback compensation mechanism, so as to minimize the influence of the lumped disturbance; A Lyapunov function V1 is constructed, and its derivation is calculated to obtain a fixed time such that the disturbance estimation error converges to a neighborhood around the origin within the fixed time.

4. The method according to claim 2 or 3, characterized in that, The fixed time sliding surface is: ; wherein is a design auxiliary variable for the slip surface.

5. The method of claim 4, wherein: The ; wherein , , and are sliding mode surface gain parameters, and are fixed time related parameters, is the error in six degrees of freedom, , is a threshold value.

6. The method of claim 4, wherein, the fixed-time sliding mode controller based on the full-drive system theory is: ； wherein, and are controller gain parameters, and are fixed time-dependent parameters set.

7. The method according to claim 5 or 6, characterized in that, the calculation of the fixed time in the step 4 comprises: A Lyapunov function V2 is constructed for the fixed-time control sliding mode surface, and derivation is performed on the fixed-time , so that the sliding mode surface converges to zero within the time constructing a Lyapunov function V3 for the system error, and calculating in the following cases: When the derivative of V3 is calculated for a fixed time so that the system error reaches the sliding surface and converges to zero within said time; when the derivative of V3 is calculated for a fixed time so that the system error reaches the sliding surface and converges to zero within said time; In summary, the convergence time of the system tracking error is .

8. The method of claim 1, wherein, The step 5 comprises: combining the expected trajectory to calculate the system error, estimating the lumped disturbance by the disturbance observer, and generating a control instruction by the controller according to the error signal and the estimated value of the disturbance, and distributing the control instruction to each propeller to drive the underwater vehicle to stably track the expected trajectory within the fixed time.

9. An electronic device for fixed-time sliding mode tracking control of an underwater vehicle based on the theory of overactuated systems, characterized by comprise: a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor implements the method of any one of claims 1-8 when executing the program.

10. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, and the computer program is used to execute the method of any one of claims 1-8.

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