A trajectory tracking method for fully-driven ships based on predictive optimal control

Abstract

This invention provides a method for tracking the trajectory of a fully driven ship based on predictive optimization control, belonging to the fields of marine technology and intelligent navigation technology. The invention involves the following steps: constructing a basic dynamic nonlinear model based on the ship's three degrees of freedom; transforming the basic dynamic nonlinear model into a linear steady-state system using a parametric design method; constructing an enhanced error system and an internal model compensator using the linear steady-state system; determining the controller form by combining the enhanced error system and the internal model compensator; and introducing a predictive term to obtain the optimal controller. This invention optimizes the calculation process of control inputs, reduces the computational burden of real-time control, and achieves an optimized control strategy; furthermore, the predictive controller can respond more quickly to dynamic trajectory changes, shorten the system's adjustment time, improve adaptability to complex trajectories, and achieve rapid response.

Description

Technical Field

[0001] This invention relates to the fields of marine technology and intelligent navigation technology, and in particular to a method for tracking the trajectory of fully driven ships based on predictive optimization control. Background Technology

[0002] Trajectory tracking control technology is widely used in ship navigation and control, especially in unmanned autonomous surface vessels (USVs), floating wind farm maintenance vessels, and marine engineering. Traditional ship navigation systems mostly employ proportional-integral-derivative (PID) control and robust control methods. These methods have the advantages of simple implementation and low computational burden, and are widely used in path tracking control of small vessels. However, traditional methods are difficult to cope with nonlinear disturbances in complex marine environments, and their control accuracy and response speed are insufficient in scenarios with rapid trajectory changes or turns. With the improvement of computing power, model predictive control technology has gradually been applied to ship trajectory tracking control. By optimizing the control input within the prediction window, model predictive control can balance tracking error and energy consumption to a certain extent. However, the linear modeling assumption of model predictive control limits its application to nonlinear ship systems, and large-scale computation leads to limited real-time performance, especially in complex environments where its effectiveness is limited.

[0003] In the field of ship trajectory tracking control, existing technologies have proposed predictive control as a feedforward control strategy, utilizing future information from a reference trajectory to improve the system's dynamic response and tracking accuracy. However, traditional predictive control methods are primarily designed for linear systems and are difficult to apply directly to ship models with nonlinear characteristics, leading to a decline in control performance. Furthermore, disturbances in the marine environment such as wind, waves, and currents significantly impact ship motion, and existing predictive control methods are insufficient in addressing these uncertainties. The complexity of predictive control algorithms also increases computational burden, affecting the system's real-time performance, especially when dealing with multivariable and strongly coupled ship systems, where control accuracy and real-time response performance are limited.

[0004] Therefore, a method for tracking the trajectory of fully driven ships based on predictive optimization control is needed. Summary of the Invention

[0005] In view of this, the present invention provides a fully driven ship trajectory tracking method based on predictive optimization control, which combines dynamic linearization and predictive control technology to improve control accuracy and meet real-time requirements.

[0006] Therefore, the present invention provides the following technical solution:

[0007] A method for tracking the trajectory of a fully driven ship based on predictive optimization control, comprising:

[0008] A basic dynamic nonlinear model is constructed based on the three degrees of freedom of the ship;

[0009] The basic nonlinear dynamic model is transformed into a linear steady-state system using a parametric design method.

[0010] The linear steady-state system is used to construct an enhanced error system and an internal model compensator;

[0011] The optimal controller configuration is determined by combining the enhanced error system and the internal model compensator.

[0012] By introducing a predictive term based on the optimization controller, an optimal controller with a predictive term is obtained.

[0013] Furthermore, the basic dynamic nonlinear model:

[0014]

[0015] in: The ship's position and yaw angle; v = [u, ν, r] T : Velocity vector, including forward velocity, lateral velocity, and yaw velocity; τ = [τ1, τ2, τ3] T Control inputs include thrust, lateral force, and yaw moment; The ship attitude transformation matrix maps the velocity vector to the geographic coordinate system; M, C(v), and D(v) represent the ship's inertia matrix, Coriolis force matrix, and damping matrix, respectively.

[0016] Furthermore, the linear steady-state system:

[0017]

[0018] Among them, state Output y = η; State matrix Control Matrix Output matrix C c =[I 0]; Virtual output is

[0019] Furthermore, the internal model compensator eliminates the effects of reference trajectory disturbances and external disturbances:

[0020]

[0021] Where ξ represents the internal compensation state variable; G1 and G2 represent the compensation gain matrices; and e represents the tracking error.

[0022] Furthermore, the enhanced error system:

[0023]

[0024] Where, η dFor reference trajectory; To enhance the state vector;

[0025] These are the system's state matrix, input matrix, and reference compensation matrix, respectively. This is the state matrix of an open-loop system.

[0026] Furthermore, the introduction of the predictive term to obtain the optimal controller includes:

[0027] By using a cost function, tracking accuracy and energy consumption can be balanced.

[0028] Solve for the optimal feedback gain matrix using the algebraic Riccati equation;

[0029] By introducing a predictive term based on the optimization controller, an optimal controller with a predictive term is obtained.

[0030] Furthermore, the cost function is:

[0031]

[0032] Where Q represents the trade-off state error; R represents the trade-off control energy consumption; This indicates an optimized controller.

[0033] Furthermore, the algebraic Riccati equation:

[0034]

[0035] The optimal feedback gain matrix: K = -R -1 B T P.

[0036] Furthermore, the prediction term is introduced based on the optimization controller:

[0037]

[0038] Where: Lyapunov function positive definite matrix P = [P x P ξ P e ];l r This represents the predicted length parameter, used to adjust the response to future trajectories.

[0039] Furthermore, the input to the optimal controller is:

[0040]

[0041] Among them, feedback gain Feedback gain

[0042] Virtual input:

[0043] Foreseeable items:

[0044] Weight matrix:

[0045] Generate a reference trajectory by referencing a dynamic model:

[0046]

[0047] η d =C d x d

[0048] In the formula: x d It is a tracking status signal, (A) d C d ( ) is a known matrix;

[0049] Inertia matrix:

[0050] Coriolis and centrifugal matrix

[0051] Damping matrix

[0052] Advantages and positive effects of the present invention:

[0053] This invention utilizes predictive information to significantly improve the dynamic response performance of the system and achieve higher trajectory tracking accuracy by obtaining future information about the reference trajectory in advance. Furthermore, it employs a parametric design method to transform the complex nonlinear ship dynamic model into a linear steady-state form, thereby enhancing the applicability of the control algorithm in nonlinear systems and achieving precise control of nonlinear systems.

[0054] This invention designs an internal model compensator and an error enhancement system to effectively resist disturbances in the marine environment such as wind, waves, and currents, ensuring the stability of trajectory tracking; for the motion of ships in the three degrees of freedom of forward, lateral, and yaw, an efficient decoupling control method is designed to achieve multi-degree-of-freedom decoupling control.

[0055] This invention optimizes the calculation process of control input by combining algebraic Riccati equations and predictive control design, reduces the computational burden of real-time control, and realizes an optimized control strategy. Furthermore, the predictive controller can respond to dynamic trajectory changes more quickly, shorten the system's adjustment time, improve adaptability to complex trajectories, and achieve rapid response.

[0056] Combining the above advantages, the present invention can improve trajectory tracking accuracy, enhance system robustness, and improve the real-time performance of the control system. Attached Figure Description

[0057] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0058] Figure 1 This is the dynamic response trajectory in the longitudinal direction in this embodiment of the invention;

[0059] Figure 2 This is the dynamic response trajectory in the lateral direction in this embodiment of the invention;

[0060] Figure 3 This is the dynamic response trajectory in the yaw direction in this embodiment of the invention;

[0061] Figure 4 This is a flowchart of the method in an embodiment of the present invention. Detailed Implementation

[0062] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0063] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0064] This invention provides a fully driven ship trajectory tracking method based on predictive optimization control. By introducing predictive terms and strictly designing controllability and observability, it provides an efficient, robust and practical trajectory tracking control method that is suitable for ship control tasks in complex dynamic environments.

[0065] S1. Modeling of nonlinear ship systems;

[0066] S11. Construct a basic nonlinear dynamic model based on the three degrees of freedom (DOF) of a ship:

[0067]

[0068] in: The ship's position and yaw angle; v = [u, ν, r] T : Velocity vector, including forward velocity, lateral velocity, and yaw velocity; τ = [τ1, τ2, τ3] T Control inputs include thrust, lateral force, and yaw moment; The ship attitude transformation matrix maps the velocity vector to the geographic coordinate system; M, C(v), and D(v) represent the ship's inertia matrix, Coriolis force matrix, and damping matrix, respectively.

[0069] S12. Transform the nonlinear model into a linear steady-state system using parametric design methods:

[0070]

[0071] Where: state Output y = η; State matrix Control Matrix Output matrix C c =[I 0]; Virtual output is

[0072] S13. Generate a reference trajectory by referencing the dynamic model:

[0073]

[0074] η d =C d x d

[0075] Among them: (A) d C d ) is a known matrix; trajectory signal η d It is piecewise continuously differentiable.

[0076] S2. Obtain the optimal controller;

[0077] S21. Define tracking error: e = y - η d The dynamic equation for the tracking error is:

[0078] S22. Introduce an internal model compensator to eliminate the influence of reference trajectory disturbances and external disturbances;

[0079] Internal model compensator:

[0080] Where: ξ represents the internal compensation state variable; G1 and G2 represent the compensation gain matrices, used to ensure the dynamic compensation capability of the system.

[0081] S23. Construct an enhanced error system:

[0082]

[0083] in: To enhance the state vector;

[0084] These are the system's state matrix, input matrix, and reference compensation matrix, respectively. This is the state matrix of an open-loop system.

[0085] S3. Verify the controllability and observability of the linear system;

[0086] S31. The controllability of a linear system is defined by the control matrix:

[0087]

[0088] If (G1, G2) is stabilizable, then the matrix has full row rank, and the system is completely controllable, meaning that all state variables can be controlled by the input.

[0089] S32. The observability of a linear system is defined by the output matrix:

[0090]

[0091] If the state weight submatrix (C) ξ C e If the matrix is ​​positive definite, then the columns of the matrix are full rank, and all states of the system can be accurately estimated through the output variables.

[0092] Through design, the system's enhanced error system and internal model compensator are theoretically made to satisfy complete controllability and observability.

[0093] S4. Determine the optimal controller;

[0094] S41. Design a cost function to balance tracking accuracy and control energy consumption;

[0095] Design the cost function:

[0096]

[0097] Where: Q represents the trade-off state error; R represents the trade-off control energy consumption; This indicates an optimized controller.

[0098] pass Verify the detectability of the system;

[0099] S42. Through the algebraic Riccati equation:

[0100]

[0101] Solve for the optimal feedback gain matrix K = -R -1 B T P, optimize system performance.

[0102] S43. Incorporate predictive terms into the controller design to optimize control input by introducing future reference trajectory information:

[0103]

[0104] Where: P = [P x P ξ P e ];l r This represents the predicted length parameter, used to adjust the response to future trajectories.

[0105] S44. The final input for the unmanned vessel trajectory tracking controller is:

[0106]

[0107] Where: feedback gain Feedback gain

[0108] Virtual input:

[0109] Foreseeable items:

[0110] Weight matrix:

[0111] In the formula: x d It is a tracking status signal, (A) d C d ( ) is a known matrix;

[0112] Inertia matrix:

[0113] Coriolis and centrifugal matrix

[0114] Damping matrix

[0115] The method of the present invention will be further illustrated by the following specific embodiments:

[0116] 1. Modeling of nonlinear ship systems;

[0117] 1.1 Establish a three-degree-of-freedom fully driven ship dynamics model, including position (η) x ,η y )and

[0118] Yaw angle The dynamic equation:

[0119]

[0120] in: The ship's position and yaw angle; v = [u, ν, r] T : Velocity vector, including forward velocity, lateral velocity, and yaw velocity; τ = [τ1, τ2, τ3] T Control input.

[0121] 1.2. By eliminating nonlinear terms through parametric design, a linearized dynamic model is obtained and used for controller design.

[0122] 2. Controller design;

[0123] 2.1 Construct an enhanced error system;

[0124] Define tracking error as: e = y - η d ;

[0125] Where, η d It is a reference trajectory;

[0126] 2.2 Design an internal model compensator to eliminate the interference of the reference trajectory on the control system: Combine the enhanced error system and the internal model compensator to construct a complete mathematical model of the predictive controller.

[0127] 2.3 Optimal Controller Design

[0128] Optimize control inputs by designing the optimal feedback gain matrix and internal model compensator gain using the algebraic Riccati equation to improve trajectory tracking performance; and add a predictive compensation term based on future information from the reference trajectory to improve control accuracy.

[0129] 3. Using the classic Cybership II ship model as the test object, its dynamic parameters are as follows: Ship mass: 23.8 kg; Damping coefficient:

[0130] Verification of dynamic sinusoidal trajectory tracking task: Initial state: η(0)=[0.1m,0.5m,0rad], velocity v(0)=[0,0,0] T Forecast length: l r =5.

[0131] Forecast length l rWhen the value is 5, the trajectory error converges rapidly to zero; as the prediction length increases, the system response time is significantly shortened, for example, l r =5's adjustment time is 8.1s, l r =0 for 73.5s. As the amplitude of the control input gradually decreases, the system becomes more stable. Simulation results for a sinusoidal trajectory verify the effectiveness of the preview optimization control method.

[0132] In summary, the method of this invention significantly improves the tracking accuracy of the system under dynamic and complex trajectories, optimizes the response time, and enhances the smoothness of the control input and the system's anti-disturbance capability, demonstrating broad applicability in complex dynamic environments. This invention exhibits excellent performance in trajectory tracking of complex nonlinear ship systems, not only significantly improving control accuracy and system stability, but also demonstrating broad engineering application potential.

[0133] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for tracking the trajectory of a fully driven ship based on predictive optimization control, characterized in that, include: A basic dynamic nonlinear model is constructed based on the three degrees of freedom of the ship; The basic nonlinear dynamic model is transformed into a linear steady-state system using a parametric design method. The linear steady-state system is used to construct an enhanced error system and an internal model compensator; The optimal controller configuration is determined by combining the enhanced error system and the internal model compensator. By using a cost function, tracking accuracy and energy consumption can be balanced. Solve for the optimal feedback gain matrix using the algebraic Riccati equation; By introducing a predictive term based on the optimization controller, an optimal controller with a predictive term is obtained; The cost function: wherein Q represents a trade-off state error; R represents a trade-off control energy consumption; represents an optimization controller; The algebraic Riccati equation: the optimal feedback gain matrix: ; Introducing predictive terms based on the optimization controller: wherein: Lyapunov function positive definite matrix ; denotes a look-ahead parameter, used to adjust the response to the future trajectory; The internal model compensator eliminates the effects of reference trajectory disturbances and external disturbances: in, Represents the internal compensation state variables; and Represents the compensation gain matrix. Indicates tracking error; The enhanced error system: wherein, is a reference trajectory; is an augmented state vector; respectively the state matrix and the input matrix of the system and the reference compensation matrix; is the open-loop system state matrix.

2. The trajectory tracking method for a fully-driven ship based on predictive optimal control according to claim 1, characterized in that, The basic dynamic nonlinear model: in: The ship's position and yaw angle; : Velocity vector, including forward velocity, lateral velocity, and yaw velocity; Control inputs include thrust, lateral force, and yaw moment; The ship attitude transformation matrix maps the velocity vector to the geographic coordinate system. , and These represent the ship's inertia matrix, Coriolis force matrix, and damping matrix, respectively.

3. The trajectory tracking method for a fully-driven ship based on predictive optimal control according to claim 2, characterized in that, The linear steady-state system: Among them, state Output State matrix Control Matrix Output matrix Virtual output is .

4. The trajectory tracking method for a fully-driven ship based on predictive optimal control according to claim 3, characterized in that, The input to the optimal controller: where the feedback gain ; Virtual input: Foreseen items: Weight matrix: ; Generate a reference trajectory by referencing a dynamic model: wherein: is a tracking state signal, , is a known matrix; Inertia matrix: ; coriolis and centrifugal matrix ; Damping matrix .

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