An underactuated unmanned surface vehicle preset performance path tracking control method and system

Abstract

The application belongs to the field of unmanned ship control, and relates to a preset performance path tracking control method and system for an underactuated unmanned ship. From the perspective of engineering practice, the application first designs an arctangent type path tracking preset performance guidance law at the kinematics level; then designs a virtual speed law, a preset time dynamics control law and a robust adaptive law at the dynamics level, so that the course tracking error is within the preset performance limit throughout the process. At the same time, the lateral error will also be within the preset limit at all times after meeting the preset performance condition, so as to achieve accurate tracking of the expected path. The designed control strategy can ensure the preset performance and preset time convergence of the system error, and ensure the safety of the unmanned ship when performing a task.

Description

Technical Field

[0001] This invention belongs to the field of unmanned surface vessels (including underwater vehicles, underwater robots, unmanned surface vessels, etc.) control, and more specifically, relates to a preset performance path tracking control method and system for underactuated unmanned surface vessels. Background Technology

[0002] In recent years, with the development and utilization of marine resources, unmanned surface vessels (USVs) (including underwater vehicles, underwater robots, and surface unmanned vessels) have begun to be widely used and developed. Path tracking control is a crucial part of enabling USVs to achieve autonomous navigation, and the design of the controller directly affects the USV's tracking accuracy and operational safety along a predetermined path. Therefore, path tracking control of USVs has become one of the hot topics in recent years.

[0003] To achieve this goal for unmanned surface vessels (USVs), domestic and international scholars have achieved significant results in designing controllers based on nonlinear algorithms such as backstepping and sliding mode. In kinematic level algorithms for USV path tracking control, the LOS guidance algorithm can smoothly guide the USV onto the desired path. However, transient performance, which is equally crucial for USV operations, often lacks constraints. Therefore, further optimization is necessary to achieve a balance between transient and steady-state performance of the path tracking error state. At the dynamic level, existing research on heading tracking controllers has largely achieved asymptotic stability, meaning the heading tracking error converges after an infinite time interval; however, the time required for convergence cannot be guaranteed. To address this issue, it is necessary to design a dynamic controller incorporating preset time theory to ensure that the heading tracking error converges within a preset time. Summary of the Invention

[0004] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a preset performance path tracking control method for underactuated unmanned surface vessels (USVs). The purpose is to achieve a balance between transient performance and preset time during the motion control of underactuated USVs, thereby solving the technical problem of safe navigation path tracking control for USVs.

[0005] To achieve the above objectives, according to one aspect of the present invention, a method for path tracking control of an underactuated unmanned surface vessel (USV) with preset performance is provided. This method aims to have the USV converge to the desired path within a preset time period, without exceeding a preset envelope range throughout the process. First, error transformation is completed by combining a preset performance function, a preset time function, and a preset performance conversion error function, laying the foundation for subsequent controller design. Then, an arctangent preset performance line-of-sight guidance law, applicable in engineering practice, is designed. At the initial large error moment, the guidance law is a proportional line-of-sight angle, driving the tracking error asymptotically to zero. Once the error converges to satisfy the performance switching inequality, the preset performance control stage begins, where the error remains strictly within constraints. This method draws on the essence of traditional line-of-sight angles, has a simple structure, requires no adaptive terms, and does not require initial condition assumptions. Next, a preset performance virtual velocity law is designed to guide the USV to achieve the preset performance target. Finally, a preset time dynamics control law is designed based on robust adaptive technology. This control law no longer expects the error to converge to zero within a preset time period, but only requires convergence to within a preset residual limit, ultimately achieving precise path tracking control. Wherein:

[0006] The preset performance function is:

[0007] ρ=(ρ0-ρ ∞ )e -κt +ρ ∞

[0008] Where ρ0 is the specified initial error limit, ρ ∞ κ represents the maximum allowable steady-state error during the steady-state phase, and κ is a constant to be set, the value of which determines the convergence rate.

[0009] The preset time function is:

[0010]

[0011] In the formula, e is the natural constant, T is the convergence time preset by the control engineer, and σ>0 and b>>ε>0 are design parameters. The selection of σ determines the system error convergence rate, while ε determines the final tracking accuracy.

[0012] The preset performance conversion error function is defined as follows:

[0013]

[0014] Among them, y e p(y) represents the lateral deviation between the actual position and the desired path of the unmanned surface vessel. e ) is a variable that switches with error, defined as e l and e u The error boundary for time-varying decay can be expressed as: In the formula δ l and δ u These are the parameters to be selected.

[0015] The arctangent preset performance line-of-sight guidance law is as follows:

[0016]

[0017] Where, γ d The path tangent angle, Let be the sideslip angle, u and v be the forward and lateral velocities defined in the unmanned surface vessel's coordinate system, and k be the lateral velocity. los For the positive definite parameters to be selected, the switching inequality is defined as follows:

[0018]

[0019]

[0020] In the formula, σ∈(0,1) are the conditional parameters selected by the control engineer. The horizontal velocity is the resultant velocity. The guidance law switches when both of the above inequalities are satisfied simultaneously. The first inequality is a performance inequality, designed to ensure that the control can achieve the preset performance target. The second inequality is an initial condition judgment inequality, designed to avoid violating the preset performance limit at the initial moment after the switch. The described arctangent path tracking preset performance line-of-sight guidance law does not require constraints on the initial position as in existing preset performance methods, and its algorithm structure is simpler, making it easier for engineering applications.

[0021] The preset performance virtual velocity law is as follows:

[0022]

[0023] Where, k ψ1 ζ is a control parameter. P It is a nonlinear transformation function. Its first derivative, ψ e This represents the heading error.

[0024] The preset time-dynamic control law is as follows:

[0025]

[0026] Where, m ij f represents the element in the i-th row and j-th column of the inertia matrix. r (r) represents the hydrodynamic term, k ψ2 For control parameters, z ψ1 =ζ P (t)ψ e ζ is the preset time conversion error variable.P (t) is the preset time function, b is the design parameter, and z ψ2 =r-α r The speed tracking error is represented by r, which is the bow angular velocity defined in the unmanned surface vessel's coordinate system. For α r The first derivative, It is the unknown upper bound of the disturbance component d3 of the external environmental disturbance in the yaw degree of freedom. Robust adaptive estimation term.

[0027] The robust adaptive law is as follows:

[0028]

[0029] In the formula, λ r and Γ r The control parameters to be set are shown. Meanwhile, the upper bound estimation error of the disturbance can be defined as...

[0030] To achieve the above objectives, according to another aspect of the present invention, a computer-readable storage medium is provided, on which a computer program is stored, which, when executed by a processor, implements the underactuated unmanned surface vessel preset performance path tracking control method as described in any of the preceding claims.

[0031] To achieve the above objectives, according to another aspect of the present invention, a preset performance path tracking control system for an underactuated unmanned surface vessel is provided, comprising a computer-readable storage medium as described above and a processor, the processor being used to call and process a computer program stored in the computer-readable storage medium.

[0032] In summary, the technical solutions conceived in this invention have the following beneficial effects compared with the prior art:

[0033] 1. This invention addresses the high-precision path tracking requirements of underactuated unmanned surface vessels (USVs). Under the proposed virtual velocity law, preset time dynamics control law, and robust adaptive law, the heading error converges to a bounded closed set with arbitrarily small errors within a preset time, and the tracking error remains within a preset performance limit throughout the entire process. This achieves a balance between transient performance and convergence time while ensuring the safe navigation of the USV.

[0034] 2. The arctangent guidance law designed in this invention does not require constraints on the initial position as in existing preset performance operations, making it more convenient for engineering applications. Furthermore, thanks to the simple structure of the algorithm, the designed arctangent guidance law can also be extended to depth surface applications.

[0035] 3. This invention designs an arctangent-type preset performance guidance law at the kinematic level, so that the heading tracking error is within the preset performance limit throughout the entire process.

[0036] 4. This invention transforms the original heading error through an actual preset time function. Simultaneously, based on the obstacle Lyapunov function and robust adaptive technology, a controller is designed to achieve preset time control under the influence of external environmental disturbances. Attached Figure Description

[0037] Figure 1 This is a block diagram of the unmanned surface vessel path tracking control method in this invention.

[0038] Figure 2 This is a schematic diagram of a preset time tracking control considering transient performance constraints.

[0039] Figure 3 Is this the arctangent preset performance guidance algorithm switching flowchart?

[0040] Figure 4 These are images showing the surface linear tracking performance of an unmanned surface vessel at different initial positions under the action of the arctangent preset performance guidance law.

[0041] Figure 5 This is a time-history curve of tracking error under the action of the arctangent preset performance guidance law. Detailed Implementation

[0042] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0043] like Figure 1 As shown, this invention provides a preferred underactuated unmanned surface vessel (USV) path tracking control method considering transient performance. This method aims to have the USV converge to the desired path within a pre-set time frame, without exceeding the pre-set envelope range throughout the entire process. A schematic diagram of the tracking control is shown below. Figure 2 As shown, error transformation was completed by combining a preset performance function, a preset time function, and a preset performance conversion error function, laying the foundation for subsequent controller design; a preset performance line-of-sight guidance law was proposed, wherein the arctangent line-of-sight angle guidance law designed in this paper is as follows: Figure 3As shown, at the initial large error moment, the guidance law is a proportional line-of-sight angle, driving the tracking error asymptotically to zero. Once the error converges to satisfy the performance switching inequality, it enters the preset performance control stage, where the error remains strictly within the constraints. This method draws on the essence of traditional line-of-sight angle methods, has a simple structure, requires no adaptive terms, and does not require initial condition assumptions. Next, a preset performance virtual velocity law is designed. Finally, a preset time-dynamic control law is designed based on robust adaptive technology to achieve precise path tracking control. The specific implementation process is as follows:

[0044] The equations of motion for the three degrees of freedom in the horizontal plane of the underactuated unmanned surface vessel are as follows:

[0045]

[0046]

[0047] Where x, y, and ψ are the position coordinates and heading angle defined in the geodetic coordinate system, respectively; u, v, and r are the forward, lateral, and turning angular velocities defined in the unmanned surface vessel's coordinate system, respectively. ij f represents the element in the i-th row and j-th column of the inertia matrix. u (u), f v (v) and f r (r) represents the hydrodynamic term, d1(t), d2(t), and d3(t) represent the disturbance components experienced by each degree of freedom, and τ1 and τ3 represent the control inputs for the forward and yaw degrees of freedom, respectively.

[0048] To achieve accurate path tracking, error transformation was first performed by combining a preset performance function, a preset time function, and a preset performance conversion error function. The specific form of this transformation is as follows:

[0049] The preset performance function is:

[0050] ρ=(ρ0-ρ ∞ )e -κt +ρ ∞

[0051] Where ρ0 is the specified initial error limit, ρ ∞ κ represents the maximum allowable steady-state error during the steady-state phase, and κ is a constant to be set, the value of which determines the convergence rate.

[0052] The preset time function is:

[0053]

[0054] In the formula, e is the natural constant, T is the convergence time preset by the control engineer, and σ>0 and b>>ε>0 are design parameters. The selection of σ determines the system error convergence rate, while ε determines the final tracking accuracy.

[0055] The preset performance conversion error function is defined as follows:

[0056]

[0057] Among them, y e p(y) represents the lateral deviation between the actual position and the desired path of the unmanned surface vessel. e ) is a variable that switches with error, defined as e l and e u The error boundary for time-varying decay can be expressed as: In the formula δ l and δ u These are the parameters to be selected.

[0058] To constrain the transient performance of the unmanned surface vessel, a simple preset performance guidance law was designed at the kinematic level, which is a preset performance guidance law for arctangent path tracking.

[0059] The arctangent preset performance line-of-sight guidance law is as follows:

[0060]

[0061] Where, γ d The path tangent angle, Let be the sideslip angle, u and v be the forward and lateral velocities defined in the unmanned surface vessel's coordinate system, and k be the lateral velocity. los The parameters to be selected are positive definite. The switching inequality is defined as follows:

[0062]

[0063]

[0064] In the formula, σ∈(0,1) are the conditional parameters selected by the control engineer. Let be the horizontal velocity. The guidance law switches when both of the above inequalities are satisfied simultaneously. The first inequality is a performance inequality, designed to ensure that the control can achieve the preset performance target. The second inequality is an initial condition judgment inequality, designed to avoid violating the preset performance limit at the initial moment after the switch.

[0065] Furthermore, the pre-defined virtual velocity law is designed as follows:

[0066]

[0067] Where, k ψ1 ζ is a control parameter. P It is a nonlinear transformation function. Its first derivative, ψ eThis represents the heading error.

[0068] Furthermore, the preset time-dynamic control law is designed as follows:

[0069]

[0070] Where, m ij f represents the element in the i-th row and j-th column of the inertia matrix. r (r) represents the hydrodynamic term, k ψ2 For control parameters, z ψ1 =ζ P (t)ψ e ζ is the preset time conversion error variable. P (t) is the preset time function, b is the design parameter, and z ψ2 =r-α r The speed tracking error is represented by r, which is the bow angular velocity defined in the unmanned surface vessel's coordinate system. For α r The first derivative, It is the unknown upper bound of the disturbance component d3 of the external environmental disturbance in the yaw degree of freedom. Robust adaptive estimation term.

[0071] Finally, the robust adaptive law is designed as follows:

[0072]

[0073] In the formula, λ r and Γ r The control parameters to be set are shown. Meanwhile, the upper bound estimation error of the disturbance can be defined as...

[0074] Implementation Case:

[0075] To verify the effectiveness of the arctangent control method described in this invention, a simulation experiment was conducted using an unmanned surface vessel (USV) as the simulation object: To fully verify the effectiveness of the designed arctangent algorithm, the USV was started from three different initial positions in the simulation. Position 1: [-2m, -4m, 10°] T Position 2: [-2m, 3m, 10°] T Position 3: [-2m, 8m, 10°] T .

[0076] Simulation results are as follows Figures 4-5 As shown, Figure 4 These are images showing the surface linear tracking performance of an unmanned surface vessel at different initial positions under the action of the arctangent preset performance guidance law. Figure 5This is a time-history curve of the tracking error under the action of the arctangent preset performance guidance law. The guidance law switching times for the three cases are 2.2 seconds, 0 seconds, and 5.9 seconds, respectively. It can be seen that although the unmanned surface vessel starts from different initial conditions, the switching conditions will be met over time, and the tracking error will always remain within the preset performance error limit after switching.

[0077] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for preset performance path tracking control of an underactuated unmanned surface vessel, characterized in that, include: First, error conversion was completed by combining preset performance functions, preset time functions, and preset performance conversion error functions, laying the foundation for subsequent controller design; Subsequently, an arctangent path tracking preset performance line-of-sight guidance law applicable to engineering practice was designed; Next, a preset performance virtual velocity law was designed and obtained; Finally, a preset time dynamics control law was designed based on robust adaptive technology to achieve precise path tracking control; The preset performance function is: ρ=(ρ0-ρ ∞ )e -κt +r ∞ Where ρ0 is the specified initial error limit, ρ ∞ κ represents the maximum allowable steady-state error during the steady-state phase, and κ is a constant to be set, the value of which determines the convergence rate. The preset time function is: In the formula, e is the natural constant, T is the convergence time preset by the control engineer, b>>ε>0 is the design parameter; the selection of σ determines the system error convergence rate, and ε determines the final tracking accuracy. The preset performance conversion error function is defined as follows: Among them, y e p(y) represents the lateral deviation between the actual position and the desired path of the unmanned surface vessel. e ) is a variable that switches with error, defined as e l and e u The error boundary for time-varying decay is denoted as: In the formula δ l and δ u These are the parameters to be selected; The designed arctangent path tracking line-of-sight guidance law has the following preset performance: Where, γ d The path tangent angle, Let be the sideslip angle, u and v be the forward and lateral velocities defined in the unmanned surface vessel's coordinate system, and k be the lateral velocity. los For the positive definite parameters to be selected, the switching inequality is defined as follows: In the formula, σ∈(0,1) are the conditional parameters selected by the control engineer. The horizontal plane velocity is given. When the above two inequalities are satisfied simultaneously, the guidance law will switch. The first inequality is a performance inequality, which aims to determine whether the control can achieve the preset performance target. The second inequality is an initial condition judgment inequality, which aims to avoid violating the preset performance limit at the initial moment after switching. The arctangent path tracking preset performance line-of-sight guidance law does not need to constrain the initial position as in the existing preset performance operation.

2. The underactuated unmanned surface vessel preset performance path tracking control method as described in claim 1, characterized in that, The designed preset performance virtual velocity law is as follows: Where, k ψ1 ζ is a control parameter. P It is a nonlinear transformation function. Its first derivative, ψ e This represents the heading error.

3. The underactuated unmanned surface vessel preset performance path tracking control method as described in claim 2, characterized in that, The designed preset time dynamics control law is as follows: Where, m ij f represents the element in the i-th row and j-th column of the inertia matrix. r (r) represents the hydrodynamic term, k Ψ2 For control parameters, z v1 =ζ P (t)ψ e ζ is the preset time conversion error variable. P (t) is the preset time function, b is the design parameter, and z ψ2 =r-α r The speed tracking error is represented by r, which is the bow angular velocity defined in the unmanned surface vessel's coordinate system. For α r The first derivative, It is the unknown upper bound of the disturbance component d3 of the external environmental disturbance in the yaw degree of freedom. Robust adaptive estimation term.

4. The underactuated unmanned surface vessel preset performance path tracking control method as described in claim 3, characterized in that, The designed robust adaptive law is as follows: In the formula, λ r and Γ r The control parameters to be set are defined as follows; meanwhile, the upper bound estimation error of the disturbance is defined as...

5. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the pre-defined performance path tracking control method for underactuated unmanned surface vessels as described in any one of claims 1 to 4.

6. A preset performance path tracking control system for an underactuated unmanned surface vessel, characterized in that, The invention includes the computer-readable storage medium as described in claim 5 and a processor, the processor being configured to invoke and process a computer program stored in the computer-readable medium.

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