Safety guided multi-tug stern thrusting ship-fixed time preset performance collaborative control method

Abstract

The application discloses a kind of safe guidance's multiple tug stern push is pushed ship fixed time preset performance coordination control method, the method includes constructing double virtual ship safety guidance mechanism, according to path tracking error combination construction fixed time preset performance function, the virtual control law of being pushed ship is designed to obtain the actual control law of being pushed ship;The actual control law of being pushed ship is distributed to stern push coordination system to obtain the push force of each tug acting on being pushed ship and the corresponding distribution direction of action by optimization;The desired pose vector of each tug is obtained to design the generalized force control law of each tug;The thrust amplitude and azimuth of each tug propeller are obtained by solving propeller optimization distribution problem model, and then the fixed time preset performance coordination control of multiple tug stern push being pushed ship based on safety guidance is realized.The application solves the problem that existing method is difficult to meet the rapid establishment of safe coordination configuration in tug auxiliary operation.

Description

Technical Field

[0001] This invention relates to the fields of ship control engineering, smart ports, unmanned tugboat collaborative operation, emergency maneuvering of pushed vessels, and ship safety obstacle avoidance control, and in particular to a safety-guided multi-tugboat stern-push-pushed vessel fixed-time preset performance collaborative control method. Background Technology

[0002] Existing control methods for intelligent ships at sea mainly focus on autonomous ship path tracking, automatic berthing, multi-ship convoy formation, and obstacle avoidance control. For unmanned vessels with their own propulsion capabilities, existing research typically uses methods such as backstepping control, sliding mode control, model predictive control, event-triggered control, or adaptive control to generate longitudinal forces, lateral forces, and yaw moments, thereby achieving path tracking and heading control. However, when a vessel being pushed loses its autonomous propulsion or maneuvering capabilities, its motion becomes entirely dependent on the forces and moments applied by external tugboats, making traditional single-ship control methods unusable directly.

[0003] In the field of multi-ship cooperative control, a large number of studies have focused on formation control, consistency control, and cooperative path tracking for ships interconnected by communication networks. These methods typically assume that each ship can independently generate its own control inputs, and that cooperation between ships is mainly achieved through communication topology. In contrast, multi-tugboat stern-push-pushed vessels are physically coupled systems where multiple tugboats need to jointly maneuver the same pushed vessel. Contact constraints, force transmission constraints, geometric configuration constraints, and actuator constraints exist between the tugboats and the pushed vessel. In tugboat-assisted maneuvering research, existing methods often simplify the tugboat's action to an ideal external force or use empirical rules for tugboat division of labor and force allocation. While some studies consider tugboat dynamics and propeller constraints, they often lack a unified framework of "safe guidance—generalized force generation—tugboat configuration generation—actuator allocation," making it difficult to simultaneously guarantee obstacle avoidance safety, fast convergence, error performance constraints, and the feasibility of real actuators. Furthermore, traditional obstacle avoidance methods such as artificial potential field methods and velocity obstacle methods are prone to problems in strongly coupled multi-tugboat systems, including local minima, over-reliance on kinematic simplification, or heavy online computational burdens. Traditional preset performance control can limit error boundaries, but most methods do not explicitly provide a fixed-time convergence guarantee independent of initial conditions, making it difficult to meet the requirements of quickly establishing a safe cooperative configuration in tugboat auxiliary operations.

[0004] In summary, the existing technologies mainly have the following drawbacks: 1) Existing multi-tugboat auxiliary maneuvering methods often lack a unified hierarchical framework and cannot simultaneously address issues such as the safety guidance of the pushed vessel, the generation of generalized forces, the distribution of tugboat action direction, tugboat tracking control, and the allocation of azimuth thrusters.

[0005] 2) Most existing obstacle avoidance guidance methods only modify the reference path at the kinematic level, making it difficult to provide a strict guarantee of the positive invariance of the safety set. When the pushed vessel and the tugboat approach the obstacle together, if the reference path lacks safety certification, it may cause the pushed vessel or the tugboat to enter the danger zone.

[0006] 3) While existing PPC methods can constrain tracking errors, their convergence speed typically depends on initial conditions, making it difficult to guarantee that the error will enter a small neighborhood within a preset time. For multi-tug stern thruster systems, if the relative error between the tug and the pushed vessel remains large for a long period, it will weaken the force transmission effect and affect maneuvering safety.

[0007] 4) Both the pushed vessel and the tugboat have unknown hydrodynamic terms and disturbances from wind, current and waves. If the controller relies on precise model parameters, its robustness in actual marine engineering applications will be insufficient.

[0008] 5) The generalized force generated by multiple tugboats must be achieved through the combined thrust and contact direction of each tugboat, while each tugboat needs to generate its own generalized torque through its port and starboard azimuth thrusters. Without considering the constraints on thrust amplitude, azimuth range, and azimuth rate of change, the control input is difficult to directly apply to actual tugboats.

[0009] To address the aforementioned issues, there is an urgent need to propose a safety-guided multi-tugboat stern thruster-assisted pusher vessel with fixed-time preset performance collaborative control method. This method aims to solve the problems of safe path tracking, rapid error convergence, force distribution, and actuator control of the multi-tugboat-assisted pusher vessel in obstacle environments. Summary of the Invention

[0010] This invention provides a method for coordinated control of the performance of a multi-tugboat stern thruster-pushed vessel at a fixed time, in order to overcome the aforementioned technical problems.

[0011] To achieve the above objectives, the technical solution of the present invention is as follows: A method for coordinated control of the performance of a multi-tugboat stern thruster-pushed vessel with fixed-time preset parameters, specifically including the following steps: S1: Obtain a stern thrust coordination system consisting of a pushed vessel and several tugboats; S2: Construct a dual-virtual-ship safety guidance mechanism based on a guided virtual ship and a safety virtual ship, and obtain the safety reference state of the pushed ship according to the dual-virtual-ship safety guidance mechanism; S3: Based on the stern thruster cooperative system, define the path tracking error of the pushed vessel according to the safety reference state; design the virtual control law of the pushed vessel based on the path tracking error and the constructed fixed-time preset performance function; define the speed error based on the virtual control law of the pushed vessel, and use an RBF neural network to approximate the unknown hydrodynamic term to obtain the actual control law of the pushed vessel. S4: The actual control law of the vessel to be pushed is optimized and distributed to the stern thrust coordination system to obtain the thrust force of each tugboat acting on the vessel to be pushed and the corresponding distribution direction. S5: Based on the assigned action direction and the safety reference state, obtain the desired pose vector of each tugboat; define the tugboat tracking error based on the desired pose vector; design the virtual speed of each tugboat based on the tugboat tracking error to define the tugboat speed error; design the generalized force control law of each tugboat based on the tugboat speed error and the constructed robust compensation function. S6: Based on the generalized force control law and the thrust of the pushed vessel, construct a propeller optimization allocation problem model, and obtain the thrust amplitude and azimuth angle of each tugboat propeller by solving the propeller optimization allocation problem model, thereby realizing fixed-time preset performance coordinated control of multiple tugboats pushing the pushed vessel based on safety guidance.

[0012] Furthermore, the expression for the stern thruster cooperative system described in S1 is:

[0013] In the formula: Indicates the ship's position and heading and Indicates the vessel being pushed. Indicates the first tugboat; This indicates the ship's longitudinal speed, lateral speed, and bow roll rate; This represents the generalized control inputs of a ship; Represents unknown hydrodynamic nonlinear terms; Indicates external environmental disturbances; Indicates the first The jacking force exerted by a tugboat on the vessel being pushed; express The direction of action relative to the coordinate system of the ship being pushed and ; Indicates the first The bow direction of the tugboat; Indicates the heading of the vessel being pushed; Represents the equivalent inertial parameters of a ship; express The first derivative; express The first derivative; Generalized control inputs of the pushed vessel for:

[0014] In the formula: This indicates that the nth tugboat provides thrust in both the bow and lateral directions. Indicates the first The position of the jacking point relative to the center of gravity of the vessel being jacked; Indicates the first The position of the jacking point relative to the center of gravity of the vessel being jacked; No. Generalized control inputs of a tugboat for:

[0015] In the formula: They represent the first The thrust amplitude and azimuth angle of the port and starboard thrusters of the tugboat; They represent the first The installation positions of the left and right thrusters of the tugboat.

[0016] Furthermore, the dual-virtual-ship safety guidance mechanism constructed in S2, based on the guided virtual ship and the safety virtual ship, is specifically as follows: S21: Obtain the kinematic model of the guided virtual ship as follows:

[0017] In the formula: These represent the position and heading of the guided virtual ship, respectively. These represent the planned speed and bow roll rate at the waypoint, respectively. express The first derivative; The kinematic model of the safe virtual ship is obtained as follows:

[0018]

[0019] In the formula: Represents the safe virtual ship position vector first derivative and ; Indicates the location of the safe virtual ship; Represents the velocity vector of the safe virtual ship and ; This indicates the longitudinal and lateral speeds of the virtual ship in the safety configuration. This represents the turning angular velocity of the virtual ship. Represents the transformation matrix; Indicates the heading of the virtual safe ship; express The first derivative; S22: Define the safety function based on the stern thrust cooperative system. for:

[0020] In the formula: Indicates the first The location of the obstacle; Indicates a safe distance; S23: Based on security functions Combining S21, the quadratic programming model is constructed as follows:

[0021]

[0022] In the formula: Indicates the safe guided ship speed after secondary planning and = ; This indicates the longitudinal speed, lateral speed, and bow roll rate of the safety-guided vessel after secondary planning. Indicates the current safe speed of the guided vessel; This indicates the guidance commands obtained from the guided virtual ship and ; This represents a positive definite weight matrix; , Indicates speed constraint; Indicates safety adjustment parameters and ; express The first derivative; Indicates constraints; S24: Solve the quadratic programming model to obtain the safe reference state of the pushed vessel:

[0023]

[0024]

[0025]

[0026] In the formula: Indicates the safety reference status of the vessel being pushed; Indicates a safe reference position; Indicates the safe reference heading; express The first derivative; This indicates the ship's position and heading obtained from the safe guided speed after secondary planning.

[0027] Furthermore, step S3 specifically includes the following steps: S31: Based on the stern thruster coordination system, the path tracking error of the pushed vessel is defined according to the safety reference state as follows:

[0028] In the formula: This represents the path tracking position error and heading error; This represents the transpose of the rotation matrix; Indicates the position and heading of the vessel being pushed; S32: Construct a fixed-time preset performance function for:

[0029] In the formula: Indicates the initial error; Indicates steady-state error; Indicates the preset convergence time; Indicate design parameters; Represents a time variable; S33: Preset performance function based on fixed time. Obtaining normalized error With transformation error for:

[0030] In the formula: Represents the path tracking error vector and = ; S34: Based on S33 and the fixed-time preset performance function constructed according to the path tracking error, a virtual control law for the pushed vessel is designed. for:

[0031] In the formula: This represents the desired longitudinal velocity and desired bow roll rate of the vessel being pushed. This represents the preset performance function obtained from S32 for the ship's position and heading; Indicates the normalization error; Design parameters representing positive gain; This represents a preset error transformation function; Indicate design parameters; Indicates the transformation error; express The first derivative; S35: Define the speed error based on the virtual control law of the pushed vessel. for:

[0032] In the formula: This indicates the longitudinal velocity, lateral velocity, and bow roll rate of the vessel being pushed. An RBF neural network is used to approximate the unknown hydrodynamic terms in the stern thruster cooperative system, and this is combined with the aforementioned velocity error. With the virtual control law To obtain the actual control law of the pushed vessel for:

[0033] 1

[0034] 1

[0035] 1

[0036]

[0037] In the formula: The equivalent inertial parameters representing the longitudinal, lateral, and bow-rolling directions of the pushed vessel; express The first derivative; This represents the estimated value of the adaptive parameters; express The first derivative; Indicate design parameters; Design parameters representing positive gain; Indicates the initial value of the adaptive parameters; This represents the neural network compression function.

[0038] Furthermore, step S4 specifically includes the following steps: S41: Construct an optimal allocation model for optimizing the actual control law allocation of the pushed vessel as follows:

[0039]

[0040] In the formula: Indicates the total number of tugboats; Indicates the weighting parameter; express The baseline value; express The upper bound of the rate of change; Indicates a time interval; This represents the total cost function; express The upper bound; S42: Solve the actual control law of the vessel being pushed by the optimized allocation model, and optimize its allocation to the stern thrust coordination system to obtain the thrusting force exerted by each tugboat on the vessel being pushed. and the corresponding distribution direction .

[0041] Furthermore, S5 specifically includes the following steps: S51: Based on the assigned action direction and the safety reference state, the expected pose vector of each tugboat is obtained as follows:

[0042]

[0043]

[0044] In the formula: The first point is calculated from the desired contact point. Desired coordinates of the center of gravity of the tugboat; Indicates the first The expected bow direction of the tugboat; Indicates the first The desired pose vector of the tugboat; Indicates the first The expected coordinates of the center of gravity of the tugboat; Represents the rotation matrix; Indicates the first The x and y coordinates of a tugboat from its center of gravity to the point of jacking; S52: The tugboat tracking error is defined as follows based on the desired pose vector:

[0045] In the formula: Indicates the first The actual position and heading of the tugboat; Represents the coordinate transformation matrix; This represents longitudinal tracking error, lateral tracking error, and bow tracking error; S53: The virtual speed of each tugboat is designed based on the tugboat tracking error as follows:

[0046]

[0047]

[0048]

[0049] In the formula: This indicates that the information obtained by S32 is for the first... tugboat Preset performance functions for each error channel; express The abbreviated form; They represent the first The virtual longitudinal velocity, virtual lateral velocity, and virtual bow roll rate of the tugboat; Indicates a positive control gain; These represent the desired longitudinal velocity and the desired bow roll rate, respectively. Indicate design parameters and , ; Indicates correspondence Normalization error; Indicates correspondence Transformation error; Denotes the tugboat tracking error vector and = ; express The first derivative; S54: Tugboat speed error defined based on S53 for:

[0050] Define the actual velocity vector With virtual velocity vector for:

[0051] Based on the actual velocity vector With virtual velocity vector Construct a robust compensation function for:

[0052] In the formula: Indicates the first tugboat The basis function vectors of the RBF neural network with each channel; Represents a known nonnegative function relating to the speed of the tugboat; S55: Based on the tugboat speed error and the constructed robust compensation function, the generalized force control law for each tugboat is designed as follows:

[0053]

[0054]

[0055]

[0056]

[0057]

[0058] In the formula: They represent the first The longitudinal generalized force, lateral generalized force, and bow moment required for a tugboat; Indicates the first Equivalent inertial parameters of a tugboat in the longitudinal, lateral, and bow-rolling directions; This represents an estimate of the adaptive parameters; Indicates a positive control gain; Indicates the adaptive gain parameter; Indicates the leakage coefficient; Indicates the initial value of the adaptive parameters; express The first derivative; express The first derivative.

[0059] Furthermore, the thruster optimization allocation problem model constructed in S6 is as follows:

[0060]

[0061]

[0062]

[0063]

[0064]

[0065]

[0066]

[0067] In the formula: They represent the first The thrust amplitude of the two propellers of the tugboat; These represent the azimuth angles of the two thrusters; They represent the first The installation positions of the two propellers of the tugboat in the tugboat's hull coordinate system; This represents the generalized force actually generated by the propulsion system on the tugboat. Indicates the thrust force of the vessel being pushed; Indicates the optimization weights; This indicates the thruster azimuth angle at the previous sampling time; This indicates the maximum thrust of the propulsion unit; This represents the rate of change of the maximum azimuth angle; Indicates the sampling time interval; This represents the objective function of the thruster optimization allocation problem model.

[0068] The present invention provides a method for coordinated control of the performance of a multi-tugboat stern thruster-pushed vessel at a fixed time, with the following beneficial effects: (1) To address the safety guidance problem of pushed ships, a dual virtual ship safety guidance mechanism is constructed based on the guidance virtual ship GVS and the safety virtual ship SVS. The guidance virtual ship GVS generates a trajectory reference based on waypoints, and the safety virtual ship SVS corrects the trajectory guidance command online through a quadratic planning safety filter, so that the original reference remains unchanged when the obstacle avoidance constraint is not activated, and a safety reference trajectory is generated with minimal intervention when the safety constraint is activated.

[0069] (2) To address the issues of slow convergence of path tracking error and insufficient boundary constraints of the pushed vessel, a fixed-time preset performance controller, i.e., the virtual control law of the pushed vessel, is designed based on the path tracking error combined with the constructed fixed-time preset performance function. This ensures that the longitudinal error, lateral error, and heading error are always kept within the preset performance boundary and converge to a small residual set within a fixed time independent of the initial conditions.

[0070] (3) To address unknown hydrodynamic and external disturbance problems, an RBF neural network and an adaptive law of compression parameters (robust compensation function) are introduced to compensate for unknown nonlinear terms and disturbances online, thereby improving the robustness of the controller and reducing the number of learning parameters.

[0071] (4) To address the actual constraints of multiple tugboats and propellers, a method based on the generalized force control law and contact direction optimization allocation is designed. Furthermore, a propeller optimization allocation problem model corresponding to each tugboat is constructed. By solving the propeller optimization allocation problem model, the thrust amplitude and azimuth angle of each tugboat propeller are obtained. This enables multiple tugboats to assist the pushed vessel in obstacle environments, thereby improving the accuracy of safe path tracking control, fast error convergence, force distribution, and effective collaborative control of actuators. Attached Figure Description

[0072] 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.

[0073] Figure 1A flowchart illustrating the method for coordinated control of the performance of a multi-tugboat stern thruster-pusher vessel with fixed-time preset parameters, as described in this invention. Figure 2 This is a schematic diagram of the coordinate relationship of the multi-tugboat stern thruster and the pushed vessel cooperative system in this embodiment; Figure 3 This is a core technology block diagram of the method described in this embodiment; Figure 4 This is a schematic diagram of the guidance framework for the safe virtual ship in this embodiment; Figure 5 This is a safety coordination trajectory diagram of the multiple tugboats' stern thrusters pushing the vessel in this embodiment; Figure 6 This is a graph showing the tracking error curves of the pushed vessel and the tugboat in this embodiment; Figure 7 This is a comparison curve of the expected generalized force and the generalized force after allocation in this embodiment; Figure 8 This is a graph showing the tugboat's top thrust versus the propeller's thrust in this embodiment; Figure 9 This is a graph showing the distance between the pushed vessel and tugboat and the obstacle in this embodiment. Detailed Implementation

[0074] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0075] This embodiment provides a safety-guided multi-tugboat stern thruster-assisted, fixed-time preset performance coordinated control method for the pushed vessel, such as... Figures 1 to 3 The specific steps shown are as follows: S1: Obtain a stern thrust coordination system consisting of a pushed vessel and several tugboats; Specifically, this embodiment considers a surface vessel that is under-propulsion and is being pushed. A coordinated stern thrust system consisting of 3 azimuth tugboats enables... Indicates the vessel being pushed. Indicates the first The three-degree-of-freedom motion model of a tugboat can be uniformly described as follows:

[0076] In the formula: Indicates the ship's position and heading and Indicates the vessel being pushed. Indicates the first tugboat; This indicates the ship's longitudinal speed, lateral speed, and bow roll rate; This represents the generalized control inputs of a ship; Represents unknown hydrodynamic nonlinear terms; Indicates external environmental disturbances; Indicates the first The jacking force exerted by a tugboat on the vessel being pushed; express The direction of action relative to the coordinate system of the ship being pushed and ; Indicates the first The bow direction of the tugboat; Indicates the heading of the vessel being pushed; Represents the equivalent inertial parameters of a ship; express The first derivative; express The first derivative; Generalized control inputs of the pushed vessel for:

[0077] In the formula: This indicates that the nth tugboat provides thrust in both the bow and lateral directions. Indicates the first The position of the jacking point relative to the center of gravity of the vessel being jacked; Indicates the first The position of the jacking point relative to the center of gravity of the vessel being jacked; No. Generalized control inputs of a tugboat for:

[0078] In the formula: They represent the first The thrust amplitude and azimuth angle of the port and starboard thrusters of the tugboat; They represent the first The installation positions of the left and right thrusters of the tugboat.

[0079] S2: Construct a dual-virtual-ship safety guidance mechanism based on a guided virtual ship and a safety virtual ship, and obtain the safety reference state of the pushed ship according to the dual-virtual-ship safety guidance mechanism; Specifically, the dual virtual ship safety guidance mechanism constructed in this embodiment is as follows: S21: Obtain the kinematic model of the guided virtual ship GVS as follows:

[0080] In the formula: These represent the position and heading of the guided virtual ship, respectively. These represent the planned speed and bow roll rate at the waypoint, respectively. express The first derivative; The kinematic model of the safe virtual ship SVS is obtained as follows:

[0081]

[0082] In the formula: Represents the safe virtual ship position vector first derivative and ; Indicates the location of the safe virtual ship; Represents the velocity vector of the safe virtual ship and ; This indicates the longitudinal and lateral speeds of the virtual ship in the safety configuration. This represents the turning angular velocity of the virtual ship. Represents the transformation matrix; Indicates the heading of the virtual safe ship; express The first derivative; SVS is used to generate security authentication references, such as Figure 4 As shown; S22: Define the safety function based on the stern thrust cooperative system. for:

[0083] In the formula: Indicates the first The location of the obstacle; Indicates a safe distance; S23: Based on security functions Combining S21, the quadratic programming model is constructed as follows:

[0084]

[0085] In the formula: Indicates the safe guided ship speed after secondary planning and = ; This indicates the longitudinal speed, lateral speed, and bow roll rate of the safety-guided vessel after secondary planning. Indicates the current safe speed of the guided vessel; This indicates the guidance commands obtained from the guided virtual ship and ; This represents a positive definite weight matrix; , Indicates speed constraint; Indicates safety adjustment parameters and ; express The first derivative; Indicates constraints; S24: Solve the quadratic programming model to obtain the safe reference state of the pushed vessel:

[0086]

[0087]

[0088]

[0089] In the formula: Indicates the safety reference status of the vessel being pushed; Indicates a safe reference position; Indicates the safe reference heading; express The first derivative; This indicates the ship's position and heading obtained from the safe guided speed after secondary planning.

[0090] S3: Based on the stern thruster cooperative system, the path tracking error of the pushed vessel is defined according to the safety reference state; based on the path tracking error and a constructed fixed-time preset performance function, a virtual control law for the pushed vessel is designed; based on the virtual control law of the pushed vessel, the velocity error is defined, and an RBF neural network is used to approximate the unknown hydrodynamic term to obtain the actual control law of the pushed vessel. The specific steps include: S31: Based on the stern thruster coordination system, the path tracking error of the pushed vessel is defined according to the safety reference state as follows:

[0091] In the formula: This represents the path tracking position error and heading error; This represents the transpose of the rotation matrix; Indicates the position and heading of the vessel being pushed; S32: To ensure that the error enters the small neighborhood within a preset time, a fixed-time preset performance function is constructed. for:

[0092] In the formula: Indicates the initial error; Indicates steady-state error; Indicates the preset convergence time; Indicate design parameters; Represents a time variable; S33: Preset performance function based on fixed time. Obtaining normalized error With transformation error for:

[0093] In the formula: Represents the path tracking error vector and = ; when Sometimes, From error dynamics, we can obtain:

[0094] S34: Based on S33 and the fixed-time preset performance function constructed according to the path tracking error, a virtual control law for the pushed vessel is designed. for:

[0095] In the formula: This represents the desired longitudinal velocity and desired bow roll rate of the vessel being pushed. This represents the preset performance function obtained from S32 for the ship's position and heading; Indicates the normalization error; Design parameters representing positive gain; This represents a preset error transformation function; Indicate design parameters; Indicates the transformation error; express The first derivative; S35: Define the speed error based on the virtual control law of the pushed vessel. for:

[0096] In the formula: This indicates the longitudinal velocity, lateral velocity, and bow roll rate of the vessel being pushed. An RBF neural network is used to approximate the unknown hydrodynamic terms in the stern thruster cooperative system, and its expression is as follows:

[0097] In the formula: Represents a radial basis function neural network; Represents radial basis functions; Represents the optimal weight matrix; Indicates the approximation error; Represents the dynamic surface control approximation term; The norm of the optimal weight matrix is ​​represented. Indicate design parameters; Based on neural network approximation and robust bound design, by incorporating the aforementioned velocity error With the virtual control law To obtain the actual control law of the pushed vessel for:

[0098] The adaptive law corresponding to the actual control law of the pushed vessel is: 1

[0099] 1

[0100] 1

[0101]

[0102] In the formula: The equivalent inertial parameters representing the longitudinal, lateral, and bow-rolling directions of the pushed vessel; express The first derivative; This represents the estimated value of the adaptive parameters; express The first derivative; Indicate design parameters; Design parameters representing positive gain; Indicates the initial value of the adaptive parameters; This represents the neural network compression function.

[0103] S4: Optimize and distribute the actual control law of the vessel to be pushed to the stern thrust coordination system to obtain the thrusting force exerted by each tugboat on the vessel to be pushed and the corresponding distribution direction. This includes the following steps: S41: Construct an optimal allocation model for optimizing the actual control law allocation of the pushed vessel as follows:

[0104]

[0105] In the formula: Indicates the total number of tugboats; Indicates the weighting parameter; express The baseline value; express The upper bound of the rate of change; Indicates a time interval; This represents the total cost function; express The upper bound; S42: Solve the actual control law of the vessel being pushed by the optimized allocation model, and optimize its allocation to the stern thrust coordination system to obtain the thrusting force exerted by each tugboat on the vessel being pushed. and the corresponding distribution direction The purpose of this embodiment is to establish an optimization allocation model for optimizing the allocation of actual control laws. The solution method or process is a known existing technical means and is not the inventive point of this application. Therefore, the solution process will not be described in detail here.

[0106] S5: Based on the assigned action direction and the safety reference state, obtain the desired pose vector of each tugboat; define the tugboat tracking error based on the desired pose vector; design the virtual velocity of each tugboat based on the tugboat tracking error to define the tugboat velocity error; design the generalized force control law of each tugboat based on the tugboat velocity error and the constructed robust compensation function, specifically including the following steps: S51: Based on the assigned action direction and the safety reference state, the expected pose vector of each tugboat is obtained as follows:

[0107]

[0108]

[0109] In the formula: The first point is calculated from the desired contact point. Desired coordinates of the center of gravity of the tugboat; Indicates the first The expected bow direction of the tugboat; Indicates the first The desired pose vector of the tugboat; Indicates the first The expected coordinates of the center of gravity of the tugboat; Represents the rotation matrix; Indicates the first The x and y coordinates of the tugboat from its center of gravity to the point of final push; in this embodiment, for the tugboat... The optimal distribution of thrust and direction of action of the tugboats are denoted as follows: and .in, Indicates the first The tugboat needs to apply a contact thrust to the vessel being pushed. This indicates the direction of the thrust relative to the coordinate system of the vessel being pushed. To ensure the tugboat maintains the correct pushing configuration, the direction is determined based on the desired bow direction of the vessel being pushed. The direction of action obtained from the allocation , generate the first The expected heading and expected condition of the tugboat; S52: The tugboat tracking error is defined as follows based on the desired pose vector:

[0110] In the formula: Indicates the first The actual position and heading of the tugboat; Represents the coordinate transformation matrix; This represents longitudinal tracking error, lateral tracking error, and bow tracking error; S53: The virtual speed of each tugboat is designed based on the tugboat tracking error as follows:

[0111] In the formula: when At that time, the tracking error is limited within the preset performance boundary. Based on the fixed-time preset performance control concept, the virtual speed of each tugboat is designed as follows:

[0112]

[0113]

[0114] In the formula: This indicates that the information obtained by S32 is for the first... tugboat Preset performance functions for each error channel; express The abbreviated form; They represent the first The virtual longitudinal velocity, virtual lateral velocity, and virtual bow roll rate of the tugboat; Indicates a positive control gain; These represent the desired longitudinal velocity and the desired bow roll rate, respectively. Indicate design parameters and , ; Indicates correspondence Normalization error; Indicates correspondence Transformation error; Denotes the tugboat tracking error vector and = ; express The first derivative; S54: Tugboat speed error defined based on S53 for:

[0115] Define the actual velocity vector With virtual velocity vector for:

[0116] In this embodiment, an RBF neural network and an adaptive law for compression parameters are used to compensate for the first... The unknown hydrodynamics and external disturbances of the tugboat, i.e., based on the actual velocity vector With virtual velocity vector Constructing a robust compensation function for:

[0117] In the formula: Indicates the first tugboat The basis function vectors of the RBF neural network with each channel; Represents a known nonnegative function relating to the speed of the tugboat; S55: Based on the tugboat speed error and the constructed robust compensation function, the generalized force control law for each tugboat is designed as follows:

[0118]

[0119]

[0120] The adaptive law corresponding to the generalized force control law is:

[0121]

[0122]

[0123] In the formula: They represent the first The longitudinal generalized force, lateral generalized force, and bow moment required for a tugboat; Indicates the first Equivalent inertial parameters of a tugboat in the longitudinal, lateral, and bow-rolling directions; This represents an estimate of the adaptive parameters; Indicates a positive control gain; Indicates the adaptive gain parameter; Indicates the leakage coefficient; Indicates the initial value of the adaptive parameters; express The first derivative; express The first derivative.

[0124] S6: In order to generalize the force of tugboats Converting this into actual azimuth thruster commands, the following thruster optimization allocation problem is established: based on the generalized force control law and the thrust of the pushed vessel, the thruster optimization allocation problem model is constructed as follows:

[0125]

[0126] The constraints are:

[0127]

[0128]

[0129]

[0130]

[0131]

[0132] In the formula: They represent the first The thrust amplitude of the two propellers of the tugboat; These represent the azimuth angles of the two thrusters; They represent the first The installation positions of the two propellers of the tugboat in the tugboat's hull coordinate system; This represents the generalized force actually generated by the propulsion system on the tugboat. Indicates the thrust force of the vessel being pushed; Indicates the optimization weights; This indicates the thruster azimuth angle at the previous sampling time; This indicates the maximum thrust of the propulsion unit; This represents the rate of change of the maximum azimuth angle; Indicates the sampling time interval; This represents the objective function of the thruster optimization allocation problem model; By solving the propeller optimization allocation problem model, the thrust amplitude and azimuth angle of each tugboat propeller are obtained, realizing the engineering execution of the multi-tugboat collaborative jacking control input, and thus realizing the fixed-time preset performance collaborative control of the multi-tugboat stern-pushed vessel based on safety guidance.

[0133] This embodiment also includes constructing a composite Lyapunov function for the pushed vessel and the tugboat in the stability analysis. By combining fixed-time preset performance error transformation, RBF neural network adaptive law, and robust term design, we can obtain:

[0134] According to the fixed-time stability lemma, the closed-loop error system is actually stable in a fixed time, and the upper bound of the convergence time does not depend on the initial conditions. When the quadratic programming safety filter is always feasible, the compact safety set where the SVS is located remains positive. Combined with the preset performance tracking error boundary, it can be guaranteed that the actual position of the pushed ship is always within the safety set.

[0135] To verify the effectiveness of the method described in this embodiment, two sets of simulation experiments were conducted using MATLAB: the first set was a multi-tugboat cooperative push-to-avoidance navigation experiment, used to verify the safety, tracking, and actuator feasibility of the complete hierarchical framework; the second set was compared with the existing PPC method to verify the transient performance and convergence speed advantages of fixed-time preset performance control.

[0136] In Experiment 1, the main parameters of the vessel being pushed and the tugboat were the same set of ship model parameters. The vessel being pushed was 105m long, 18m wide, had an average draft of 5.4m, and a displacement volume of 5710.2 m³; the tugboat was 28m long, 12m wide, had an average draft of 4.95m, and a displacement volume of 659 m³. Waypoints were set as follows: , , and The desired guidance velocity is 1 m / s. The two jacking points are set as follows: m and m, the tugboat contact point offset is m. The maximum thrust of each tugboat is N, azimuth angular velocity constraint is .

[0137] Figure 5 The cooperative trajectories of the pushed vessel and tugboats are presented when obstacle constraints are present. Blue dots represent obstacle locations, yellow circles represent the nominal safety domain of the obstacle, and brown annular areas represent the extended safety margin considering the overall dimensions of the pushed vessel and tugboats. It can be seen that the safety virtual ship guidance layer can smoothly correct the reference path near the obstacle and gradually return the trajectory to the original waypoint path after obstacle avoidance; the pushed vessel and both tugboats remain outside the safety zone.

[0138] Figure 6The tracking errors of the pushed vessel and the tugboat are given. It can be seen that the longitudinal error, lateral error, and heading error are all limited within the preset performance boundaries, indicating that the fixed-time preset performance controller can guarantee the transient and steady-state accuracy of the entire cooperative system. Figure 7 A comparison between the expected generalized force and the actual generalized force after allocation is presented. Due to the existence of thrust and azimuth angular velocity constraints, a certain allocation error will occur in the rapid transient phase, but this error does not violate the preset performance boundary.

[0139] Figure 8 The top thrust and propeller thrust curves of the tugboat are presented, and the results show that the distribution of upper-level forces and the distribution of tugboat actuators can output control inputs that meet physical constraints. Figure 9 The distances between the pushed vessel and the tugboat and the obstacle were given, and all distances remained above the safety threshold, verifying the effectiveness of safety guidance and tracking error margin in ensuring the safety of actual vessels.

[0140] Based on the simulation results above, compared with existing technologies, the beneficial effects of the method described in this embodiment are as follows: 1) By using a dual-virtual-ship safety guidance mechanism based on a guided virtual ship and a safety virtual ship, and a quadratic planning safety filter, a safety certification reference path can be generated without disrupting the smoothness of the nominal waypoint guidance, and the safety set remains positive.

[0141] 2) By using fixed-time preset performance control, the tracking error of the pushed vessel and tugboat is always kept within the preset performance boundary and enters the small neighborhood within a fixed time independent of the initial conditions, which improves the problem of unclear convergence speed of the traditional PPC method.

[0142] 3) By using RBF neural networks and adaptive compression parameter laws to compensate for unknown hydrodynamics and disturbances, the dependence on accurate ship model parameters is reduced, and the robustness under wind, current and wave disturbance environments is improved.

[0143] 4) Through the generalized force control law and contact direction distribution, coordinated thrust sharing among multiple tugboats is achieved; through the distribution of the bottom-level azimuth thrusters, the generalized force of the tugboats is transformed into... It meets the limitations of thrust, angle, and angular velocity.

[0144] 5) The method described in this embodiment can simultaneously achieve safe obstacle avoidance, rapid error convergence, cooperative configuration maintenance, and actuator control, and is applicable to engineering scenarios such as disabled vessel rescue, emergency towing in port, unmanned tugboat cooperative berthing, and safe operation of intelligent ports.

[0145] 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; and these 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 coordinated control of the performance of a multi-tugboat stern thruster-pushed vessel at a fixed time, characterized in that: The specific steps include: S1: Obtain a stern thrust coordination system consisting of a pushed vessel and several tugboats; S2: Construct a dual-virtual-ship safety guidance mechanism based on a guided virtual ship and a safety virtual ship, and obtain the safety reference state of the pushed ship according to the dual-virtual-ship safety guidance mechanism; S3: Based on the stern thruster cooperative system, define the path tracking error of the pushed vessel according to the safety reference state; and design the virtual control law of the pushed vessel based on the path tracking error and the constructed fixed-time preset performance function. The speed error is defined based on the virtual control law of the pushed vessel, and the unknown hydrodynamic term is approximated using an RBF neural network to obtain the actual control law of the pushed vessel. S4: The actual control law of the vessel to be pushed is optimized and distributed to the stern thrust coordination system to obtain the thrust force of each tugboat acting on the vessel to be pushed and the corresponding distribution direction. S5: Based on the assigned action direction and the safety reference state, obtain the desired pose vector of each tugboat; define the tugboat tracking error based on the desired pose vector; design the virtual speed of each tugboat based on the tugboat tracking error to define the tugboat speed error; design the generalized force control law of each tugboat based on the tugboat speed error and the constructed robust compensation function. S6: Based on the generalized force control law and the thrust of the pushed vessel, construct a propeller optimization allocation problem model, and obtain the thrust amplitude and azimuth angle of each tugboat propeller by solving the propeller optimization allocation problem model, thereby realizing fixed-time preset performance coordinated control of multiple tugboats pushing the pushed vessel based on safety guidance.

2. The method for coordinated control of the performance of a multi-tugboat stern thruster-pushed vessel with fixed-time preset according to claim 1, characterized in that, The expression for the stern thruster cooperative system described in S1 is: In the formula: Indicates the ship's position and heading and Indicates the vessel being pushed. Indicates the first tugboat; This indicates the ship's longitudinal speed, lateral speed, and bow roll rate; This represents the generalized control inputs of a ship; Represents unknown hydrodynamic nonlinear terms; Indicates external environmental disturbances; Indicates the first The jacking force exerted by a tugboat on the vessel being pushed; express The direction of action relative to the coordinate system of the ship being pushed and ; Indicates the first The bow direction of the tugboat; Indicates the heading of the vessel being pushed; Represents the equivalent inertial parameters of a ship; express The first derivative; express The first derivative; Generalized control inputs of the pushed vessel for: In the formula: This indicates that the nth tugboat provides thrust in both the bow and lateral directions. Indicates the first The position of each jacking point relative to the center of gravity of the vessel being jacked; Indicates the first The position of each jacking point relative to the center of gravity of the vessel being jacked; No. Generalized control inputs of a tugboat for: In the formula: They represent the first The thrust amplitude and azimuth angle of the port and starboard thrusters of the tugboat; They represent the first The installation positions of the port and starboard thrusters of the tugboat.

3. A method for coordinated control of the performance of a multi-tugboat stern thruster-pushed vessel with fixed-time preset according to claim 2, characterized in that, The dual-virtual-ship safety guidance mechanism constructed in S2, based on a guided virtual ship and a safety virtual ship, is as follows: S21: Obtain the kinematic model of the guided virtual ship as follows: In the formula: These represent the position and heading of the guided virtual ship, respectively. These represent the planned speed and bow roll rate at the waypoint, respectively. express The first derivative; The kinematic model of the safe virtual ship is obtained as follows: In the formula: Represents the position vector of the safe virtual ship first derivative and ; Indicates the location of the safe virtual ship; Describes the velocity vector of the safe virtual ship and ; This indicates the longitudinal and lateral speeds of the virtual ship in safety. This represents the turning angular velocity of the virtual ship. Represents the transformation matrix; Indicates the heading of the virtual safe ship; express The first derivative; S22: Define the safety function based on the stern thruster cooperative system. for: In the formula: Indicates the first The location of the obstacle; Indicates a safe distance; S23: Based on security functions Combining S21, the quadratic programming model is constructed as follows: In the formula: Indicates the safe guided ship speed after secondary planning and = ; This indicates the longitudinal speed, lateral speed, and bow roll rate of the safety-guided vessel after secondary planning. Indicates the current safe speed of the guided vessel; This indicates the guidance commands obtained from the guided virtual ship and ; This represents a positive definite weight matrix; , Indicates speed constraint; Indicates safety adjustment parameters and ; express The first derivative; Indicates constraints; S24: Solve the quadratic programming model to obtain the safe reference state of the pushed vessel: In the formula: Indicates the safety reference status of the vessel being pushed; Indicates a safe reference position; Indicates the safe reference heading; express The first derivative; This indicates the ship's position and heading obtained from the safe guided speed after secondary planning.

4. The method for coordinated control of the performance of a multi-tugboat stern thruster-pushed vessel with fixed-time preset according to claim 3, characterized in that, S3 specifically includes the following steps: S31: Based on the stern thruster coordination system, the path tracking error of the pushed vessel is defined according to the safety reference state as follows: In the formula: This represents the path tracking position error and heading error; This represents the transpose of the rotation matrix; Indicates the position and heading of the vessel being pushed; S32: Construct a fixed-time preset performance function for: In the formula: Indicates the initial error; Indicates steady-state error; Indicates the preset convergence time; Indicate design parameters; Represents a time variable; S33: Preset performance function based on fixed time. Obtaining normalized error With transformation error for: In the formula: Represents the path tracking error vector and = ; S34: Based on S33 and the fixed-time preset performance function constructed according to the path tracking error, a virtual control law for the pushed vessel is designed. for: In the formula: This represents the desired longitudinal velocity and desired bow roll rate of the vessel being pushed. This represents the preset performance function obtained from S32 for the ship's position and heading; Indicates the normalization error; Design parameters representing positive gain; This represents the preset error transformation function; Indicate design parameters; Indicates the transformation error; express The first derivative; S35: Define the speed error based on the virtual control law of the pushed vessel. for: In the formula: This indicates the longitudinal velocity, lateral velocity, and bow roll rate of the vessel being pushed. An RBF neural network is used to approximate the unknown hydrodynamic terms in the stern thruster cooperative system, and this is combined with the aforementioned velocity error. With the virtual control law To obtain the actual control law of the pushed vessel for: 1 1 1 In the formula: The equivalent inertial parameters representing the longitudinal, lateral, and bow-rolling directions of the pushed vessel; express The first derivative; This represents the estimated value of the adaptive parameters; express The first derivative; Indicate design parameters; Design parameters representing positive gain; Indicates the initial value of the adaptive parameters; This represents a neural network compression function; This represents the radial basis function of the RBF neural network.

5. A method for coordinated control of the performance of a multi-tugboat stern thruster-pushed vessel with fixed-time preset according to claim 4, characterized in that, S4 specifically includes the following steps: S41: Construct an optimal allocation model for optimizing the actual control law allocation of the pushed vessel as follows: In the formula: Indicates the total number of tugboats; Indicates the weighting parameter; express The baseline value; express The upper bound of the rate of change; Indicates a time interval; This represents the total cost function; express The upper bound; S42: Solve the actual control law of the vessel being pushed in the optimization allocation model, and optimize its allocation to the stern thrust coordination system to obtain the thrusting force exerted by each tugboat on the vessel being pushed. and the corresponding distribution direction .

6. A method for coordinated control of the performance of a multi-tugboat stern thruster-pushed vessel with fixed-time preset according to claim 5, characterized in that, S5 specifically includes the following steps: S51: Based on the assigned action direction and the safety reference state, the expected pose vector of each tugboat is obtained as follows: In the formula: The first point is calculated from the desired contact point. Desired coordinates of the center of gravity of the tugboat; Indicates the first The expected bow direction of the tugboat; Indicates the first The desired pose vector of the tugboat; Indicates the first The expected coordinates of the center of gravity of the tugboat; Represents the rotation matrix; Indicates the first The x and y coordinates of a tugboat from its center of gravity to the point of jacking; S52: The tugboat tracking error is defined as follows based on the desired pose vector: In the formula: Indicates the first The actual position and heading of the tugboat; Represents the coordinate transformation matrix; This represents longitudinal tracking error, lateral tracking error, and bow tracking error; S53: The virtual speed of each tugboat is designed based on the tugboat tracking error as follows: In the formula: This indicates that the information obtained by S32 is for the first... tugboat Preset performance functions for each error channel; express The abbreviated form; They represent the first The virtual longitudinal velocity, virtual lateral velocity, and virtual bow roll rate of the tugboat; Indicates a positive control gain; These represent the desired longitudinal velocity and the desired bow roll rate, respectively. Indicate design parameters and , ; Indicates correspondence Normalization error; Indicates correspondence Transformation error; Denotes the tugboat tracking error vector and = ; express The first derivative; S54: Tugboat speed error defined based on S53 for: Define the actual velocity vector With virtual velocity vector for: Based on the actual velocity vector With virtual velocity vector Construct a robust compensation function for: In the formula: Indicates the first tugboat The basis function vectors of the RBF neural network with each channel; Represents a known nonnegative function relating to the speed of the tugboat; S55: Based on the tugboat speed error and the constructed robust compensation function, the generalized force control law for each tugboat is designed as follows: In the formula: They represent the first The longitudinal generalized force, lateral generalized force, and bow moment required for a tugboat; Indicates the first Equivalent inertial parameters of a tugboat in the longitudinal, lateral, and bow-rolling directions; This represents an estimate of the adaptive parameters; Indicates a positive control gain; Indicates the adaptive gain parameter; Indicates the leakage coefficient; Indicates the initial value of the adaptive parameters; express The first derivative; express The first derivative.

7. A method for coordinated control of the performance of a multi-tugboat stern thruster-pushed vessel with fixed-time preset according to claim 6, characterized in that, The thruster optimization allocation problem model constructed in S6 is as follows: In the formula: They represent the first The thrust amplitude of the two propellers of the tugboat; These represent the azimuth angles of the two thrusters; They represent the first The installation positions of the two propellers of the tugboat in the tugboat's hull coordinate system; This represents the generalized force actually generated by the propulsion system on the tugboat. Indicates the thrust force of the vessel being pushed; Indicates the optimization weights; This indicates the thruster azimuth angle at the previous sampling time; This indicates the maximum thrust of the propulsion unit; This represents the rate of change of the maximum azimuth angle; Indicates the sampling time interval; This represents the objective function of the thruster optimization allocation problem model.

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