Intelligent tugboat cooperative towing path tracking control method based on dynamic synchronization event triggering

Abstract

The application discloses a kind of intelligent tugboat cooperative towing path tracking control methods based on dynamic synchronization event trigger, including constructing adaptive attenuation repulsion field guidance law;According to dynamic event trigger mechanism, the derivative of kinetic tracking error is solved in combination with nonlinear mathematical model, and the uncertain term in nonlinear mathematical model is approximated using neural network, to obtain the derivative of optimized kinetic tracking error;According to the intermediate continuous updating control law of tugboat and actual updating control law, the towing force control law and yaw moment control law of towed ship are designed, and the cooperative towing path tracking control of tugboat is realized in combination with the intermediate continuous updating control law of tugboat and actual updating control law.Solve the continuity and accessibility requirements of path generation in the existing method under multi-obstacle environment, when using continuous updating mechanism, effectively realize the adaptive compensation problem of system nonlinearity, uncertainty and external disturbance while reducing communication bandwidth occupation and updating frequency of actuator.

Description

Technical Field

[0001] This invention relates to the field of intelligent tugboat marine towing operation technology, and in particular to an intelligent tugboat cooperative towing path tracking control method based on dynamic synchronization event triggering. Background Technology

[0002] To address the path tracking and collision avoidance control challenges of multi-ship towing systems in complex marine environments, the system comprises two intelligent tugboats and one unpowered towed vessel connected by towlines, exhibiting clear dynamic coupling characteristics. The tugboats generate propulsion and steering torque via propellers and rudders respectively, transmitting traction to the towed vessel via the towlines, thus driving the overall system motion. During closed-loop control, control commands are calculated in real-time by the controller based on the error between the actual attitude of each vessel and the reference path, and transmitted to the actuators of each tugboat via a communication link to adjust the system's motion state.

[0003] In multi-ship towed path tracking and collision avoidance control, actuators and communication update mechanisms are core components of the multi-ship cooperative control system. Inappropriate updates or frequent triggering can lead to decreased system control performance or even failure, causing the towed system to deviate from its intended course, resulting in obstacle avoidance failure or structural instability. While existing methods can mitigate the effects of system nonlinearity, external disturbances, and multi-ship coupling to some extent, they often present long-term, multi-obstacle, and dynamically changing situations in complex marine environments. To fully consider the impact of complex environments on path planning and control performance, an adaptive decaying repulsive field model is introduced to describe complex and variable obstacle avoidance scenarios. By unifying obstacle influences and target guidance within a potential field framework, the impact of path planning on the overall control system in complex environments is more clearly reflected. On the other hand, continuous updates of control inputs increase communication burden and actuator wear. Current methods have not fully achieved the goal of constraining the control update frequency while ensuring system stability. A control strategy addressing this issue can further improve the system's control accuracy and resource utilization efficiency.

[0004] Based on the above analysis, existing multi-ship towing control methods have the following two drawbacks: 1) Existing guidance methods are difficult to fully reflect the continuity and reachability requirements of path generation in multi-obstacle environments, and are prone to problems such as local minima and path oscillation, which are not conducive to the engineering application of the algorithm in complex sea areas.

[0005] 2) Considering the need for control accuracy and resource utilization efficiency in multi-ship towing systems, existing control algorithms, when using continuous update mechanisms, are unable to effectively achieve adaptive compensation for system nonlinearity, uncertainty and external disturbances while reducing communication bandwidth usage and the update frequency of actuators. Summary of the Invention

[0006] This invention provides an intelligent tugboat cooperative towing path tracking control method based on dynamic synchronization event triggering to overcome the above-mentioned technical problems.

[0007] To achieve the above objectives, the technical solution of the present invention is as follows: A method for intelligent tugboat cooperative towing path tracking control based on dynamic synchronization event triggering specifically includes the following steps: S1: Construct a nonlinear mathematical model based on the dynamics of a multi-ship towing system and the coupling relationship between the towing cables; S2: Construct an adaptive attenuation repulsive field guidance law to obtain a reference trajectory for guidance of a multi-ship towing system. Based on the reference trajectory and the nonlinear mathematical model, obtain the path tracking error of the multi-ship towing system. Design virtual control laws for the forward direction and the yaw direction based on the path tracking error. Obtain the filtered signal by filtering the virtual control laws through the introduction of DSC technology. S3: Define the measurement error of the multi-ship towing system and construct a dynamic event triggering mechanism based on the measurement error; obtain the dynamic tracking error based on the filtered signal and the nonlinear mathematical model; Based on the dynamic event triggering mechanism and the nonlinear mathematical model, the derivative of the dynamic tracking error is obtained. The RBF neural network is then used to approximate the uncertain terms in the nonlinear mathematical model to obtain the optimized dynamic tracking error derivative. S4: Based on the derivative of the dynamic tracking error, construct the intermediate continuous control law and the actual control law of the corresponding tugboat in the multi-ship towing system; at the same time, design the adaptive law of the tugboat and the neural network weight update law to update the intermediate continuous control law and the actual control law in real time, and obtain the intermediate continuous update control law and the actual update control law of the tugboat. S5: Based on the dynamic analysis of the towed vessel in a multi-vessel towing system, and according to the intermediate continuous update control law and the actual update control law of the towed vessel, design the traction force control law and yaw moment control law of the towed vessel, which include the adaptive law of the towed vessel and the neural network weight update law. S6: Based on the intermediate continuous update control law and the actual update control law of the tugboat, combined with the traction force control law and yaw moment control law of the towed vessel, intelligent tugboat cooperative towing path tracking control based on dynamic synchronous event triggering is realized for the multi-vehicle towing system.

[0008] Furthermore, the nonlinear mathematical model constructed in S1 based on the dynamics of the multi-ship towing system and the coupling relationship of the towing cable is as follows:

[0009]

[0010] In the formula: Indicates tugboat With the tugboat Position and heading angle in the geodetic coordinate system ; These represent the forward speed, drift speed, and bow roll rate of the tugboat and the towed vessel, respectively. ; Describes the velocity vector and ,and express The abbreviated form; Indicates tugboat with tugboat The traction force exerted on the towed vessel via the tow cable; This represents the nonlinear damping term used to describe hydrodynamics; This indicates the angle formed between the towing cable and the longitudinal axis of the towed vessel; It represents the combined disturbances caused by external environmental factors such as wind, waves, and currents; Indicates the captain of the towed vessel; Indicates the tugboat captain; Indicates the design parameters related to equivalent mass and moment of inertia; This indicates the tension exerted by the towing cable on the tugboat; Indicates the angle between the direction of the towing cable tension and the bow direction of the tugboat; Indicates the propeller speed of the tugboat; Indicates the rudder angle of a tugboat; These represent the thrust gain and rudder efficiency gain of the tugboat propeller, respectively. express The first derivative.

[0011] Furthermore, step S2 specifically includes the following steps: S21: Construct an adaptive attenuation repulsion field guidance law to obtain a reference trajectory for guidance of a multi-ship towing system; and the adaptive attenuation repulsion field guidance law is:

[0012] In the formula: These represent the desired position and heading angle of the multi-ship towing system, respectively. Indicates the desired forward speed; This indicates the desired direction angle of motion, which is the direction of the resultant force combining all the gravitational forces of the target and the repulsive forces of the obstacle. express The first derivative; S22: Based on the reference route trajectory and the aforementioned nonlinear mathematical model, the path tracking error of the multi-ship towing system is obtained as follows:

[0013] In the formula: These represent the ship's transverse direction error, longitudinal direction error, and heading angle error, respectively. Indicates positional error; This represents the compensation offset of the multi-ship towing system formation configuration in the horizontal and vertical directions; S23: Based on the path tracking error, the virtual control laws for the forward and yaw directions are designed as follows:

[0014]

[0015] In the formula: Virtual control laws representing the forward direction and the pitch direction, respectively; Indicates the error compensation offset; Indicates the amount of intermediate parameters; Indicates a positive design parameter; S24: The virtual control law is filtered using DSC technology to obtain a filtered signal. The expression for filtering the virtual control law is as follows:

[0016] In the formula: , This represents a time constant that is greater than zero. These represent the filter compensation terms, i.e., the filter signals, introduced in the forward and yaw directions, respectively; These represent the initial values ​​of the filter compensation terms introduced in the forward and yaw directions, respectively; They represent The initial value; express The first derivative.

[0017] Furthermore, step S3 specifically includes the following steps: S31: Define the measurement error of a multi-ship towing system as:

[0018] In the formula: Indicates measurement error; Indicates intermediate control input in continuous time; This indicates the actual control commands sent to the actuator; express The abbreviated form; S32: The dynamic event triggering mechanism based on measurement error is as follows:

[0019] In the formula: These represent dynamically adjustable gain threshold and bounded bias threshold, respectively. These represent the weight update rates of the neural network in continuous time and at the trigger time, corresponding to the forward and yaw directions, respectively. ; Indicates the first Next trigger moment Indicates the first The next trigger moment; S33: Obtain the dynamic tracking error based on the filtered signal and the nonlinear mathematical model. for:

[0020] S34: Based on the dynamic event triggering mechanism and the nonlinear mathematical model, the derivative of the dynamic tracking error is obtained. Then, the RBF neural network is used to approximate the uncertain terms in the nonlinear mathematical model to obtain the optimized dynamic tracking error derivative:

[0021] In the formula: They represent the first Optimized dynamic error derivatives of a tugboat in the longitudinal and bow roll directions; These represent the optimized dynamic error derivatives of the towed vessel in the longitudinal and bow-rolling directions, respectively. This represents the approximation term of the RBF neural network for the uncertainties in the ship model; Represents a weight vector; Represents the basis function vector of an RBF neural network; This represents the longitudinal thrust and bow control torque provided by the propeller; This indicates that the gain is controlled in both the forward and pitch directions; This represents the neural network approximation error in the forward and yaw directions; These represent the derivatives of the filter compensation terms introduced in the forward and yaw directions, respectively.

[0022] Furthermore, step S4 specifically includes the following steps: S41: Perform stability analysis on the derivative of the optimized dynamic tracking error to construct the intermediate continuous control law and the actual control law for the corresponding tugboat in the multi-ship towing system:

[0023] In the formula: They represent the first The intermediate continuous control law corresponding to the propeller speed and rudder angle of a tugboat; These represent the control gain estimates for the corresponding thruster and servo motor, respectively. These represent the actual control laws for the forward direction and the pitch direction, respectively. Indicates a positive design parameter; These represent the upper bound estimates of the disturbances in the forward and yaw directions, respectively. Indicates a positive design parameter; This represents an estimate of the actuator gain uncertainty for the forward and yaw directions; S42: Design the adaptive law and neural network weight update law of the tugboat to update the intermediate continuous control law and the actual control law in real time, and obtain the intermediate continuous update control law and the actual update control law of the tugboat; and the adaptive law and neural network weight update law of the tugboat are as follows:

[0024] In the formula: These represent the estimated values ​​of the thrust gain of the propeller and the rudder effect gain, respectively. Indicates a positive design parameter; Represents the initial value of the control gain uncertainty estimate and ; Indicates a positive design constant; express The first derivative; express The initial estimate; This indicates the measurement error of the tugboat's forward speed and bow roll speed. Indicates the upper bound estimate of the perturbation. The first derivative; This represents the approximation term estimation of the uncertainties in the ship model by the RBF neural network. The first derivative; express The initial estimate; Represents a basis function vector. express The abbreviated form of .

[0025] Furthermore, the towing traction control law and yaw moment control law designed in S5, which include the adaptive law of the towed vessel and the neural network weight update law, are as follows:

[0026]

[0027] In the formula: These represent the traction force and yaw moment acting on the tugboat, respectively. This represents the estimated gain of the two tugboats in the traction and torque channels; Indicates correspondence The designed continuous control law; Indicates the traction force and torque distribution coefficient; This indicates the tracking error of the towed vessel in terms of longitudinal speed and yaw rate. Indicates a positive design parameter; These represent the derivatives of the filter compensation terms introduced in the forward and yaw directions, respectively. express The estimated value; These represent the basis function vectors corresponding to the forward direction and the bow roll direction of the towed vessel, respectively. This represents the estimated values ​​of the external disturbances to the towed vessel in the forward and bow directions; Indicates a positive design parameter; This indicates the longitudinal traction force and yaw moment of the towed vessel; Indicates the traction force distribution coefficient; Indicates the yaw moment distribution factor; The adaptive law and neural network weight update law of the towed vessel are as follows:

[0028] In the formula: They represent the first Estimates of the distribution gain of a tugboat in the traction channel and yaw moment channel; express The first derivative; The control laws governing the towed vessel's forward direction and bow roll direction; This indicates the weighting coefficient for tugboat allocation; Indicates a positive design parameter; Indicates a positive design constant; express The initial estimate; This represents the estimated external disturbances to the towed vessel in the direction of travel and the direction of bow roll. express The initial estimate; This represents the weight estimation vector of the RBF neural network for the towed vessel in the forward and bow directions. The initial value; express The abbreviated form; express The first derivative; This indicates the measurement error of the forward speed and bow roll speed of the towed vessel.

[0029] This invention provides an intelligent tugboat cooperative towing path tracking control method based on dynamic synchronization event triggering, with the following beneficial effects: (1) Construct an adaptive attenuation repulsive field guidance law so that the multi-ship towing system has the ability to dynamically adjust to complex environments during the path planning process, and can achieve smooth obstacle avoidance and effectively avoid local minima under multiple obstacles and dynamic interference conditions.

[0030] (2) By constructing an adaptive control method based on a dynamic synchronous event-triggered neural mechanism, that is, using the dynamic event-triggered mechanism to update the control command, neural network weights and adaptive parameters as needed, and combining the RBF neural network to approximate and compensate for system uncertainties and external disturbances online, the intermediate continuous update control law and actual update control law of the tugboat, and the traction force control law and yaw moment control law of the towed vessel are obtained. This effectively improves the system control accuracy while reducing the communication and computing burden, and significantly enhances the robustness of the multi-ship towing system in complex environments. Attached Figure Description

[0031] 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.

[0032] Figure 1 This is a flowchart of the intelligent tugboat cooperative towing path tracking control method based on dynamic synchronization event triggering according to the present invention. Figure 2 This is a diagram of the multi-ship towing control structure based on dynamic synchronization event triggering in this embodiment; Figure 3 This is a flowchart of the core process of multi-ship towing control based on dynamic synchronization event triggering in this embodiment; Figure 4 This is a schematic diagram of the tugboat guidance frame in this embodiment; Figure 5 This is a trajectory comparison curve diagram in this embodiment; Figure 6 This is a comparison chart of error variation curves in this embodiment; Figure 7 This is a comparison chart of control input change curves in this embodiment; Figure 8This is a comparison chart of trigger intervals in this embodiment; Figure 9 This is a diagram showing the trigger interval results for the ship's propeller and rudder in this embodiment. Detailed Implementation

[0033] 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.

[0034] This embodiment provides an intelligent tugboat cooperative towing path tracking control method based on dynamic synchronization event triggering, such as... Figures 1 to 2 As shown, the specific steps include: S1: Construct a nonlinear mathematical model based on the dynamics of a multi-ship towing system and the coupling relationship between the towing cables; specifically, the nonlinear mathematical model is:

[0035]

[0036] In the formula: Indicates tugboat With the tugboat Position and heading angle in the geodetic coordinate system ; These represent the forward speed, drift speed, and bow roll rate of the tugboat and the towed vessel, respectively. ; Describes the velocity vector and ,and express The abbreviated form; Indicates tugboat with tugboat The traction force exerted on the towed vessel via the tow cable; This represents the nonlinear damping term used to describe hydrodynamics; This indicates the angle formed between the towing cable and the longitudinal axis of the towed vessel; It represents the combined disturbances caused by external environmental factors such as wind, waves, and currents; Indicates the captain of the towed vessel; Indicates the tugboat captain; Indicates the design parameters related to equivalent mass and moment of inertia; This indicates the tension exerted by the towing cable on the tugboat; Indicates the angle between the direction of the towing cable tension and the bow direction of the tugboat; Indicates the propeller speed of the tugboat; Indicates the rudder angle of a tugboat; These represent the thrust gain and rudder efficiency gain of the tugboat propeller, respectively. express The first derivative.

[0037] S2: Construct an adaptive attenuation repulsive field guidance law to obtain a reference trajectory for guidance of a multi-ship towed system, such as... Figure 3 As shown, the path tracking error of the multi-ship towing system is obtained based on the reference route trajectory and the nonlinear mathematical model; virtual control laws for the forward direction and the yaw direction are designed based on the path tracking error; and the filtered signal is obtained by filtering the virtual control laws through the introduction of DSC technology. The specific steps include: S21: In this embodiment, the reference route of the multi-ship towing system can be generated by a dynamic virtual ship, while the integrated potential field is used to guide the system's motion direction to solve the problems of path deviation and obstacle avoidance instability in complex environments. For example... Figure 4 As shown, based on this, an adaptive attenuation repulsive field guidance law is constructed. By fusing the target's gravitational force and the obstacle's repulsive force, and introducing a distance-related attenuation mechanism, smooth path guidance and effective obstacle avoidance are achieved. Furthermore, the direction of the comprehensive potential field is mapped to the desired motion direction of the dynamic virtual ship, thereby generating a continuously differentiable reference trajectory. The constructed adaptive attenuation repulsive field guidance law is as follows:

[0038] In the formula: These represent the desired position and heading angle of the multi-ship towing system, respectively. Indicates the desired forward speed; This indicates the desired direction angle of motion, which is the direction of the resultant force combining all the gravitational forces of the target and the repulsive forces of the obstacle. express The first derivative; To ensure that the multi-ship towing system can accurately achieve path tracking and collision avoidance control in complex marine environments while reducing the frequency of control command updates and communication burden, a multi-ship towing cooperative control scheme based on adaptive guidance and dynamic synchronization event triggering mechanism is designed. This scheme mainly consists of two steps: the first step is to design a virtual control law, and the second step is to design a control law based on the dynamic synchronization event triggering mechanism, specifically as follows: S22: Based on the reference route trajectory and the aforementioned nonlinear mathematical model, the path tracking error of the multi-ship towing system is obtained as follows:

[0039] In the formula: These represent the ship's transverse direction error, longitudinal direction error, and heading angle error, respectively. Indicates positional error; This represents the compensation offset of the multi-ship towing system formation configuration in the horizontal and vertical directions; S23: To achieve stability of kinematic errors and ensure asymptotic stability of path tracking errors, the virtual control laws for the forward and yaw directions are designed based on the path tracking errors as follows:

[0040]

[0041] In the formula: Virtual control laws representing the forward direction and the pitch direction, respectively; Indicates the error compensation offset; Indicates the amount of intermediate parameters; Indicates a positive design parameter; S24: To avoid the complexity explosion caused by repeated differentiation of the virtual controller, DSC technology is introduced to filter the virtual control law and obtain a filtered signal. The expression for filtering the virtual control law is as follows:

[0042] In the formula: , This represents a time constant that is greater than zero. These represent the filter compensation terms, i.e., the filter signals, introduced in the forward and yaw directions, respectively; These represent the initial values ​​of the filter compensation terms introduced in the forward and yaw directions, respectively; They represent The initial value; express The first derivative; S3: Define the measurement error of the multi-ship towing system and construct a dynamic event triggering mechanism based on the measurement error; obtain the dynamic tracking error based on the filtered signal and the nonlinear mathematical model; obtain the derivative of the dynamic tracking error by taking the derivative of the dynamic tracking error based on the dynamic event triggering mechanism and the nonlinear mathematical model; and use an RBF neural network to approximate the uncertain terms in the nonlinear mathematical model to obtain the optimized dynamic tracking error derivative. The specific steps include: S31: To reduce the communication overhead of multi-ship towing systems, reduce the update frequency of actuators, and save computing resources, a dynamic synchronous event-triggered neural control mechanism is introduced, so that control commands, neural network weights, and adaptive parameters are updated only when the triggering conditions are met, rather than being updated continuously in cycles. The measurement error of a multi-ship towing system is defined as:

[0043] In the formula: Indicates measurement error; Indicates intermediate control input in continuous time; This indicates the actual control commands sent to the actuator; express The abbreviated form; S32: The dynamic event triggering mechanism based on measurement error is as follows:

[0044] In the formula: These represent dynamically adjustable gain threshold and bounded bias threshold, respectively. These represent the weight update rates of the neural network in continuous time and at the trigger time, corresponding to the forward and yaw directions, respectively. ; Indicates the first Next trigger moment Indicates the first The next trigger moment; S33: Obtain the dynamic tracking error based on the filtered signal and the nonlinear mathematical model. for:

[0045] S34: Based on the dynamic event triggering mechanism and the nonlinear mathematical model, the derivative of the dynamic tracking error is obtained. Then, the RBF neural network is used to approximate the uncertain terms in the nonlinear mathematical model to obtain the optimized dynamic tracking error derivative:

[0046] In the formula: They represent the first Optimized dynamic error derivatives of a tugboat in the longitudinal and bow roll directions; These represent the optimized dynamic error derivatives of the towed vessel in the longitudinal and bow-rolling directions, respectively. This represents the approximation term of the RBF neural network for the uncertainties in the ship model; Represents a weight vector; Represents the basis function vector of an RBF neural network; This represents the longitudinal thrust and bow control torque provided by the propeller; This indicates that the gain is controlled in both the forward and pitch directions; This represents the neural network approximation error in the forward and yaw directions; These represent the derivatives of the filter compensation terms introduced in the forward and yaw directions, respectively; S4: Based on the derivative of the dynamic tracking error, construct the intermediate continuous control law and the actual control law of the corresponding tugboat in the multi-ship towing system; at the same time, design the adaptive law of the tugboat and the neural network weight update law to update the intermediate continuous control law and the actual control law in real time, and obtain the intermediate continuous update control law and the actual update control law of the tugboat. The specific steps include: S41: To achieve stability of the kinematic error and ensure the asymptotic stability of the path tracking error, the intermediate continuous control law and the actual control law of the corresponding tugboat in the multi-ship towing system are constructed as follows:

[0047] In the formula: They represent the first The intermediate continuous control law corresponding to the propeller speed and rudder angle of a tugboat; These represent the control gain estimates for the corresponding thruster and servo motor, respectively. These represent the actual control laws for the forward direction and the pitch direction, respectively; Indicates a positive design parameter; These represent the upper bound estimates of the disturbances in the forward and yaw directions, respectively. Indicates a positive design parameter; The term representing the estimate of the actuator gain uncertainty in the forward and yaw directions is used in conjunction with the hyperbolic tangent function. Construct robust compensation terms; S42: Design the adaptive law and neural network weight update law of the tugboat to update the intermediate continuous control law and the actual control law in real time, and obtain the intermediate continuous update control law and the actual update control law of the tugboat; and the adaptive law and neural network weight update law of the tugboat are as follows:

[0048] In the formula: These represent the estimated values ​​of the thrust gain of the propeller and the rudder effect gain, respectively. Indicates a positive design parameter; Represents the initial value of the control gain uncertainty estimate and ; Indicates a positive design constant; express The first derivative; express The initial estimate; This indicates the measurement error of the tugboat's corresponding forward speed and bow roll speed; Indicates the upper bound estimate of the perturbation. The first derivative; This represents the approximation term estimation of the uncertainties in the ship model by the RBF neural network. The first derivative; express The initial estimate; Represents a basis function vector. express The abbreviated form; S5: Based on the dynamic analysis of the towed vessel in a multi-vessel towing system, and according to the intermediate continuous update control law and the actual update control law of the towed vessel, design the traction force control law and yaw moment control law of the towed vessel, which include the adaptive law of the towed vessel and the neural network weight update law. Specifically, in this embodiment, considering the dynamic characteristics of the towed vessel, the distribution relationship between the traction force and yaw moment of the towed vessel can be expressed as follows:

[0049] In the formula: , ; These represent the distribution coefficients for traction force and yaw moment, respectively. These represent the traction force and yaw moment of the towed vessel, respectively. Therefore, in this embodiment, the propulsion force and maneuvering moment generated by the two tugboats can be jointly mapped to the longitudinal traction force and yaw moment of the towed vessel through the coupling relationship of the tow cables. This embodiment establishes the correspondence between the tugboat control input and the combined traction force and yaw moment of the towed vessel, thereby realizing a unified control design from the tugboat control layer to the towed vessel collaborative control layer. The correspondence between the tugboat control input and the combined traction force and yaw moment of the towed vessel is as follows:

[0050] In the formula: The actual control inputs for the two tugboats are the actual control laws for the forward direction and the bow roll direction; Indicates the traction force distribution coefficient; This represents the yaw moment distribution coefficient; the above correspondence shows that the intermediate continuous control law and the actual control law (i.e., the tugboat control law) of the corresponding tugboat in the multi-ship towing system obtained in S41 can be further mapped to the longitudinal traction force of the towed vessel through the coupling effect of the towing cable. With yaw moment Therefore, based on the established force and torque distribution relationship in this embodiment, the traction force control law and yaw moment control law of the towed vessel can be further derived. That is, by utilizing the control inputs of the two tugboats, the gain estimate, and the neural network compensation term, the coordinated control of the longitudinal speed and heading motion of the towed vessel can be achieved. Specifically: To ensure the stability of the controlled object, based on the dynamic characteristics of the towed vessel and according to the intermediate continuous update control law and the actual update control law of the towed vessel, the traction force control law and yaw moment control law of the towed vessel, which include the adaptive law of the towed vessel and the neural network weight update law, are designed as follows:

[0051]

[0052] In the formula: These represent the traction force and yaw moment acting on the tugboat, respectively. This represents the estimated gain of the two tugboats in the traction and torque channels; Indicates correspondence The designed continuous control law; Indicates the traction force and torque distribution coefficient; This indicates the tracking error of the towed vessel in terms of longitudinal speed and yaw rate. Indicates a positive design parameter; These represent the derivatives of the filter compensation terms introduced in the forward and yaw directions, respectively. express The estimated value; These represent the basis function vectors corresponding to the forward direction and the bow roll direction of the towed vessel, respectively. This represents the estimated values ​​of the external disturbances to the towed vessel in the forward and bow directions; Indicates a positive design parameter; This indicates the longitudinal traction force and yaw moment of the towed vessel; Indicates the traction force distribution coefficient; Indicates the yaw moment distribution factor; The adaptive law and neural network weight update law of the towed vessel are as follows:

[0053] In the formula: They represent the first Estimates of the distribution gain of a tugboat in the traction channel and yaw moment channel; express The first derivative; The control laws governing the towed vessel's forward direction and bow roll direction; This indicates the weighting coefficient for tugboat allocation; Indicates a positive design parameter; Indicates a positive design constant; express The initial estimate; This represents the estimated external disturbances to the towed vessel in the direction of travel and the direction of bow roll. express The initial estimate; This represents the weight estimation vector of the RBF neural network for the towed vessel in the forward and bow directions. The initial value; express The abbreviated form; express The first derivative; This indicates the measurement error of the forward speed and bow roll speed of the towed vessel. S6: Based on the intermediate continuous update control law and the actual update control law of the tugboat, combined with the traction force control law and yaw moment control law of the towed vessel, intelligent tugboat cooperative towing path tracking control based on dynamic synchronous event triggering is realized for the multi-vehicle towing system.

[0054] To verify that the method described in this embodiment can achieve stable path tracking of a multi-ship towing system in a complex marine environment, and to ensure that the control system effectively applies control commands to the tugboat actuators to achieve the desired trajectory, while guaranteeing good adaptive performance of the entire control system under model uncertainty and external disturbances, this embodiment utilizes computer simulation experiments to conduct numerical comparison simulations under multi-obstacle and wind, wave, and current interference environments. The effectiveness and superiority of the method described in this embodiment are verified by comparing it with comparative algorithm A (Guo Q, Zhang X, Han X. Robust adaptive event-triggeredpath following control for autonomous surface vehicles in shallow waters[J]. Ocean Engineering, 2023, 286: 115571.). The main differences between the method described in this embodiment and comparative algorithm A are shown in Table 1.

[0055] Table 1. Similarities and differences between the method described in this embodiment and Algorithm A

[0056] The method and algorithm A described in this embodiment were compared and simulated on an industrial computer (Intel(R) Core(TM) i5-7300 HQ CPU@2.50GHz, RAM: 8.00GB). Figures 5 to 1 0 shows the main comparison results; such as Figure 5 As shown, although both algorithms can achieve path tracking, the algorithm proposed in this invention introduces a dynamic synchronization event triggering strategy. In comparison, Algorithm A, which uses a traditional event triggering method, exhibits certain trajectory deviations in complex environments. Therefore, the method described in this embodiment demonstrates superior path guidance and cooperative control performance in complex marine environments. Figure 6 The error variation of the method described in this embodiment and the comparison algorithm A is described. As can be seen from the figure, the method described in this embodiment has smaller error and more stable convergence, and has a significant advantage in path tracking accuracy. Figure 7 The diagram illustrates the control input changes of the method described in this embodiment and comparison algorithm A. As can be seen from the figure, compared to comparison algorithm A, the method described in this embodiment reduces the control input update frequency through a dynamic synchronization event triggering mechanism and combines a neural network to compensate for uncertainties and disturbances, resulting in a smoother control input. Figure 8 The comparison results of event triggering intervals are given. It can be seen that the triggering interval of the method described in this embodiment is significantly longer than that of the event triggering interval update of the comparison algorithm A, indicating that the designed dynamic synchronous event triggering mechanism effectively reduces the control input update frequency and communication burden. Figure 9 This refers to the triggering time interval between the tugboat's propeller and rudder under the method described in this embodiment. In summary, the method described in this embodiment demonstrates excellent robustness in handling path tracking control problems in complex marine environments.

[0057] Compared with existing technologies, the method described in this embodiment, based on the design and numerical comparison simulation of a multi-ship towing cooperative controller with adaptive guidance and dynamic synchronization event triggering mechanism, has achieved the following three beneficial effects in the field of motion control of multi-ship towing systems: 1) Compared with existing multi-ship towed path tracking and collision avoidance control algorithms, the adaptive guidance and cooperative control mechanism proposed in this embodiment exhibits significant advantages in several aspects. First, by constructing an adaptive attenuating repulsive field guidance law, the system possesses the ability to dynamically adjust to complex environments during path planning, enabling smooth obstacle avoidance under conditions of multiple obstacles and dynamic disturbances, and effectively avoiding local minima. Second, this method comprehensively considers path guidance and collision avoidance constraints, and the guidance strategy designed based on this is more in line with the actual needs of multi-ship towed systems operating in complex sea areas.

[0058] 2) As the requirements for operational accuracy and stability in multi-ship towing systems continue to increase, robust adaptive control methods have become crucial. The neural adaptive control scheme based on a dynamic synchronization event triggering mechanism proposed in this embodiment effectively solves the performance degradation problem under model uncertainty and external disturbances. Considering the limited control resources, the method in this embodiment updates the control input on demand through a dynamic synchronization event triggering mechanism, reducing communication burden and actuator update frequency while ensuring control accuracy.

[0059] 3) Numerical simulations verified that the method described in this embodiment achieves good control performance in multi-ship towing path tracking and collision avoidance control tasks. It not only achieves stable path tracking and safe obstacle avoidance in complex environments, but also significantly improves the system's adaptability and reliability under multiple obstacle and disturbance conditions by introducing adaptive guidance and dynamic synchronous event-triggered control mechanisms. This provides an efficient and stable method for multi-ship towing cooperative control, with promising application prospects in complex marine engineering operations. The method described in this embodiment can accelerate the transformation of tugboat systems towards greater resilience, intelligence, and safety.

[0060] 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 intelligent tugboat cooperative towing path tracking control based on dynamic synchronization event triggering, characterized in that, Specifically, the following steps are included: S1: Construct a nonlinear mathematical model based on the dynamics of a multi-ship towing system and the coupling relationship between the towing cables; S2: Construct an adaptive attenuation repulsive field guidance law to obtain a reference trajectory for guidance of a multi-ship towing system. Based on the reference trajectory and the nonlinear mathematical model, obtain the path tracking error of the multi-ship towing system. Design virtual control laws for the forward direction and the yaw direction based on the path tracking error. Obtain the filtered signal by filtering the virtual control laws through the introduction of DSC technology. S3: Define the measurement error of the multi-ship towing system and construct a dynamic event triggering mechanism based on the measurement error; The dynamic tracking error is obtained based on the filtered signal and the nonlinear mathematical model. Based on the dynamic event triggering mechanism and the nonlinear mathematical model, the derivative of the dynamic tracking error is obtained. The RBF neural network is then used to approximate the uncertain terms in the nonlinear mathematical model to obtain the optimized dynamic tracking error derivative. S4: Based on the derivative of the dynamic tracking error, construct the intermediate continuous control law and the actual control law of the corresponding tugboat in the multi-ship towing system; at the same time, design the adaptive law of the tugboat and the neural network weight update law to update the intermediate continuous control law and the actual control law in real time, and obtain the intermediate continuous update control law and the actual update control law of the tugboat. Specifically including step: S41: Perform stability analysis on the derivative of the optimized dynamic tracking error to construct the intermediate continuous control law and the actual control law for the corresponding tugboat in the multi-ship towing system: In the formula: They represent the first The intermediate continuous control law corresponding to the propeller speed and rudder angle of a tugboat; These represent the control gain estimates for the corresponding thruster and servo motor, respectively. These represent the actual control laws for the forward direction and the pitch direction, respectively; Indicates a positive design parameter; These represent the upper bound estimates of the disturbances in the forward and yaw directions, respectively. Indicates a positive design parameter; This represents an estimate of the actuator gain uncertainty for the forward and yaw directions; The derivative of the filter compensation terms introduced by the forward and yaw directions; S42: Design the adaptive law and neural network weight update law of the tugboat to update the intermediate continuous control law and the actual control law in real time, and obtain the intermediate continuous update control law and the actual update control law of the tugboat; and the adaptive law and neural network weight update law of the tugboat are as follows: In the formula: These represent the estimated values ​​of the thrust gain of the propeller and the rudder effect gain, respectively. Indicates a positive design parameter; Represents the initial value of the control gain uncertainty estimate and ; Indicates a positive design constant; express The first derivative; express The initial estimate; This indicates the measurement error of the tugboat's forward speed and bow roll speed. Indicates the upper bound estimate of the perturbation. The first derivative; This represents the approximation term estimation of the uncertainties in the ship model by the RBF neural network. The first derivative; express The initial estimate; Represents a basis function vector. express The abbreviated form; S5: Based on the dynamic analysis of the towed vessel in a multi-vehicle towing system, and according to the intermediate continuous update control law and the actual update control law of the towed vessel, the traction force control law and yaw moment control law of the towed vessel, which include the adaptive law of the towed vessel and the neural network weight update law, are designed as follows: In the formula: These represent the traction force and yaw moment acting on the tugboat, respectively. This represents the estimated gain of the two tugboats in the traction and torque channels; Indicates correspondence The designed continuous control law; Indicates the traction force and torque distribution coefficient; This indicates the tracking error of the towed vessel in terms of longitudinal speed and yaw rate. Indicates a positive design parameter; These represent the derivatives of the filter compensation terms introduced in the forward and yaw directions, respectively. express The estimated value; These represent the basis function vectors corresponding to the forward direction and the bow roll direction of the towed vessel, respectively. This represents the estimated values ​​of the external disturbances to the towed vessel in the forward and bow directions; Indicates a positive design parameter; This indicates the longitudinal traction force and yaw moment of the towed vessel; Indicates the traction force distribution coefficient; Indicates the yaw moment distribution factor; The adaptive law and neural network weight update law of the towed vessel are as follows: In the formula: They represent the first Estimates of the distribution gain of a tugboat in the traction channel and yaw moment channel; express The first derivative; The control laws governing the towed vessel's forward direction and bow roll direction; This indicates the weighting coefficient for tugboat allocation; Indicates a positive design parameter; Indicates a positive design constant; express The initial estimate; This represents the estimated external disturbances to the towed vessel in the direction of travel and the direction of bow roll. express The initial estimate; This represents the weight estimation vector of the RBF neural network for the towed vessel in the forward and bow directions. The initial value; express The abbreviated form; express The first derivative; This indicates the measurement error of the forward speed and bow roll speed of the towed vessel. S6: Based on the intermediate continuous update control law and the actual update control law of the tugboat, combined with the traction force control law and yaw moment control law of the towed vessel, intelligent tugboat cooperative towing path tracking control based on dynamic synchronous event triggering is realized for the multi-vehicle towing system.

2. The intelligent tugboat cooperative towing path tracking control method based on dynamic synchronization event triggering according to claim 1, characterized in that, The nonlinear mathematical model constructed in S1 based on the dynamics of a multi-ship towing system and the coupling relationship between the towing cables is as follows: In the formula: Indicates tugboat With the tugboat Position and heading angle in the geodetic coordinate system ; These represent the forward speed, drift speed, and bow roll rate of the tugboat and the towed vessel, respectively. ; Describes the velocity vector and ,and express The abbreviated form; Indicates tugboat with tugboat The traction force exerted on the towed vessel via the tow cable; This represents the nonlinear damping term used to describe hydrodynamics; This indicates the angle formed between the towing cable and the longitudinal axis of the towed vessel; It represents the combined disturbances caused by external environmental factors such as wind, waves, and currents; Indicates the captain of the towed vessel; Indicates the tugboat captain; Indicates the design parameters related to equivalent mass and moment of inertia; This indicates the tension exerted by the towing cable on the tugboat; Indicates the angle between the direction of the towing cable tension and the bow direction of the tugboat; Indicates the rotational speed of the tugboat's propeller; Indicates the rudder angle of a tugboat; These represent the thrust gain and rudder efficiency gain of the tugboat propeller, respectively. express The first derivative.

3. The intelligent tugboat cooperative towing path tracking control method based on dynamic synchronization event triggering according to claim 2, characterized in that, S2 specifically includes the following steps: S21: Construct an adaptive attenuation repulsion field guidance law to obtain a reference trajectory for guidance of a multi-ship towing system; and the adaptive attenuation repulsion field guidance law is: In the formula: These represent the desired position and heading angle of the multi-ship towing system, respectively. Indicates the desired forward speed; This indicates the desired direction angle of motion, which is the direction of the resultant force combining all the gravitational forces of the target and the repulsive forces of the obstacle. express The first derivative; S22: Based on the reference route trajectory and the aforementioned nonlinear mathematical model, the path tracking error of the multi-ship towing system is obtained as follows: In the formula: These represent the ship's transverse direction error, longitudinal direction error, and heading angle error, respectively. Indicates positional error; This represents the compensation offset of the multi-ship towing system formation configuration in the horizontal and vertical directions; S23: Based on the path tracking error, the virtual control laws for the forward and yaw directions are designed as follows: In the formula: Virtual control laws representing the forward direction and the pitch direction, respectively; Indicates the error compensation offset; Indicates the amount of intermediate parameters; Indicates a positive design parameter; S24: The virtual control law is filtered by introducing DSC technology to obtain a filtered signal. The expression for filtering the virtual control law is as follows: In the formula: , This represents a time constant that is greater than zero. These represent the filter compensation terms, i.e., the filter signals, introduced in the forward and yaw directions, respectively; These represent the initial values ​​of the filter compensation terms introduced in the forward and yaw directions, respectively; They represent The initial value; express The first derivative.

4. The intelligent tugboat cooperative towing path tracking control method based on dynamic synchronization event triggering according to claim 3, characterized in that, S3 specifically includes the following steps: S31: Define the measurement error of a multi-ship towing system as: In the formula: Indicates measurement error; Indicates intermediate control input in continuous time; This indicates the actual control commands sent to the actuator; express The abbreviated form; S32: The dynamic event triggering mechanism based on measurement error is as follows: In the formula: These represent dynamically adjustable gain threshold and bounded bias threshold, respectively. These represent the weight update rates of the neural network in continuous time and at the trigger time, corresponding to the forward and yaw directions, respectively. ; Indicates the first Next trigger time Indicates the first The next trigger moment; S33: Obtain the dynamic tracking error based on the filtered signal and the nonlinear mathematical model. for: S34: Based on the dynamic event triggering mechanism and the nonlinear mathematical model, the derivative of the dynamic tracking error is obtained. Then, the RBF neural network is used to approximate the uncertain terms in the nonlinear mathematical model to obtain the optimized dynamic tracking error derivative: In the formula: They represent the first Optimized dynamic error derivatives of a tugboat in the longitudinal and bow roll directions; These represent the optimized dynamic error derivatives of the towed vessel in the longitudinal and bow-rolling directions, respectively. This represents the approximation term of the RBF neural network for the uncertainties in the ship model; Represents a weight vector; Represents the basis function vector of an RBF neural network; This represents the longitudinal thrust and bow control torque provided by the propeller; This indicates that the gain is controlled in both the forward and pitch directions; This represents the neural network approximation error in the forward and yaw directions; These represent the derivatives of the filter compensation terms introduced in the forward and yaw directions, respectively.

Images